Maverick Philosopher

Trope Troubles: An Exercise in Aporetics

Elliot C. asked me about tropes. What follows is a re-post from 30 March 2016, slightly emended, which stands up well under current scrutiny.  Perhaps Elliot will find the time to tell me whether he finds it clear and convincing and whether it answers his questions.

................................

A reader  has been much exercised of late by trope theory and other questions in ontology.  He has been sharing his enthusiasm with me.   He espies 

. . . an apparent antinomy at the heart of trope theory. On the one hand, tropes are logically prior to objects. But on the other hand, objects (or, more precisely, the trope-bundles constituting objects) are logically prior to tropes, because without objects tropes have nowhere to be – without objects (or the trope-bundles constituting objects) tropes cannot be. Moreover, as has I hope been shown, a trope cannot be in (or constitute) any object or trope-bundle other than that in which it already is.

How might a trope theorist plausibly respond to this?  Can she? [My use of the feminine third-person singular pronoun does not signal my nonexistent political correctness, but is an anticipatory reference to Anna-Sofia Maurin whom I will discuss below.  'Anna-Sofia'! What a beautiful name, so aptronymic. Nomen est omen.)

What are tropes?

It is a 'Moorean fact,' a pre-analytic datum, that things have properties.  This is a pre-philosophical observation.  In making it we are not yet doing philosophy.  If things have properties, then there are properties.  This is a related pre-philosophical observation.  We begin  to do philosophy when we ask: given that there are properties, what exactly are they?  What is their nature?  How are we to understand them?  This is not the question, what properties are there, but the question, what are properties?  The philosophical question, then, is not whether there are properties, nor is it the question what properties there are, but the question what properties are.

On trope theory, properties are assayed not as universals but as particulars: the redness of a tomato is as particular, as unrepeatable, as the tomato. Thus a tomato is red, not in virtue of exemplifying a universal, but by having a redness trope as one of its constituents (on the standard  bundle version of trope theory) or by being a substratum in which a redness trope inheres (on a nonstandard theory championed by C. B. Martin which I will not further discuss). A trope is a simple entity in that there is no distinction between it and the property it ‘has.’ 'Has' and cognates are words of ordinary English: they do not commit us to ontological theories of what the having consists in.  So don't confuse 'a has F-ness' with 'a instantiates F-ness.'  Instantiation is a term of art, a terminus technicus in ontology.  Or at least that is what it is in my book.  More on instantiation in a moment.

Thus a redness trope is red, but it is not red by instantiating redness, or by having redness as a constituent, but by being (a bit of) redness. So a trope is what it has. It has redness by being identical to (a bit of) redness.

It is therefore inaccurate to speak of tropes as property instances.  A trope is not a property instance on one clear understanding of the latter.  First-order instantiation is a dyadic asymmetrical relation: if a instantiates F-ness, then it is not the case that F-ness instantiates a.  (Higher order instantiation is not asymmetrical but  nonsymmetrical.  Exercise for the reader: prove it!)  Suppose the instantiation relation connects the individual Socrates here below to the universal wisdom in the realm of platonica.  Then a further item comes into consideration, namely, the wisdom of Socrates. This is a property instance.  It is a particular, an unrepeatable, since it is the wisdom of Socrates and of no one else. This distinguishes it from the universal, wisdom, which is repeated in each wise individual.  On the other side, the wisdom of Socrates is distinct from Socrates since there is more to Socrates that his being wise.  There is his being snub-nosed, etc.  Now why do I maintain that a trope is not a property instance? Two arguments. 

Tropes are simple, not complex.  (See Maurin, here.)  They are not further analyzable.  Property instances, however, are complex, not simple.   'The F-ness of a'  --  'the wisdom of Socrates,' e.g. -- picks out a complex item that is analyzable into F-ness, a, and the referent of 'of.'  Therefore, tropes are not property instances.

A second, related,  argument.  Tropes are in no way proposition-like.  Property instances are proposition-like as can be gathered from the phrases we use to refer to them.  Ergo, tropes are not property instances. 

One can see from this that tropes on standard trope theory, as ably presented by Maurin in her Stanford Encyclopedia of Philosophy entry, are very strange items, so strange indeed that one can wonder whether they are coherently conceivable at all by minds of our discursive constitution.  Here is one problem.

How could anything be both predicable and impredicable?

Properties are predicable items.  So if tropes are properties, then tropes are predicable items.  If the redness of my tomato, call it 'Tom,'  is a trope, then this trope is predicable of Tom. Suppose I assertively utter a token of 'Tom is red.'  On one way of parsing this we have a subject term 'Tom' and a predicate term '___ is red.'  Thus the parsing: Tom/is red.  But then the trope would appear to have a proposition-like structure, the structure of what Russell calls a propositional function.  Clearly, '___ is red' does not pick out a proposition, but it does pick out something proposition-like and thus something complex.  But now we have trouble since tropes are supposed to be simple.  Expressed as an aporetic triad or antilogism:

a. Tropes are simple.
b. Tropes are predicable.
c.  Predicable items are complex.

The limbs of the antilogism are each of them rationally supportable, but they cannot all be true. Individually plausible, collectively inconsistent. The conjunction of any two limbs entails the negation of the remaining one.  Thus the conjunction of (b) and (c) entails ~(a).

We might try to get around this difficulty by parsing 'Tom is red' differently, as: Tom/is/red.  On this scheme, 'Tom' and 'red' are both names.  'Tom' names a concrete particular whereas 'red' names an abstract particular.  ('Abstract' is here being used in the classical, not the Quinean, sense.)   As Maurin relates, D. C. Williams, who introduced the term 'trope' in its present usage back in the '50s, thinks of the designators of tropes as akin to names and demonstratives, not as definite descriptions. But then it becomes difficult to see how tropes could be predicable entities. 

A tomato is not a predicable entity.  One cannot predicate a tomato of anything.  The same goes for the parts of a tomato; the seeds, e.g., are not predicable of anything.  Now if a tomato is a bundle of tropes, then it is a whole of ontological parts, these latter being tropes.  If we think of the tomato as a (full-fledged) substance, then the tropes constituting it are "junior substances." (See D. M. Armstrong, 1989, 115) But now the problem is: how can one and the same item -- a trope --  be both a substance and a property, both an object and a concept (in Fregean jargon), both impredicable and predicable?  Expressed as an aporetic dyad or antinomy:

d. Tropes are predicable items.
e. Tropes are not predicable items.

Maurin seems to think that the limbs of the dyad can both be true:  ". . . tropes are by their nature such that they can be adequately categorized both as a kind of property and as a kind of substance."  If the limbs can both be true, then they are not contradictory despite appearances.

How can we defuse the apparent contradiction in the d-e dyad?  Consider again Tom and the redness trope R.  To say that R is predicable of Tom  is to say that Tom is a trope bundle having R as an ontological (proper) part.  To say that R is impredicable or  a substance is to say that R is capable of independent existence.  Recall that Armstrong plausibly defines a substance as anything logically capable of independent existence.

It looks as if we have just rid ourselves of the contradiction.  The sense in which tropes are predicable is not the sense in which they are impredicable.  They are predicable as constituents of trope bundles; they are impredicable in themselves. Equivalently, tropes are properties when they are compresent with sufficiently many other tropes to form trope bundles (concrete particulars); but they are substances in themselves apart from trope bundles as the 'building blocks' out of which such bundles are (logically or rather ontologically) constructed.

Which came first: the whole or the parts?

But wait!  This solution appears to have all the advantages of jumping from the frying pan into the fire.   For now we bang up against the above Antinomy, or something like it, to wit:

f. Tropes as substances, as ontological building blocks, are logically prior to concrete particulars.
g. Tropes as properties, as predicable items, are not logically prior to concrete particulars.

This looks like an aporia in the strict and narrow sense: an insoluble problem.  The limbs cannot both be true.  And yet each is an entailment of standard (bundle) trope theory.  If tropes are the "alphabet of being" in a phrase from Williams, then they are logically prior to what they spell out.  But if tropes are unrepeatable properties, properties as particulars, then a trope cannot exist except as a proper ontological part of a trope bundle, the very one of which it is a part.  For if a trope were not tied to the very bundle of which it is a part, it would be a universal, perhaps only an immanent universal, but a universal all the same. 

Furthermore, what makes a trope abstract in the classical (as opposed to Quinean) sense of the term is that it is abstracted from a concretum.  But then the concretum comes first, ontologically speaking, and (g) is true.

Interim conclusion: Trope theory, pace Anna-Sofia Maurin, is incoherent. But of course we have only scratched the surface. 

Pictured below, left-to-right:  Anna-Sofia Maurin, your humble correspondent, Arianna Betti, Jan Willem Wieland. Geneva, Switzerland, December 2008.  It was a cold night.

Related articles

Armstrong, Quine, Universals, Abstract Objects, and Naturalism

Peter van Inwagen, "A Theory of Properties," Exposition and Critique

Atheism and Ontological Simplicity: A Retraction and a Repair

God and Mann: Divine Simplicity and Property-Instances

God, Simplicity, and Tropes

Tropes as Truth-Makers? Or Do We Need Facts?

In a Philosophical Conversation, Three's a Crowd

 

Elliot C. asked me about tropes. What follows is a re-post from 30 March 2016, slightly emended, which stands up well under current scrutiny.  Perhaps Elliot will find the time to tell me whether he finds it clear and convincing and whether it answers his questions.

................................

A reader  has been much exercised of late by trope theory and other questions in ontology.  He has been sharing his enthusiasm with me.   He espies 

. . . an apparent antinomy at the heart of trope theory. On the one hand, tropes are logically prior to objects. But on the other hand, objects (or, more precisely, the trope-bundles constituting objects) are logically prior to tropes, because without objects tropes have nowhere to be – without objects (or the trope-bundles constituting objects) tropes cannot be. Moreover, as has I hope been shown, a trope cannot be in (or constitute) any object or trope-bundle other than that in which it already is.

How might a trope theorist plausibly respond to this?  Can she? [My use of the feminine third-person singular pronoun does not signal my nonexistent political correctness, but is an anticipatory reference to Anna-Sofia Maurin whom I will discuss below.  'Anna-Sofia'! What a beautiful name, so aptronymic. Nomen est omen.)

What are tropes?

It is a 'Moorean fact,' a pre-analytic datum, that things have properties.  This is a pre-philosophical observation.  In making it we are not yet doing philosophy.  If things have properties, then there are properties.  This is a related pre-philosophical observation.  We begin  to do philosophy when we ask: given that there are properties, what exactly are they?  What is their nature?  How are we to understand them?  This is not the question, what properties are there, but the question, what are properties?  The philosophical question, then, is not whether there are properties, nor is it the question what properties there are, but the question what properties are.

On trope theory, properties are assayed not as universals but as particulars: the redness of a tomato is as particular, as unrepeatable, as the tomato. Thus a tomato is red, not in virtue of exemplifying a universal, but by having a redness trope as one of its constituents (on the standard  bundle version of trope theory) or by being a substratum in which a redness trope inheres (on a nonstandard theory championed by C. B. Martin which I will not further discuss). A trope is a simple entity in that there is no distinction between it and the property it ‘has.’ 'Has' and cognates are words of ordinary English: they do not commit us to ontological theories of what the having consists in.  So don't confuse 'a has F-ness' with 'a instantiates F-ness.'  Instantiation is a term of art, a terminus technicus in ontology.  Or at least that is what it is in my book.  More on instantiation in a moment.

Thus a redness trope is red, but it is not red by instantiating redness, or by having redness as a constituent, but by being (a bit of) redness. So a trope is what it has. It has redness by being identical to (a bit of) redness.

It is therefore inaccurate to speak of tropes as property instances.  A trope is not a property instance on one clear understanding of the latter.  First-order instantiation is a dyadic asymmetrical relation: if a instantiates F-ness, then it is not the case that F-ness instantiates a.  (Higher order instantiation is not asymmetrical but  nonsymmetrical.  Exercise for the reader: prove it!)  Suppose the instantiation relation connects the individual Socrates here below to the universal wisdom in the realm of platonica.  Then a further item comes into consideration, namely, the wisdom of Socrates. This is a property instance.  It is a particular, an unrepeatable, since it is the wisdom of Socrates and of no one else. This distinguishes it from the universal, wisdom, which is repeated in each wise individual.  On the other side, the wisdom of Socrates is distinct from Socrates since there is more to Socrates that his being wise.  There is his being snub-nosed, etc.  Now why do I maintain that a trope is not a property instance? Two arguments. 

Tropes are simple, not complex.  (See Maurin, here.)  They are not further analyzable.  Property instances, however, are complex, not simple.   'The F-ness of a'  --  'the wisdom of Socrates,' e.g. -- picks out a complex item that is analyzable into F-ness, a, and the referent of 'of.'  Therefore, tropes are not property instances.

A second, related,  argument.  Tropes are in no way proposition-like.  Property instances are proposition-like as can be gathered from the phrases we use to refer to them.  Ergo, tropes are not property instances. 

One can see from this that tropes on standard trope theory, as ably presented by Maurin in her Stanford Encyclopedia of Philosophy entry, are very strange items, so strange indeed that one can wonder whether they are coherently conceivable at all by minds of our discursive constitution.  Here is one problem.

How could anything be both predicable and impredicable?

Properties are predicable items.  So if tropes are properties, then tropes are predicable items.  If the redness of my tomato, call it 'Tom,'  is a trope, then this trope is predicable of Tom. Suppose I assertively utter a token of 'Tom is red.'  On one way of parsing this we have a subject term 'Tom' and a predicate term '___ is red.'  Thus the parsing: Tom/is red.  But then the trope would appear to have a proposition-like structure, the structure of what Russell calls a propositional function.  Clearly, '___ is red' does not pick out a proposition, but it does pick out something proposition-like and thus something complex.  But now we have trouble since tropes are supposed to be simple.  Expressed as an aporetic triad or antilogism:

a. Tropes are simple.
b. Tropes are predicable.
c.  Predicable items are complex.

The limbs of the antilogism are each of them rationally supportable, but they cannot all be true. Individually plausible, collectively inconsistent. The conjunction of any two limbs entails the negation of the remaining one.  Thus the conjunction of (b) and (c) entails ~(a).

We might try to get around this difficulty by parsing 'Tom is red' differently, as: Tom/is/red.  On this scheme, 'Tom' and 'red' are both names.  'Tom' names a concrete particular whereas 'red' names an abstract particular.  ('Abstract' is here being used in the classical, not the Quinean, sense.)   As Maurin relates, D. C. Williams, who introduced the term 'trope' in its present usage back in the '50s, thinks of the designators of tropes as akin to names and demonstratives, not as definite descriptions. But then it becomes difficult to see how tropes could be predicable entities. 

A tomato is not a predicable entity.  One cannot predicate a tomato of anything.  The same goes for the parts of a tomato; the seeds, e.g., are not predicable of anything.  Now if a tomato is a bundle of tropes, then it is a whole of ontological parts, these latter being tropes.  If we think of the tomato as a (full-fledged) substance, then the tropes constituting it are "junior substances." (See D. M. Armstrong, 1989, 115) But now the problem is: how can one and the same item -- a trope --  be both a substance and a property, both an object and a concept (in Fregean jargon), both impredicable and predicable?  Expressed as an aporetic dyad or antinomy:

d. Tropes are predicable items.
e. Tropes are not predicable items.

Maurin seems to think that the limbs of the dyad can both be true:  ". . . tropes are by their nature such that they can be adequately categorized both as a kind of property and as a kind of substance."  If the limbs can both be true, then they are not contradictory despite appearances.

How can we defuse the apparent contradiction in the d-e dyad?  Consider again Tom and the redness trope R.  To say that R is predicable of Tom  is to say that Tom is a trope bundle having R as an ontological (proper) part.  To say that R is impredicable or  a substance is to say that R is capable of independent existence.  Recall that Armstrong plausibly defines a substance as anything logically capable of independent existence.

It looks as if we have just rid ourselves of the contradiction.  The sense in which tropes are predicable is not the sense in which they are impredicable.  They are predicable as constituents of trope bundles; they are impredicable in themselves. Equivalently, tropes are properties when they are compresent with sufficiently many other tropes to form trope bundles (concrete particulars); but they are substances in themselves apart from trope bundles as the 'building blocks' out of which such bundles are (logically or rather ontologically) constructed.

Which came first: the whole or the parts?

But wait!  This solution appears to have all the advantages of jumping from the frying pan into the fire.   For now we bang up against the above Antinomy, or something like it, to wit:

f. Tropes as substances, as ontological building blocks, are logically prior to concrete particulars.
g. Tropes as properties, as predicable items, are not logically prior to concrete particulars.

This looks like an aporia in the strict and narrow sense: an insoluble problem.  The limbs cannot both be true.  And yet each is an entailment of standard (bundle) trope theory.  If tropes are the "alphabet of being" in a phrase from Williams, then they are logically prior to what they spell out.  But if tropes are unrepeatable properties, properties as particulars, then a trope cannot exist except as a proper ontological part of a trope bundle, the very one of which it is a part.  For if a trope were not tied to the very bundle of which it is a part, it would be a universal, perhaps only an immanent universal, but a universal all the same. 

Furthermore, what makes a trope abstract in the classical (as opposed to Quinean) sense of the term is that it is abstracted from a concretum.  But then the concretum comes first, ontologically speaking, and (g) is true.

Interim conclusion: Trope theory, pace Anna-Sofia Maurin, is incoherent. But of course we have only scratched the surface. 

Pictured below, left-to-right:  Anna-Sofia Maurin, your humble correspondent, Arianna Betti, Jan Willem Wieland. Geneva, Switzerland, December 2008.  It was a cold night.

Related articles

Armstrong, Quine, Universals, Abstract Objects, and Naturalism

Peter van Inwagen, "A Theory of Properties," Exposition and Critique

Atheism and Ontological Simplicity: A Retraction and a Repair

God and Mann: Divine Simplicity and Property-Instances

God, Simplicity, and Tropes

Tropes as Truth-Makers? Or Do We Need Facts?

In a Philosophical Conversation, Three's a Crowd

The Hatfields and the McCoys

Whether or not it is true, the following  has a clear sense:

1. The Hatfields outnumber the McCoys.

(1) says that the number of Hatfields is strictly greater than the number of McCoys.  It obviously does not say, of each Hatfield, that he outnumbers some McCoy.  If Gomer is a Hatfield and Goober a McCoy, it is nonsense to say of Gomer that he outnumbers Goober. The Hatfields 'collectively' outnumber the McCoys. 

It therefore seems that there must be something in addition to the individual Hatfields (Gomer, Jethro, Jed, et al.) and something in addition to the individual McCoys (Goober, Phineas, Prudence, et al.) that serve as logical subjects of number predicates.  In

2. The Hatfields are 100 strong

it cannot be any individual Hatfield that is 100 strong.  This suggests that there must be some one single entity, distinct but not wholly distinct from the individual Hatfields, and having them as members, that is the logical subject or bearer of the predicate '100 strong.'

So here is a challenge to Ed Buckner the nominalist.  Provide truth-preserving analyses of (1) and (2) that make it unnecessary to posit a collective entity (whether set, mereological sum, or whatever) in addition to individual Hatfields and McCoys.

Nominalists and realists alike agree that one must not "multiply entities beyond necessity."   Entia non sunt multiplicanda praeter necessitatem!  The question, of course, hinges on what's necessary for explanatory purposes.  So the challenge for Buckner the nominalist is to provide analyses of (1) and (2) that capture the sense and preserve the truth of the analysanda and yet obviate the felt need to posit entities in addition to concrete particulars.

Now if such analyses could be provided, it would not follow that there are no 'collective entities.'  But a reason for positing them would have been removed.

The Ramsey Problem and the Problem of the Intrinsically Unpropertied Particular

Here at Maverick Philosopher: Strictly Philosophical

Frege's Horse Paradox, Bradley's Regress, and the Problem of Predication

The concept horse is not a concept.  Thus spoke Frege, paradoxically.  Why does he say such a thing?  Because the subject expression 'the concept horse' refers to an object.  It names an object.  Concepts and objects on his scheme are mutually exclusive. No concept is an object and conversely.   Only objects can be named.  No concept can be named. Predicates are not names.  If you try to name a concept you will fail.  You will succeed only in naming an object.  You will not succeed in expressing the predicativity of the concept.  Concepts are predicable while objects are not. It is clear that one cannot predicate Socrates of Socrates. We can, however, predicate wisdom of Socrates.  It is just that wisdom is not an object.

But now we are smack in the middle of the paradox. For to explain Frege's view I need to be able to talk about the referent of the gappy predicate ' ___ is wise.'  I need to be able to say that it is a predicable entity, a concept.  But how can I do this without naming it, and thus objectifying it?  Ineffability may be the wages of Frege's absolute object-concept distinction.

To savor the full flavor of the paradox, note that the sentence 'No concept can be named'  contains the general name 'concept.'  It seems we, or rather the Fregeans, cannot say what we or they mean.  But if we cannot say what we mean, how do we know that we mean anything at all?  Is an inexpressible meaning a meaning?  Are there things that cannot be said but only shown? (Wittgenstein) Perhaps we cannot say that concepts are concepts; all we can do is show that they are by employing open sentences or predicates such as '___ is tall.'  Unfortunately, this is also paradoxical.  For I had to say what the gappy predicate shows. I had to say that concepts are concepts and that concepts are what gappy predicates (predicates that are not construed as names) express.

Why can't concepts be named?  Why aren't they a kind of higher-order object? Why can't they be picked out using abstract substantives?  Why can't we say that, in a sentence such as 'Tom is sad,' 'Tom' names an object while 'sad' names a different sort of object, a concept/property?  Frege's thought seems to be that if concepts are objects, then they cannot exercise their predicative function.  Concepts are essentially and irreducibly predicative, and if you objectify them -- think or speak of them as objects -- then you destroy their predicative function. A predicative proposition is not a juxtaposition of two objects.  If  there is Tom and there is sadness, it doesn't follow that sadness is true of Tom. What makes a property true of its subject?  An obvious equivalence: if F-ness is true of a, then *a is F* is true.  So we might ask the questions this way: What makes *a is F* true?

The Problem of the Unity of the Proposition and the Fregean Solution

We are brought back to the problem of the unity of the proposition. It's as old as Plato. It is a genuine problem, but no one has ever solved it. (Of course, I am using 'solve' as a verb of success.)

A collection of two objects is not a proposition.  The mereological sum Tom + sadness is neither true nor false; propositions are either true or false.  The unity of a proposition is a type of unity that attracts a truth value, whereas the unity of a sum does not attract a truth value.  The unity of a proposition is mighty puzzling even in the simplest cases.   It does no good to say that the copula 'is' in 'Tom is sad' refers to the instantiation relation R and that this relation connects the concept/property to the object, sadness to Tom, and in such a way as to make sadness true of Tom.  For then you sire Mr Bradley's relation regress.  It's infinite and it's vicious.  Note that if the sum Tom + sadness can exist without it being true that Tom is sad, then the sum Tom + R + sadness can also exist without it being true that Tom is sad. 

Enter Frege with his obscure talk of the unsaturatedness of concepts. Concepts exist whether or not they are instantiated, but they are  'gappy':  if a first-level concept is instantiated by an object, there is no need for a tertium quid to connect concept and object. They fit together like plug and socket, where the plug is the object and the concept the socket.  The female receptacle accepts the male plug without the need of anything to hold the two together.

On this approach no regress arises.  For if there is no third thing that holds concept and object together, then no worries can arise as to how the third thing is related to the concept on the one side and the object on the other.  But our problem about the unity of the proposition remains unsolved.  For if the concept can exist uninstantiated, then both object and concept, Tom and sadness, can exist without it being true that Tom is sad. 

The dialectic continues on and on. Philosophia longa, vita brevis. Life is brief; blog posts ought to be.

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Against Ostrich Nominalism

As magnificent a subject as philosophy is, grappling as it does with the ultimate concerns of human existence, and thus surpassing in nobility any other human pursuit, it is also miserable in that nothing goes uncontested, and nothing ever gets established to the satisfaction of all competent practitioners.  (This is true of other disciplines as well, but in philosophy it is true in excelsis.) Suppose I say, as I have in various places:

That things have properties and stand in relations I take to be a plain Moorean fact beyond the reach of reasonable controversy. After all, my cat is black and he is sleeping next to my blue coffee cup.  ‘Black’ picks out a property, an extralinguistic feature of my cat.

Is that obvious?  Not to some.  Not to the ornery and recalcitrant critter known as the ostrich nominalist.  My cat, Max Black, is black.  That, surely, is a Moorean fact. Now consider the following biconditional and consider whether it too is a Moorean fact:

1. Max is black iff Max has the property of being black.

As I see it, there are three main ways of construing a biconditional such as (1):

A.  Ostrich Nominalism.  The right-hand side (RHS) says exactly what the left-hand side (LHS) says, but in a verbose and high-falutin' and dispensable way.  Thus the use of 'property' on the RHS does not commit one ontologically to properties beyond predicates.  (By definition, predicates are linguistic items while properties are extralinguistic and extramental.)  Predication is primitive and in need of no philosophical explanation.  On this approach, (1) is trivially true.  One needn't posit properties, and in consequence one needn't worry about the nature of property-possession. (Is Max related to his blackness, or does Max have his blackness quasi-mereologically  by having it as an ontological constituent of him?)

B. Ostrich Realism.  The RHS commits one ontologically to properties, but in no sense does the RHS serve to ground or explain the LHS.  On this approach, (1) is false if there are no properties.  For the ostrich realist, (1) is true, indeed necessarily true, but it is not the case that the LHS is true because the RHS is true.  Such notions as metaphysical grounding and philosophical explanation are foreign to the ostrich realist, but not in virtue of his being a realist, but  in virtue of his being an ostrich.

C. Non-Ostrich Realism.  On this approach, the RHS both commits one to properties, but also proffers a metaphysical ground of the truth of the LHS: the LHS is true because (ontologically or metaphysically speaking)  the concrete particular Max has the property of being black, and not vice versa.

Note 1: Explanation is asymmetrical; biconditionality is symmetrical.

Note 2: Properties needn't be universals.  They might be (abstract) particulars (unrepeatables) such as the tropes of D. C. Williams and Keith Campbell.  Properties must, however, be extralinguistic and extramental,  by definition.

Note 3: Property-possession needn't be understood in terms of instantiation or exemplification or Fregean 'falling-under'; it might be construed quasi-mereologically as constituency: a thing has a property by having it as a proper ontological part.

Against Ostrich Nominalism

On (A) there are neither properties, nor do properties enter into any explanation of predication.  Predication is primitive and in need of no explanation.  In virtue of what does 'black' correctly apply to Max? In virtue of nothing.  It just applies to him and does so correctly.  Max is black, but there is no feature of reality that explains why 'black' is true of Max, or why 'Max is black' is true.  It is just true!  There is nothing in reality that serves as the ontological ground of this contingent truth.  Nothing 'makes' it true.  There are no truth-makers and no need for any.

I find ostrich nominalism preposterous.  'Black' is true of Max, 'white' is not, but there is no feature of reality, nothing in or at or about Max that explains why the one predicate is true of him and the other is not!?  This is not really an argument but more an expression of incomprehension or incredulity, an autobiographical comment, if you will.  I may just be petering out, pace Professor van Inwagen.

Can I do better than peter?  'Black' is a predicate of English.  Schwarz is a predicate of German.  If there are no properties,  then Max is black relative to English, schwarz relative to German, noir relative to French, and no one color.  But this is absurd.  Max is not three different colors, but one color, the color we use 'black' to pick out, and the Germans use schwarz to pick out. When Karl, Pierre, and I look at Max we see the same color.  So there is one color we both see -- which would not be the case if there were no properties beyond predicates.  It is not as if I see the color black while Karl sees the color schwarz.  We see the same color.  And we see it at the cat.  This is not a visio intellectualis whereby we peer into some Platonic topos ouranos.  Therefore, there is something in, at, or about the cat, something extralinguistic, that grounds the correctness of the application of the predicate to the cat.

A related argument.  I say, 'Max is black.'  Karl says, Max ist schwarz.  'Is' and ist are token-distinct and type-distinct words of different languages.  If there is nothing in reality (no relation whether of instantiation or of constituency, non-relational tie, Bergmannian nexus, etc.) that the copula picks out, then it is only relative to German that Max ist schwarz, and only relative to English that Max is black.  But this is absurd.  There are not two different facts here but one.  Max is the same color for Karl and me, and his being black is the same fact for Karl and me.

Finally, 'Max is black' is true.  Is it true ex vi terminorum?  Of course not.  It is contingently true.  Is it just contingently true?  Of course not.  It is true because of the way extralinguistic reality is arranged. It is modally contingent, but also contingent upon the way the world is.  There's this cat that exists whether or not any language exists, and it is black whether or not any language exists.

Therefore, I say that for a predicate to be contingently true of an individual, (i) there must be individuals independently of language; (ii) there must be properties independently of language; and there must be facts or truth-making states of affairs independently of language.  Otherwise, you end up with (i) total linguistic idealism, which is absurd; or (ii) linguistic idealism about properties which is absurd; or (iii) a chaos, a world of disconnected particulars and properties.

The above is a shoot-from-the hip, bloggity-blog exposition of ideas that can be put more rigorously, but it seems to to me to show that ostrich nominalism and ostrich realism for that matter are untenable -- and this despite the fact that a positive theory invoking facts has its own very serious problems.

Metaphilosophical Coda: If a theory has insurmountable problems, these problems are not removed by the fact that every other theory has problems.  For it might be that no theory is tenable,while the problem itself is genuine.

Predication as Identity: Another Round

The Opponent is a patient man:

Trying again.

(1) Sam is poor at t1 iff Sam is identical with some poor person at t1
(2) Sam is poor at t1 iff Sam is self-identical at t1

(1) is self-evidently true. For it cannot be true that Sam is poor, but not identical with some poor person. Nor can it be false that Sam is poor, but true that he is identical with some poor person.

But (2) is false. Sam is necessarily self-identical, but not necessarily poor. Therefore (2) does not follow from (1), for a false statement cannot follow from a true one.

The fallacy is in assuming that being identical with some poor person is the same fact as being identical with oneself.

I plead innocent of the charge of having committed a logical mistake.  I accept (1) but I reject (2) and for the very reason the Opponent supplies: "Sam is necessarily self-identical, but not necessarily poor."  In fact, this is the very point I use against him. I claim that his theory cannot accommodate it. 

The Issue

The issue is whether predication can be assimilated to identity. 'Sam is poor' is an example of a sentence which, on the face of it, features a predicative use of 'is' as opposed to an identitarian use.   Connected with this is the fact that 'poor' is a predicate adjective, not a noun proper or common.  So surface indications are that predication cannot be assimilated to identity, or vice versa, and that the 'is' of identity and the 'is' of predication are distinct and mutually irreducible.

When we say that Sam is poor we cannot possibly mean that Sam is identical to the property of being poor. Why not? First, if Sam is identical to a property, then he is a property -- which is precisely what he isn't. Second,  if Sam is poor and his father Dave is poor, and to be poor is to be identical to the property of being poor, then, by the Transitivity of Identity, Sam is identical to Dave, which is absurd.

On the other hand, 'Sam is poor' is equivalent to 'Sam is a poor man.'  What we have done is replace the adjective with a (common) name. This lends sanction to the notion that our original sentence can be construed to express  an identity between the denotatum of 'Sam' and exactly one of the denotata of 'poor man.'  We can give this poor guy a (proper) name: 'Poboy.'  

I now ask: what is the truth-maker of 'Sam is a poor man' given that the 'is' expresses numerical identity? What in the world makes-true 'Sam is a poor man'?  (If the Opponent declares that there is no need for a truth-maker for this obviously contingent true sentence, then Game Over, and we have nothing more to discuss.)  The answer has to be, on the theory under discussion: the numerical identity of Sam with Poboy. Since Sam and Poboy are one and the same, this amounts to saying that the truth-maker of 'Sam is a poor man' is Sam's being Sam.

The Problem

The difficult with this identity theory of predication ought to be obvious.  It succumbs to two related objections as I said earlier:

Objection 1. Sam might not have been poor.  But it is not the case that Sam might not have been Sam. So the manifestly contingent truth  of 'Sam is poor' cannot be explained in terms of identity. 

Objection 2. That was a modal objection; now for a temporal one. The poor have been known to become rich. Suppose Sam goes from poor to rich.  The identity theory implies that Sam, who was identical to Poboy, ceases to be identical to Poboy and becomes identical to Richboy.  But surely this is absurd inasmuch as it is equivalent to saying that Sam, who was numerically the same as himself, is now no longer numerically the same as himself.

This is absurd because, if Sam changes in respect of wealth, going from poor to rich, there has to be a self-same substrate of this change. Sam must remain numerically the same through the change. After all, the change is accidental, not substantial. The identity theory of predication, however, cannot accommodate these truisms. For if Sam is poor in virtue of being identical to one of the poor individuals, then he cannot become rich without ceasing to be himself.

An Alternative Which Avoids These Objections

Suppose we construe 'Sam is poor' to express the instantiation by Sam of the property of being poor.  Then the objections can't get started. The Opponent, however, cannot avail himself of this way out since he is a nominalist, one who rejects properties.  He may appreciate that man does not live by bread, or bed, alone, but he does not appreciate that the philosopher does not live by predicates alone -- even if he turns them into names.

But I am not endorsing the alternative since it too has difficulties. Here is one.  Sam's going from poor to rich or hot to cold or whatever is an intrinsic accidental change, a real change in Sam. It is not a relational change.  But if Sam merely instantiates the property of being poor, and this property is a universal, and indeed a universal that is not a constituent of Sam, then it would seem that what is plainly an intrinsic change has been misconstrued as a relational change. 

Related articles

Grammar School

Bill O'Reilly Makes His Abortion Mistake Again

Maverick Philosopher: An Identity Theory of Predication

The 'Is' of Identity and the 'Is' of Predication: Contra Sommers

Maimonides on Existence as an Accident and on Divine Simplicity

Maverick Philosopher: Nominalism and an Identity Theory of Predication

What is Potentiality? An Exploration

Just Say 'No' to 'No Self'

An Identity Theory of Predication

I will sketch a two-name, quasi-Scholastic, nominalistic/reistic  theory of predication that I believe is quite hopeless. But it may serve as a foil against which and in comparison to which a more plausible theory may be developed.

Suppose it is true that Sam is poor. What are the truth-conditions of 'Sam is poor'?  Rewrite the sentence as 'Sam is a poor individual.' Think of 'Sam' ('S') and ''poor individual' ('P') as names where the first name is proper and the second common. We assume that there are no universals. Accordingly, 'poor' in our original sentence cannot be construed as an abstract substantive, as a proper name for the universal poorness.  It must be construed as a common name for poor individuals.

And because we are assuming that there are no universals, we cannot parse 'Sam is poor' as 'Sam instantiates poorness.' Nor can we take the truth-maker of 'Sam is poor' to be the state of affairs, Sam's being poor.

First idea. 'Sam is a poor individual' is true just in case:

A. For some x, 'S' denotes x and for some x, 'P' denotes x.

This is obviously insufficient since it doesn't guarantee that the item denoted by 'S' is numerically the same as one of the items denoted by 'P.'  While the second two occurrences of 'x' are bound variables, they are not bound by the same quantifier. So we try 

B. For some x, 'S' denotes x and 'P' denotes x.

This is much better. The second and third occurrences of 'x' are bound by the same quantifier. This ensures that the item denoted by 'S' is identical to one of the items denoted by 'P.'  The first item is called 'Sam' and the second we can call 'Poboy.'  Obviously these names denote one and the same item given that our sentence is true.

This yields an identity theory of predication. A simple predicative sentence such as 'Sam is poor' is true just in case the denotatum of the subject term is identical to one of the denotata of the predicate term.  The truth-maker of the sentence is the identity of Sam with Poboy, i.e., the identity of Sam with himself.

Objection 1. Sam might not have been poor.  But it is not the case that Sam might not have been Sam. So the manifestly contingent truth  of 'Sam is poor' cannot be explained in terms of identity. 

Objection 2. That was a modal objection; now for a temporal one. The poor have been known to become rich. Suppose Sam goes from poor to rich.  The identity theory implies that Sam, who was identical to Poboy, ceases to be identical to Poboy and become identical to Richboy.  But surely this is absurd inasmuch as it is equivalent to saying that Sam, who was numerically the same as himself, is now no longer numerically the same as himself.

This is absurd because, if Sam changes in respect of wealth, going from poor to rich, there has to be a self-same substrate of this change. Sam must remain numerically the same through the change. After all, the change is accidental, not substantial. The identity theory of predication, however, cannot accommodate these truisms. For if Sam is poor in virtue of being identical to one of the poor individuals, then he cannot become rich without ceasing to be himself.

Notice how these problems disappear if properties are admitted.  Sam instantiates the property of being poor, but he might not have. Sam instantiates the property of being poor at one time but not at others.

I now invite the Noble Opponent to show how his version of the identity theory circumvents these objections, if it does.  

Related articles

Carnap and Clarity

Potentiality and the Substance View of Persons

Objective Truth as a Condition of Intelligibility

Divine Simplicity and God's Contingent Knowledge: An Aporetic Tetrad

 

Two Good Articles on Predication Theory

Ignacio Angelelli, Predication Theory: Classical versus Modern

Gyula Klima, The Essentialist Nominalism of John Buridan

The 'Is' of Identity and the 'Is' of Predication: Contra Sommers

Dedication: To Bill Clinton who taught us that much can ride on what the meaning of 'is' is.

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The Opponent has a very good post in which he raises the question whether the standard analytic distinction between the 'is' of identity and the 'is' of predication is but fallout from an antecedent decision to adhere to an absolute distinction between names and predicates according to which no name is a predicate and no predicate is a name. If the distinction is absolute, as Gottlob Frege and his epigoni maintain, then names cannot occur in predicate position, and a distinction between the two uses of 'is' is the consequence.  But what if no such absolute distinction is made?  Could one then dispense with the standard analytic distinction between the two uses of 'is'?  Or are there reasons independent of Frege's function-argument analysis of propositions for upholding the distinction between the two uses? 

To illustrate the putative distinction, consider

1. George Orwell is Eric Blair

and

2. George Orwell is famous.

Both sentences feature a token of 'is.'  Now ask yourself: is 'is' functioning in the same way in both sentences? The standard analytic line is that 'is' functions differently in the two sentences.  In (1) it expresses (numerical) identity; in (2) it expresses predication. Identity, among other features, is symmetrical; predication is not.  That suffices to distinguish the two uses of 'is.'  'Famous' is predicable of Orwell, but Orwell is not predicable of  'famous.'  But if Blair is Orwell, then Orwell is Blair.

Now it is clear, I think, that if one begins with the absolute name-predicate distinction, then the other distinction is also required. For if  'Eric Blair' in (1) cannot be construed as a predicate, then surely the 'is' in (1) does not express predication.  The question I am raising, however, is whether the distinction between the two uses of 'is' arises ONLY IF one distinguishes absolutely and categorially between names and predicates.

Fred Sommers seems to think so.  The Opponent follows him in this. Referencing the example 'The morning star is Venus,' Sommers  writes, "Clearly it is only after one has adopted the syntax that prohibits the predication of proper names that one is forced to read 'a is b' dyadically and to see in it a sign of identity." (The Logic of Natural Language, Oxford 1982, p. 121, emphasis added)  The contemporary reader will of course wonder how else 'a is b' could be read if it is not read as expressing a dyadic relation between a and b.  How the devil could the 'is' in 'a is b' be read as a sign of predication?

The question can be put like this. Can we justify a distinction between the 'is' of identity and the 'is' of predication even if we do not make an absolute distinction between names (object words) and predicates (concept words)?  I think we can.

Is it not obvious that if an individual has a property, then it is not identical to that property? Tom is hypertensive. But it would be absurd to say that Tom is identical to this property.  This is so whether you think of properties as universals or as particulars (tropes). Suppose the property of being hypertensive (H-ness) is a universal and that Tom's brother Sal is also hypertensive. It follows that they share this property.  So if Tom = H-ness, and Sal = H-ness, then, by the transitivity and symmetry of identity, Tom = Sal, which is absurd.

If properties are tropes, we also get an absurdity. On a trope bundle theory, Tom is a bundle of tropes. But surely Tom cannot be identical to one of his tropes, his H-trope.  On a trope substratum theory, tropes are like Aristotelian accidents inhering in a substance. But surely no substance is identical to one of its accidents.

So whether properties are universals or tropes, we cannot sensibly think of an individual's having a property in terms of identity with that property.  If H-ness is a universal, then we would speak of Tom's instantiating H-ness, where this relation is obviously asymmetrical and for this reason and others distinct from identity.

Now 'H' is a predicate whereas 'H-ness' is a name. But nothing stops us from parsing 'Tom is hypertensive' as 'Tom instantiates hypertensiveness.' This shows that we can uphold the distinction between the 'is' of identity and the 'is' of predication with a two-name theory of predication, and thus without making Frege's absolute distinction between names and predicates.  It appears that Sommers is mistaken in his claim that  "Clearly it is only after one has adopted the syntax that prohibits the predication of proper names that one is forced to read 'a is b' dyadically and to see in it a sign of identity."

I am assuming of course that we cannot eke by on predicates alone: we need properties.  By my lights this should not be controversial in the least. My nominalist Opponent will demur. In 'Orwell is famous' he seems to be wanting to say that 'Orwell' and 'famous' refer to the same thing.  But what could that mean? 

First of all, 'Orwell' and 'famous' do not have the same extension: there are many famous people, but only one Orwell. 'Orwell is famous' is true. What makes it true? Presumably the fact that 'Orwell' and 'famous' denote one and the same individual. And which individual is that? Why, it's Orwell! But Orwell might not have been famous.  Since it is contingent that Orwell is famous, but noncontingent that Orwell is Orwell, the truth-maker of 'Orwell is famous' cannot be Orwell alone.  It has has to be the fact of Orwell's being famous, which fact involves the property of being famous in addition to Orwell.  

Nominalists insist that we ought not multiply entities beyond necessity. They are right! But there is no multiplication beyond necessity here since we need to admit properties as features of extralinguistic reality.  To explain why 'Orwell is famous' is contingent, one must distinguish Orwell from his contingently possessed properties.  Man does not live or think truly by predicates alone. 

Nominalism and an Identity Theory of Predication

The Worthy Opponent comments,

We nominalists hold that 'God is good' is true when what is signified by 'God' and what is signified by 'good' are numerically one and the same thing.

I stumble over this. 

Apparently, it is The Opponent's view that a sentence such 'Socrates is good' is true when what is signified by 'Socrates' and what is signified by 'good' are numerically one and the same thing. I don't understand. 'Good,' unlike 'Socrates,' is a common term: it applies to many individuals. So there cannot be numerically one thing that both 'Socrates' and 'good' signify. 'Socrates' signifies one thing; 'good' signifies many things.

If, contrary to fact, there were only one good thing, then it would make some sense to say that 'Socrates is good,' which is by its surface grammar a predication, could be read as asserting the numerical identity of Socrates with the one good thing.  But if Socrates is good, or seated, or conversing with Theaetetus, this is only contingently the case. So how analyze the possibly true 'Socrates is not good' on the assumption that there is only one good thing?  We would have to say that Socrates is distinct from himself -- which is absurd.  For if, in actuality, Socrates is good in virtue of being identical to the one good thing, then, in the possible counterfactual situation in which he -- the very same individual --  is not good, he would have to be numerically diverse from the one good thing, namely, himself!

The same argument goes through even if there are many good things. For the Opponent's claim is that Socrates is good in virtue of being identical to one of the many good things. Call this good thing G.  The claim is that 'Socrates is good' is an identity proposition in disguise, and that its deep logical form is: S = G.

The problem is that 'Socrates is good' is contingently true. But 'S = G' is not contingently true. So the predication is not an identity proposition in disguise.  

This looks to be a pretty powerful objection.

I am assuming something that is well-nigh self-evident, but which I fear the Illustrious Opponent will deny, namely, that if a = b, then this is non-contingently the case.  In other words, I am assuming that if a = b, then there is no possible situation in which a and b both exist but are numerically distinct.

Curiously, the Opponent's theory works in one case and one case only. But he has to admit the divine simplicity.  So assume that God exists, that God is essentially good, and that God is identical to his attributes, and that therefore God alone is good in this sense. If God is identical to his attributes, then God = the one and only good thing. (Socrates is good only in an analogical and derivative sense.) In this one case, 'God is good' is an identity proposition in disguise.  

Related articles

Peter van Inwagen, "A Theory of Properties," Exposition and Critique

Review of Barry Miller, A Most Unlikely God

<i>Luke</i> 2:21: Can the Not-Yet-Existent be Named?

Is God Beyond All Being?

Half-Way Fregeanism About Existence

Another subtle existence entry to flummox and fascinate the Londonistas.  Hell, this Phoenician is flummoxed by it himself.  Ain't philosophy grand?

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In section 53 of The Foundations of Arithmetic, Gottlob Frege famously maintains that

. . . existence is analogous to number.  Affirmation of existence is in fact nothing but denial of the number nought.  Because existence is a property of concepts the ontological argument for the existence of God breaks down. (65)

Frege is here advancing a double-barreled thesis that splits into two subtheses.

ST1. Existence is analogous to number.

ST2. Existence is a property (Eigenschaft) of concepts and not of objects.

In the background is the sharp distinction between property (Eigenschaft) and mark (Merkmal).  Three-sided is a mark of the concept triangle, but not a property of this concept; being instantiated is a property of this concept but not a mark of it.  The Cartesian-Kantian ontological argument "from mere concepts" (aus lauter Begriffen), according to Frege, runs aground because existence cannot be a mark of any concept, but only a property of some concepts.  And so one cannot validly argue from the concept of God to the existence of God.

Existence as a property of concepts is the property of being-instantiated.  We can therefore call the Fregean account of existence an instantiation account.  A concept is instantiated just in case it has one or more instances.  So on a Fregean reading, 'Cats exist' says that the concept cat is instantiated.  This implies, of course, that 'Cats exist' is not about cats, but about a non-cat, a concept, and what it says about this concept is not that it (singulatly) exists, but that it is instantiated!  A whiff of paradox? Or more than just a whiff?

My concern in this entry is the logical relation between the above two subtheses.  Does the first entail the second or are they logically independent?  There is a clear sense in which (ST1) is true.  Necessarily, if horses exist, then the number of horses is not zero, and vice versa.  So 'Horses exist' is logically equivalent to 'The number of horses is not zero.'  This is wholly unproblematic for those of us who agree that there are no Meinongian nonexistent objects.  But note that, in general, equivalences, even logical equivalences, do not sanction reductions or identifications.  So it remains an open question whether one can take the further step of reducing existence to instantiation, or identifying existence with instantiation, or even eliminating existence in favor of instantiation. Equivalence, reduction, elimination: those are all different.  But I make this point only to move on.

(ST1), then, is unproblematically true if understood as expressing the following logical equivalence: 'Necessarily Fs exist iff the number of Fs is not zero.'  My question is whether (ST1) entails (ST2).  Peter van Inwagen in effect denies the entailment by denying that the 'the number of . . . is not zero' is a predicate of concepts:

I would say that, on a given occasion of its use, it predicates of certain things that they number more than zero.  Thus, if one says, 'The number of horses is not zero,' one predicates of horses that they number more than zero.  'The number of . . . is not zero' is thus what some philosophers have called a 'variably polyadic' predicate.  But so are many predicates that can hardly be regarded as predicates of concepts.  The predicates 'are ungulates' and 'have an interesting evolutionary history,' for example, are variably polyadic predicates.  When one says, 'Horses are ungulates' or 'Horses have an interesting evolutionary history' one is obviously making a statement about horses and not about the concept horse.  ("Being, Existence, and Ontological Commitment," pp. 483-484)

It is this passage that I am having a hard time understanding.   It is of course clear what van Inwagen is trying to show, namely, that the Fregean subtheses are logically independent and that one can affirm the first without being committed to the second.  One can hold that existence is denial of the number zero without  holding that existence is a property of concepts.  One can go half-way with Frege without going 'whole hog' or all the way.

But I am having trouble with the claim that the predicate 'the number of . . . is not zero' is  'variably polyadic' and the examples van Inwagen employs.  'Robbed a bank together' is an example of a variably polyadic predicate.  It is polyadic because it expresses a relation and it is variably polyadic because it expresses a family of relations having different numbers of arguments.  For example, Bonnie and Clyde robbed a bank together, but so did Ma Barker and her two boys, Patti Hearst and three members of the ill-starred Symbionese Liberation Army, and so on.  (Example from Chris Swoyer and Francesco Orilia.) 

Now when I say that the number of horses is not zero, what am I talking about? It is plausible to say that I am talking about horses, not about the concept horse. (Recall the whiff of paradox, supra.)  What I don't understand are van Inwagen's examples of variably polyadic predicates.  Consider 'are ungulates.'  If an ungulate is just a mammal with hooves, then I fail to see how 'are ungulates' is polyadic, let alone variably polyadic.  'Are hooved mammals' is monadic.

The other example is 'Horses have an interesting evolutionary history.'  This sentence is clearly not about the concept horse. But it is not about any individual horse either.  Consider Harry the horse.  Harry has a history.  He was born in a certain place, grew up, was bought and sold, etc. and then died at a certain age.  He went through all sorts of changes.  But Harry didn't evolve, and so he had no evolutionary history.  No individual evolves; populations evolve:

Evolutionary change is based on changes in the genetic makeup of populations over time. Populations, not individual organisms, evolve. Changes in an individual over the course of its lifetime may be developmental (e.g., a male bird growing more colorful plumage as it reaches sexual maturity) or may be caused by how the environment affects an organism (e.g., a bird losing feathers because it is infected with many parasites); however, these shifts are not caused by changes in its genes. While it would be handy if there were a way for environmental changes to cause adaptive changes in our genes — who wouldn't want a gene for malaria resistance to come along with a vacation to Mozambique? — evolution just doesn't work that way. New gene variants (i.e., alleles) are produced by random mutation, and over the course of many generations, natural selection may favor advantageous variants, causing them to become more common in the population.

'Horses have an interesting evolutionary history,' then, is neither about the concept horse nor about any individual horse.  The predicate in this sentence appears to be non-distributive or collective.  It is like the predicate in 'Horses have been domesticated for millenia.'  That is certainly not about the concept horse.  No concept can be ridden or made to carry a load.  But it is also not about any individual horse.  Not even the Methuselah of horses, whoever he might be, has been around for millenia.

A predicate F is distributive just in case it is analytic that whenever some things are F, then each is F.  Thus a distributive predicate is one the very meaning of which dictates that if it applies to some things, then it applies to each of them.  'Blue' is an example.  If some things are blue, then each of them is blue.

If a predicate is not distributive, then it is non-distributive (collective).  If some Occupy-X nimrods have the building surrounded, it does not follow that each such nimrod has the building surrounded.  If some students moved a grand piano into my living room, it does not follow that each student did.  If bald eagles are becoming extinct, it does not follow that each bald eagle is becoming extinct.  Individual animals die, but no individual animal ever becomes extinct. If the students come from many different countries, it does not follow that each comes from many different countries.  If horses have an interesting evolutionary history, it does not follow that each horse has an interesting evolutionary history.

My problem is that I don't understand why van Inwagen gives the 'Horses have an interesting evolutionary history' example when he is committed to saying that each horse exists.  His view , I take it, is that 'exist(s)' is a first-level distributive predicate.  'Has an interesting evolutionary history,' however, is a first-level non-distributive predicate.  Or is it PvI's view that 'exist(s)' is a first-level non-distributive predicate?

Either I don't understand van Inwagen's position due to some defect in me, or it is incoherent.  I incline toward the latter.  He is trying to show that (ST1) does not entail (ST2).  He does this by giving examples of predicates that are first-level, i.e., apply to objects, but are variably polyadic as he claims 'the number of . . . is not zero' is variably polyadic.  But the only clear example he gives is a predicate that is non-distributive, namely 'has an interesting evolutionary history.'  'Horses exist,' however, cannot be non-distributive.  If some horses exist, then each of them exists.  And if each of them exists, then 'exists' is monadic, not polyadic, let alone variably polyadic.

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On an Argument for the Univocity of 'Exist(s)'

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A List of Bars Philosophers Opened On Being Denied Tenure

In section 53 of The Foundations of Arithmetic, Gottlob Frege famously maintains that

. . . existence is analogous to number.  Affirmation of existence is in fact nothing but denial of the number nought.  Because existence is a property of concepts the ontological argument for the existence of God breaks down. (65)

Frege is here advancing a double-barreled thesis that splits into two subtheses.

ST1. Existence is analogous to number.

ST2. Existence is a property (Eigenschaft) of concepts and not of objects.

In the background is the sharp distinction between property (Eigenschaft) and mark (Merkmal).  Three-sided is a mark of the concept triangle, but not a property of this concept; being instantiated is a property of this concept but not a mark of it.  The Cartesian-Kantian ontological argument "from mere concepts" (aus lauter Begriffen), according to Frege, runs aground because existence cannot be a mark of any concept, but only a property of some concepts.  And so one cannot validly argue from the concept of God to the existence of God.

Existence as a property of concepts is the property of being-instantiated.  We can therefore call the Fregean account of existence an instantiation account.  A concept is instantiated just in case it has one or more instances.  So on a Fregean reading, 'Cats exist' says that the concept cat is instantiated.  This implies, of course, that 'Cats exist' is not about cats, but about a non-cat, a concept, and what it says about this concept is not that it (singulatly) exists, but that it is instantiated!  A whiff of paradox? Or more than just a whiff?

My concern in this entry is the logical relation between the above two subtheses.  Does the first entail the second or are they logically independent?  There is a clear sense in which (ST1) is true.  Necessarily, if horses exist, then the number of horses is not zero, and vice versa.  So 'Horses exist' is logically equivalent to 'The number of horses is not zero.'  This is wholly unproblematic for those of us who agree that there are no Meinongian nonexistent objects.  But note that, in general, equivalences, even logical equivalences, do not sanction reductions or identifications.  So it remains an open question whether one can take the further step of reducing existence to instantiation, or identifying existence with instantiation, or even eliminating existence in favor of instantiation. Equivalence, reduction, elimination: those are all different.  But I make this point only to move on.

(ST1), then, is unproblematically true if understood as expressing the following logical equivalence: 'Necessarily Fs exist iff the number of Fs is not zero.'  My question is whether (ST1) entails (ST2).  Peter van Inwagen in effect denies the entailment by denying that the 'the number of . . . is not zero' is a predicate of concepts:

I would say that, on a given occasion of its use, it predicates of certain things that they number more than zero.  Thus, if one says, 'The number of horses is not zero,' one predicates of horses that they number more than zero.  'The number of . . . is not zero' is thus what some philosophers have called a 'variably polyadic' predicate.  But so are many predicates that can hardly be regarded as predicates of concepts.  The predicates 'are ungulates' and 'have an interesting evolutionary history,' for example, are variably polyadic predicates.  When one says, 'Horses are ungulates' or 'Horses have an interesting evolutionary history' one is obviously making a statement about horses and not about the concept horse.  ("Being, Existence, and Ontological Commitment," pp. 483-484)

It is this passage that I am having a hard time understanding.   It is of course clear what van Inwagen is trying to show, namely, that the Fregean subtheses are logically independent and that one can affirm the first without being committed to the second.  One can hold that existence is denial of the number zero without  holding that existence is a property of concepts.  One can go half-way with Frege without going 'whole hog' or all the way.

But I am having trouble with the claim that the predicate 'the number of . . . is not zero' is  'variably polyadic' and the examples van Inwagen employs.  'Robbed a bank together' is an example of a variably polyadic predicate.  It is polyadic because it expresses a relation and it is variably polyadic because it expresses a family of relations having different numbers of arguments.  For example, Bonnie and Clyde robbed a bank together, but so did Ma Barker and her two boys, Patti Hearst and three members of the ill-starred Symbionese Liberation Army, and so on.  (Example from Chris Swoyer and Francesco Orilia.) 

Now when I say that the number of horses is not zero, what am I talking about? It is plausible to say that I am talking about horses, not about the concept horse. (Recall the whiff of paradox, supra.)  What I don't understand are van Inwagen's examples of variably polyadic predicates.  Consider 'are ungulates.'  If an ungulate is just a mammal with hooves, then I fail to see how 'are ungulates' is polyadic, let alone variably polyadic.  'Are hooved mammals' is monadic.

The other example is 'Horses have an interesting evolutionary history.'  This sentence is clearly not about the concept horse. But it is not about any individual horse either.  Consider Harry the horse.  Harry has a history.  He was born in a certain place, grew up, was bought and sold, etc. and then died at a certain age.  He went through all sorts of changes.  But Harry didn't evolve, and so he had no evolutionary history.  No individual evolves; populations evolve:

Evolutionary change is based on changes in the genetic makeup of populations over time. Populations, not individual organisms, evolve. Changes in an individual over the course of its lifetime may be developmental (e.g., a male bird growing more colorful plumage as it reaches sexual maturity) or may be caused by how the environment affects an organism (e.g., a bird losing feathers because it is infected with many parasites); however, these shifts are not caused by changes in its genes. While it would be handy if there were a way for environmental changes to cause adaptive changes in our genes — who wouldn't want a gene for malaria resistance to come along with a vacation to Mozambique? — evolution just doesn't work that way. New gene variants (i.e., alleles) are produced by random mutation, and over the course of many generations, natural selection may favor advantageous variants, causing them to become more common in the population.

'Horses have an interesting evolutionary history,' then, is neither about the concept horse nor about any individual horse.  The predicate in this sentence appears to be non-distributive or collective.  It is like the predicate in 'Horses have been domesticated for millenia.'  That is certainly not about the concept horse.  No concept can be ridden or made to carry a load.  But it is also not about any individual horse.  Not even the Methuselah of horses, whoever he might be, has been around for millenia.

A predicate F is distributive just in case it is analytic that whenever some things are F, then each is F.  Thus a distributive predicate is one the very meaning of which dictates that if it applies to some things, then it applies to each of them.  'Blue' is an example.  If some things are blue, then each of them is blue.

If a predicate is not distributive, then it is non-distributive (collective).  If some Occupy-X nimrods have the building surrounded, it does not follow that each such nimrod has the building surrounded.  If some students moved a grand piano into my living room, it does not follow that each student did.  If bald eagles are becoming extinct, it does not follow that each bald eagle is becoming extinct.  Individual animals die, but no individual animal ever becomes extinct. If the students come from many different countries, it does not follow that each comes from many different countries.  If horses have an interesting evolutionary history, it does not follow that each horse has an interesting evolutionary history.

My problem is that I don't understand why van Inwagen gives the 'Horses have an interesting evolutionary history' example when he is committed to saying that each horse exists.  His view , I take it, is that 'exist(s)' is a first-level distributive predicate.  'Has an interesting evolutionary history,' however, is a first-level non-distributive predicate.  Or is it PvI's view that 'exist(s)' is a first-level non-distributive predicate?

Either I don't understand van Inwagen's position due to some defect in me, or it is incoherent.  I incline toward the latter.  He is trying to show that (ST1) does not entail (ST2).  He does this by giving examples of predicates that are first-level, i.e., apply to objects, but are variably polyadic as he claims 'the number of . . . is not zero' is variably polyadic.  But the only clear example he gives is a predicate that is non-distributive, namely 'has an interesting evolutionary history.'  'Horses exist,' however, cannot be non-distributive.  If some horses exist, then each of them exists.  And if each of them exists, then 'exists' is monadic, not polyadic, let alone variably polyadic.

Modality, Possible Worlds, and the Accidental-Essential Distinction

This from a reader:

The Stanford Encyclopedia notes in its article on Essential vs. Accidental Properties, "A modal characterization of the distinction between essential and accidental properties is taken for granted in nearly all work in analytic metaphysics since the 1950s.”  Personally, I find modal definitions of this type very hand wavy.  Ed Feser states my objection more eloquently than I can: 

 

From an Aristotelian-Thomistic point of view, the possible worlds analysis of essence has things backwards: we need to know what the essence of a thing is, before we can know what it would be like in various possible worlds; talk of possible worlds, if legitimate at all, must get explained in terms of essence, not essence in terms of possible worlds ( Aquinas, iBooks edition, page 90).  

 

I think the modal characterization will be a dead end for us.

Response

Two points.  First, I do not understand how one could characterize the essential versus accidental distinction except modally.  Second, a modal characterization need not be in terms of so-called 'possible worlds.'  One should not suppose that a characterization is modal if and only if it is in terms of possible worlds.

First point first.  I am a blogger and a native Californian.  I might not have been either.  So being a blogger and being a native Californian are accidental properties of me.  I could have existed without possessing these properties.  But I could not have existed without being human.  So being human is an essential property of me.  Generalizing, if P is an essential property of x, then x must have P, it cannot not have P.  If P is an accidental property of x, then x need not have P, it could lack P.  And conversely in both cases.

Note that I had to use modal words to characterize the distinction: 'might,' 'could,' 'must,' 'need not,' 'cannot.'  I conclude that the accidental-essential distinction is irreducibly modal: it cannot be made except modally.  It is indeed essentially modal!

To appreciate this, consider the first two accidental properties I mentioned.  I was not always a blogger: speaking tenselessly, there are times at which I am not a blogger.  But I was always and will always be a native Californian.  Speaking tenselessly again, there are no times at which I am not a native Californian.*  It follows that we cannot define an essential (accidental) property of x as a property x has (does not have) at every time at which it exists.  The distinction cannot be made in temporal terms; one needs to employ modal language.

If a thing has a property essentially, then it has the property at every time at which it exists.  But not conversely:  if a thing has a property at every time at which it exists, it does not follow that it has the property essentially.  So again it should be clear that the distinction in question is ineliminably modal.

I should make it clear that the modality in question here is non-epistemic/non-doxastic.  Suppose Tom died an hour ago, unbeknownst to me.  I ask you, "Is Tom teaching now?"  You say, "Could be!"  But of course it can't be that he is teaching now if he is dead now.  You are not saying that it is (really) possible that he be teaching now; you are saying that his teaching now is logically consistent with what you know or believe, that it is not ruled out by what you know/believe. 

Second point second.  From what I have written it should be clear that we don't need the jargon of possible worlds to talk modally.   But it is a very useful and graphic way of talking.  Accordingly,

D1. P is an accidental property of x =_df there are possible worlds in which x exists but does not instantiate P.

D2. P is an essential property of x =_df there are no possible worlds in which x exists but does not instantiate P.

We can add a third definition:

D3. P is a necessary property of x =_df there are no possible worlds in which x exists but does not instantiate P, and x exists in every possible world.  Example:  Omniscience is a necessary property of God: he has it in every world in which he exists, and, since he is a necessary being, he exists in every world.  Non-theological example: Being prime is a necessary property of the number 7:  7 has it in every metaphysically possible world in which it exists, and it exists in every such world.

The above definitions do not sanction the reduction of the modal to the non-modal.  For modal terms appear on both sides of the biconditionals.  Nor could we say that the right-hand sides explicates or analyzes the left-hand sides.  So I agree with Feser as quoted above.  What is first in the order of metaphysical explanation is a thing's being essentially thus and so or accidentally thus and so.  We can then go on to represent these states of affairs in possible worlds terms, but we need not do so.

Jenner and Dolezal.  Is Jenner essentially male?  I should think so.  Being male is a biological determination.  It can be spelled out in terms of sex chromosomes.   They are different in males and females.  Jenner as he is today is a sort of super-transvestite: he is not just a male in women's clothing, but a male who has had his body surgically altered to have female anatomical features.  But he is still male.  How could he be a woman?  You can't be a woman without first being a girl, and he was never a girl.

If you deny that Jenner is essentially biologically male, will you also deny that he is essentially biologically human?  If not, why not?  If literal sex change is possible, is species change possible? 

Is Rachel Dolezal essentially Caucasian?  Well, of course.  Race, like sex, is biologically based.  It is not something you choose.  Nor is it a social construct.  Barack Obama thinks that we Americans have racism in our DNA.  That's bullshit, of course.  There is nothing biological about being a racist.  But there is something biological about race.  You can be a traitor to your country, but not to your race.

Biology matters!  And so does clear thinking and honest talk.  Obama take note.

______________________

*Ignoring the fact, if it is a fact, that I existed pre-natally.  If this wrinkle troubles you, I can change my example.

 

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Van Inwagen, Properties, and Bare Particulars

In this entry I expand on my claim that Peter van Inwagen's theory of properties commits him to bare particulars, not in some straw-man sense of the phrase, but in a sense of the phrase that comports with what proponents of bare particulars actually have claimed.  I begin by distinguishing among four possible senses of 'bare particular.'

Four Senses of 'Bare Particular'

1. A bare particular is an ordinary concrete particular that lacks properties.  I mention this foolish view only to set it aside.  No  proponent of bare particulars that I am aware of ever intended the phrase in this way.  And of course, van Inwagen is not committed to bare particulars in this sense.

2. A bare particular is an ontological constituent of an ordinary concrete particular, a constituent that has no properties.  To my knowledge, no proponent of bare particulars ever intended the phrase in this way.  In any case, the view is untenable and may be dismissed.  Van Inwagen is of course not committed to this view.  He is a 'relation' ontologist, not a 'constituent' ontologist.

3. A bare particular is an ontological constituent of an ordinary concrete particular, a constituent that does have properties, namely, the properties associated with the ordinary particular in question, and has them by instantiating (exemplifying) them.  This view is held by Gustav Bergmann and by David Armstrong in his middle period.  Armstrong, however, speaks of  thin particulars rather than bare particulars, contrasting them with thick particulars (what I am calling ordinary concrete particulars).  When he does uses 'bare particular,' he uses the phrase incorrectly and idiosyncratically to refer to something like (1) or (2).  For example, in Universals and Scientific Realism, Cambridge UP, 1978, vol. I, p. 213, he affirms something he calls the "Strong Principle of the Rejection of Bare Particulars":

For each particular, x, there exists at least one non-relational property, P, such that x is P.

(I should think that the first occurrence of 'P' should be replaced by 'P-ness' despite the unfortunate sound of that.)  This principle of Armstrong is plausibly read as a rejection of (1) and (2).  It is plainly consistent with (3).

But of course I do not claim that van Inwagen is committed to bare or thin particulars in the sense of (3). For again, van Inwagen is not a constituent ontologist.

4. A bare particular is an ordinary concrete particular that has properties by instantiating them, where instantiation is a full-fledged external asymmetrical relation (not a non-relational tie whatever that might come to) that connects  concrete objects to abstract objects, where abstract objects are objects that are not in space, not in time, and are neither causally active nor causally passive. 

What is common to (3) and (4) is the idea that bare particulars  have properties all right, but they have them in a certain way, by being externally related to them.  A bare particular, then, is nothing like an Aristotelian primary substance which has, or rather is, its essence or nature.   The bareness of a bare particular, then, consists in its lacking an Aristotle-type nature, not it its lacking properties. 

My claim is that van Inwagen is committed to bare particulars in sense (4).  Let me explain.

Van Inwagen's Bare Particulars

Consider my cat Max.  Van Inwagen is committed to saying that Max is a bare particular.  For while Max has properties, these properties are in no sense  constituents of him, but lie (stand?) outside him in a realm apart.  These properties are in no sense at him or in him or on him, not even such properties as being black or being furry, properties that are plausibly held to be sense-perceivable.  After all, one can see black where he is and feel furriness where he is.  None of Max's properties, on van Inwagen's  construal of properties, are where he is or when he is.  As I made clear earlier, the realms of the concrete and the abstract are radically disjoint for van Inwagen.  They are jointly exhaustive and mutually exclusive realms: for all x, x is either concrete or abstract, but not both and not neither.  So Max is here below in the realm of space, time, change, and causality while his properties exist in splendid  isolation up yonder in the realm of abstracta.

Max and his properties are of course connected by instantiation which is a relation that is both external and abstract.  In what sense is the relation external?  X and y are externally related just in case there is nothing intrinsic about the relata that entails their being related.  Max is two feet from me at the moment.  This relation of being two feet from is external in that there are no intrinsic properties of me or Max or both that entail our being two feet from each other.  Our intrinsic properties would be just the same if we were three feet from each other.  But Max and his brother Manny are both black.  In virtue of their both being intrinsically black, they stand in the same color as relation.  Hence the latter relation is not external but internal. Internal relatedness is supervenient upon the intrinsic features of the relata; external relatedness is not.

Suppose I want to bring it about that two balls have the same color.  I need do only two things: paint the one ball red, say, and then paint the other ball red.  But if I want to bring it about that there are two balls having the same color ten feet from each other, I have to do three things: paint the one ball red, say; paint the other ball red; place them ten feet from each other.   The external relatedness does not supervene upon the intrinsic properties of the relata.

Given that concrete particulars are externally related to their properties, these particular are bare particulars in the sensedefined in #4 above. 

And What is Wrong with That?

Suppose you agree with me that van Inwagen's concrete particulars are bare, not in any old  sense, but in the precise sense I defined, a sense that comports well with what the actual proponents of bare/thin particulars had in mind.  So what?  What's wrong with being committed to bare particulars?  Well, the consequences seem unpalatable if not absurd.

A. One consequence is that all properties are accidental and none are essential.  For if Max is bare, then there is nothing in him or at him or about him that dictates the properties he must instantiate or limits the  properties he can instantiate.  He can have any old set of properties so long as he has some set or other.  Bare particulars are 'promiscuous' in their connection with properties.   The connection between particular and property is contingent and all properties are accidental.  It is metaphysically (broadly logically) possible that Max combine with any property.  He happens to be a cat, but he could have been a poached egg or a valve lifter.  He could have had the shape of a cube.  Or he might have been a dimensionless point.  He might have been an act of thinking (temporal and causally efficacious, but not spatial). 

B. A second consequence is that all properties are relational and none are intrinsic.  For if Max is black in virtue of standing in an external instantiation relation to the abstract object, blackness, then his being black is a relational property and not an intrinsic one.

C. A third consequence is that none of Max's properties are sense-perceivable. PvI-properties are abstract objects and none of them are perceivable.  But if I cup my hands around a ball, don't I literally feel its sphericalness or spheroidness?  Or am I merely being appeared to spheroidally?

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Peter van Inwagen, "A Theory of Properties," Exposition and Critique

Peter van Inwagen, "A Theory of Properties," Exposition and Critique

This entry is a summary and critique of  Peter van Inwagen's "A Theory of Properties," an article which first appeared in 2004 and now appears as Chapter 8 of his Existence: Essays in Ontology (Cambridge University Press, 2014, pp. 153-182.)  Andrew Bailey has made it available on-line. (Thanks Andrew!)  I will be quoting from the Existence volume.  I will also be drawing upon material from other articles in this collection. This post is a warm-up for a review of the book by me commissioned by a European journal. The review wants completing by the end of February.  Perhaps you can help me. Comments are enabled for those who know this subject.

Exposition

1. The Abstract and the Concrete. 

Platonism is "the thesis that there are abstract objects." (153)  Van Inwagen uses 'object' synonomously with 'thing,' 'item,' and 'entity.' (156)  Everything is an object, which is to say: everything exists.  Thus there are no nonexistent objects, pace Meinong.  There are two categories of object, the abstract and the concrete.  These categories are mutually exclusive and jointly exhaustive.  Thus for any  x, x is either abstract or concrete, but not both, and not neither. Van Inwagen is a bit  coy when it comes to telling us what 'abstract' and concrete' mean; he prefers a roundabout way of introducing these terms.  He stipulates that the terms and predicates of ordinary, scientific, and philosophical discourse can be divided  into two mutually exclusive and jointly exhaustive classes. The denotata of the members of these two classes of terms and predicates, if they have denotata, are concrete and abstract objects.  Thus 'table,' 'God,' and 'intelligent Martian,' if they pick out anything, pick out concreta, while 'number,' 'the lion,' (as in 'The lion is of the genus Felis') and 'sentence' (as in 'The same sentence can express different propositions in different contexts'), pick out abstracta. (154) (See footnote * below)

Van Inwagen holds that platonism is to  be avoided if at all possible.  On platonism, there are abstract objects.  This characteristic thesis does not entail, but it is consistent with, the proposition that there are also concrete objects.  Van Inwagen is a platonist who accepts both abstract and concrete objects but thinks we would be better of if we could avoid commitment to abstract objects.  Why?  Well, apart from considerations of parsimony, the difference between members of the two categories is abysmal (my word): "the differences between God and this pen pale into insignificance when they are compared with the differences between this pen and the number 4 . . . ." (156)  Such a radical difference is puzzling.  So it would be preferable if the category of abstracta were empty.  That the category of concreta cannot be empty is obvious: we know ourselves to be concreta. (157) Van Inwagen goes on to belabor the point that the things we can say about concrete things are practically endless, while little can be said about abstracta.

In short, reality, unlike ancient Gaul, "is divided into two parts . . . ." (158, emphasis added). The two parts of reality are radically disjoint.  Everything is either abstract or concrete, nothing is both, and nothing is neither.  Among the abstracta are instantiated properties.  Instantiation or 'having' would seem to forge a connection between the disjoint realms.  But the instantiation relation is "abstract and external." (206, 242)  So it too resides in the realm of abstracta and hence (as it seems to me) does nothing to mitigate the radical dualism or span the abyss that yawns between reality's two parts.  So if we could eke by without abstracta, that would be preferable.  But we cannot manage without them, says van Inwagen. (158)

2. Why We Need Abstract Objects. 

The short reason is that we need them because we need properties, and properties are one sort of abstract object, along with propositions and "proper relations." (240) A proper relation is a relation whose adicity is two or more; van Inwagen thinks of properties as one-place relations and propositions as zero-place relations. Every abstract object is a relation (a relation-in-intension) in the broad or improper sense, and everything else is a substance, a concrete object. (239)

But why do we need properties?  We need properties because things have common features.  The class of humans, for example, has something in common.  This appears to be an existential claim: there is something, humanity, that the members of this class share.  Platonists take the appearance at face value while nominalists maintain that the appearance is a mere appearance such that in reality there are no properties.  How do we decide the issue that divides the platonists and the nominalists?  Here van Inwagen is referring to what he calls "austere" nominalists, the nominalists more standardly called extreme: those who deny that there are properties at all.  There are also the nominalists van Inwagen calls "luxuriant" nominalists, the ones more standardly called moderate: those who admit the existence of tropes or individual accidents or particularized properties. (203, 203 fn 5)  The extreme nominalist denies that there are properties at all -- a lunatic view if I may inject my opinion -- while the moderate nominalists admit properties but deny that they are universals.  Platonists are not austere nominalists because they accept properties; they are not luxuriant nominalists because they accept universals.

3. Van Inwagen's Method. 

The method derives from Quine.  We start with the beliefs we already have, couched in the sentences we already accept.  We then see if these sentences commit us to properties.  We do this by translating these sentences into "the canonical language of quantification." (160)  If we need to quantify over properties for the sentences we accept as true to count as true, then we are ontologically committed to the existence of properties.  If, on the other hand, we can 'paraphrase away' the apparent reference to properties in the sentences we accept that appear to refer to properties, then the ontological commitment is merely apparent.

Van Inwagen's main idea here is that our discourse commits us to quantification over properties, and thus to the existence of properties.  We deduce the existence of properties from certain sentences we accept.  The argument is not epistemological: it does not seek to provide evidence for the existence of properties.  Nor is it transcendental, or an inference to the best explanation. (167)  The operative methodological principle, if there is one, is only this:  "if one does not believe that things of a certain sort exist, one shouldn't say anything that demonstrably  implies that things of that sort exist." (167) 

Example. We accept 'Spiders share some of the anatomical features of insects.'  (159) This says nothing different from 'There are anatomical features that insects have and spiders also have.'  This then is translated into canonical English.  I will spare you the rigmarole.  The upshot is that there are anatomical features.  Hence there are properties.

The most promising way of rebutting platonism so derived is by finding a paraphrase of the original sentence that says the same thing but does not even seem to commit its acceptor to properties.  (The nominalists would of course have to do this for every sentence proposed by  platonists that supposedly commits its users to abstracta.) Van Inwagen, predictably, argues against the paraphrastic way out. Nominalist paraphrases are not to be had. (164-167)

4. Van Inwagen's Theory of Properties.

Given that there are properties, what are they like?  What are the properties of properties? To specify them is the task of a theory of properties. What follows is my list, not his, but gleaned from what he writes.  Properties are

a. abstract objects, as we have already seen.  As abstract, properties are non-spatiotemporal and causally inert. (207) Better: abstract objects are categorially such as to be neither causally active nor causally passive.

b. universals, as we have already gleaned, with the exception of haecceities such as the property of being identical to Plantinga. (180)  Van Inwagen has no truck with tropes. (241) See my Peter van Inwagen's Trouble with Tropes.

c. the entities that play the property role.  And what role would that be? This is the role "thing that can be said of something."  It is a special case of the role "thing that can be said." (175)  Properties are things that can be said of or about something.  Propositions are things that can be said, period, or full stop.

d. unsaturated assertibles.  Things that can be said are assertibles.  They are either unsaturated, in which case they are properties, or saturated, in which case they are propositions. 

e. necessary beings. (207)

f. not necessarily instantiated.  Many properties exist uninstantiated.

g. not all of them instantiable.  Some unsaturated assertibles are necessarily uninstantiated, e.g., what is said of x if one says 'x is both round and square.'

h. such that the usual logical operations apply to them. (176)  Given any two assertibles, whether saturated or unsaturated, there is 'automatically' their conjunction and their disjunction.  Given any one assertible, there is 'automatically' its negation. 

i. abundant, not sparse.  There is a property corresponding to almost every one-place open sentence with a precise meaning. The 'almost' alludes to a variant of Russell's paradox that van Inwagen is fully aware of but that cannot be discussed here. (243)  Thus, contra David Armstrong, it is not the task of what the latter calls "total [empirical] science" to determine what properties there are.  Perhaps we could say that properties for van Inwagen are logical fallout from one-place predicates. (My phrase)  But since properties are necessary beings, there are all the properties there might have been; hence they 'outrun' actual one-place predicates. (My way of putting it.)

j. not parts or constituents in any sense of the concrete things that have them.  Indeed, it makes no sense to say that an assertible is a part of a concrete object.  And although properties or unsaturated assertibles are universals, it makes no sense that such an item is 'wholly present' in concrete objects. (178) Concrete things are 'blobs' in David Armstrong's sense.  They lack ontological structure. "Their only constituents are their parts, their parts in the strict and mereological sense." (243)

k. not more basic ontologically than the things whose properties they are. A concrete thing is not a bundle or cluster of properties.  The very suggestion is senseless on van Inwagen's scheme.  A property is an unsaturated assertible.  It is very much like a Fregean (objective) concept or Begriff, even though van Inwagen does not say this in so many words.  (But his talk of unsaturatedness points us back to Frege.) Clearly it would be senseless to think of a dog as a bundle of Fregean concepts.  That which can be truly said of a thing like a dog, that it is furry, for example, is no part of the critter. (178-79)

I should point out that while talk of saturated and unsaturated assertibles conjures the shade of Frege, van Inwagen has no truck with Frege's concept-object dichotomy according to which no concept is an object, no object is a concept, and the concept horse is not a concept.  You could say, and I mean no disrespect, that he 'peters out' with respect to this dichotomy: "I do not understand the concept-object distinction. The objects I call properties are just that: objects." (206, fn 11)

l. are not objects of sensation. (179)   To put it paradoxically, and this is my formulation, not van Inwagen's, such perceptual properties as being blue and being oval in shape are not perceptible properties.  One can see that a coffee cup is blue, but one cannot literally see the blueness of the coffee cup.

Critique

My readers will know that almost everything (of a substantive and controversial nature) that van Inwagen maintains, I reject and for reasons that strike me as good.  Ain't philosophy grand?

1. Perceivability

I'll begin the critique with the last point. "We never see properties, although we see that certain things have certain properties." (179)  If van Inwagen can 'peter out,' so can I: I honestly don't know what to make of the second  clause of the quoted sentence.  I am now, with a brain properly caffeinated, staring at my blue coffee cup in good light.  Van Inwagen's claim is that I do not see the blueness of the cup, though I do see that the cup is blue.  Here I balk.  If I don't see blueness, or blue, when I look at the cup, how can I see (literally see, with the eyes of the head, not the eye of the mind) that the cup is blue?

'That it is blue' is a thing that can be said of the cup, and said with truth.  This thing that can be said is an unsaturated assertible, a property in van Inwagen's sense.  Van Inwagen is telling us that it cannot be seen. 'That the cup is blue' is a thing that can be said, full stop.  It is a saturated assertible, a proposition, and a true one at that.  Both assertibles are abstract objects.  Both are invisible, and not  because of any limitation in my visual power or in human visual power in general, but because abstract objects cannot be terms of causal relations, and perception involves causation. Both types of assertible are categorially disbarred from visibility. But if both the property and the proposition are invisible, then how can van Inwagen say that "we see that certain things have certain properties"?  What am I missing?

How can he say that we don't see the property but we do see the proposition?  Both are abstract and invisible.  How is it that we can see the second but not the first?  Either we see both or we see neither.  If van Inwagen says that we don't see the proposition, then what do we see when we see that the cup is blue?  A colorless cup?  A cup that is blue but is blue in a way different from the way the cup is blue by instantiatiating the abstract unsaturated assertible expressed by 'that it is blue'?  But then one has duplicated at the level of abstracta the property that one sees at the concrete cup.  If there is blueness at the cup and abstract blueness in Plato's heaven, why do we need the latter? Just what is going on here?

To van Inwagen's view one could reasonably oppose the following view.  I see the cup (obviously!) and I see blueness at the cup (obviously!)  I don't see a colorless cup.  To deny the three foregoing sentences would be to deny what is phenomenologically given.  What I don't literally see, however, is that the cup is blue.   (Thus I don't literally see what van Inwagen says we literally see.)  For to see that the cup is blue is to see the instantiation of blueness by the cup.  And I don't see that.  The correlate of the 'is' in 'The cup is blue' is not an object of sensation.  If you think it is, tell me how I can single it out, how I can isolate it.  Where in the visual field is it?  The blueness is spread out over the visible surfaces of the cup.  The cup is singled out as a particular thing on the desk, next to the cat, beneath the lamp, etc.  Now where is the instantiation relation?  Point it out to me!  You won't be able to do it.  I see the cup, and I see blue/blueness where the cup is.  I don't see the cup's BEING blue.

It is also hard to understand how van Inwagen, on his own assumptions, can maintain that we see that certain things have certain properties.  Suppose I see that Max, a cat of my acquaintance, is black.  Do I see a proposition?  Not on van Inwagen's understanding of 'proposition.'  His propositions are Fregean, not Russellian: they are not resident in the physical world.  Do I see a proposition-like entity such as an Armstrongian state of affairs?  Again, no.  What do I see?

Van Inwagen claims that properties are not objects of sensation; no properties are, not even perceptual properties.  I should think that some properties are objects of sensation, or better, of perception: I perceive blueness at the cup by sight; I perceive smoothness and hardness and heat at the cup by touch.  If so, then (some) properties are not abstract objects residing in a domain unto themselves.

Van Inwagen's view appears to have the absurd consequence that things like coffee cups are colorless.  For if colors are properties (179) and properties are abstract objects, and abstract objects are colorless (as they obviously are), then colors are colorless, and whiteness is not white and blueness is not blue.  Van Inwagen bites the bullet and accepts the consequence.  But we can easily run the argument in reverse:  Blueness is blue; colors are properties; abstract objects are colorless; ergo, perceptual properties are not abstract objects.  They are either tropes or else universals wholly present in the things that have them.  Van Inwagen, a 'relation ontologist' cannot of course allow this move into 'constituent ontology.'

There is a long footnote on p. 242 that may amount to a response to something like my objection.  In the main text, van Inwagen speaks of "such properties as are presented to our senses as belonging to the objects we sense . . . ."  How does this square with the claim on p. 179 that properties are not objects of sensation?  Can a property such as blueness be presented to our senses without being an object of sensation?  Apparently yes, "In a noncausal sense of 'presented.'" (243, fn 3)

How does this solve the  problem?  It is phenomenologically evident that (a definite shade of) blue appears to my senses when I stare at my blue coffee cup. Now if this blueness is an abstract object as van Inwagen claims then it cannot be presented to my senses any more than it can be something with which I causally interact.

2. But Is This Ontology?

Why does van Inwagen think he is doing ontology at all?  It looks more like semantics or philosophical logic or philosophy of language.  I say this because van Inwagen's assertibles are very much like Fregean senses. They are intensional items. (As we noted, he reduces all his assertibles to relations-in-intension.) Taking his cue from Quine, he seeks an answer to the question, What is there?  He wants an inventory, by category, of what there is.  He wants to know, for example, whether in addition to concrete things there are also properties, as if properties could exist in sublime disconnection from concrete things in a separate sphere alongside this sublunary sphere.  That no property is an object of sensation is just logical fallout from van Inwagen's decision to install them in Plato's heaven; but then their connection to things here below in space and time become unintelligible.  It does no good, in alleviation of this unintelligibility, to say that abstract blueness -- the unsaturated assertible expressed by 'that it is blue' -- is instantiated by my  blue cup.  For instantiation is just another abstract object, a dyadic external relation, itself ensconced in Plato's heaven.

But not only the formulation of the question but also the method of attack come from Quine.  Van Inwagen thinks he can answer what he and Quine idiosyncratically call the ontological question by examining the ontological commitments of our discourse.  Starting with sentences we accept as true, he looks to see what these sentences entail as regards the types of entity there are when the sentences are properly regimented in accordance with the structures of modern predicate logic with identity.

The starting point is not things in their mind- and language-independent being, but beliefs we already have and sentences we already accept.  The approach is oblique, not direct; subjective, not objective.  Now to accept a sentence is to accept it as true; but a sentence accepted as true need not be true.  Note also that if one sentence entails another, both can be false.  So if sentences accepted as true entail the existence of properties in van Inwagen's sense, according to which properies are unsaturated assertibles, it is logically possible that there be no properties in reality.  The following is not a contradiction:  The sentences we accept as true entail that there are properties & There are no properties.  For it may be -- it is narrowly-logically possible that --  the sentences we accept as true that entail that there are properties are all of them false.  Not likely, of course, and there may be some retorsive argument against this  possibility.  But it cannot be ruled out by logic alone.

So there is something fishy about the whole method of 'ontological' commitment. One would have thought that ontology is concerned with the Being of beings, not with the presuppositions of sentences accepted as true by us.  To put it vaguely, there is something 'transcendental' (in the Kantina sense) and 'subjective' and 'modern' about van Inwagen's Quinean method that unsuits it for for something that deserves to be called ontology.

This is connected with the point that van Inwagen's assertibles, saturated and unsaturated, are hard to distinguish from Fregean senses.  They are denizens of Frege's Third Reich or Third World if you will, not his First Reich, the realm of primary reference.  To illustrate: Venus is an item in the First World, while the senses of 'Morning Star' and 'Evening Star'  and the sense of the sentence 'The Morning Star is the Evening Star' are three items all in the Third World.  Senses, however, are logico-semantic items: their job is to mediate reference.  Van Inwagen is arguably just hypostatizing items that are needed for us to secure reference -- whether thinking reference or linguistic reference -- to things that truly exist extramentally and extralinguistically.

Again, this is vague and sketchy.  But good enough for a weblog entry!  Is think my Czech scholastic friends will know what I am driving at.

3. Van Inwagen's Ostrich Realism and Commitment to Bare Particulars

Van Inwagen rejects both extreme and moderate nominalism.  So he can't possibly be an ostrich nominalist.  He is, however, as he himself appreciates, an ostrich realist or ostrich platonist. (214-15)

Suppose Max is black. What explains the predicate's being true of Max?   According to the ostrich nominalist, nothing does.   It is just true of him.  There is nothing in or about Max that serves as the ontological ground of the correctness of his satisfying  the predicate.  Now 'F' is true of a iff 'a is F' is true.  So we may also ask: what is the ontological ground of the truth of 'Max is black'?  The ostrich reply will be: nothing.  The sentence is just true.  There is no need for a truth-maker.

The ostrich realist/platonist says something very similar except that in place of predicates he puts abstract properties, and in place of sentences he puts abstract propositions.  In virtue of what does Max instantiate blackness? In virtue of nothing.  He just instantiates it.  Nothing explains why the unsaturated assertible expressed by 'x is black' is instantiated by Max.  Nothing explains it because there is nothing to explain.  And nothing explains why the saturated assertible expressed by 'Max is black' is true. Thus there is nothing concrete here below that could be called a state of affairs in anything like Armstrong's sense.  There is in the realm of concreta no such item as Max-instantiating-blackness, or the concrete fact of Max's being black. 

Here below there is just Max, and up yonder in a topos ouranos are 'his' properties (the abstract unsaturated assertibles that he, but not solely, instantiates).  But then Max is a bare particular in one sense of this phrase, though not in Gustav Bergmann's exact sense of the phrase.  (Bergmann is a constituent ontologist.) In what sense, then?

A bare particular is not a particular that has no properties in any sense of 'having properties'; a bare particular is a particular that has properties, but has them  in a certain way: by being externally related to them.  Thus bare particulars, unlike Aristotelean substances, have neither natures nor essences.  Indeed, the best way to understand what a bare particular is is by contrast with the primary substances of Aristotle. These concrete individuals have natures by being (identically) natures: they are not externally related to natures that exist serenely and necessarily in Plato's heaven.  

In this sense, van Inwagen's concrete things are bare particulars.  There are no properties 'in' or 'at' Max; there are no properties where he is and when he is.  What's more, on van Inwagen's scheme -- one he shares with Chisholm, Plantinga, et al. -- Max can only be externally related to his properties.  This has the consequence that all of Max's properties are accidental.  For if x, y are externally related, then x can exist without y and y can exist without x.  So Max can exist without being feline just as he can exist without being asleep. 

Could Max have been a poached egg?  It is narrowly-logically possible.  For if he has all of his properties externally, then he has all of his properties accidentally.  Even if it is necessary that he have some set of properties or other, there is no necessity that he have any particular set.  If properties are externally related to particulars, then any particular can have any set of properties so long as it has some set or other.

If you deny that concrete things are bare in the sense I have explained, then you seem to be committed to saying that there are two sorts of properties, PvI-properties in Plato's heaven and 'sublunary' properties at the particulars here below.  But then I will ask two questions.  First, what is the point of introducing PvI-properties if they merely duplicate at the abstract intensional level the 'real' properties in the sublunary sphere?  Second, what justifies calling PvI-properties properties given that you still are going to need 'sublunary' properties to avoid saying that van Inwagen's concreta are bare particulars?

4. Existence

One can say of a thing that it might not have existed.  For example, I can say this of myself.  If so, it must be possible to say of a thing that it exists.  For example, it must be possible for me to say of myself that I exist.  As van Inwagen remarks, "it is hard to see how there could be such an assertible as 'that it might not have existed' if there were no such assertible as 'that it exists.'" (180)  Existence, then, is a property, says van Inwagen, for properties are unsaturated assertibles, and 'that it exists' is an assertible.

There are many problems with the notion that existence is a first-level property on a van Inwagen-type construal of properties.  Instantiation for van Inwagen is a full-fledged dyadic relation. (It is not a non-relational tie or Bergmannian nexus).  He further characterizes it as abstract and external as we have seen.  Now it is perfectly obvious to me that the very existence of Socrates cannot consist in his instantiation of any PvI-type property, let alone the putative property, existence.  For given the externality of the instantiation relation, both Socrates and the putative property must 'already' exist for said relation to hold between them.  So one moves in an explanatory circle of embarrassingly short diameter if one tries to account for existence in this way.

This circularity objection which I have developed in painful detail elsewhere will, I expect,  leave van Inwagen stone cold.  One reason is that he sees no role for explanation in metaphysics whereas I think that metaphysics without explanation is not metaphysics at all in any serious sense.  This is large topic that cannot be addressed here.

I'll mention one other problem for van Inwagen.  I'll put it very briefly since this entry is already too long.  Van Inwagen is a Fregean about existence; but on a Fregean view existence cannot be a  first-level property.  For Frege, 'x exists' where 'x' ranges over individuals is a senseless open sentence or predicate.  There is no unsaturated assertible corresponding to it.  I have a number of posts on van Inwagen and existence. Here is one.  My latest published article on existence is "Existence: Two Dogmas of Analysis" in Novak and Novotny, eds., Neo-Aristotelian Perspectives in Metaphysics, Routledge 2014, 45-75.

5. Haecceities

Among the properties, van Inwagen counts haecceities.  They are of course abstract objects like all properties.  But they are not universals because, while they are instantiable, they are not multiply instantiable.  The property of being identical with Alvin Plantinga is an example van Inwagen gives. (180) This property, if instantiated, is instantiated by Plantinga alone in the actual world and by nothing distinct from Plantinga in any possible world.  Plantingitas -- to give it a name -- somehow involves Plantinga himself, that very concrete object.  For this property is supposed to capture the nonqualitative thisness of Plantinga. (Haecceitas is Latin for 'thisness.') 

I submit that these haecceity properties are metaphysical monstrosities.  For given that they are properties, they are necessary beings.  A necessary being exists at all times in all possible worlds that have time, and in all worlds, period.  Plantinga, however, does not exist in all worlds since he is  a contingent being; and he doesn't exist at all times in all worlds in which he exists, subject as he is to birth and death, generation and corruption.   I conclude that before Plantinga came into being there could not have been any such property as the property of being identical to Plantinga.  I conclude also that in worlds in which he does not exist there is no such haecceity property.  For at pre-Plantingian times and non-Plantingian worlds, there is simply nothing to give content to the unsaturated assertible expressed by 'that it is Alvin Plantinga.'  (Alvin Plantingas hung out at those times and in those worlds, but not our Alvin Plantinga.)  Plantinga himself enters essentially into the very content of his haecceity property.

But this is absurd because PvI-properties are merely intensional entities.  No such entity can have a concrete, flesh and blood man as a constituent.  Just as a PvI-property cannot be a constituent of a concretum such as Plantinga, Plantinga cannot be a constituent in any sense of 'constituent' of a  PvI-property. 

But if Plantinga hadn't existed, might it nonetheless have been true that he might have existed? (180).  Van Inwagen says yes and introduces haecceities.  Plantingitas exists in every world; it is just that it is instantiated only in some.  I say no, precisely because I take haecceities to be metaphysical monstrosities.

Conclusion

I am not out to refute van Inwagen or anyone.  Philosophical theories, except for some sophomoric ones,  cannot be refuted.  At most I am out to neutralize van Inwagen's theory, or rather his type of theory, to explain why it is not compelling and how it is open to powerful objections, only some of which I have adduced in this entry.  And of course I do not have a better theory. I incline toward constituent ontology myself, but it too is bristling with difficulties.

As I see it, the problems of philosophy are most of them genuine, some of them humanly important, but all of them insoluble.

______________________

*At this point I should like to record a misgiving.  If sentences (sentence types, not tokens)  are abstract objects, and abstract objects are necessary beings as van Inwagen holds (cf., e.g., p. 242), then sentences are necessary beings.  But sentences are tied to contingently existing languages and cannot exist apart from them.  Thus 'I am hungry' is a sentence of English while 'Ich habe Hunger' is a sentence of German, and neither sentence can exist apart from its respective language.  A natural language, however, would seem to be a contingent being: German came into existence, but it might never have come into existence.  Given all this, a contradiction appears to follow: Sentences are and are not necessary beings.

The Ramsey Problem and the Problem of the Intrinsically Unpropertied Particular

What exactly is the distinction between a universal and a particular?  Universals are often said to be repeatable entities, ones-over-many or ones-in-many.  Particulars, then, are unrepeatable entities.  Now suppose the following: there are universals; there are particulars; particulars instantiate universals; first-order facts are instantiations of universals by particulars. 

One and the same universal, F-ness, is repeated in the following facts: Fa, Fb, Fc.  But isn't one and the same particular repeated in Fa, Ga, Ha?  If so, particulars are as repeatable as universals, in which case repeatability cannot be the mark of the universal. How can it be that all and only universals are repeatable? I stumbled upon this problem the other day.  But Frank Ramsey saw it first.  See his "Universals," Mind 34, 1925, 401-17.

Instantiation as holding between particulars and universals is asymmetric: if a instantiates F-ness, then F-ness does not instantiate a.  (Instantiation is not in general asymmetric, but nonsymmetric: if one universal instatiates a second, it may or may not be the case that the second instantiates the first.)  The asymmetry of first-level instantiation may provide a solution to the Ramsey problem.  The asymmetry implies that particulars are non-instantiable: they have properties but cannot themselves be properties.  By contrast, universals are properties and have properties.

So we can say the following.  The repeatability of a universal is its instantiability while the  unrepeatability of a particular is its non-instantiability.  So, despite appearances, a is not repeated in Fa, Ga, and Ha.  For a is a particular and no particular is instantiable (repeatable).

Solve a problem, create one or more others.  I solved the Ramsey problem by invoking the asymmetry of instantiation.  But instantiation is a mighty perplexing  'relation' (he said with a nervous glance in the direction of Mr. Bradley).  It is dyadic and asymmetric.  But it is also external to its terms.  If a particular has its properties by instantiating them, then its properties are 'outside' it, external to it.  Note first that to say that a is F is not to say that a is identical to F-ness.  The 'is' of predication is not the 'is' of identity.  (For one thing, identity is symmetric, predication is not.)  It would seem to follow that a is wholly distinct from F-ness. But then a is connected to F-ness by an external relation and Bradley's regress is up and running.  But let's set aside Bradley's regress and the various responses to it to focus on a different problem.

If a and F-ness are external to each other, then it is difficult to see how a could have any intrinsic (nonrelational) properties.  Suppose a is an apple and that the apple is red.  Being red is an intrinsic property of the apple; it is not a relational property like being in my hand. But if a is F in virtue of standing in an external instantiation relation to the universal F-ness, then it would seem that F-ness cannot be an intrinsic property of a.  So an antinomy rears its ugly head: a is (intrinsically) F and a is not (intrinsically) F.

Call this the Problem of the Intrinsically Unpropertied Particular.  If there are particulars and universals and these are mutually irreducible categories of entity, then we have the problem of bringing their members together.  Suppose it is contingently true that a is F.  We cannot say that a is identical to F-ness, nor, it seems, can we say that a and F-ness are wholly distinct and connected by the asymmetric, external tie of instantiation.  Is there a way between the horns of this dilemma?

David Armstrong at the end of his career suggested that instantiation is partial identity.  The idea is that a and F-ness overlap, are partially identical.  This bring a and F-ness together all right, but it implies that the connection is necessary.  But then the contingency of the connection is lost.  It also implies that instantiation is symmetrical!  But then Ramsey is back in the saddle.

More later.

Related articles

Bare Particulars versus Aristotelian Substances

Being is Said in Many Ways: On the Uses of 'Is'

Chad reports:

In the opening pages of More Kinds of Being: A Further Study of Individuation, Identity, and the Logic of Sortal Terms (Blackwell, 2009), E. J. Lowe distinguishes five uses of ‘is’ as a copula: 1. The ‘is’ of attribution, as in ‘Socrates is wise’ and ‘Grass is green’.2. The ‘is’ of identity, as in ‘Napoleon is Bonaparte’ and ‘Water is H2O’.3. The ‘is’ of instantiation, as in ‘Mars is a planet’ and ‘A horse is a mammal’.4. The ‘is’ of constitution, as in ‘This ring is gold’ and ‘A human body is a collection of cells’.5. The ‘is’ of existence, as in ‘The Dodo is no more’.He says some may be reducible to others, and that one or two must be primitive. I thought this was a helpful spread.

That is indeed helpful, but here are some comments and questions.

1. First of all, I would be surprised if Lowe referred to the five uses as five uses of 'is' as a copula.  The 'is' of existence is not a copula because it doesn't couple.  There is no copulation, grammatical or logical, in 'God is.'  The 'is' of existence does not pick out any sort of two-termed relation such as identity, instantiation, or constitution. Calling the 'is' of identity a copula is a bit of a stretch, and I don't think most philosophers would.

2. Is there a veritative use of 'is'?  'It is so.'  'It is the case that Frege died in 1925.'  One could say, though it is not idiomatic: 'Obama's being president is.'  One would be expressing that the state of affairs obtains or that the corresponding proposition is true.  So it looks as if there is a veritative use of 'is.'

3. Reducibility of one use to another does not show that they are not distinct uses.  Perhaps the veritative use can be reduced to what Lowe calls the attributive use.  Attributions of truth, however, imply that truth is a property.  Frege famously argued that truth cannot be a property.  That is a messy separate can of worms.

4.  There are also tensed and tenseless uses of 'is.'  'Obama is president' versus '7 + 5 is 12.'  With respect to the latter, it would be a bad joke, one reminiscent of Yogi Berra, were I to ask,"You mean now?"  Yogi Berra was once asked the time.  He said,"You mean now?"

'Hume is an empiricist' can be used both in a tensed way and an untensed way.  If I say that Hume is an empiricist what I say is true despite the present nonexistence of Hume.  'Grass is green,' however, is never used in a tensed way, though one can imagine circumstances in which it could.

5. One and the same tokening of 'is' can do more than one job. Is the 'is' in 'Max is black' as used by me in the presence of my cat Max the 'is' of predication merely?  I don't think so.  It also expresses existence.  But this requires argument:

1. 'Max is black' and 'Black Max exists' are intertranslatable. 
2. Intertranslatable sentences have the same sense.
Therefore
3. 'Max is black' and 'Black Max exists' express the very same (Fregean) sense.
Therefore
4. Both sentences express both predication and existence: a property is predicated of something that cannot have properties unless it exists.
Therefore
5. The 'is' in 'Max is black' has a double function: it expresses both predication and existence. 

Note that both sentences include a sign for the predicative tie.  The sign is 'is' in the first sentence and in the second sentence the sign is the immediate concatenation of 'black' and 'Max' in that order. This shows that to refer to logical (as opposed to grammatical) copulation does not require a separate stand-alone sign.  'Black Max exists' expresses both existence via the sign 'exsts' and predication via the immeditae concatenation of 'black' and 'Max' in that order in the context of the sentence in question. 

Related articles

A Question About Predication and Identity

Against Ostrich Nominalism

As magnificent a subject as philosophy is, grappling as it does with the ultimate concerns of human existence, and thus surpassing in nobility any other human pursuit, it is also miserable in that nothing goes uncontested, and nothing ever gets established to the satisfaction of all competent practitioners.  (This is true of other disciplines as well, but in philosophy it is true in excelsis.) Suppose I say, as I have in various places:

That things have properties and stand in relations I take to be a plain Moorean fact beyond the reach of reasonable controversy. After all, my cat is black and he is sleeping next to my blue coffee cup.  ‘Black’ picks out a property, an extralinguistic feature of my cat.

Is that obvious?  Not to some.  Not to the ornery and recalcitrant critter known as the ostrich nominalist.  My cat, Max Black, is black.  That, surely, is a Moorean fact. Now consider the following biconditional and consider whether it too is a Moorean fact:

1. Max is black iff Max has the property of being black.

As I see it, there are three main ways of construing a biconditional such as (1):

A.  Ostrich Nominalism.  The right-hand side (RHS) says exactly what the left-hand side (LHS) says, but in a verbose and high-falutin' and dispensable way.  Thus the use of 'property' on the RHS does not commit one ontologically to properties beyond predicates.  (By definition, predicates are linguistic items while properties are extralinguistic and extramental.)  Predication is primitive and in need of no philosophical explanation.  On this approach, (1) is trivially true.  One needn't posit properties, and in consequence one needn't worry about the nature of property-possession. (Is Max related to his blackness, or does Max have his blackness quasi-mereologically  by having it as an ontological constituent of him?)

B. Ostrich Realism.  The RHS commits one ontologically to properties, but in no sense does the RHS serve to ground or explain the LHS.  On this approach, (1) is false if there are no properties.  For the ostrich realist, (1) is true, indeed necessarily true, but it is not the case that the LHS is true because the RHS is true.  Such notions as metahysical grounding and philosophical explanation are foreign to the ostrich realist, but not in virtue of his being a realist, but  in virtue of his being an ostrich.

C. Non-Ostrich Realism.  On this approach, the RHS both commits one to properties, but also proffers a metaphysical ground of the truth of the LHS: the LHS is true because (ontologically or metaphysically speaking)  the concrete particular Max has the property of being black, and not vice versa.

Note 1: Explanation is asymmetrical; biconditionality is symmetrical.

Note 2: Properties needn't be universals.  They might be (abstract) particulars (unrepeatables) such as the tropes of D. C. Williams and Keith Campbell.  Properties must, however, be extralinguistic and extramental,  by definition.

Note 3: Property-possession needn't be understood in terms of instantiation or exemplification or Fregean 'falling-under'; it might be construed quasi-mereologically as constituency: a thing has a property by having it as a proper ontological part.

Against Ostrich Nominalism

On (A) there are neither properties, nor do properties enter into any explanation of predication.  Predication is primitive and in need of no explanation.  In virtue of what does 'black' correctly apply to Max? In virtue of nothing.  It just applies to him and does so correctly.  Max is black, but there is no feature of reality that explains why 'black' is true of Max, or why 'Max is black' is true.  It is just true!  There is nothing in reality that serves as the ontological ground of this contingent truth.  Nothing 'makes' it true.  There are no truth-makers and no need for any.

I find ostrich nominalism preposterous.  'Black' is true of Max, 'white' is not, but there is no feature of reality, nothing in or at or about Max that explains why the one predicate is true of him and the other is not!?  This is not really an argument but more an expression of incomprehension or incredulity, an autobiographical comment, if you will.  I may just be petering out, pace Professor van Inwagen.

Can I do better than peter?  'Black' is a predicate of English.  Schwarz is a predicate of German.  If there are no properties,  then Max is black relative to English, schwarz relative to German, noir relative to French, and no one color.  But this is absurd.  Max is not three different colors, but one color, the color we use 'black' to pick out, and the Krauts use schwarz to pick out. When Karl, Pierre, and I look at Max we see the same color.  So there is one color we both see -- which would not be the case if there were no properties beyond predicates.  It is not as if I see the color black while Karl sees the color schwarz.  We see the same color.  And we see it at the cat.  This is not a visio intellectualis whereby we peer into some Platonic topos ouranos.  Therefore, there is something in, at, or about the cat, something extralinguistic, that grounds the correctness of the application of the predicate to the cat.

A related argument.  I say, 'Max is black.'  Karl says, Max ist schwarz.  'Is' and ist are token-distinct and type-distinct words of different languages.  If there is nothing in reality (no relation whether of instantiation or of constituency, non-relational tie, Bergmannian nexus, etc.) that the copula picks out, then it is only relative to German that Max ist schwarz, and only relative to English that Max is black.  But this is absurd.  There are not two different facts here but one.  Max is the same color for Karl and me, and his being black is the same fact for Karl and me.

Finally, 'Max is black' is true.  Is it true ex vi terminorum?  Of course not.  It is contingently true.  Is it just contingently true?  Of course not.  It is true because of the way extralinguistic reality is arranged. It is modally contingent, but also contingent upon the way the world is.  There's this cat that exists whether or not any language exists, and it is black whether or not any language exists.

Therefore, I say that for a predicate to be contingently true of an individual, (i) there must be individuals independently of language; (ii) there must be properties independently of language; and there must be facts or truth-making states of affairs independently of language.  Otherwise, you end up with (i) total linguistic idealism, which is absurd; or (ii) linguistic idealism about properties which is absurd; or (iii) a chaos, a world of disconnected particulars and properties.

The above is a shoot-from-the hip, bloggity-blog exposition of ideas that can be put more rigorously, but it seems to to me to show that ostrich nominalism and ostrich realism for that matter are untenable -- and this despite the fact that a positive theory invoking facts has its own very serious problems.

Metaphilosophical Coda: If a theory has insurmountable problems, these problems are not removed by the fact that every other theory has problems.  For it might be that no theory is tenable,while the poroblem itself is genuine.

Related articles

A Question About Predication and Identity

Metaphysical Grounding I: True Of

A Question About Predication and Identity

Chad M. sent me a paper of his in which he illustrates the distinction between the 'is' of predication and the 'is' of identity using the following examples:

1. Joseph Ratzinger is [the] Pope

and

2. Water is H₂O

where the first sentence is proposed as an example of a predication and the second as an identity sentence.  If I were to explain the distinction, I would use these examples:

3. Joseph Ratzinger is German

and  (for consistency of subject matter)

4. Joseph Ratzinger is Pope Benedict XVI.

(2) and (4) are clearly sentences expressing strict, numerical, identity.  Identity is an equivalence relation: reflexive, symmetrical, transitive.  It is also governed by the Indiscernibility of Identicals: if x = y, then whatever is true of  x is true of y, and vice versa.  By these four tests, the 'is' in (4) is the 'is' of identity.  The 'is' in (3) expresses a different relation.  Frege would say that it is the relation of falling under: the object JR falls under the concept German.  That relation fails each of the four tests. It is not reflexive, not symmetrical, etc.

Now my problem is that I don't find (1) to be a clear example of a predication in the way that (3) is a clear example. 

Although 'The Pope' is a definite description, not a name (Kripkean rigid designator), (1) could be construed as asserting an identity, albeit a contingent identity, between the object picked out by 'JR' and the object picked out by 'the Pope.'  After all, the sentence passes the four tests, at least if we confine ourselves to the present time and the actual world.  The relation is reflexive, symmetrical, and transitive.  For example, if JR is the Pope, and the Pope is the vicar of Christ, then JR is the vicar of Christ.  Furthermore, whatever is true of JR now is also true of the Pope now, and vice versa. So the indiscernibility test is satisfied as well.

Why not then say that (1) expresses contingent identity and that the 'is' is an 'is' of identity, not of predication?  The fact that one could maintain this, with some show of plausibility, indicates that Chad's example is not a clear one.  That is my only point, actually.

I grant that the notion of contingent identity can be questioned.  How could x and y just happen to be identical?  For Kripke, identity is governed by the Necessity of Identity: if x = y, then necessarily x = y.  This has the interesting implication that if it is so much as possible that x and y are distinct, then x and y are distinct.  (Shades of the ontological argument!)

But there are philosophers who propose to speak of contingent sameness relations.  Hector Castaneda is one.  So I am merely asking Chad why he uses the puzzling and provocative (1) as illustrative of the 'is' of predication.

There is a labyrinth of deep questions lurking  below the surface, questions relevant to Chad's real concern, namely the coherence of the Trinity doctrine and its (in)coherence with the doctrine of divine simplicity. 

Related articles

The 'Is' of Identity and the 'Is' of Predication

Properties as Parts: More on Constituent Ontology

Skin and seeds are proper parts of a tomato, and the tomato is an improper part of itself.  But what about such properties as being red, being ripe, being a tomato?  Are they parts of the tomato?  The very idea will strike many as born of an elementary confusion, as a sort of Rylean category mistake.  "Your tomato is concrete and so are its parts; properties are abstract; nothing concrete can have abstract parts."  Or:  "Look, properties are predicable entities; parts are not.  Having seeds is predicable of the tomato but not seeds!  You're talking nonsense!"

I concede that the notion that the properties of an ordinary particular are parts thereof, albeit in some extended unmereological sense of 'part,' is murky.  Murky as it is, the motivation for the view is fairly clear, and the alternative proposed by relational ontologists is open to serious objection.  First I will say something in motivation of the constituent-ontological (C-ontological view).  Then I will raise objections to the relational-ontological (R-ontological) approach.

For C-Ontology

Plainly, the blueness of my coffee cup belongs to the cup; it is not off in a realm apart.  The blueness (the blue, if you will) is at the cup, right here, right now.  I see that the cup before me now is blue.  This seeing is not a quasi-Platonic visio intellectualis but a literal seeing with the eyes.  How else would I know that the cup is blue, and in need of a re-fill, if not by looking at the cup?   Seeing that the cup is blue, I see blueness (blue).  I see blueness here and now in the mundus sensibilis.  How could I see (with the eyes) that the cup is blue without seeing (with the same eyes) blueness?  If blueness is a universal, then I see a universal, an instantiated universal.  If blueness is a trope, then I see a trope, a trope compresent with others.   Either way I see a property.  So some properties are visible.  This would be impossible if properties are abstract objects as van Inwagen and the boys maintain. Whether uninstantiated or instantiated abstract properties are invisible.

Properties such as blueness and hardness, etc. are empirically detectable. Blueness is visible while hardness is tangible.  That looks to be a plain datum.  Their being empirically detectable  rules out their being causally inert abstracta off in a quasi-Platonic realm apart.   For I cannot see something without causally interacting with it.  So not only is the cup concrete, its blueness is as well.

This amounts to an argument that properties are analogous to parts.  They are not parts in the strict mereological sense.  They are not physical parts.  So let's call them metaphysical or ontological constituents.  The claim, then, is that ordinary particulars such as tomatoes and cups have their properties, or at least some of them,  by having them as ontological constituents.  To summarize the argument:

1. Some of the properties of ordinary concrete material particulars are empirically detectable at the places the particulars occupy and at the times they occupy them.

2. No abstract object is empirically detectable.  Therefore:

3. Some properties of ordinary concrete material particulars are not abtract objects.  Therefore:

4. It is reasonable to conjecture that some of the properties of ordinary concrete material particulars are analogous to (proper) parts of them.

Against R-Ontology

I grant that the above is not entirely clear, and that it raises questions that are not easy to answer.  But does R-ontology fare any better?  I don't think so.

Suppose an R-ontologist is staring at my blue cup.  Does he see something colorless?  Seems he would have to if the blueness of the cup is an abstract object merely related by exemplification to the concrete cup.  Abstracta are invisible. Suppose we introduce 'stripped particular' to designate the R-ontological counterpart of what C-ontologists intend with 'bare particular' and 'thin particular.'  A stripped particular is an ordinary particular devoid of empirically detectable properties.  If the R-ontologist thinks that my cup is a stripped particular, then he is surely wrong.  Call this the Stripped Particular Objection.

But if the R-ontologist agrees with me that the blueness is empirically detectable, then he seems to be involved in an unparsimonious duplication of properties.  There is the invisible abstract property in Plato's heaven or Frege's Third Reich that is expressed by the open sentence or predicate '___ is blue.'  And there is the property (or property-instance) that even the R-ontologist sees when he stares at a blue coffee cup.

Isn't that one property too many?  What work does the abstract property do?  More precisely, what ontological work does it do?  I needn't deny that it does some semantic work: it serves as the sense (Fregean Sinn) of the corresponding predicate.  But we are doing ontology here, not semantics.  We want to understand what the world -- extramental, extralinguistic reality -- must be like if a sentence like 'This cup is blue' is true.  We want to understand the property-possession in reality that underlies true predications at the level of language.  We are not concerned here with the apparatus by which we represent the world; we are concerned with the world represented.

In my existence book I called the foregoing the Duplication Objection, though perhaps I could have hit upon a better moniker.  The abstract property is but an otiose duplicate of the property that does the work, the empirically detectable propery that induces causal powers in the thing that has it.

So I present the R-ontologist with a dilemma: either you are embracing stripped particulars or you are involved in a useless multiplication of entities.

Coda

It's Christmas Eve and there is more to life than ontology.  So I'll punch the clock for today.  But there are two important questions we need to pursue. (1) Couldn't we reject the whole dispute  and be neither a C- nor an R-ontologist?  (2) Should ontologists be in the business of explanation at all? (My point that abstract properties are useless for purposes of accounting for predication and property-possession presupposes that there is such a legitimate enterprise as philosophical explanation.)

Related articles

Constituent Ontology Versus Relational Ontology and an Argument Against the Latter

What Exactly is an Ontological Constituent?

Does the Notion of a Bare Particular Make Sense Only in Constituent Ontology?

Constituent Ontology and the Problem of Change

Stanislav Sousedik's "Towards a Thomistic Theory of Predication"

Bare Particulars and Lukáš Novák's Argument Against Them

Stanislav Sousedik's "Towards a Thomistic Theory of Predication"

Enough of politics, back to some hard-core technical philosophy.  If nothing else, the latter offers exquisite escapist pleasures not unlike those of chess. Of course I don't believe that technical philosophy is escapist; my point is a conditional one: if it is, its pleasures suffice to justify it as a form of recuperation from  this all-too-oppressive world of 'reality.'  It's what I call a 'fall-back position.'

I have been commissioned to review the collection of which the above-captioned article is a part.  The collection is entitled Metaphysics: Aristotelian, Scholastic, Analytic (Ontos Verlag 2012) and includes contributions by Peter van Inwagen, Michael Loux, E. J. Lowe, and several others.  My review article will address such topics as predication, truth-makers, bare particulars, and the advantages and liabilities of constituent ontology.  I plan a series of posts in which I dig deep into some of the articles in this impressive collection.

Stanislav Sousedik argues for an "identity theory of predication" according to which a predicative sentence such as 'Peter is a man' expresses an identity of some sort between the referent of the subject 'Peter' and the referent of the predicate 'man.'  Now to someone schooled in modern predicate logic (MPL) such an identity  theory will appear wrongheaded from the outset.  For we learned at Uncle Gottlob's knee to distinguish between the 'is' of identity ('Peter is Peter') and the 'is' of predication ('Peter is a man').

But let's give the Thomist theory a chance.  Sousedik, who is well aware of Frege's distinction, presents an argument for the identity in some sense of subject and predicate.  He begins by making the point that in the declarative 'Peter is a man' and the vocative 'Peter, come here!' the individual spoken about is (or can be) the same as the individual addressed.  But common terms such as 'man' can also be used to address a person.  Instead of saying,  'Peter, come here!' one can say 'Man, come here!'  And so we get an argument that I will put as follows:

1. Both 'Peter' and 'man' can be used to refer to the same individual. Therefore

2. A common term can be used to refer to an individual.  But

3. Common terms also refer to traits of individuals.  Therefore

4. The traits must be identical in some sense to the individuals.  E.g., the referent of 'Peter' must be in some sense identical to the referent of 'man.'

But in what sense are they identical?  Where Frege distinguishes between predication and identity, Sousedik distinguishes between weak and strong identity. 'Peter is Peter' expresses strong identity while 'Peter is a man' expresses weak identity.  "Strong identity is reflexive, symmetric, and transitive, weak identity has none of these formal properties." (254)  It thus appears that strong identity is the same as what modern analytic philosophers call (numerical) identity.  It is clear that 'Peter is a man' cannot be taken to express strong identity. But what is weak identity?

S. is a constituent ontologist.  He holds that ordinary substances such as Peter have what he calls "metaphysical parts."  Whereas Peter's left leg is a physical part of him, his traits are metaphysical parts of him.  Thus the referents of the common terms 'man,' 'animal,' living thing,' etc. are all metaphysical parts of Peter.  Clearly, these are different traits of Peter.  But are they really distinct in Peter?  S. says that they are not: they are really identical in Peter and only "virtually distinct" in him.  The phrase is defined as follows.

(Def. 1)  Between x, y there is a virtual  distinction iff (i) x, y are really identical; (ii) x can become an object of some cognitive act Φ without y being the object  of the same act Φ . . . . (251)

For example, humanity and animality in Peter are really identical but virtually distinct in that humanity can be the intentional object of a cognitive act without animality being the object of the same act.  I can focus my mental glance so to speak on Peter's humanity while leaving out of consideration his animality even though he is essentially both a man and an animal and even though animality is included within humanity. 

The idea, then, is that Peter has metaphysical parts (MPs) and that these items are really identical in Peter but virtually distinct, where the virtual distinctness of any two MPs is tied to the possibility of one of them being the object of a cognitive act without the other being the object of the same act.

Is S. suggesting that virtual distinctness is wholly mind generated?   I don't think so.  For he speaks of a potential distinction of MPs in concrete reality, a distinction that becomes actual when the understanding grasps them as distinct.  (253) And so I take the possibility mentioned in clause (ii) of the above definition to be grounded not only in the mind's power to objectify and abstract but also in a real potentiality in the MPs in substances like Peter.

One might be tempted to think of weak identity as a part-whole relation.  Thus one might be tempted to say that 'Peter' refers to Peter and 'man' to a property taken in the abstract that is predicable not only of Peter but of other human beings as well.  'Peter is a man' would then say that this abstract property is a metaphysical part of Peter.  But this is not Sousedik's or any Thomist's view.  For S. is committed to the idea that "Every empirical individual and every part or trait of it is particular." (251)  It follows that no metaphysical part of any concrete individual is a universal.  Hence no MP is an abstract property.  So weak identity is not a part-whole relation.

What is it then?

First of all, weak identity is a relation that connects a concrete individual such as Peter to a property taken abstractly.  But in what sense is Peter identical to humanity taken abstractly?   In this sense:  the humanity-in-Peter and the humanity-in-the-mind have a common constituent, namely, humanity taken absolutely as common nature or natura absoluta or natura secundum se.  (254)  What makes weak identity identity is the common constituent shared by the really existing humanity in Peter and the intentionally existing  humanity in the mind of a person who judges that Peter is human.

So if we ask in what sense the referent of 'Peter' is identical to the referent of 'man,' the answer is that they are identical in virtue of the fact that Peter has a proper metaphysical part that shares a constituent with the objective concept referred to by 'man.'  Sousedik calls this common constituent the "absolute subject."  In our example, it is human nature taken absolutely in abstraction from its real existence in Peter and from its merely intentional existence in the mind.

Critical Observations

I am deeply sympathetic to Sousedik's constituent-ontological approach, his view that existence is a first-level 'property,' and the related view that there are modes of existence. (253)  But one of the difficulties I  have with S.'s  identity theory of predication is that it relies on common natures, and I find it difficult to make sense of them as I already spelled out in a previous post.    Common natures are neither one nor many, neither universal nor particular.  Humanity is many in things but one in the mind.  Hence taken absolutely it is neither one nor many.  It is this absolute feature that allows it be the common constituent in humanity-in-Peter and humanity-in-the-mind.  And as we just saw, without this common constituent there can be no talk of an identity between Peter and humanity.  The (weak) identity 'rides on' the common constituent, the natura absoluta.  Likewise, humanity is particular in particular human beings but universal in the mind (and only in the mind).  Hence taken absolutely it is neither particular nor universal. 

But it also follows that the common nature is, in itself and taken absolutely, neither really existent nor intentionally existent.  It enjoys neither esse naturale (esse reale) nor esse intentionale.  Consequently it has no being (existence) at all. This is not to say that it is nonexistent.  It is to say that it is jenseits von Sein und Nichtsein to borrow a phrase from Alexius von Meinong, "beyond being and nonbeing." 

The difficulty is to understand how there could be a plurality of distinct items that are neither universal nor particular, neither one nor many, neither existent nor nonexistent.  Note that there has to be a plurality of them: humanity taken absolutely is distinct from animality taken absolutely, etc.  And what is the nature of this distinctness?  It cannot be mind-generated.  This is because common natures are logically and ontologically prior to mind and matter as that which mediates between them. They are not virtually distinct.  Are they then really distinct?  That can't be right either since they lack esse reale.

And how can these common or absolute natures fail to be, each of them, one, as opposed to neither one nor many?  The theory posits a plurality of items distinct among themselves.  But if each is an item, then each is one.  An item that is neither one nor many is no item at all.

There is also this consideration.  Why are common natures more acceptable than really existent universals as constituents of ordinary particulars such as Peter?    The Thomists allow universals only if they have merely intentional existence, existence 'in' or rather for a mind.  "Intentional existence belongs to entities which exist only in dependence upon the fact that they are objects of our understanding." (253)  They insist that, as S. puts it,  "Every empirical individual and every part or trait of it is particular." (251)  S. calls the latter an observation, but it is not really a datum, but a bit of theory.  It is a datum that 'man' is predicable of many different individuals.  And it is a datum that Peter is the subject of plenty of essential predicates other than 'man.'  But it is not a clear datum that Peter is particular 'all the way through.'  That smacks of a theory or a proto-theory, not that it is not eminently reasonable.

One might 'assay' (to use G. Bergmann's term) an ordinary particular as a complex consisting of a thin or 'bare'  particular instantiating universals.  This has its own difficulties, of course, but why should a theory that posits common natures be preferrable to one that doesn't but posits really existent universals instead?  Either way problems will arise.

The main problem in a nutshell is that it is incoherent to maintain that some items are such that they have no being whatsoever.  'Some items are such that they have no being whatsoever' is not a formal-logical contradiction, pace van Inwagen, but it is incoherent nonetheless.  Or so it seems to me. 

Still Trying to Understand Van Inwagen's Half-Way Fregeanism about Existence

In section 53 of The Foundations of Arithmetic, Gottlob Frege famously maintains that

. . . existence is analogous to number.  Affirmation of existence is in fact nothing but denial of the number nought.  Because existence is a property of concepts the ontological argument for the existence of God breaks down. (65)

Frege is here advancing a double-barreled thesis that splits into two subtheses.

ST1. Existence is analogous to number.

ST2. Existence is a property (Eigenschaft) of concepts and not of objects.

In the background is the sharp distinction between property (Eigenschaft) and mark (Merkmal).  Three-sided is a mark of the concept triangle, but not a property of this concept; being instantiated is a property of this concept but not a mark of it.  The Cartesian-Kantian ontological argument "from mere concepts" (aus lauter Begriffen), according to Frege, runs aground because existence cannot be a mark of any concept, but only a property of some concepts.  And so one cannot validly argue from the concept of God to the existence of God.

Existence as a property of concepts is the property of being-instantiated.  We can therefore call the Fregean account of existence an instantiation account.

My concern in this entry is the logical relation between the subtheses.  Does the first entail the second or are they logically independent?  There is a clear sense in which (ST1) is true.  Necessarily, if horses exist, then the number of horses is not zero, and vice versa.  'So 'Horses exist' is logically equivalent to 'The number of horses is not zero.'  This is wholly unproblematic for those of us who agree that there are no Meinongian nonexistent objects.  But note that, in general, equivalences, even logical equivalences, do not sanction reductions or identifications.  So it remains an open question whether one can take the further step of reducing existence to instantiation, or identifying existence with instantiation, or even eliminating existence in favor of instantiation. 

(ST1), then, is unproblematically true if understood as expressing the following logical equivalence: 'Necessarily Fs exist iff the number of Fs is not zero.'  My question is whether (ST1) entails (ST2).  Peter van Inwagen in effect denies the entailment by denying that the 'the number of . . . is not zero' is a predicate of concepts:

I would say that, on a given occasion of its use, it predicates of certain things that they number more than zero.  Thus, if one says, 'The number of horses is not zero,' one predicates of horses that they number more than zero.  'The number of . . . is not zero' is thus what some philosophers have called a 'variably polyadic' predicate.  But so are many predicates that can hardly be regarded as predicates of concepts.  The predicates 'are ungulates' and 'have an interesting evolutionary history,' for example, are variably polyadic predicates.  When one says, 'Horses are ungulates' or 'Horses have an interesting evolutionary history' one is obviously making a statement about horses and not about the concept horse.  ("Being, Existence, and Ontological Commitment," pp. 483-484)

It is this passage that I am having a hard time understanding.   It is of course clear what van Inwagen is trying to show, namely, that the Fregean subtheses are logically independent and that one can affirm the first without being committed to the second.  One can hold that existence is denial of the number zero without  holding that existence is a property of concepts.

But I am having trouble with the claim that the predicate 'the number of . . . is not zero' is  'variably polyadic' and the examples van Inwagen employs.  'Robbed a bank together' is an example of a variably polyadic predicate.  It is polyadic because it expresses a relation and it is variably polyadic because it expresses a family of relations having different numbers of arguments.  For example, Bonnie and Clyde robbed a bank together, but so did Ma Barker and her two boys, Patti Hearst and three members of the ill-starred Symbionese Liberation Army, and so on.  (Example from Chris Swoyer and Francesco Orilia.) 

Now when I say that the number of horses is not zero, what am I talking about? It is plausible to say that I am talking about horses, not about the concept horse.  What I don't understand is why van Inwagen says that 'the number of . . . is not zero' is a variably polyadic predicate. As far as I can see, it is not even polyadic, let alone variably polyadic.  What is the relation that the predicate expresses, and why is that relation multigrade?  I grant that there are indefinitely many ways the number of horses could be not zero: there could be one horse, two, three, and so on.  But what is the relation between or among horses that this supposedly polyadic predicate expresses? 

'. . .exist(s)' is monadic.  It expresses no relation.  Why not say the same about 'such that their number is not zero'?

Now consider 'are ungulates.'  If an ungulate is just a mammal with hooves, then I fail to see how 'are ungulates' is polyadic, let alone variably polyadic.  'Are hooved mammals' is monadic.

The other example is 'Horses have an interesting evolutionary history.'  This sentence is clearly not about the concept horse. But it is not about any individual horse either.  Consider Harry the horse.  Harry has a history.  He was born in a certain place, grew up, was bought and sold, etc. and then died at a certain age.  He went through all sorts of changes.  But Harry didn't evolve, and so he had no evolutionary history.  No individual evolves; populations evolve:

Evolutionary change is based on changes in the genetic makeup of populations over time. Populations, not individual organisms, evolve. Changes in an individual over the course of its lifetime may be developmental (e.g., a male bird growing more colorful plumage as it reaches sexual maturity) or may be caused by how the environment affects an organism (e.g., a bird losing feathers because it is infected with many parasites); however, these shifts are not caused by changes in its genes. While it would be handy if there were a way for environmental changes to cause adaptive changes in our genes — who wouldn't want a gene for malaria resistance to come along with a vacation to Mozambique? — evolution just doesn't work that way. New gene variants (i.e., alleles) are produced by random mutation, and over the course of many generations, natural selection may favor advantageous variants, causing them to become more common in the population.

'Horses have an interesting evolutionary history,' then, is not about the concept horse or about any individual horse.  The predicate in this sentence appears to be non-distributive or collective.  It is like the predicate in 'Horses have been domesticated for millenia.'  That is certainly not about the concept horse.  No concept can be ridden or made to carry a load.  But it is also not about any individual horse.  Not even the Methuselah of horses, whoever he might be, has been around for millenia.

A predicate F is distributive just in case it is analytic that whenever some things are F, then each is F.  Thus a distributive predicate is one the very meaning of which dictates that if it applies to some things, then it applies to each of them.  'Blue' is an example.  If some things are blue, then each of them is blue.

If a predicate is not distributive, then it is non-distributive (collective).  If some Occupy-X nimrods have the building surrounded, it does not follow that each such nimrod has the building surrounded.  If some students moved a grand piano into my living room, it does not follow that each student did.  If bald eagles are becoming extinct, it does not follow that each bald eagle is becoming extinct.  Individual animals die, but no individual animal ever becomes extinct. If the students come from many different countries, it does not follow that each comes from many different countries.  If horses have an interesting evolutionary history, it does not follow that each horse has an interesting evolutionary history.

My problem is that I don't understand why van Inwagen gives the 'Horses have an interesting evlutionary history' example when he is committed to saying that each horse exists.  His view , I take it, is that 'exist(s)' is a first-level non-distributive predicate.  'Has an interesting evolutionary history,' however, is a first-level non-distributive predicate.  Or is it PvI's view that 'exist(s)' is a first-level non-distributive predicate?

Either I don't understand van Inwagen's position due to some defect in me, or it is incoherent.  I incline toward the latter.  He is trying to show that (ST1) doe not entail (ST2).  He does this by giving examples of predicates that are first-level, i.e., apply to objects, but are variably polyadic as he claims 'the number of . . . is not zero' is variably polyadic.  But the only clear example he gives is a predicate that is non-distributive, namely 'has an interesting evilutionary history.'  'Horses exist,' however, cannot be non-distributive.  If some horses exist, then each of them exists.  And if each of them exists, then 'exists' is monadic, not polyadic, let alone variably polyadic.

The ComBox is open if there is anyone who knows this subject and has read PvI's paper and can set me straight. 

My Argument That 'Exist(s)' is not Univocal Revisited: No 'Is' of Predication?

On August 11th I wrote:

Suppose we acquiesce for the space of this post in QuineSpeak. 

Then 'Horses exist' says no more and no less than that 'Something is a horse.'  And 'Harry exists' says no more and no less than that 'Something is Harry.'  But the 'is' does not have the same sense in both translations.  The first is the 'is' of predication while the second is the 'is' of identity.  The difference  is reflected in the standard notation.  The propositional function in the first case is Hx.  The propositional function in the second case is x = h.  Immediate juxtaposition of predicate constant and free variable [with the predicate constant coming first] is the sign for predication.  '=' is the sign for identity.  Different signs for different concepts.  Identity is irreducible to predication which is presumably why first-order predicate logic with identity is so-called.

Those heir to the 'Fressellian' position, such as Quine and his epigoni, dare not fudge the distinction between the two senses of 'is' lately noted. That, surely, is a cardinal tenet of their brand of analysis.

So even along Quinean lines, the strict univocity of 'exist(s)' across all its uses cannot [pace van Inwagen] be upheld.  It cannot be upheld across the divide that separates general from singular existentials.

But the next morning I had a doubt about what I had written.  Is there an 'is' of predication in MPL (modern predicate logic)? I argued (above) that 'exist(s)' is not univocal: it does not in MPL have the same sense in 'Fs exist' and 'a exists.' The former translates as 'Something is (predicatively) an F' while the latter translates as 'Something is (identically) a.'  Kicked out the front door, the equivocity returns through the back door disguised as  an equivocation on 'is' as between predication and identity.

But if the 'is' in 'Grass is green' or 'Something is green' is bundled into the predicate in the Fregean manner, then it could be argued that there is no 'is' of predication in MPL distinct from the 'is' of identity and the 'is' of existence.  If so, my equivocity argument above collapses, resting as it does on the unexpungeable distinction between the 'is' or identity and the 'is' of predication.

Yesterday a note from Spencer Case shows that he is on to the same (putative) difficulty with my argument:

Hey Bill, I have a professor whose pet peeve is the claim that there is an 'is' of identity and an 'is' of predication. I don't know his arguments for thinking so, but his view is that 'is' is univocal and what differs is the content of the copula. If he's right, that would be a problem for you here. Do you know more about this position than I do?           

To sort this out we need to distinguish several different questions:

Q1. Is there a predicative use of 'is' in English?  Yes, e.g., 'Al is fat.'  This use is distinct from the existential use and the identitative use (and others that I needn't mention).  So I hope Spencer's professor is not denying the plain linguistic fact that in English there is an 'is' of predication and an 'is' of identity and that they are distinct.

Q2. Must there be a separate sign for the predicative tie in a logically perspicuous artificial language such as MPL (modern predicate logic, i.e., first-order predicate logic with identity)?  No.  When we symbolize 'Al is fat' by Fa, there is no separate sign for the predicative tie.  But there is a sign for it, namely, the immediate juxtaposition of the predicate constant and the individual constant with the predicate constant to the left of the individual constant. So we shouldn't confuse a separate or stand-alone sign with a sign.  Other non-separate signs are conceivable exploiting different fonts and different colors, etc. 

Q3.  Must there be some sign or other for predication in a logically adequate language such as MPL? How could there fail to be?  If our logical language is adequate, then it has to be able to symbolize predications such as 'Al is fat.'  And note that existentials such as 'Fat cats exist' cannot be put into MPL without a sign for predication.  '(∃x)(Fx & Cx)' employs non-separate signs for predication.

Q4.  Is the predicative tie reducible or eliminable?  No.  For Frege, there is no need for a logical copula or connector to tie object a to concept F when a falls under F.  The concept is "unsaturated" (ungesaettigt).  Predicates and their referents (Bedeutungen) are inherently gappy or incomplete.   So the predicate 'wise' would be depicted as follows: '___ wise.'  What is thereby depicted is a sentential function or open sentence.  A (closed) sentence results when a name is placed in the gap. The concept to which this predicate or sentential function refers is gappy in an analogous sense. Hence there is no need for for an 'is' of predication in the logical language or for an instantiation relation. Object falls under concept without the need of a tertium quid to connect them.

I would imagine that Spencer Case's professor has some such scheme in mind.  One problem is that it is none too clear what could be meant by a gappy or incomplete or unsaturated entity.  That a predicate should be gappy is tolerably clear, but how could the referent of a predicate be gappy given that the referent of a predicate is a single item and not the manifold of things to which the predicate applies?  The idea is not that concepts exist only when instantiated, but that  their instantiation does not require the services of a nexus of predication: the concept has as it were a slot in it that accepts the object without the need of a connector to hold them together.  (Think of a plug and a socket: there is no need for a third thing to connect the plug to the socket: the 'female' receptacle just accepts the 'male' plug.)

There are other problems as well.

But here is the main point.  Frege cannot avoid speaking of objects falling under concepts, of a's falling under F but not under G.  If the notion of the unsaturatedness of concepts is defensible, then Frege can avoid speaking of a separate predicative tie that connects objects and concepts.  But he cannot get on without predication and without a sign for predication.

I conclude that my original argument is sound.  There is is and must be a sign for predication in any adequate logic, but it needn't be a stand-alone sign.  (Nor need its referent be a stand-alone entity.)   Compare '(∃x)Hx' to '(∃x)(x = h)' as translations of 'Horses exist' and 'Harry exists,' respectively.  The identity sign occurs in only one of the translations, the second.  And the sign for predication occurs only in the first.  There is no univocity of 'exist(s)' because there is no univocity of 'is' in the translations. 

David Brightly's Weblog and a Punctilio Anent Predication and Inclusion

The unduly modest David Brightly has begun a weblog entitled tillyandlola, "scribblings of no consequence."   In a recent post he criticizes my analysis of the invalidity of the argument: Man is a species; Socrates is a man; ergo, Socrates is a species.  I claimed that the argument equivocates on 'is.'  In the major premise, 'is' expresses a relation of conceptual inclusion: the concept man includes the subconcept species.  In the minor premise, however, the 'is' is the 'is' of predication: Socrates falls under man, he doesn't fall within it.

I am afraid that my analysis is faulty, however, and for the reasons that David gives.  There is of course a difference between the 'is' of inclusion and the 'is' of predication.  'Man is an animal' expresses the inclusion of the concept animal within the concept man.  'Socrates is a man,' however, does something different: it expresses the  fact that Socrates falls under the concept man. 

But as David notes, it is not clear that species is included within the concept man.  If we climb the tree of Porphyry we will ascend from man to mammal to animal; but nowhere in our ascent will we hit upon species. 

Transitivity of Predication?

I dedicate this post to London Ed, who likes sophisms and scholastic arcana.

Consider these two syllogistic arguments:

A1. Man is an animal; Socrates is a man; ergo, Socrates is an animal.
A2. Man is a species; Socrates is a man; ergo, Socrates is a species.

The first argument is valid.  On one way of accounting for its validity, we make two assumptions.  First, we assume that each of the argument's constituent sentences is a predication.  Second, we assume the principle of the Transitivity of Predication: if x is predicable of y, and y is predicable of z, then x is predicable of z.  This principle has an Aristotelian pedigree.  At Categories 3b5, we read, "For all that is predicated of the predicate will be predicated also of the subject." So if animal is predicable of man, and man of Socrates, then animal of Socrates.  

Something goes wrong, however, in the second argument.  The question is: what exactly?  Let's first of all see if we can diagnose the fallacy while adhering to our two assumptions.  Thus we assume that each occurrence of 'is' in (A2) is an 'is' of predication, and that predication is transitive.  One suggestion  -- and I take this to be the line of some Thomists -- is that (A2) equivocates on 'man.'  In the major, 'man' means 'man-in-the-mind,' 'man as existing with esse intentionale.'  In the minor, 'man' means 'man-in-reality,' 'man as existing with esse naturale.'  We thus diagnose the invalidity of (A2) by saying that it falls afoul of quaternio terminorum, the four-term fallacy.  On this diagnosis, Transitivity of Predication is upheld: it is just that in this case the principle does not apply since there are four terms.

But of course there is also the modern Fregean way on which we abandon both of our assumptions and locate the equivocation in (A2) elsewhere.  On a Fregean diagnosis, there is an equivocation on 'is' in (A2) as between the 'is' of inclusion and the 'is' of predication.  In the major premise, 'is' expresses, not predication, but inclusion: the thought is that the concept man includes within its conceptual content the subconcept species.  In the minor and in the conclusion, however, the 'is'  expresses predication: the thought is that Socrates falls under the concepts man and species.  Accordingly, (A2) is invalid because of an equivocation on 'is,' not because of an equivocation on 'man.'

The Fregean point is that the concept man falls WITHIN but not UNDER the concept animal, while the object Socrates falls UNDER but not WITHIN the concepts man and animal.  Man does not fall under animal because no concept is an animal.  Animal is a mark (Merkmal) not a property (Eigenschaft) of man.  In general, the marks of a concept are not its properties.  But concepts do have properties.  The property of being instantiated, for example, is a property of the concept man.  But it is not a mark of it.  If it were a mark, then man by its very nature would be instantiated and it would be a conceptual truth that there are human beings, which is false.

Since on the Fregean scheme the properties of concepts needn't be properties of the items that fall under the concepts, Transitivity of Predication fails.  Thus, the property of being instantiated is predicable of the concept philosopher, and the concept philosopher is predicable  of Socrates; but the property of being instantiated is not predicable of Socrates. 

Another Round with Hennessey on Accidental Predication

Having had my say about what is known in the trade as Occam's Razor, and having secured some welcome agreement with the proprietor of Beyond Necessity in the combox of the aforelinked post, I am now ready to address the meat of Richard Hennessey's response to my three-post critique of what I took to be his theory of accidental predication.

There is no need to stray from our hoary example of accidental predication: 'Socrates is seated.'  I took Hennessey to be saying that in a true accidental predication of this simple form subject and predicate refer to exactly the same thing.  If they didn't, the sentence could not be true.  Here is how Hennessey puts it:

Let us take the proposition “Socrates is sitting” or the strictly equivalent “Socrates is a sitting being.” The referent of the subject term here is the sitting Socrates and that of the predicate term is one and the same sitting Socrates. . . . only if the referent of the “Socrates” and that of the “sitting” of “Socrates is sitting” are identical can it be true that Socrates is actually the one sitting.

Since Hennessey uses the word 'identity' we can call this an identity theory of accidental predication: in true predications of this sort, the referent of the subject term and the referent of the predicate term are identical, and this identty is what insures that the predication is true.  If so, then the same goes for all other true predications which are about Socrates.  So consider 'Socrates is standing' which is the logical contrary (not contradictory) of 'Socrates is sitting.'  These sentences cannot both be true at the same time, but they can be true at different times.  Suppose we ask what the truth-maker is in each case.  Given that subject and predicate terms refer to exactly the same thing, namely, Socrates, it follows that in each case it is Socrates and Socrates alone that is the truth-maker of both sentences.  When he is sitting, Socrates makes-true 'Socrates is sitting' and when he is standing Socrates makes-true 'Socrates is standing.' 

What I do not understand, however, is how these obviously different sentences, which differ in their truth-conditions, can have one and the same entity as truth-maker.  The same problem does not seem to arise for such essential predications as 'Socrates is human.'  For there is no time when he is not human, and (this is a distinct modal point), at every time at which he is human he is not possibly such as to be nonhuman.  In the case of essential predications an identity theory may be workable.  Perhaps we can say that Socrates himself is the truth-maker of 'Socrates is human,' 'Socrates is rational,' and Socrates is animal.'

In the case of accidental predications, however, it seems definitely unworkable. This is because different accidental predications about Socrates need different truth-makers. It is not Socrates, but Socrates'  being seated that is the truth-maker of 'Socrates is seated' and it is not Socrates, but Socrates' standing that is the truth-maker of 'Socrates is standing.'

Without worrying about what exactly the italicized phrases pick out (facts? states of affairs? tropes?), one thing seems crystal clear: there cannot be a strict identity of, e.g., the referent of 'Socrates' and the referent of 'seated.'  And since there cannot be a strict identity, there must be some difference between the referents of the subject and predicate terms.  Hennessey seems to show an appreciation of this in his response (second hyperlink above):

If we tweak the [B.V.] passage a bit, we can, it strikes me, improve the thesis about the referencing at work in the sentence “Socrates is sitting” so that it offers a more satisfactory support of the neo-Aristotelian thesis of anti-realism in the theory of universals, one indeed getting along “without invoking universals.” First, let us speak of “particular property” instead of “particularized property,” for the latter expression suggests, at least to me, that the property would be, prior to some act of particularization, a universal and not a particular. Let us then accept, but with a precision, Bill’s statement that “‘sitting’ refers to a particularized property (a trope),” saying instead that while the “Socrates” in our statement refers to Socrates, the person at present sitting, the “sitting” primarily refers to Socrates, the person at present sitting, and also co-refers to the particular property of sitting that inheres in Socrates. (An alternative terminology might have it that the “Socrates” in our statement denotes Socrates and the “sitting” primarily denotes Socrates, still the person sitting, and also connotesthe property of sitting that inheres in Socrates; come to think of it, I believe I recall having read, long ago, a similar distinction in the Petite logique of Jacques Maritain, a book which I no longer have, thanks to a flooded basement.)

This is definitely an improvement.  It is an improvement because it tries to accommodate the perfectly obvious point that there must be some difference or other between the worldly referents of the subject and predicate terms in accidental predications.  Hennessey is now telling us that 'Socrates' in our example refers to exactly one item, Socrates, while 'sitting' refers to two items, Socrates and the particular property (trope, accident) seatedness which inheres in Socrates.

But Hennessey is not yet in the clear.  For I will now ask him what the copula 'is' expresses.  It seems he must say that it expresses inherence.  He must say that it is because seatedness inheres in Socrates that 'Socrates is seated' is true.  Now inherence is an asymmetrical relation: if x inheres in y, then it is not the case that y inheres in x.  But there is no sameness relation (whether strict identity, contingent identity, accidental sameness, Castaneda's consubstantiaton, etc) that is not symmetrical.  Thus if x is in any sense the same as y, then y is (in the same sense) the same as x.  Therefore, Hennessey's bringing of inherence into the picture is at odds with his claims of identity.  Inherence, being asymmetrical,  is not a type of identity or sameness.  So why the talk of identity in the first passage quoted above?

Why does Hennessey say that 'seated' refers primarily to Socrates but also to the particular property seatedness?   Why not just say this: 'Socrates' refers to the primary substance (prote ousia) Socrates and nothing else; 'is' refers to the inherence relation or nexus and nothing else; 'seated/sitting' refers to the particular property (trope, accident) seatedness and nothing else.  This would give him what he wants, a theory of predication free of universals.

But this is not what Hennessey says.  He is putting forth some sort of identity theory of predication.  He thinks that in some sense the subject and predicate terms refer to the very same thing.  He tells us that 'seated' refers both to a substance and to an accident.  The upshot is that Hennessey has given birth to a hybrid theory which I for one do not find  intelligible. 

Here is the question he needs to confront directly: what, in the world, makes it true that 'Socrates is seated' (assuming of course that the sentence is true)?  Here is a clear answer: the sentence is true because seatedness inheres in Socrates.  But then of course there can be no talk of the identity of Socrates and seatedness.  They are obviously not identical: one is a substance and the other an accident.  The relation between them, being asymmetrical, cannot be any sort of sameness relation.

The other clear answer which, though clear, is absurd is this:  the sentence is true because 'Socrates' and 'seated' refer to the very same thing with the result that the copula expresses identity.  Now this is absurd for the reasons given over several posts. This was his original theory which he has wisely moved away from.

Instead of plumping for one of these clear theories, Hennessey gives us an unintelligible hybrid, a monster if you will, as we approach Halloween.

Accidental Sameness and its Logical Properties

I should thank Richard Hennessey for motivating me to address a topic I haven't until these last few days discussed in these pages, namely, that of accidental sameness.  Let us adopt for the time being a broadly Aristotelian ontology with its standard nomenclature of substance and accident, act and potency, form and matter, etc.  Within such a framework, how can we account for an accidental predication such as 'Socrates is seated'? 

In particular, what is expressed by 'is' in a sentence like this?  Hennessey seems to maintain that it expresses an identity which holds, if the sentence is true, between the referent of the subject term 'Socrates' and the referent of the predicate term  'seated.'  Here is what Hennessey says:

Let us take the proposition “Socrates is sitting” or the strictly equivalent “Socrates is a sitting being.” The referent of the subject term here is the sitting Socrates and that of the predicate term is one and the same sitting Socrates. Similarly, the referent of the subject term of “Plato is sitting” is the sitting Plato and that of its predicate term is one and the same sitting Plato. Here, once again, only if the referent of the “Socrates” and that of the “sitting” of “Socrates is sitting” are identical can it be true that Socrates is actually the one sitting. And, only if the referent of the “Plato” and that of the “sitting” of “Plato is sitting” are identical can it be true that Plato is actually the one sitting.

Hennessey is making two moves in this passage.  The first is the replacement of 'Socrates is seated' with 'Socrates is a seated being.' (I am using 'seated' instead of 'sitting' for idiosyncratic stylistic reasons;  the logic and ontology of the situation should not be affected.) I grant that the original sentence and its replacement are logically equivalent.  Hence I have no objection to the first move.

The second move is to construe the 'is' of the replacement sentence as expressing identity.  Together with this move goes Hennessey's  claim that ONLY in this way can the truth of the sentence be insured.  This claim is false for reasons given earlier, but this is not my present concern.  My concern at present is the second move by itself.  Can the 'is' of the replacement sentence be construed as expressing identity?

The answer to this is in the negative if by 'identity' is meant strict identity.  Strict identity, symbolized by '=,'  is an equivalence relation: it is reflexive, symmetrical, and transitive.  It is furthermore governed by the Indiscernibility of Identicals (If a = b, then everything true of a is true of b and vice versa) and the Necessity of Identity (If a = b, then necessarily a = b).  Now if the referent of 'Socrates' and the referent of 'seated' are strictly identical, then this is necessarily so, true in every possible world in which Socrates exists, in which case our sentence cannot be contingently true as it obviously is.  Socrates is seated only at some of the times at which he exists, not at all such times.  And at any time at which he is seated he is possibly such as not to be seated at that time.  (The modality in question is broadly logical.)

So if Hennessey wants to construe the 'is' as expressing a type of sameness, it cannot be that sameness which is strict identity.  An option which is clearly open to him as an Aristotelian is to construe the 'is' as expressing accidental sameness.  But what is that?

It is a dyadic relation that connects one substance and one accidental compound.  (Thus by definition it never connects two substances or two compounds.)  An accidental compound is a particular, not a universal.  It is a hylomorphic compound the matter of which is a substance and the form of which an accident inhering in that substance.  It is admittedly a somewhat 'kooky' object, to borrow an epithet from Gareth Mathews.  An example is seated-Socrates.  Socrates is a substance.  His seatedness is an accident inhering in him.  The two together form an accidental compound which can be denoted by 'seated-Socrates' or by 'Socrates + seatedness.'  Seated-Socrates is neither a substance nor an accident, but a transcategorial hybrid composed of one substance and one accident, but only if the accident inheres in the substance. (An accidental compund is therefore not a mereological sum of a substance and any old accident.)

The compound is not a substance because it cannot exist on its own, but it is parasitic upon its parent substance, in our example, Socrates. It is also not a substance because it is not subject to alterational change.  Change for an accidental compound is existential change, either coming into being or passing out of being.  When Socrates sits down, seated-Socrates comes into being, and when he stands up it passes out of being.  An accidental compound is not an accident because it is not related to its parent substance by inherence, but by accidental sameness.  A key difference is that inherence is an asymmetrical relation, while accidental sameness is symmetrical.

Hennessey can say the following: 'Socrates is seated' expresses the accidental sameness of Socrates with the accidental compound, seated-Socrates.  He needs to posit two objects, not one: a substance and an accidental compound.  If he holds that the referent of 'Socrates' and the referent of 'seated' are strictly identical, then the accidentality of the predication cannot be accommodated, and all predications become essential. That was my initial objection to Hennessey's view before I figured out a way to salvage it. 

What are the logical properties of the accidental sameness relation?  Like strict identity, it is symmetrical.  This should be obvious.  If Socrates is accidentally the same as seated-Socrates, then the latter is accidentally the same as the former.  The inherence relation, by contrast, is asymmetrical: if A inheres in S, then S does not inhere in A. This is one of the differences between the accidental sameness relation and the inherence relation. 

Accidental sameness is irreflexive.  This can be proven as follows:

1. No substance is an accidental compound.
2. If a is accidentally the same as b, then either a is a subtance and b a compound, or vice versa.
Therefore
3. No object, whether substance or compound, is accidentally the same as itself.

It can also be proven that accidental sameness is intransitive.  Thus, if a is accidentally the same as b, and b accidentally the same as c, it follows that a is not accidentally the same as c.  Suppose a is a substance.  Then b is a compound.  But if b is a compound, then c is a substance, with the result that a substance is accidentally the same as a substance, which violates the definition of accidental sameness.  On the other hand, if a is a compound, then b is a substance, which makes c a compound, with the result that a  compound is accidentally the same as a compound, which also violates the definition.  So accidental sameness is intransitive.

Clearly, there is accidental sameness only if there are accidental compounds.  But are there any of the latter?  Consider a fist.  A fist is not strictly identical to the hand whose fist it is. (They have different persistence conditions.) But a fist is not strictly different from the hand whose fist it is.  But surely there are fists, and surely what we have in a situation like this is not two individuals in the same place.  So it is reasonable to maintain that a fist is an accidental compound which is accidentally the same as the hand whose fist it is.

Still, there is something 'kooky' about accidental compounds.  So I'll end with a challenge to Hennessey, enemy of universals.  Why are accidental compounds less 'kooky' than universals, whether immanent or transcendent? 

Accidental Sameness: Defending Hennessey Against My Objection

Yesterday I made an objection to Richard Hennessey's neo-Aristotelian theory of accidental predication.  But this morning I realized that he has one or more plausible responses.  By the way, this post has, besides its philosophical purpose, a metaphilosophical one.  I will be adding support to my claim lately bruited that philosophy -- the genuine article -- is not a matter of debate, as I define both 'philosophy' and 'debate.'  For have you ever been to a debate in which debater A, having made an objection to something debater B has said, says, "Wait a minute!  I just realized that you have one or more plausible ways of turning aside my objection.  The first is . . . ."?

1. 'Socrates is seated' is an example of an accidental predication.  For surely it is no part of Socrates' essence or nature that he be seated.  There is no broadly logical necessity that  he be seated at any time at which he is seated, and there are plenty of times at which he is not seated.  'Socrates is seated' contrasts with the essential predication 'Socrates is human.'  Socrates is human at every time at which he exists and at every world at which he exists.

2. Hennessey's theory is that ". . . only if the referent of the 'Socrates' and that of the 'sitting' of 'Socrates is sitting' are identical can it be true that Socrates is actually the one sitting."  The idea seems to be that accidental predications can be understood as identity statements.  Thus 'Socrates is seated' goes over into (what is claimed to be) the logically equivalent  'Socrates is (identical to) seated-Socrates.'  Accordingly, our sample sentence is construed, not as predicating a property of Socrates, a property he instantiates, but as affiming the identity of Socrates with the referent of 'seated-Socrates.'

3.  But what is the referent of 'seated-Socrates'?  If the referent is identical to the referent of 'Socrates,' namely Socrates, then my objection kicks in:  how can the predication be contingently true, as it obviously is, given that it affirms the identity of Socrates with himself?  Socrates is essentially Socrates but only accidentally seated.

4. Perhaps Hennessey could respond to this objection by saying that 'Socrates' and 'Socrates-seated' do not refer to the same item: they refer to different items which are, nonetheless, contingently identical.  This would involve distinguishing between necessary identity and contingent identity where both are equivalence relations (reflexive, symmetrical, transitive) but only the former satisfies in addition the Indiscernibility of Identicals (InId) and the Necessity of Identity (NI).  It is obvious that if a and b are contingently identical, but distinct, then these items must be discernible in which case InId fails.  It is also obvious that NI must fail for contingent identity.

5. Closer to Aristotle is a view described by Michael C. Rea in "Sameness Without Identity: An Aristotelian Solution to the Problem of Material Constitution" in Form and Matter, ed. Oderberg, Blackwell 1999, pp. 103-115.  I will now paraphrase and interpret from Rea's text, pp. 105-107.  And I won't worry about how the view I am about to sketch differs -- if it does differ -- from the view sketched in #4.

When Socrates sits down, seated-Socrates comes into existence. When he stands up or adopts some other nonseated posture, seated-Socrates passes out of existence.  This 'kooky' or 'queer' object is presumably a particular, not a universal, though it is not a substance.  It is an accidental unity whose existence is parasitic upon the existence of its parent substance, Socrates.   It cannot exist without the parent substance, but the latter can exist without it.  The relation is like that of a fist to a hand made into a fist.  The fist cannot exist without the hand, but the hand can exist without being made into a fist.Though seated-Socrates is not a substance it is like a substance in that it is a hylomorphic compound: it has Socrates as its matter and seatedness as its form.  As long as Socrates and seated-Socrates exist, the relation between them is accidental sameness, a relation weaker than strict identity. 

Accidental sameness is not strict identity presumably because  the former is not governed by the Indiscernibility of Identicals.  Clearly, Socrates and seated-Socrates do not share all properties despite their sameness.  They differ temporally and modally. Socrates exists at times at which seated-Socrates does not exist (though not conversely).  And it is possible that Socrates exist without seated-Socrates existing (though not conversely). 

Are Socrates and seated-Socrates numerically the same?  They count as one and so they are one in number though not one in being.   So says Aristotle according to Rea.  After all, if Socrates and Alcibiades are seated at table we count two philosophers not four.  We don't count: Socrates, seated-Socrates, Alcibiades, seated-Alcibiades.

But I will leave it to Hennessey to develop this further.  It looks as if this is the direction in which he must move if his theory is to meet my objection.

What about essential predication?  Is there a distinction between Socrates and human-Socrates?  These two cannot be accidentally the same.  They must be strictly identical. If 'Socrates is human' is parsed as 'Socrates is identical to human-Socrates' then how does the latter differ from 'Socrates is Socrates'?  The sense of 'Socrates is human' differs from the sense of 'Socrates is Socrates.'  How account for that?  'Socrates is Socrates' is a formal-logical truth, trivial and uninformative.  'Socrates is human' is not a formal-logical truth; it is informative. 

Comments on Richard Hennessey's Neo-Aristotelian Theory of Predication

Richard Hennessey of Gnosis and Noesis sketches a neo-Aristotelian theory of predication in Another Aristotelian Basis for a Neo-Aristotelian Anti-Realism in the Theory of Universals.  Drawing as he does upon my discussion in Scholastic Realism and Predication, he has asked me to comment on his post.  I will do so with pleasure.

I first want to agree partially with something he says at the close of his post: 

. . . we have in the so-called problem of universals not a genuine problem, but merely a pseudo-problem. That is, we have a problem of universals only if we posit their existence. If we do not posit them, there is no genuine problem.

I would put the point somewhat differently.  The phrase 'problem of universals' is a misnomer. For what is in dispute in the so-called problem of universals is the nature of properties.  Not their existence, but their nature.  That there are properties is a given, a datum.  What alone can be reasonably questioned is their nature.  If you deny that sugar is sweet, then I show you the door.  But if you deny that sweetness is a universal, then I listen to your arguments.  For it is not at all obvious that the sweetness of a sugar cube is a universal. (Nor is it obvious that it isn't) That it is a universal is a theoretical claim that goes beyond the data.  It is consistent with the data that the sweetness be a particular, an unrepeatable item, such as a trope (as in the theories of D. C. Williams and Keith Campbell, et al.) or some other sort of particular. 

The correct phrase, then, is 'problem of properties,' not 'problem of universals.'  But that is not to say that there is no legitimate use for 'problem of universals.'  If one posits universals, then one will face various problems such as the problem of how they connect to particulars.  Those problems are genuine, not pseudo, given that there are universals.

In any case, Richard sees no need to posit universals, whether Platonic or Aristotelian, to explain either essential or accidental predication.  Here is the gist of Richard's theory:

Let us take the proposition “Socrates is sitting” or the strictly equivalent “Socrates is a sitting being.” The referent of the subject term here is the sitting Socrates and that of the predicate term is one and the same sitting Socrates. Similarly, the referent of the subject term of “Plato is sitting” is the sitting Plato and that of its predicate term is one and the same sitting Plato. Here, once again, only if the referent of the “Socrates” and that of the “sitting” of “Socrates is sitting” are identical can it be true that Socrates is actually the one sitting. And, only if the referent of the “Plato” and that of the “sitting” of “Plato is sitting” are identical can it be true that Plato is actually the one sitting.

What we have here could be called an identity theory of predication: if 'Socrates is a sitting being' is true, then the referent of the subject term 'Socrates' and the referent of the predicate term 'sitting being' are numerically identical.  Accordingly, the 'is' is the 'is' of identity.  ONLY on this analysis, says Richard, can the sentence be true. I rather doubt that, but first we need to consider whether Richard's theory is not open to serious objection.

If x and y are identical, then this is necessarily so. Call this the Necessity of Identity.  More precisely: for any x, y, if x = y, then necessarily, x = y.   Equivalent contrapositive: if possibly ~(x = y), then ~(x = y).  It follows that if Socrates is identical to some sitting being, then necessarily he is identical to that sitting being.  But in that case it would not be possible for Socrates not to be a sitting being.  This, however, is possible.  Sometimes he is on his feet walking around, other times he is flat on his back, and he has even been observed standing on his head.  And please note that even if, contrary to fact, Socrates was always seated, it would still be possible for him not to be seated.  The mere possibility of his not being seated shows that he cannot be identical to some sitting being.

This is an objection that Richard needs to address if his theory is to be tenable.  Note that my objection can be met without invoking universals.  One could say that 'Socrates' in our sample sentence refers to Socrates, that 'sitting' refers to a particularized property (a trope), and that the 'is' is the 'is' of predication, not identity.  Accordingly, there is not an identity between Socrates and a sitting being; the particularized property being-seated inheres in Socrates, where inherence, unlike identity, is asymmetrical.

The other claim that Richard makes is that ONLY on his theory can the truth of 'Socrates is sitting' be accommodated.  That strikes me as false.  I just gave an analysis on which the truth of the predication is preserved.  And of course there are others. 

 

Two Questions About the Bundle Theory Answered

On the bundle-of-universals theory of ordinary concrete particulars, such a particular is a bundle of its properties and its properties are universals.  This theory will appeal to those who, for various ontological and epistemological reasons, resist substratum theories and think of properties as universals.  Empiricists like Bertrand Russell, for example.  Powerful objections can be brought against the theory, but the following two questions suggested by  some comments of Peter Lupu  in an earlier thread are, I think, easily answered.

Q1.  How may universals does it take to constitute a particular?  Could there be a particular composed of only one or only two universals?

Q2.  We speak of particulars exemplifying properties.  But if a particular is a bundle of its properties, what could it mean to say of a particular that it exemplifies a property?

A1.  The answer is that it takes a complete set.  I take it to be a datum that the ordinary meso-particulars of Sellars' Manifest Image -- let's stick with these -- are completely determinate or complete in the following sense:

D₁. X is complete =_df for any predicate P, either x satisfies P or  x satisfies the complement of  P.

If predicates express properties, and properties are universals, and ordinary particulars are bundles of properties, then for each such particular there must be a complete set of universals.  For example, there cannot be a red rubber ball that has as constituents exactly three universals: being red, being made of rubber, being round.  For it must also have a determinate size, a determinate spatiotemporal location, and so on.  It has to be such that it is either covered with Fido's saliva or not so distinguished.  If it is red, then it must have a color; if it is round, it must have a shape, and so on.  This brings in further universals.  Whatever is, is complete.  That is a law of metaphysics, I should think.  Or perhaps it is only a law of phenomenological ontology, a law of the denizens of the Manifest Image.  (Let's not get into quantum mechanics.) 

A2.  If a particular is a bundle of universals, then it is a whole of parts, the universals being the (proper) parts, though not quite in the sense of classical mereology.  Why do I say that? Well, suppose you have a complete set of universals, and suppose further that they are logically and nomologically compossible.  It doesn't follow that they form a bundle.  But it does follow, by Unrestricted Summation, that there is a classical mereological sum of the universals.  So the bundle is not a sum.  Something more is required, namely, the contingent bundling to make of the universals a bundle, and thus a particular.

Now on a scheme like this there is no exemplification (EX) strictly speaking.  EX is an asymmetrical relation -- or relational tie:  If x exemplifies P-ness, then it is not the case that P-ness exemplifies x.  Bundling is not exemplification because bundling is symmetrical: if U1 is bundled with U2, then U2 is bundled with U1.  So what do we mean when we say of a particular construed as a bundle that is has -- or 'exemplifies' or 'instantiates' using these terms loosely -- a property?  We mean that it has the property as a 'part.'   Not as a spatial or temporal part, but as an ontological part.  Thus:

D₂. Bundle B has the property P-ness =_df P=ness is an ontological 'part' of B.

Does this scheme bring problems in its train?  Of course!  They are for me to know and for you to figure out.

 

Collective Inconsistency and Plural Predication

We often say things like

1. The propositions p, q, r are inconsistent.

Suppose, to keep things simple, that each of the three propositions is self-consistent.  It will then be false that each proposition is self-inconsistent. (1), then, is a plural predication that cannot be given a distributive paraphrase.  What (1) says is that the three propositions are collectively inconsistent.  This suggests to many of us  that there must be some one single entity that is the bearer of the inconsistency.  For if the inconsistency does not attach distributively to each of p, q, and r, then it attaches to something distinct from them of which they are members.  But what could that be?

If you say that it is the set {p, q, r} that is inconsistent, then the response will be that a set is not the sort of entity that can be either consistent or inconsistent.  Note that it is not helpful to say

A set is consistent (inconsistent) iff its members are consistent (inconsistent).

For that leaves us with the problem of the proper parsing of the right-hand side, which is the problem with which we started.

And the same goes for the mereological sum (p + q + r).  A sum or fusion is not the sort of entity that can be either consistent or inconsistent.

What about the conjunction p & q & r?  A conjunction of propositions is itself a proposition.  (A set of propositions is not itself a proposition.) This seems to do the trick. We can parse (1) as

2. The conjunctive proposition p & q & r is (self)-inconsistent.

In this way we avoid construing (1) as an irreducibly plural predication.  For we now have a single entity that can serve as the logical subject of the predicate ' . . . is/are inconsistent.'  We can avoid saying, at least in this case, something that strikes me as only marginally intelligible, namely, that there are irreducible monadic non-distributive predicates.  My problem with irreducibly plural predication is that I don't know what it means to say of some things that they are F if that doesn't mean one of the following: (i) each of the things is F; (ii) there is a single 'collective entity' that is F; or (iii) the predicate 'is F'  is really relational. 

One could conceivably object that in the move from (1) to (2) I have 'changed the subject.'  (1) predicates inconsistency of some propositions, while (2) predicates (self)-inconsistency of a single conjunctive proposition.  Does this amount to a changing of thr subject?  Does (2) say something different about something different?

A Problem With the Multiple Relations Approach to Plural Predication

Consider

1. Sam and Dave are meeting together.

2. Al, Bill, and Carl are meeting together.

3. Some people are meeting together.

Obviously, neither (1) nor (2) can be decomposed into a conjunction of singular predications.  Thus (2) cannot be analyzed as 'Al is meeting together & Bill is meeting together & Carl is meeting together.'  So it is natural to try to analyze (1) and (2) using relational predicates.  (1) becomes

1R. Meeting(Sam, Dave)   In symbols: Msd

But if 'meeting' is a dyadic (two-place) predicate, then we should expect (2) to give way to

2R. Mab & Mbc & Mac.

Unfortunately, (2R) is true in circumstances in which (2) is false.  Suppose there are three separate meetings.  Then (2R) is true and (2) false.  To get around this difficulty, we can introduce a triadic relation M* which yields as analysans of (2):

2R*. M*abc.

But then we need a tetradic relation should Diana come to the meeting.  And so on, with the result that 'meeting together' picks out a family of relations of different polyadicities.  But what's wrong with that?  Well, note that (1) and (2) each entail (3) by Existential Generalization in the presence of the auxiliary premise 'Al, Bill, Carl, Dave, and Sam are people.' 

But then we are going to have difficulty explaining the validity of the two instances of Existential Generalization.  For the one instance features a dyadic meeting relation and  the other a triadic.  If two different relations are involved, then what is the logical form of (3) -- Some people are meeting together -- which is the common conclusion of both instances of Existential Generalization?  If 'meeting together picks out a family of relations of different 'adicities, then (3) has no one definite logical form.

Does this convince you that the multiple relations approach is unworkable?

REFERENCE:  Thomas McKay, Plural Predication (Oxford 2006), pp. 19-21.

 

Irreducibly Plural Predication: 'They are Surrounding the Building'

Let's think about the perfectly ordinary and obviously intelligible sentence,

1. They are surrounding the building.

I borrow the example from Thomas McKay, Plural Predication (Oxford 2006), p. 29.  They could be demonstrators.  And unless some of them have very long arms, there is no way that any one of them could satisfy the predicate, 'is surrounding the building.'  So it is obvious that (1) cannot be analyzed in terms of 'Al is surrounding the building & Bill is surrounding the building & Carl is surrounding the building & . . . .'  It cannot be analyzed in the way one could analyze 'They are demonstrators.'  The latter is susceptible of a distributive reading; (1) is not.  For example, 'Al is a demonstrator & Bill is a demonstrator & Carl is a demonstrator & . . . .'  So although 'They are demonstrators' is a plural predication, it is not an irreducibly plural predication.  It reduces to a conjunction of singular predications.

The Hatfields and the McCoys

Whether or not it is true, the following  has a clear sense:

1. The Hatfields outnumber the McCoys.

(1) says that the number of Hatfields is strictly greater than the number of McCoys.  It obviously does not say, of each Hatfield, that he outnumbers some McCoy.  If Gomer is a Hatfield and Goober a McCoy, it is nonsense to say of Gomer that he outnumbers Goober. The Hatfields 'collectively' outnumber the McCoys. 

It therefore seems that there must be something in addition to the individual Hatfields (Gomer, Jethro, Jed, et al.) and something in addition to the individual McCoys (Goober, Phineas, Prudence, et al.) that serve as logical subjects of number predicates.  In

2. The Hatfields are 100 strong

it cannot be any individual Hatfield that is 100 strong.  This suggests that there must be some one single entity, distinct but not wholly distinct from the individual Hatfields, and having them as members, that is the logical subject or bearer of the predicate '100 strong.'

So here is a challenge to William the nominalist.  Provide analyses of (1) and (2) that make it unnecessary to posit a collective entity (whether set, mereological sum, or whatever) in addition to individual Hatfields and McCoys.

Nominalists and realists alike agree that one must not "multiply entities beyond necessity."   Entia non sunt multiplicanda praeter necessitatem!  The question, of course, hinges on what's necessary for explanatory purposes.  So the challenge for William the nominalist is to provide analyses of (1) and (2) that capture the sense of the analysanda and obviate the felt need to posit entities in addition to concrete particulars.

Now if such analyses could be provided, it would not follow that there are no 'collective entities.'  But a reason for positing them would have been removed.

I Need to Study Plural Predication

Here is a beautiful aphorism from Nicolás Gómez Dávila (1913-1994), in Escolios a un Texto Implicito (1977), II, 80, tr. Gilleland: 

Stupid ideas are immortal. Each new generation invents them anew.

Clearly this does not mean:

1. Each stupid idea is immortal and is invented by each new generation anew.

So we try:

2. The set of stupid ideas is immortal in the sense that every new generation invents some stupid idea or other.

(2) is much closer to the intended meaning. The idea is that there are always stupid ideas around, not that any one stupid idea is always around. (2) seems to capture this notion. But (2) presents its own puzzles. A set is a collection, and a collection is not the mere manifold of its members: it is "a further entity over and above them" as Michael Potter puts it in Set Theory and its Philosophy (Oxford 2004, p. 22).

Potter speaks of collections versus fusions. The distinction emerges starkly when we consider that there is a distinction between a singleton collection and its member, but no distinction between a 'singleton' fusion and its member. Thus Quine is distinct from {Quine}, the set consisting of Quine and nothing else. But there is no distinction between Quine and the sum or fusion, (Quine). {Quine}, unlike Quine, has a member; but neither (Quine) nor Quine have members. A second difference is that, while it makes sense to speak of a set with no members, the celebrated null set, it makes no sense to speak of a null fusion. The set consisting of nothing, the null set { } is something; the fusion of nothing is nothing.

Getting back to stupid ideas, what I want to say is that 'stupid ideas are immortal' can be understood neither along the lines of (1) nor along the lines of (2). The generality expressed is quite obviously not distributive, but it is not quite collective either. We are not expressing the idea that there is some one entity "over and above" its members to which immortality is being ascribed. 'Stupid ideas' seems to pick out a fusion; but if a fusion is a pure manifold, how can it be picked out?  

The puzzle is that immortality is not being predicated of each stupid idea, but it is also not being predicated of some one item distinct from stupid ideas which has them as members, whether this one item be a mathematical set or a mereological sum.

We know what we mean when we say that stupid ideas are immortal, but we cannot make it precise, or at least I can't make it precise given my present level of logical acumen.

So rather than contribute any stupid ideas of my own, I will go to the library and check out Thomas McKay's Plural Predication.  

 

Richard Gaskin on the Unity of the Proposition

The current issue of Dialectica (vol. 64, no. 2, June 2010) includes a symposium on Richard Gaskin, The Unity of the Proposition (Oxford 2008).  Gaskin's precis of his work is followed by critical evaluations by William F. Vallicella ("Gaskin on the Unity of the Proposition"), Manuel Garcia-Carpintero ("Gaskin's Ideal Unity"), and Benjamin Schnieder ("Propositions United: Gaskin on Bradley's Regress and the Unity of the Proposition").  The symposium concludes with Gaskin's replies ("The Unity of the Proposition: Replies to Vallicella, Schnieder, and Garcia-Carpintero"). 

Predicates and Properties

We are warming up to an examination of deflationary theories of truth according to which truth is either not a property or not a metaphysically substantive property.  (I oppose deflationary theories of truth just as I oppose deflationary theories of existence.) But first some clarification of 'predicate' and 'property.'

1. I begin by resisting the traditional conflation of predicates and properties, a conflation in evidence when we hear a philosopher claim that "existence is not a predicate."  That claim makes no sense unless a predicate is a property.  After all, 'existence,' as an abstract substantive, is not grammattically tuited to occupy predicate position.  If, however, a predicate is a bit of language used to express a property, then the claim should be that " '. . . exists' is not a predicate."  That's in order, as is "Existence is not a property."  As expressing properties, predicates are distinct from properties.  Predicates are linguistic while properties are extralinguistic.

To be a bit more precise, predicates (whether types or tokens) are tied to particular languages whereas the properties they express are not so tied.  Thus schwarz is tied to German in the way black is tied to English, but the property of being black is tied to neither.  Equally, the property of being disyllabic is tied to no one language even though it is a property that only linguistic items can have.  Thus 'Boston' but not Boston is disyllabic.

2. Some of you will question whether there are properties distinct from predicates.  Question away.  But just realize that in order to raise this very question you must first have distinguished predicates and properties.  You must already have made the distinction 'at the level of intension' if not 'at the level of extension.'  For you cannot maintain that there are no properties distinct from predicates unless you understand the term 'property' just as you cannot maintain that there are no unicorns distinct from horses unless you understand the term 'unicorn.'

3. By my lights, you are a very foolish philosopher if you deny properties, but not if you deny universals.  If you deny universals you are merely mistaken.  So let's be clear that 'property' and 'universal' are not to be used interchangeably.  It is a substantive question whether properties are universals or particulars (as trope theorists maintain).  Universals I define as repeatable entities, particulars as unrepeatable entities.

4. The predicate/property distinction under our belts, we need to note three views on their relation.

5. One view is that  no predicate expresses a property.  I rejected this view in #3.  To put it bluntly, there is a real world out there, and the things in it have properties whether or not there are any languages and language-users. Some of our predicates succeed more or less in expressing some of these properties.

6. A second view is that every predicate expresses or denotes a property.  The idea is that for every predicate 'P' there is a property P corresponding to 'P.'  But then, given that 'exists' and 'true' are predicates, it would follow straightaway that existence and truth are properties.  And that seems too easy.  Deflationists, after all, deny for reasons that cannot simply be dismissed that truth is a property.  They cannot be refuted by pointing out that 'true' is a predicate of English.  The following equivalence is undeniable but also not formulable unless 'true'  is a predicate:

'Grass is green' is true iff grass is green.

The deflationist will take an equivalence like this to show that 'true' is a dispensable predicate and therefore one that does not pick out a property.  (On Quine's disquotationalism, for example, 'is true' is a device of disquotation: it merely undoes the semantic ascent displayed on the LHS of the biconditional.)  We should therefore be uneasy about the view that every predicate expresses or denotes a property.  The existence of a predicate does not show the existence of a corresponding property.  A predicate need not predicate a property.  It should not be a matter of terminological fallout that wherever there is a predicate there is a property.

7.  Determined to maintain  that every predicate expresses or denotes a property, a deflationist  could of course hold that existence and truth are properties, but not metaphysically substantive properties.  A deflationist could argue like this:

Every predicate expresses a property

'True' is a predicate

Ergo: Truth is a property, but not a substantive one.

But he could also argue like this:

Every genuine predicate expresses a substantive property

Truth is not a substantive property

Ergo: 'True' is not a genuine predicate.

8.  A third view about the predicate-property relation has it that some predicates pick out properties and some don't.  I suggest this is how we should use 'predicate.'  It then becomes a matter of investigation, not of terminology, whether or not there is a property for a given predicate.

The Truthmaker Theory of Predication and Divine Simplicity

In this post I first try to get clear about the truthmaker theory of predication proposed by Michael Bergmann and Jeffrey E. Brower in their A Theistic Argument Against Platonism.  I then try to understand how it solves a certain problem in the doctrine of divine simplicity (DDS). Finally, I raise a question about the authors' solution.

The truthmaker theory of predication is a rival to the following theory of predication which, with a little inaccuracy, we can label 'Platonistic' so as to have a handy label:

P: The truth of all true predications, or at least of all true predications of the form "a is F", is to be explained in terms of a subject and an exemplifiable (however exemplifiables are themselves to be conceived). (p. 7)

This post will not address the authors' impressive theistic argument  against P.  For present purposes we can assume that it is sound the better to evaluate the alternative which  Bergmann and Brower put  as follows:

P*: The truth of all 

true predications, or at least of all true predications of the form "a is F", is to be explained in terms of truthmakers. (p. 25)

To appreciate how the two theories differ, consider the proposition expressed by the true essential predication, 'God is divine.'  The Platonistic theory explains the truth of this proposition in terms of the subject God and the exemplifiable, the property of being divine.  The proposition is true because the subject exemplifies the property.  By contrast, the truthmaker theory of predication explains the proposition's truth in terms of its truthmaker.  Three questions:  What is a truthmaker?  What is the truthmaker of the proposition *God is divine*?  What exactly is the difference between P and P*? The authors offer the following as a "partial analysis" of the notion of a truthmaker:

TM: If an entity E is a truthmaker for a predication P, then 'E exists' entails the truth expressed by P. (p. 22)

From TM and the fact that 'God is divine' is an essential predication it can be inferred that the truthmaker of this truth is God himself.  For 'God exists' entails the truth expressed by 'God is divine.'  This is because there is no possible world in which God exists and the proposition in question is not true.  Thus God himself suffices as truthmaker for 'God is divine,' and there is no need for an exemplifiable entity or a concrete state of affairs (the subject's exemplifying of the exemplifiable entity.) This allows us to appreciate the difference between the Platonistic and the truthmaker theories of predication.  The first, but not the second, requires that the explanation of a truth's being true invoke a subject and an exemplifiable.  On the truthmaker theory it is not the case that every predication is such that its explanation requires the positing of a subject and an exemplifiable.  The subjects of all essential predications of the form a is F suffice as truthmakers of the propositions expressed by these predications.

In the case of such accidental predications as 'Tom is tired,' the truthmaker cannot be Tom by himself, as the authors appreciate. (p. 26)  Neither Tom nor Tom's existence nor *Tom exists* necessitates the truth of 'Tom is tired.'  On one approach, the truthmaker of true accidental predications is a concrete state of affairs.  On another, the truthmaker is a trope.  I think it follows that P is a special case of P*.  I don't find the authors stating this but it seems to be a clear implication of what they do say.  According to the truthmaker theory of predication, the truth of every true affirmative monadic predication, whether essential or accidental, is explained by a truthmaker, an entity which can belong to any ontological category.  The Platonistic theory is the special case in which the truthmaker either is or involves an exemplifiable.  (A special case of this is the case in which the truthmaker is a concrete state of affairs.)  The truthmaker theory is more general because it allows for truthmakers that neither are nor involve exemplifiables.

Application to Divine Simplicity

One of the entailments of the doctrine of divine simplicity (DDS) is that there is no distinction between God and his attributes.  Thus God is (identical to) his goodness, his power, etc.  We have discussed the motivation for this doctrine in earlier posts.  But how could an individual be identical to its attributes or properties? If God is identical to one of his properties, such as the property of being divine, then it follows that he is a property or exemplifiable -- which is absurd.  It is absurd because God is a person and persons are not exemplifiable entities.  But if the truthmaker theory of predication is correct, then there is a way to make coherent sense of the notion that God is identical to his nature, goodness, power, wisdom, and other such attributes.

Consider 'God is his omnipotence.'  If the abstract singular term 'God's omnipotence' is taken to refer to a property, then we get the unacceptable consequence that God is identical to a property.  Proponents of the truthmaker theory of predication, however, can maintain that the referents of abstract singular terms are truthmakers.  Accordingly, 'God's omnipotence'  and 'God's divinity' refer respectively to the truthmakers of 'God is omnipotent' and 'God is divine' respectively.  Because both of these predications are essential, the truthmaker of both is God himself.  To say that God is identical to his omnipotence is to say that the referent of 'God' is identical to the referent of 'God's omnipotence.'  And that amounts to the unproblematic claim that God is identical to God.

A Question

The authors have shown us a way to demonstrate the coherence of 'God is identical to his divinity'  assuming we are prepared to accept P* and TM.   But I wonder whether their demonstration 'proves too much.'  Consider the parallel but presumably incoherent  'Socrates is identical to his humanity.'  We now must ask whether the strategy that works in the case of God also works in the case of Socrates.  If it does, then the radical difference between God and creature, which is part of the motivation for DDS, will not have been  properly accommodated.

The authors will grant that Socrates is truthmaker enough for (the propositions expressed by) all essential predications about him.  Thus Socrates himself makes true 'Socrates is human' by TM.  Because they hold P* they will grant that no exemplifiable need  be invoked to explain 'Socrates is human.'  We needn't say that this is true because Socrates exemplifies the property of being human; we can say that it is true because 'Socrates' and 'Socrates humanity' have the same referent, namely Socrates. But then does it not follow that Socrates is ontologically simple, at least in respect of such essential predicates as 'human,' 'rational,' and the like?  Does it not follow that Socrates is identical to his humanity, his rationality, animality, etc.?  Rhetorical questions aside, I am arguing as follows:

a. Socrates  is the truthmaker of 'Socrates is human' and like essential predications.  (From TM)

b. Socrates is the referent of both 'Socrates' and 'Socrates' humanity.' (From P*)  Therefore:

c. Socrates is identical to Socrates' humanity. (From b) 

But we surely do not want to say that Socrates is identical to his humanity, rationality, etc.  which would imply that his humanity, rationality,etc. are identical to one another.  Socrates, unlike God, is a metaphysically composite being.  So something appears to have gone wrong.  The Bergmann-Brower approach appears to 'prove too much.'  Their approach seems to imply what is false, namely, that both God and Socrates are ontologically simple  in respect of their essential attributes.

Scholastic Realism and Predication

This post continues our explorations in the philosophy of The School. What is a scholastic realist? John Peterson (Introduction to Scholastic Realism, Peter Lang, 1999, p. 6) defines a scholastic realist as follows:

S is a scholastic realist =df i) S is a moderate realist and ii) S believes that universals exist in some transcendent mind, i.e., the mind of God.

A moderate realist is defined like this:

S is a moderate realist =df i) S denies that universals exist transcendently and ii) S affirms that universals exist immanently both in matter and minds.

A universal exists transcendently just in case it exists "independently of matter and mind." One who holds that universals exist independently of matter and mind is a Platonic or extreme realist. A moderate realist who is not a scholastic realist Peterson describes as an Aristotelian realist. Such a philosopher is a moderate realist who "denies that universals exist in some transcendent mind."   In sum, and interpreting a bit:

Platonic or extreme  realist:  maintains that there are universals and that they can exist transcendently, i.e., unexemplified (uninstantiatied) and so apart from matter and mind.

Moderate realist:  denies that there are any transcendent universals and maintains that universals exist only immanently in minds and in matter.

Scholastic realist: moderate realist who believes that there is a transcendent mind in which universals exist.

Aristotelian realist:  moderate realist who denies that there is a transcendent mind in which universals exist.

Divine Simplicity and Truthmakers: Notes on Brower

1. One of the entailments of the doctrine of divine simplicity (DDS) is that God is identical to: God's omniscience, God's omnipotence, and in general God's X-ness, where 'X' ranges over the divine attributes.  And it is easy to see that if God = God's F-ness, and God = God's G-ness, then (by transitivity of identity) God's F-ness = God's G-ness.  I suggest that we use 'divine attribute' to refer to those properties of God that are both essential and intrinsic.  The problem, of course, is to make sense of these identities given the fact that, prima facie, they do not make sense.  The pattern is the same as with Trinity and Incarnation.  These doctrines imply identities which, on the face of it, beggar understanding.  It thus falls to the philosopher of religion to try to render coherent that which, on the face of it, is incoherent.

2. One of the questions that arise when we try to make sense of DDS concerns which category of entity such phrases as 'God's omniscience' pick out.  One possibility is that such phrases pick out properties, whether universal (multiply exemplifiable) properties or particular (not multiply exemplifiable) properties, also known as tropes. But this leads to trouble as Brower points out.  For if God is identical either to omniscience or to his omniscience, then God is identical to a property -- which sounds absurd: how can God, a person, be a property?  Properties are predicable entities, but God is an individual and so not predicable.  Properties are exemplifiable entities (whether multiply or non-multiply); but God is an individual and so not exemplifiable.  Properties are abstract (causally inert)  whereas God is concrete (causally active/passive).  No property is a person, but God is a person.  No property creates or knows or loves.  These are some hastily sketched reasons for thinking that God cannot be identical to his properties.

3. Jeffrey E. Brower forwards an interesting proposal.  He suggests that such phrases as 'God's nature,' 'God's goodness' and 'God's power' refer to "entities of a broadly functional type -- namely, truthmakers." (Simplicity and Aseity, sec. 2)  The idea is that 'God's omniscience' refers to the trruthmaker of 'God is omniscient' or perhaps to the truthmaker of the proposition expressed by 'God is omniscient.'  If (Fregean) propositions are the primary truthbearers, then (tokenings of) declarative sentences that express such propositions can be said to be secondary truthbearers.  I trust that it is clear that truthbearers and truthmakers are not to be confused.  One key difference is that while some truthbearers are are false, no truthmaker is false.  Truth and falsity are properties of certain representations (propositions, declarative sentences, beliefs, judgments, etc.)  whereas truthmakers are the ontological grounds of some true truthbearers.  If I understand Brower's view, it is not only that truthmakers are neither true nor false -- every TM theorist will hold this -- but also that truthmakers are not at all proposition-like.  By contrast, I follow D. M. Arstrong in holding that truthmakers must have a proposition-like structure.  But more on this in a moment.

4. Roughly, a truthmaker is whatever plays a certain role or performs a certain function; it is whatever makes true a true truthbearer.  The 'truthmaker intuition' -- which I share with Brower -- is that a sentence such as 'Tom is blogging' cannot just be true; there is need of some worldly entity to 'make' it true, to serve as the ontological ground of its truth, to 'verify' it in an ontological, not epistemological, sense of this term.  To say that some or all truthbearers need truthmakers is not yet to specify which sort of entity plays the truthmaker role.  Among philosophers who accept the need for truthmakers there is disagreement about the ontological category to which they belong. 

 Brower says rather incautiously that the functional characterization of truthmakers "places no restriction on the specific nature or ontological category to which a truthmaker can belong." (sec 2.1)  That can't be right.  Surely there are some restrictions.  For one thing, a truthmaker cannot be a Fregean proposition for the simple reason that such items are among the items made true by truthmakers.  And the same goes for declarative sentences, beliefs, and judgments.  My belief that the cat is asleep is either true or false and as such is a truthbearer.  It is in need of a truthmaker but is not itself one.  Of course, the fact of my believing that the cat is asleep can serve as truthmaker for the sentence ' BV now believes that the cat is asleep'  if concrete facts are admitted as truthmakers -- but that is something else again.  So not just anything can be a truthmaker.  Charitably interpreted, what Brower is telling us is that TM theorists are allowed some ontological latitude when it comes to specifying which category of entity is fit to play the truthmaker role. 

5. Let us note that if a true Fregean proposition p entails a Fregean proposition q, then one could say that the first 'makes true' the second.  And so one could speak of the first as a 'truthmaker' of the second.  But this is not what is meant  by 'truthmaking' in these discussions despite the fact that p broadly logically necessitates q.   What is intended is a relation of broadly logical necessitation that connects a nonpropositional entity (but on some theories a proposition-like entity) to a propositional entity, or more precisely, to an entity that can serves as the bearer or vehicle of a truth-value.  As I see it, the entailment relation and the truthmaking relation are species of broadly logical necessitation; but truthmaking is not entailment.  Entailment will never get you 'outside the circle of propositions'; but that is exactly what truthmaking is supposed to do.  A truthmaker is an ontological, not propositional or representational truth-ground.  Philosophers who are attracted to truthmakers typically have a realist sense that certain of our representations need to be anchored in reality.

Brower sees it a little differently.  He would agree with me that entailment and truthmaking cannot be identical, but he thinks of it as "a form of broadly logical necessitation or entailment" and says that entailment is necessary but not sufficient for truthmaking. (Sec. 2.1)  So Brower seems to be maintaining that while there is more to truthmaking than entailment, every truthmaker entails the truth it makes true.  But this makes little or no sense.  Entailment is a relation defined on propositions.  If x entails y, then you can be sure that x and y are propositions or at least proposition-like entities, whether these be sentences or judgments or beliefs or even concrete states of affairs such as the fact of (not the fact that) Peter's being tired, which concrete fact contains Peter himself as constituent, warts and all.  But for Brower, as we will see in a moment, concrete individuals such as Socrates, entities that are neither propositions nor proposition-like, can serve as truthmakers.  As far as I can see, it makes no sense to say that Socrates entails a proposition.  It makes no sense because entailment is defined in terms of truth, and no individual can be true or false.  To say that p entails q is to say that it is impossible that p be true and q false.  Since it makes no sense to say of an individual that it is true, it makes no sense to say of an individual that it entails a proposition.  So truthmaking cannot be a type or species of entailment if individuals are truthmakers.

6.  But setting aside for the moment the above worry, if it makes sense to say that God is the truthmaker of 'God is omniscient,' and if 'God's omniscience' refers to this truthmaker, then it will be clear how God can be identical to God's omniscience.  For then 'God is identical to his omniscience' is no more problematic than 'God is God.' It will also be clear how God's omniscience can be identical to God's omnipotence. 

7.  But can it really be this easy to show that DDS is coherent? Although I agree with Brower that some truthbearers need truthmakers, I don't see how truthmakers could be ontologically structureless individuals or 'blobs' as opposed to 'layer-cakes' in Armstrong's terminology.  By 'ontologically structureless' I mean lacking in propositional or proposition-like structure.  Consider the following true intrinsic essential predicative sentences: 'Socrates is human,' 'Socrates is an animal,' Socrates is a material object,' 'Socrates exists,' and 'Socrates is self-identical.'  (It is not obvious that 'Socrates exists' is an essential predication inasmuch as Socrates exists contingently, but let's not enter into this thorny thicket just now.)

Brower's claim is that in each of these cases (which parallel the true intrinsic essential predications of divine attributes) the truthmaker is the concrete individual Socrates himself.  Thus Socrates is the truthmaker of 'Socrates is human' just as God is the truthmaker of 'God is omniscient.'  Unfortunately, no individual lacking propositional or proposition-like structure can serve as a truthmaker as I argued in #5 above.  Just as it makes no sense to say that Socrates is true, it makes no sense to say that Socrates entails the proposition expressed by 'Socrates is human.' 

There is more to say, but tomorrow's another day.  Time to punch the clock.