Maverick Philosopher

Referring to Two Things

Ed writes,

Does ‘these two things’ refer to two things, or not? (Suppose the things are shoes.)

Perhaps not. For there are the two things, but also the plurality of them. The plurality is one thing, identical with neither the first thing, nor the second.

So the phrase ‘these two things’ actually refers to three things? Makes no sense to me.

BV:  Perhaps it makes no sense to you because  you think that 'thing' can only mean 'material thing.'  We agree that 'these two shoes' refers to exactly two shoes, each of which is a material thing, and that there is no third material thing of which they are members.  So if that is what our nominalist means when he denies that the two shoes form a plurality, then we agree.

Here is a slightly more complicated example. You have a bolt B and a nut N that fits the bolt, i.e., N can be screwed onto B.  Now there is clearly a difference between B, N unconnected and B, N connected. But even here I will grant that there is no third material thing wholly distinct from B and wholly distinct from N when B, N are connected.  There is no third material thing 'over and above' the connected bolt and nut.  Here is exactly what you have and no material third thing in addition:

Disagreement may begin to set in when I point out that the weight of the object depicted above is strictly greater that the weights of the bolt and the nut taken separately.  The total weight is additive such that if the nut weighs 2 ounces and the bolt 16 ounces, then the weight of the object depicted is equal to 2 + 16 = 18 ounces. The predicate '___weighs 18 ounces' is not true of the nut, and it is not true of the bolt, and it is not true of any material third thing 'over and above' the object depicted, and this  for the simple reason that there is no such third material thing.

So what is the predicate '___ weighs 18 ounces' true of?  I say that it is true of the plurality the sole members of which are N and B.  I am not further specifying the nature of this plurality. Thus I am not saying that it is a mathematical set, nor am I saying that it is a mereological sum.  I am saying that there is a distinction to be made between a plurality of items and the items.

Note that if our nominalist were to say that a plurality is exhausted by, or reduces to, its members, then will have given up the game by his use of 'its.'  So he has to somehow avoid that locution.

Our nominalist will grant that the predicate '___weighs 18 ounces' is not true of the nut, not true of the bolt, and not true of any third material thing  wholly distinct from the bolt and the nut.  But he might say that it is not true of anything. The predicate is flatus vocis, a mere word, phrase or sound to which nothing extramental and extralinguistic corresponds.  I reject this view. It implies that the nut threaded onto the bolt has in objective reality no weight that is the sum of the objective weights of the nut and bolt taken separately.

Our nominalist seems committed to an intolerable linguistic idealism. Suppose all language users were to cease to exist. It would remain that case that the weight of our nut-bolt combo would equal 18 ounces. It would remain the case that Earth is spheroid in shape and has exactly one natural satellite.

But why is he a nominalist in the first place? Is it because he thinks that only material particulars exist? If that is true then of course there cannot be a plurality of two material particulars.  Hilary Putnam: "Nominalists must at heart be materialists . . . otherwise their scruples are unintelligible." (Phil Papers, vol. I, 338)

Is he a nominalist because he is an empiricist who thinks that only sensible particulars exist?  I see the nut, I see the bolt, I see the nut threaded onto the bolt; but I don't see any plurality of material particulars. Is our man restricting what exists to that which is empirically detectable via our senses and their instrumental extensions (e.g., microscopes, telescopes, etc.)? 

Is he both a materialist and an empiricist? How do those two positions cohere?

Pluralities

To what does the plural referring expression, 'the cats in my house,' refer? Not to plurality, but to a plurality. A plurality is one item, not many items. It is one item with many members. 'The guitars in my house' refers to a numerically different plurality. It too refers to one item with many members.  It follows that a plurality cannot be identical to its members.  For if it were there would be no 'it.'

I am not saying that a plurality is a mathematical set. I am saying that a plurality is not just its members.  I am rejecting Composition as Identity. If the Londonistas do not agree with the Phoenician on this one, then I fear that there is little point to further discussion. We are at the non-negotiable.  We are at bedrock and "my spade is turned." 

Occam's Razor: Its Use and Abuse

I am not historian enough to pronounce upon the relation of what is standardly called Occam's Razor to the writings of the 14th century William of Ockham. The different spellings of his name will serve as a reminder to be careful about reading contemporary concerns into the works of philosophers long dead. Setting aside historical concerns, Occam's Razor is standardly taken to be a principle of theoretical economy or  parsimony that states:

   

OR. Do not multiply entities beyond necessity.

It is sometimes formulated in Latin: Entia non sunt multiplicanda praeter necessitatem. The principle is presumably to be interpreted qualitatively rather than quantitatively, thus:

   OR*. Do not multiply TYPES of entity beyond necessity.

Thus it is not individual entities that are not to be multiplied, but types or kinds or categories of entity.  To illustrate.  Some criticized David Lewis' extreme modal realism on the ground that it proliferates concreta: there are not only all the actual  concreta, on his view, there are all those merely possible ones as well.  He responded quite plausibly to the proliferation charge by pointing out that the Razor applies to categories of entity, not individual entities, and that category-wise his ontology is sparse indeed.

'Multiply' is a picturesque way of saying posit. (Obviously, there are as many categories of entity as there are, and one cannot cause them to 'multiply.')  And let's not forget the crucial qualification: beyond necessity.  That means: beyond what is needed for purposes of adequate explanation of the data that are to be explained.  Hence:

OR**  Do not posit types of entity in excess of what is needed for purposes of explanation.

So the principle enjoins us to refrain from positing more types of entity than we need to explain the phenomena that need to be explained. It is obvious that (OR**) does not tell us to prefer theory T1 over theory T2 if T1 posits fewer types of entity than T2. What it tells us is to prefer T1 over T2 if T1 posits fewer types of entity AND accounts adequately for all  the data. So there is a trade-off between positing and accounting.

It seems to me that the Razor as I have just described it ought to be in every philosopher's tool box.  But how useful is it? Not very. For it tells us not to posit more than we need, but it does not tell us what we need. For example, do we need mathematical sets? Given Manny, Moe, and Jack, do we need to add to the ontological inventory the set {Manny, Moe, Jack}?  It is not obvious that we do. But it is also not obvious that we don't. There are arguments on both sides which I won't go into now.

Here's the punch line: simply brandishing the Razor has no tendency to show that there are not such abstract objects as sets. That would be an abuse of the Razor.  It would be the mistake of thinking that T1 is to be preferred to T2 solely on the ground that T1 posits fewer types of entity.

Note that I presupposed above that philosophy is an explanatory enterprise. Is that obvious? As Hilary Putnam says somewhere, "It ain't obvious what's obvious."

Nominalism Presupposes What it Denies

What makes a pair of shoes a pair and not just two physical artifacts? Nominalist answer: nothing in reality. Our resident nominalist tells us that it is our use of 'a pair' that imports a unity, conventional and linguistic in nature, a unity that does not exist in reality apart from our conventional importation. We are being told that out there in the world there are no ones-in-many, let alone any ones-over-many. If that is  right, then there are no sets. For a set is a one-over-many in this sense: it is one item distinct from its many members. (Let's not worry about the null set, which has no members and unit-sets or singletons which have exactly one member each. Here lies yet another rich source of aporiai, but one problem at a time.) 

If there are no sets, then there are neither finite sets nor infinite sets. There are just pluralities, and all grouping, collecting, subsuming under common rubrics, unifying, etc. is done in language by language-users. What I will try to show is that if you think carefully about all of this you will have to make distinctions that are inconsistent with nominalism. 

My aim is purely negative: to show that the nominalism of the resident nominalist is untenable. If you have read a good amount of what I have written you will recall that I am a solubility skeptic, which in this instance means that I am not endorsing any realist solution of the problem. I am not pushing an opposing theory. 

I will start with some data that I find 'Moorean,' i.e., rationally indisputable and pre-theoretical.  (Unfortunately, one man's datum is another man's theory.) The phrase 'a pair' has a sense that remains the same over time and space, a sense that is the same for all competent speakers of English whether here or abroad. The same holds for ein Paar in German, and similarly for all languages. The sense or meaning of an expression, whether word, phrase, sentence, etc. must be distinguished from the expression.  An expression is something physical and thus sensible. The sensible is that which is able to be sensed via one of our senses.  I hear the sound that conveys to me the meaning of 'cat,' say, or I see the marks on paper. Hearing and seeing are outer senses that somehow inform us or, more cautiously, purport to inform us of the existence and properties of physical or material things that exist whether or not we perceive them. But I don't hear or see the meaning conveyed to me by your utterance of  a sentence such 'The cats are asleep.' The sentence, being a physical particular, is sensible; the meaning is intelligible. That's just Latin for understandable. I hear the words you speak, and if all goes well, I understand their meaning or sense, thereby understanding the proposition you intend to convey to me, namely, that the cats are asleep. Note that while one can trip over sleeping cats, one cannot trip over that the cats are asleep.

There are two distinctions implicit in the above that need to be set forth clearly.  I argue that neither is compatible with nominalism

A. The distinction between the sense/meaning of a linguistic expression and the expression. Why must we make this distinction? (a) Because the same sense can be expressed at different times by the same person using the same expression. (b) Because the same sense can be expressed at the same and at different times by different people using the same expression. (c) Because the same sense can be expressed in different languages using different expressions by the same and different people at the same and at different times. For example the following sentences express, or rather can be used to express, the same sense (meaning, proposition):

The cat is black.
Il gatto è nero. 
Die Katze ist schwarz.
Kedi siyah.
Kočka je černá.

So the sense of a word or phrase or sentence is a one-in-many in that each tokening of the word or phrase expresses numerically the same sense.  A tokening, by definition, is the production of a token, in this case, a linguistic token.  One way a speaker can produce such a token is by uttering the word or phrase in question. Another way is by writing the word or phrase down on a piece of paper. (There are numerous other ways as well.)  This production of tokens therefore presupposes a further distinction:

B. The distinction between linguistic types and linguistic tokens. In the following array, how many words are there?

cat
cat
cat

Three or one? Is the same word depicted three times? Or are there three words? Either answer is as good as the other but they contradict each other. So we need to make a distinction: there are three tokens of the same type. We are forced by elementary exegesis of the data to make the type-token distinction.  If you don't make it, then you will not be able to answer my simple question: three words or one?

You see (using the optical transducers in your head, and not by any visio intellectualis) the three tokens. And note that the tokens you now see are not the tokens I saw when I wrote this entry. Those were different tokens of the same type, tokens which, at the time of your reading are wholly past. Linguistic tokens are in time, and in space, which is not obviously the case for linguistic types. I said: not obviously the case, not: obviously not the case.   You see the three tokens, but do you see the type of which they are the tokens? If you do, then you have powers I lack. And yet the tokens are tokens of a type. No type, no tokens. So types exist. How will our nominalist accommodate them? He cannot reduce types to sets of tokens since he eschews sets. No sets, no sets of linguistic tokens. Linguistic types are multiply instantiable. That makes them universals. But no nominalist accepts universals.  Nominalists hold that everything is a particular.  I grant that the rejection of sets and the rejection of universals are different rejections. But if one rejects sets because they are abstract objects, one ought also to reject universals for the same reason.

Now glance back at the first array. What we have there are five different sentence tokens from five different languages.  Each is both token - and type-distinct from the other four. 

To conclude, I present our nominalist with two challenges. The first is to give a nominalist account of linguistic types without either reducing them to sets or treating them as ones-in-many or ones-over-many. The second challenge is to explain the distinction between the sense or meaning of an expression, which is not physical/material and the expression which is.

Suppose he responds to the second challenge by embracing conceptualism according to which  meanings are mental.  Conceptualism is concept-nominalism, as D. M. Armstrong has maintained. My counterargument would be that the meaning/sense expressed by a tokening of 'The cats are asleep'  is objectively either true or false, and thus either true or false for all of us, not just for the speaker. Sentential meanings are not private mental contents.  Fregean Gedanken, for example, are not dependent for their existence or truth-value on languages or language-users.  

 

A Nominalist Walks into a Bar . . .

. . . looking sad.

Bartender: "What's the matter, pal?"

"My girlfriend says we have nothing in common!"

Bartender: "But you are a nominalist! Isn't that the way it's supposed to be?"

This short video is sloppy, but will give you some idea of what nominalism is if you don't have a clue.

Why Not be a Nominalist about Sets?

The resident nominalist comments:

Nominalists say that the conception of an actual infinity of natural numbers depends on there being a set of all such numbers. But Ockhamists do not believe in sets. They say that the term ‘a pair of shoes’ is a collective noun which deceives by the singular expression ‘a pair’. Deceives, because it means no more than ‘two shoes’, and if there is only a pair of shoes, then there are only two things. But if a ‘pair’ of two things is a single thing, there are three things, the two things and the pair. Ergo etc.

I agree that there cannot be an actual infinity of natural numbers unless there is a (mathematical as opposed to commonsense) set of all such numbers. But of course this holds for all numbers, rational, irrational, transcendental, etc. Indeed, it holds for any category of item that is actually infinite. If there is an actual infinity of propositions, for example, then there must be a set of all propositions. I would point out however that there is nothing nominalistic about our friend's opening remark.

Nominalism kicks in with the claim that there are no sets.  What there are are plural referring devices such as 'a pair of shoes' which fools us into thinking that in reality, i.e., extralinguistically, there are three things, a left shoe, a right shoe, and the pair, when there are only two things, the two shoes.  The same goes for the following seemingly singular but really plural phrases: a gaggle of geese, a pride of lions, a parliament of owls, a coven of witches, etc.   

This all makes good sense up to a point. When I put on my shoes, I put on one, then the other. It would be a lame joke were you to say to me, "You put on the left shoe and then the right one; when are you going to put on the pair?" To eat a bunch of grapes is to eat each grape in the bunch; after that task is accomplished there is nothing left to do.  The bunch is not something 'over and above' the individual grapes that I still need to eat.

Consider now the Hatfields and the McCoys. These are two famous feuding Appalachian families, and therefore two pluralities. They cannot be (mathematical) sets on the nominalist view.  But there is also the two-membered plurality of these pluralities to which we refer with the phrase 'the Hatfields and the McCoys' in a sentence like 'The Hatfields and the McCoys are families  feuding with each other.'

If, however, a plurality of pluralities has exactly two members, as in the case of the Hatfields and the McCoys -- taking those two collections collectively -- then the latter cannot themselves be mere pluralities, but must be single items, albeit single items that have members. They must be both one and many. That is to say: In the sentence, 'The Hatfields and the McCoys are two famous feuding Appalachian families,' 'the Hatfields' and 'the McCoys' must each be taken to be referring to a single item, a family, and not to a plurality of persons. For if each is taken to refer to a plurality of items, then the plurality of pluralities could not have exactly two members but would many more than two members, as many members as there are Hatfields and MCoys all together. Compare the following two sentences:

1. The Hatfields and the McCoys number 100 in toto.

2. The Hatfields and the McCoys are two famous feuding Appalachian families.

In (1),'the Hatfields and the McCoys' can be interpreted as referring to a plurality of persons as opposed to a mathematical set of persons. But in (2), 'the Hatfields and the McCoys' cannot be taken to be referring to a plurality of persons; it must be taken to be referring to a plurality of two single items.

Or consider the following said to someone who mistakenly thinks that the Hatfields and the McCoys are one and the same family under two names:

3. The Hatfields and the McCoys are two, not one.

Clearly, in (3) 'the Hatfields and the McCoys' refers to a two-membered plurality of single items, each of which has many members, and not to a plurality of pluralities. And so we must introduce mathematical sets into our ontology.

My conclusion, contra the resident nominalist, is that we cannot scrape by on  pluralities alone. (Man does not live by manifold alone! He needs unity!) We need mathematical sets or something like them: entities that are both one and many.  A set, after all, is a one-in-many. It is not a mere many, and it is not a one 'over and above' a many.  The nominalist error is to recoil from the latter absurdity and end up embracing the former.  The truth is in the middle.

What I have given is  an argument from ordinary language to mathematical sets. But there are also mathematical arguments for sets. Here is a very simple one. The decimal expansion of the fraction 1/3 is nonterminating: .33333333 . . . . But if I trisect a line, i.e., divide it into three equal lengths, I divide it into three quite definite actual lengths.  This can be the case only if the the decimal expansion is a completed totality, an actual infinity, not a merely potential one.  An even better example is that of the irrational number, the square root of 2 -- it is irrational because it cannot be expressed as a ratio of two numbers, the numerator and the denominator of a fraction as in the case of of the rational 1/3.  If the hypotenuse of a right triangle is   units of length, that is a quite definite and determinate length.  How could it be if the decimal expansion however protracted did not point to a completed totality, an actual infinity?

 

REFERENCES

Max Black, "The Elusiveness of Sets," Review of Metaphysics, vol. XXIV, no. 4 (June 1971), 614-636.

Stephen Pollard, Philosophical Introduction to Set Theory, University of Notre Dame Press, 1990. 

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.

Nominalism and Being

Ed Buckner is threatening to write a book on the history of philosophy from the perspective of nominalism. I encourage him to do so for his sake and ours. One of the things he will have to do early on is to define 'nominalism' as he will use the term given its varied use in the history of philosophy. The following redacted re-post from over ten years ago (7 March 2012) may help him focus his thoughts.

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Today I preach on an old text of long-time commenter and sparring partner, London Ed:

Nominalism is the doctrine that we should not multiply entities  according to the multiplicity of terms. I.e., we shouldn't  automatically assume that there is a thing corresponding to every  term. Das Seiende is a term, so we shouldn't automatically assume there is a thing corresponding to it. Further arguments are needed to show that there is or there isn't. A classic nominalist strategy is to rewrite the sentence in such a way that the term disappears.

My first concern is whether this definition of 'nominalism' is perhaps too broad, so broad that it pulls in almost all of us. Does anyone think that every term has a referent? (No) Don't we all hold that there can be no automatic assumption that every occurrence of a term in a stretch of discourse picks out an entity? (Yes) For example, one would be hard pressed to find a philosopher who holds that 'nothing' in

   1. Nothing is in the drawer

refers to something. (Carnapian slanders aside, Heidegger does not maintain this, but this is a separate topic about which I have written a long unpublished paper.) Following Ed's excellent advice, the apparently referential 'nothing' can be paraphrased away:

   2. It is not the case that there is something in the drawer.

This then goes into quasi-canonical notation as

   2*. ~(∃x)(x is in the drawer).

In (2*) the tilde and the particular quantifier are syncategorematic elements. On the face of it, then, there is no call to be anything other than a nominalist about 'nothing,' using 'nominalism' as per the suggestion above.

Whether there is call to be a nominalist about 'being' is another matter. Before proceeding to it, consider the following example:

   3. Peter and Paul are blond

which could be parsed as

   3*. Peter is blond and Paul is blond.

Now I rather doubt that anyone maintains that every word in (3*) -- or rather every word in a tokening of this sentence-type whether via utterance or inscription or some other mode of encoding -- has an entity corresponding to it. This suggests a taxonomy of nominalisms:

Mad Dog Nominalism: No word has an existing referent, not even 'Peter' and 'Paul.' (I write 'existing referent' to disallow Meinongian objects as referents. The waters are muddy enough without bringing Meinong into the picture -- please pardon the mixed metaphors.)

Extreme Nominalism: The only words that have existing referents are names like 'Peter' and Paul'; nothing in reality corresponds to such predicates as 'blond.' And a fortiori nothing corresponds to copulae and logically connective words such as 'and' and 'or.'

Nominalism Proper: Particulars (unrepeatables) alone exist: there are no universals (repeatables). This view allows that something in reality corresponds to predicates such as 'blond.' It is just that what this predicate denotes is not a universal but a particular, a trope say, or an Aristotelian accident.  I am using particular to refer to any unrepeatable item, whether concrete or abstract. Thus Socrates is a particular while his whiteness is an abstract particular, where 'abstract' is being used in the traditional as opposed to the new-fangled Quinean way.  Both are particulars because neither is repeatable in the way in which a universal is repeatable.   Thus the whiteness of Socrates is numerically distinct from the whiteness of Plato. 

Methodological Nominalism: This is just Ed's suggestion that we not assume that for each word there is a corresponding entity.

I hope no one is crazy enough to be a mad-dog nominalist, and that everyone is sane enough to be a methodological nominalist. The two middle positions, however, are subject to reasonable controversy. What I am calling Extreme Nominalism has little to recommend it, but I think Nominalism Proper is quite a reasonable position.  There has to be something extralinguistic (and extramenal) corresponding to the predicate in 'Peter is blond,' but it is not obvious that it must be a universal.  

If I understand Ed's position, he holds that all reference is intra-linguistic.   That makes him a linguistic idealist. Is that a 'mad dog' position? 

Now let's think about whether we should be nominalists with respect to words like das Seiende, that-which-is, the existent, beings, and the like. Heidegger has been known to say such things as Das Seiende ist,  or

   4. That-which-is is. (Beings are.)

Now is there anything in reality corresponding to 'that-which-is' and 'beings'? Well of course: absolutely everything comes under 'that-which-is.' There is nothing that is named by 'Nothing.' And if I met nobody on the trail, that is not to say that I met someone named 'Nobody.' But absolutely everything falls under 'a being,' 'an existent,' ein Seiendes, das Seiende.

So I see no reason to have any nominalist scruples about the latter expressions. I don't see any problem with forming the substantive das Seiende from the present participle seiend.  But you will be forgiven if you balk at the transformation of the infinitive sein into the the substantive das Sein and take the latter to refer to Majuscule Being.

Against Ostrich Nominalism (2021 Update)

Cyrus asked me whether being an ostrich indicates a moral defect. He is invited to repeat his question in his own words in the Comments. Logically prior question: what is an ostrich? The entry below is a redacted version of one from January 2013.

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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 is 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.)  For the ostrich nominalist, predication is primitive and in no need of  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?) And if one needn't posit properties, no questions need arise about what they are: sets? universals? tropes? mereological sums? and so on.

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. Peter van Inwagen is an ostrich realist.

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, not causally)  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 the abstract particulars of 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  Peter 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 thus 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 ouranios.  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, no 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. Copulae as bits of language belonging to different languages are token-distinct and type-distinct. But they pick out the copulative tie that is logically and metaphysically antecedent to language.  Or will you say that reality is language all the way down? That way lies the madness of an absurd linguistic idealism.

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 (possibly false if true; possibly true if false), 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.  If I argue against a position, that does not make me for its opposite. So when I argue against presentism in the philosophy of time that does not make me for eternalism, even if eternalism is the contradictory opposite of presentism.

One cannot exclude a priori the existence of genuine  aporiai or insolubilia.  Curators of logic museums take note.

Nominalism, Existence, and Subsistence

Here are five versions of nominalism by my current count:

Mad-Dog Nominalism: No word has an extra-linguistic referent, not even proper names such as 'Peter' and 'Paul.' 

Extreme Nominalism: The only words that have existing referents are proper names like 'Peter' and Paul'; nothing in reality corresponds to such predicates as 'blond.' And a fortiori nothing corresponds to copulae and logically connective words such as 'and' and 'or.'

Nominalism Proper: Particulars (unrepeatables) alone exist: there are no universals (repeatables). This view allows that something in reality corresponds to predicates such as 'blond' as in 'Peter is blond.' It is just that what this predicate denotes is not a universal but a particular, a trope say, or an Aristotelian accident. What I am calling nominalism proper also allows for abstract particulars where an item is abstract just in case it is non-spatio-temporal and causally inert. Mathematical sets, for example are abstract particulars. The set: {x: x is a prime number and x is less than 1o} is abstract because it has no spatiotemporal location and is causally inert. It is particular because it is unrepeatable which is equivalent to saying that it is not possibly such as to be instantiated. Sets have members -- the null set aside -- but no instances. (Quiz for the reader: tell me the cardinality of the set just mentioned.)

Reistic Nominalism: Attach the codicil 'There are no abstract items' to nominalism proper and the result is reistic nominalism.  On this view only particulars exist, and all particulars are concrete (non-abstract).  Franz Brentano is his later years was a reist.  See the SEP entry, Reism.

Methodological Nominalism: This is the view that we ought never assume that for each word there is a corresponding entity.

I hope no one is crazy enough to be a mad-dog nominalist, and that everyone is sane enough to be a methodological nominalist. The three middle positions, however, are subject to reasonable controversy. They are not obviously false and they are not obviously true. What I am calling extreme nominalism has little to recommend it, but I think nominalism proper is quite a reasonable position.  As it seems to me, there has to be something extra-linguistic (and extra-mental) corresponding to the predicate in 'Peter is blond,' but it is not obvious that it must be a universal.  

Thomas Beale sent me to a blog post of his that begins as follows:

Nominalism is a philosophical doctrine usually understood to entail a rejection of universals, in favour of the belief that only the concrete exists. Universals are understood as instantiable entities, i.e. something like types. Another flavour of nominalism involves rejection of abstracta, such as mathematical entities, propositions, fictional entities (including possible worlds). 

I personally think that most nominalist arguments are straightforwardly wrong, but not for the usual reasons that universals and/or abstracta are said by realists to exist, but for the opposite reason: types and abstracta are just there, even if they don’t ‘exist’, in the sense of being spatio-temporally concretised. The real problem is that we misuse the word exists at least half the time in philosophy. The way we should talk is to say things like: there are universals . . . .

So that’s why nominalists are wrong. There are universals, but they don’t exist. 

First of all, it is no misuse of 'exist/exists' to use these expressions interchangeably with 'is/are.' It is standard English to use them interchangeably. Examples: I am; I exist. God is; God exists. Island volcanoes exist; there are island volcanoes. Unicorns do not exist; unicorns are not; there exist no unicorns; there are no unicorns.  Scollay Square once existed; Scollay Square once was.  Socrates would never have come to be had his parents never met; Socrates would never have come to exist had his parents never met. And so on.

Nevertheless, we are not the slaves of ordinary language and one is free to distinguish between existence and being as Bertrand Russell did in Principles of Mathematics. 

Now if existence is the mode of being enjoyed by all and only spatiotemporal items, then abstracta and transcendent universals do not exist. (A transcendent universal is one that needn't be instantiated to be. An immanent universal is one that cannot be unless it is instantiated.) If transcendent universals are, but do not exist, then they enjoy the mode of being called subsistence. This seems to be what Mr Beale is telling us. 

Here is an interesting question. Suppose with David Armstrong that universals are immanent --ones-in-many, not ones-over many -- and that first-order immanent universals are constituents of thick spatio-temporal particulars. Would not these universals be "spatio-temporally concretised" in Beale's words?  Suppose universal U is a constituent of a, b, and c -- concrete existing spatiotemporal particulars -- and is wholly present in each without prejudice to its unity as a universal. Would U then not be "spatio-temporally concretised" and therefore existent?

One more question. If there were a good argument for either nominalism proper and/or reistic nominalism, would  that not also be a good argument against universals and abstracta that are but do not exist?  He who fights shy of multiplying entities beyond necessity does not care whether the entities exist or subsist.

Finally, aren't there good objections to the notion that there are modes of being?

A Realist Walks into a Bar . . .

. . . looking glum.

Bartender: "What's the matter, pal?"

Realist: "My nominalist girl friend says we have nothing in common!"

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.

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?

On the Status of Thomistic Common Natures

Aquinas says that any given nature can be considered in three ways: in respect of the esse it has in concrete singulars; in respect of the esse it has in minds; absolutely, in the abstract, without reference to either material singulars or minds, and thus without reference to either mode of esse.  The two modes are esse naturale (esse reale) and esse intentionale.  We can speak of these in English as real existence (being) and intentional existence (being).  Real existence is existence 'outside' the (finite) mind. Intentional existence is existence 'in' or 'before' the mind.  The mentioned words are obviously not to be taken spatially.  Esse is the Latin infinitive, to be.  Every human mind is a finite mind, but don't assume the converse.

According to Schopenhauer, the medievals employed but three examples: Socrates, Plato, and an ass.  Who am I to deviate from a tradition at once so hoary and noble?  So take Socrates.  Socrates is human.  The nature humanity exists really in him, and in Plato, but not in the ass.  The same nature exists intentionally in a mind that thinks about or knows Socrates.  For Aquinas, there are no epistemic deputies standing between mind and thing: thought reaches right up to and grasps the thing itself.   There is an isomorphism between knowing mind and thing known.  The ground of this isomorphism is the natura absoluta, the nature considered absolutely.  Call it the common nature (CN).  It is so-called because it is common to both the knower and the known, informing both, albeit in different ways.  It is also common to all the  singulars of the same nature and all the thoughts directed to the same sort of thing.  So caninity is common to all doggy thoughts, to all dogs, besides linking the doggy thoughts to the dogs.

Pause to appreciate how attractive this conception is. It secures the intrinsic intelligibility of the world while avoiding the 'gap problem' that bedevils post-Cartesian thought.

I need to know more, however, about  the exact ontological status of the common nature (CN) which is, as it were, amphibious as between knowing mind and thing known. 

With the help of Anthony Kenny, I realized that there are four possible views, not three as I stated in earlier forays:

A. The CN really exists as a separate, self-subsistent item.

B. The CN exists only intentionally in the mind of one who abstracts it from concrete extramental singulars and mental acts.  (Note: a mental act is a concrete singular because in time, though not in space.)

C. The CN has Meinongian Aussersein status: it has no mode of being whatsoever, and yet is is something, not nothing.  It actually has properties, it does not merely possibly have them, but is property-incomplete (and therefore in violation of the Law of Excluded Middle) in that it is neither one nor many, neither universal nor particular, neither intentionally existent nor really existent.

D. The CN exists intentionally in the mind of God, the creator.

(A) is a nonstarter and is rejected by both me and Lukas Novak.  (B) appears to be Novak's view.  (C) is the interpretation I was tentatively suggesting in earlier entries..  My thesis was that the CN must have Aussersein status, but then it inherits -- to put it anachronistically -- all the problems of Meinongianism.  The doctor angelicus ends up in the jungle with a  Meinongian monkey on his back. 

Let me now try to explain why I reject (B), Novak's view, and incline toward (C), given that (A) cannot possibly be what Aquinas had in mind. 

Consider a time t before there were any human animals and any finite minds, and ask yourself: did the nature humanity exist at t?  The answer has to be in the negative if there are only two modes of existence, real existence in concrete extramental singulars and intentional existence in finite (creaturely) minds.  For at t there were no humans and no finite minds.  But surely it is true at t that man is rational, that humanity includes rationality.  This implies that humanity at t cannot be just nothing at all.  For if it were nothing at all at t, then 'Man is rational'' at t would lack a truth-maker.  Furthermore, we surely don't want to say that 'Man is rational' first becomes true when the first human being  exists.  In some sense, the common nature must be prior to its existential realization in concrete singulars and in minds.  The common nature cannot depend on these modes of realization.  Kenny quotes Aquinas (Aquinas on Being, Oxford 2002, p. 73):

Socrates is rational, because man is rational, and not vice versa; so that even if Socrates and Plato did not exist, rationality would still be a characteristic of human nature.

Socrates est rationalis, quia homo est rationalis, et non e converso; unde dato quod Socrates et Plato non essent, adhuc humanae naturae rationalitas competeret. (Quodl. VIII, I, c, 108-110)

Aquinas' point could be put like this.  (i) At times and in possible worlds in which humans do not exist, it is nevertheless the case that rationality is included in humanity, and (ii)  the metaphysical ground of humans' being rational is the circumstance that rationality is included in humanity, and not vice versa.

Now this obviously implies that the common nature humanity has some sort of status independent of real and intentional existence.  So we either go the Meinongian route or we say that comon natures  exist in the mind of God.  Kenny:

Aquinas' solution is to invoke the divine mind.  There are really four, not three ways of considering natures: first, as they are in the mind of the creator; second, as they are in the abstract; third, as they are in individuals; and finally, as they are in the human mind. (p. 74)

This may seem to solve the problem I raised.  Common natures are not nothing because they are divine accusatives.  And they are not nothing in virtue of being ausserseiend. This solution avoids the three options of Platonism, subjectivism (according to which CNs exist only as products of abstraction), and Meinongianism.

The problem with the solution is that it smacks of deus ex machina: God is brought in to solve the problem similarly as Descartes had recourse to the divine veracity to solve the problem of the external world.  Solutions to the problems of universals, predication, and intentionality ought to be possible without bringing God into the picture. 

I  think about deus ex machina objections in philosophy in Deus ex Machina: Leibniz Contra Malebranche.

But if we don't bring God into the picture then we may face a trilemma:  either Platonism, or subjectivism, or Meinongianism.

Related articles

A Question About God and Existence

Genuine Inquiry and Two Forms of Pseudo-Inquiry: Sham Reasoning and Fake Reasoning

Senses of 'Abstract' with a Little Help from Hegel

The Grand Central Conundrum in the Philosophy of Fiction

J. P. Moreland on Constituent Ontology: Is Exemplification a Spatial Container Relation?

J. P. Moreland defines an "impure realist" as one who denies the Axiom of Localization (Universals, McGill-Queen's UP, 2001, p. 18):

No entity whatsoever can exist at different spatial locations at once or at interrupted time intervals.

An example of an impure realist is D. M. Armstrong.  An example of a pure realist is R. Grossmann.   Moreland writes,

Impure realists like D. M. Armstrong deny the axiom of localization.  For them, properties are spatially contained inside the things that have them.  Redness is at the very place Socrates is and redness is also at the very place Plato is. Thus, redness violates the axiom of localization.  Impure realists are naturalists at heart.  Why?  Because they accept the fact that properties are universals; that is, as entities that can be exemplified by more than one thing at once.  But they do not want to deny naturalism and believe in abstract entities that are outside space and time altogether.  Thus, impure realists hold that all entities are, indeed, inside space and time.  But they embrace two different kinds of spatial entities: concrete particulars (Socrates) that are in only one place at a time, and universals (properties like redness) that are at different spatial locations at the very same time. For the impure realist, the exemplification relation is a spatial container relation.  Socrates exemplifies  redness in that redness is spatially contained inside of or at the same place as Socrates. (18-19)

The above doesn't sound right to me either in itself or as an interpretation  of Armstrong. 

Is Exemplification a Container Relation?

Take a nice simple 'Iowa' example.  There are two round, red spots on a piece of white paper.  It is a datum, a Moorean fact, that both are of the same shape and both are of the same color.  Moving from data to theory:  what is the ontological ground of the sameness of shape and the sameness of color?  The impure realist responds with alacrity:  the spots are of the same color because one and the same universal redness and one and the same universal roundness are present in both spots.  The qualitative sameness of the two spots is grounded in sameness of universals.  What is the ontological ground of the numerical difference of the two spots?  The bare or thin particular in each.  Their numerical difference grounds the numerical difference of the two spots.  The bare/thin particular does a second job: it is that which instantiates the universals 'in' each spot.  For not only do we need an account of numerical difference, we also need an account of why the two spots are particulars and not (conjunctive) universals.

The upshot for both Bergmann and Armstrong is that each spot is a fact or state of affairs.  How so?  Let 'A' designate one spot and 'B' the other.  Each spot is a thick particular, a particular together with all its monadic properties.  Let 'a' and 'b' designate the thin particulars in each.  A thin particular is a particular taken in abstraction from its monadic properties.  Let 'F-ness' designate the conjunctive universal the conjuncts of which are roundness and redness.  Then A = a-instantiating F-ness, and B = b-instantiating-F-ness.  A and B are concrete facts or states of affairs.  A is a's being F and B is b's being F.

From what has been said so far it should be clear that instantiation/exemplification cannot be a spatial container relation.  Even if F-ness is spatially inside of the thick particulars A and B, that relation is different from the relation that connects the thin particular a to the universal F-ness and the thin particular b to the universal F-ness. The point is that instantiation cannot be any sort of container, constituency, or part-whole relation on a scheme like Armstrong's or Bergmann's in which ordinary concrete particulars are assayed as states of affairs or facts.  A's being red is not A's having the universal redness as a part, spatial or not.  A's being red is a's instantiating the universal redness.  Instantiation, it should be clear, is not a part-whole relation.  If a instantiates F-ness, then  neither is a a part of F-ness nor is F-ness a part of a.

Contra Moreland, we may safely say that for Armstrong, and for any scheme like his, exemplification/instantiation is not a container relation, and therefore not a spatial container relation.

Could an Ontological Part be a Spatial Part?

Moreland makes two claims in the quoted passage.  One is that exemplification is a spatial container relation.  The other is that there are two different kinds of spatial entities.  The claims seem logically independent.  Suppose you agree with me that exemplification cannot be any sort of container relation.  It seems consistent with this to maintain that universals are spatial parts of ordinary concrete particulars.  But this notion is difficult to swallow as well.

A constituent ontologist like Bergmann, Armstrong, or the author of A Paradigm Theory of Existence maintains that ordinary concrete particulars have ontological parts structured ontologically.  Thus thin particulars and constituent universals are among the  ontological parts of ordinary particulars when the latter are assayed as states of affairs or facts.  The question is: could these ontological parts be spatial parts? 

Consider a thin or bare particular.  Is it a spatial part of a round red spot?  By my lights, this makes no sense.  There is no conceivable process of physical decomposition that could lay bare (please forgive the wholly intended pun) the bare particular at the metaphysical core of a red spot or a ball bearing.  Suppose one arrived at genuine physical atoms, literally indivisible bits of matter, in the physical decomposition of a ball bearing.  Could one of these atoms be the bare or thin particular of the ball bearing?  Of course not.  For any such atom you pick will have intrinsic properties.  And so any atom you pick will be a thick particular.  As such, it will have at its metaphysical core a thin particular which -- it should now be obvious -- cannot be a bit of matter.  Bare particulars, if there are any, lie too deep, metaphysically speaking, to be bits of matter.

Obviously, then, bare particulars cannot be material parts of ordinary particulars.  Hence they cannot be spatial parts of ordinary particulars.

What about universals?  Could my two red spots -- same shade of red, of course -- each have as a spatial part numerically one and the same universal, a universal 'repeated' in each spot, the universal redness?  If so, then the same goes for the geometrical property, roundness: it is too is a universal spatially present in both spots.  But then it follows that the two universals spatially coincide: they occupy the same space in each spot.  So not only can universals be in different places at the same time; two or more of them can be in the same place at the same time.

If nothing else, this conception puts considerable stress on our notion of a spatial part.  One can physically separate the spatial parts of a thing.  A spherical object can be literally cut into two hemispheres.  But if a ball is red all over and sticky all over, the redness and the stickiness cannot be physically separated.  If physical separability in principle is a criterion of spatial parthood, then universals cannot be spatial parts of spatial concrete particulars.

Any thoughts?

Three Views

Van Inwagen:  The only parts of  material particulars are ordinary spatial parts.  The only structure of a material particular is spatial or mereological structure.  The notion of an ontological part that is not a spatial part in the ordinary mereological sense is unintelligible. And the same goes for ontological structure.  See here.

Armstrong as Misread by Moreland:  There are ontological parts in addition to ordinary spatial parts and they too are spatial.

Vallicella (2002):  There are ontological parts but they are not spatial.

Related articles

Bare Particulars versus Aristotelian Substances

Trope Troubles: An Exercise in Aporetics with the Help of Professor Levy

Potentiality and the Substance View of Persons

Senses of 'Abstract' with a Little Help from Hegel

In Defense of Modes of Being: Substance and Accident

God: A Being among Beings or Being Itself?

Armstrong, Quine, Universals, Abstract Objects, and Naturalism

Trope Troubles: An Exercise in Aporetics with the Help of Professor Levy

Eric P. Levy, an emeritus professor of English at the University of British Columbia, 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?

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, but 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 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 snubnosed, 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 SEP 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. 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 us 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 fying pan into the fire, or from the toilet into the cesspool. (I apologize to the good professor for the mixture and crudity of my metaphors.)  For now we bang up against Levy's 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 a genuine aporia.  The limbs cannot both be true.  And yet each is an entailment of standard trope theory.  If tropes are the "alphabet of being" in a phrase from Williams, then they are 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 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 [what a beautiful aptronym!] Maurin, is incoherent. But of course we have only scratched the surface. 

Picture 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

Some Philosophical Positions Valuable Only as Foils: Extreme Nominalism and Eliminative Materialism

By a philosophical foil I mean a view or position that contrasts with other positions in such a way as to highlight the often superior qualities of the other positions.  Foils are useful for mapping the spaces of theories and as termini of theoretical spectra.  Consider the spectrum of positions stretching from extreme nominalism to Plato's Theory of Forms.  The end points are reasonably viewed  as foils.  It seems to me that some philosophical positions are valuable and worthy of study only as foils and not as serious candidates for the office of 'true theory.'  Here are two of several  examples.  Since everything in philosophy is controverted, I expect these will be too.  The foil of one is the truth of another.  Ain't philosophy grand?  But I like the following examples, and I am the man whose intellectual and spiritual exigencies I am most interested in satisfying.

• Extreme Nominalism. This is the view that there are no properties.  If you tell me that there are no properties, I will be inclined to 'show you the door.'  Of course there are properties.  The only reasonable questions pertain to their nature.  Are they universals or particulars?  Can they exist unexemplified or not?  Are they constituents of the things that have them or not?  Is there a property for every meaningful predicate?  Are there disjunctive properties? And so on.  The reasonable question is not whether there are properties, but what they are.
• Eliminative Materialism. This is surely a lunatic philosophy of mind.  An eliminative materialist is a bit like a person who blows her brains out to be rid of a headache.  No head, no headache, no problem!  Too quick you say? Perhaps.  So let me expatiate further. 

  The most obvious objection to eliminative materialism (EM) is that it denies obvious data, the very data without which there would be no philosophy of mind in the first place. Introspection directly reveals the existence of pains, anxieties, pleasures, and the like. Suppose I have a headache. The pain, qua felt, cannot be doubted or denied. Its esse is its percipi. To identify the pain with a brain state makes a modicum of sense, at least initially; but it makes no sense at all to deny the existence of the very datum that gets us discussing this topic in the first place. But Paul M. Churchland (Matter and Consciousness, rev. ed. MIT Press, 1988, pp. 47-48) has a response to this sort of objection:

  The eliminative materialist will reply that that argument makes the same
  mistake that an ancient or medieval person would be making if he insisted that
  he could just see with his own eyes that the heavens form a turning sphere, or
  that witches exist. The fact is, all observation occurs within some system of
  concepts, and our observation judgments are only as good as the conceptual
  framework in which they are expressed. In all three cases — the starry sphere,
  witches, and the familiar mental states — precisely what is challenged is the
  integrity of the background conceptual frameworks in which the observation
  judgments are expressed. To insist on the validity of one's experiences,
  traditionally interpreted, is therefore to beg the very question at issue. For
  in all three cases, the question is whether we should reconceive the
  nature of some familiar observational domain.

  Even if we grant that "all observation occurs within some system of concepts," is the experiencing of a pain a case of observation? If you know your Brentano, you know that early on in Psychology From an Empirical Standpoint he makes a distinction between inner observation (innere Beobachtung) and inner perception (innere Warhnehmung). Suppose one suddenly becomes angry. The experiencing of anger is an inner perception, but not an inner observation. The difference is between living in and through one's anger and objectifying it in an act of reflection. The act of inner observation causes the anger to subside, unlike the inner perception which does not.

  Reflecting on this phenomenological difference, one sees how crude Churchland's scheme is. He thinks that mental data such as pains and pleasures are on a par with outer objects like stars and planets. It is readily granted with respect to the latter that seeing is seeing-as. A medieval man who sees the heavens as a turning sphere is interpreting the visual data in the light of a false theory; he is applying an outmoded conceptual framework. But there is no comparable sense in which my feeling of pain involves the application of a conceptual framework to an inner datum.

  Suppose I feel a pain. I might conceptualize it as tooth-ache pain in which case I assign it some such cause as a process of decay in a tooth. But I can 'bracket' or suspend that conceptualization and consider the pain in its purely qualitative, felt,  character. It is then nothing more than a sensory quale. I might even go so far as to abstract from its painfulness.  This quale, precisely as I experience it, is nothing like a distant object that I conceptualize as this or that.

  Now the existence of this rock-bottom sensory datum is indubitable and refutes the eliminativist claim. For this datum is not a product of conceptualization, but is something that is the 'raw material' of conceptualization. The felt pain qua felt is not an object of observation, something external to the observer, but an Erlebnis, something I live-through (er-leben). It is not something outside of me that I subsume under a concept, but a content (Husserl: ein reeller Inhalt) of my consciousness. I live my pain, I don't observe it. It is not a product of conceptualization -- in the way a distant light in the sky can be variously conceptualized as a planet, natural satellite, artificial satellite, star, double-star, UFO, etc. -- but a matter for conceptualization.

  So the answer to Churchland is as follows. There can be no question of re-conceptualizing fundamental sensory data since there was no conceptualization to start with. So I am not begging the question against Churchland when I insist that pains exist: I am not assuming that the "traditional conceptualization" is the correct one. I am denying his presupposition, namely, that there is conceptualization in a case like this.

  Most fundamentally, I am questioning the Kantian-Sellarsian presupposition that the data of inner sense are in as much need of categorial interpretation as the data of outer sense. If there is no categorization at this level, then there is no possibility of a re-categorization in neuroscientific
  terms. 

  What is astonishing about eliminative materialists is that they refuse to take the blatant falsity of their conclusions as showing that they went wrong somewhere in their reasoning.  In the grip of their scientistic assumptions, they deny the very data that any reasonable person would take as a plain refutation of their claims.

Pre-Print: Peter van Inwagen, Existence: Essays in Ontology

The following review article is scheduled to appear later this year in Studia Neoscholastica.  The editor grants me permission to reproduce it here should anyone have comments that might lead to its improvement.

REVIEW ARTICLE

William F. Vallicella

 Peter van Inwagen, Existence: Essays in Ontology, Cambridge University Press, 2014, viii + 261 pp.

This volume collects twelve of Peter van Inwagen's recent essays in ontology and meta-ontology, all of them previously published except one, “Alston on Ontological Commitment.” It also includes an introduction, “Inside and Outside the Ontology Room.” It goes without saying that anyone who works in ontology should study this collection of rigorous, brilliant, and creative articles. One route into the heart of van Inwagen's philosophical position is via the theory of fictional entities he develops in chapter 4, “Existence, ontological commitment, and fictional entities.”

 Fictional Entities

One might reasonably take it to be a datum that a purely fictional item such as Sherlock Holmes does not exist. After all, most of us know that Holmes is a purely fictional character, and it seems analytic that what is purely fictional does not exist. Van Inwagen, however, demurs:

The lesson I mean to convey by these examples is that the nonexistence of [Sherlock] Holmes is not an ontological datum; the ontological datum is that we can use the sentence 'Sherlock Holmes does not exist' to say something true. (105)

So, while many of us are inclined to say that the nonexistence of Holmes is an ontological datum in virtue of his being a purely fictional entity, one wholly made up by Sir Arthur Conan Doyle, van Inwagen maintains that Holmes exists and that his existence is consistent with his being purely fictional. One man's datum is another man's (false) theory! To sort this out, we need to understand van Inwagen's approach to ficta.

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?

Related articles

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

Armstrong, Quine, Universals, Abstract Objects, and Naturalism

A Serbian reader inquires,

I have read your latest post on truthmakers. Among other things, you mention [David] Armstrong's view on abstract objects. As I read elsewhere (not in Armstrong own works, I have not read anything by him yet) he was realist about universals and gives a very voluminous defense of his view. Does this view entail realism about abstract objects?

I think that Quine was realist about abstract objects and at the same time naturalist and also holds that his Platonism was consequence of his naturalized ontology.  Moreover, I have the impression that several preeminent analytic philosophers hold realist views on abstract objects, mostly under influences from Quine and in a smaller degree from Putnam.

Do Armstrong's views about universals entail realism about abstract objects?

No, they do not.  Rejecting extreme nominalism, Armstrong maintains that there are properties.  (I find it  obvious that there properties, a Moorean fact, though I grant that it is not entirely obvious what is obvious.)  Armstrong further maintains that properties are universals (repeatables), not particulars (unrepeatables) as they would be if properties were tropes.  But his is a theory of immanent universals.  This means two things.  First, it means that there are no unexemplified universals. Second, it means that universals are constituents of the individuals (thick particulars) that 'have' them.  In Wolterstorff's terminology, Armstrong is a constituent ontologist as opposed to a relation ontologist.  His universals are ontological parts of the things that 'have' them; they are not denizens of a realm apart only related by an asymmetrical exemplification tie to the things that have them. 

So for Armstrong universals are immanent in two senses: (a) they cannot exist unexemplified, and (b) they enter into the structure of ordinary (thick) particulars.  It follows that his universals are not abstract objects on the Quinean understanding of abstract objects as neither spatial nor temporal nor causally active/passive.  For given (b), universals are where and when the things that have them are, and induce causal powers in these things.  And yet they are universals, immanent universals: ones-in-many, not ones-over-many.  Some philosophers, including Armstrong, who are not much concerned with historical accuracy, call them 'Aristotelian' universals.

Does Armstrong reject all abstract objects?

Yes he does.  Armstrong is a thorough-going naturalist.  Reality is exhausted by space-time and the matter that fills it.  Hence there is nothing outside of space-time, whether abstract (causally inert) or concrete (causally active/passive).  No God, no soul capable of disembodied existence, or embodied existence for that matter, no unexemplified universals, not even exemplified nonconstituent universals, no Fregean propositions, no numbers, no mathematical sets, and of course no Meinongian nonenties. 

How do Armstrong and Quine differ on sets or classes?

For Quine, sets are abstract entities outside space and time.  They are an addition to being, even in those cases in which the members of a set are concreta.  Thus for Quine, Socrates' singleton is an abstract object in addition to the concrete Socrates.  For Armstrong, sets supervene upon their members.  They are not additions to being.  Given the members, the class or set adds nothing ontologically.  Sets are no threat to a space-time ontology.  (See D. M. Armstrong, Sketch for a Systematic Metaphysics, Oxford UP, 2010, p. 8.)

What about the null set or empty class?

For Armstrong, there is no such entity.  "It would be a strange addition to space-time!" he blusters. (Sketch, p. 8, n. 1).  Armstrong makes a bad mistake in that footnote.  He writes, "Wade Martin has reminded me about the empty class which logicians make a member of every class."  Explain the mistake in the ComBox.  Explain it correctly and I'll buy you dinner at Tres Banderas. 

Are both Quine and Armstrong naturalists?

Yes.  The Australian is a thorough-going naturalist: there is nothing that is not a denizen of space-time.  The American, for reasons I can't go into, countenances some abstract objects, sets.   It is a nice question, which is more the lover of desert landscapes.

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Properties as Parts: More on Constituent Ontology

Relational Ontology, Constituent Ontology, and Divine Simplicity

What Exactly is an Ontological Constituent?

Reply to Ken Hochstetter on Divine Simplicity

Ken Hochstetter of the College of Southern Nevada kindly sent me some comments on my SEP Divine Simplicity entry.  They are thoughtful and challenging and deserve a careful reply.  My remarks are in blue.  I have added some subheadings.

Comments enabled.

A Question About Constituent Ontology: Sensible Properties as 'Parts'

The following from a reader.  I've edited it for clarity.

Here is a quick question for you: suppose someone were to grant you that there is the sensible character blue that you say that there is, a character of your coffee cup, but then still wanted to know why it is "in" or a "constituent" of  a substance such as a cup.  So, take this person to have read and understood your argument about nude particulars and to have said: "Indeed, whatever red is, it cannot be an abstractum, for certainly something of the sort could never enter into visual experience.  Nor could "the fact that" some sensible particular stands in an instantiation relation to such an abstract object enter into visual experience, for we theorize such metaphysical facts, we do not see them.  So I grant that blue is a visible property, but why should we say that blue, so characterized is "in" or is a "constituent" of a sensible particular item?"

Well, one assumption I am making is that a certain form of nominalism is untenable. Suppose someone said that what makes a blue object blue is that English speakers apply the predicate 'blue' to it.  Nelson Goodman actually maintains something as crazy as this in one of his books.   (Intellectual brilliance and teaching at Harvard are not prophylactic against silliness.)  Why is it crazy?  Because it is the metaphysically antecedent blueness of the thing in question, my trusty coffee cup, for example, that grounds the correctness of the application of 'blue' to the cup.  I am tempted to say that this realism is just Moorean common sense. 

In other words, 'blue' is true of the cup because the cup is blue.  And not the other way around.  It is false that the cup is blue because 'blue' is true of it.  Obviously, this use of 'because' is not causal, as causation is understood by most contemporary philosophers.  But neither is it logical.  It is not logical because it does not express a relation that connects a proposition to a proposition.  It expresses an asymmetrical relation of metaphysical grounding. This relation is a relation between what is at most a proposition-like entity such as a concrete fact or state of affairs and a proposition.

The truthmaker of 'This cup is blue' cannot be anything of a linguistic nature.  (More generally, it cannot be anything of a representational nature.)  And yet something makes our sample sentence true.    There must be a truthmaker.  It would be silly to say that the sentence is "just true."  Given that there must be a truthmaker, it is going to involve the cup and the property, both construed as 'real,' i.e., extramental and extralinguistic.  There is more a truthmaker than this, but we don't need to go into this 'more.'

My reader grants that blue is a visible property.  One literally sees the blueness of the cup.  This is not a Platonic visio intellectualis.  It is not a seeing with the 'eyes' of the mind, but a seeing with the eyes of the head.  Now if this is the case, then the property I see when I see a blue cup as blue cannot be an item off in a realm apart.  It cannot be a denizen of a Platonic topos ouranos, and I am not peering into such a heavenly place when I see blue.  Blueness  cannot be an abstract object as many contemporary philosophers use this phrase.

Now if I see the blueness where the cup is, and when the cup is (although only at times at which the cup is in fact blue), then the pressure is on to say that blueness is some sort of 'proper part' of the cup, albeit in an extended, unmereological sense of 'part.'  It can't be the whole of the cup because the cup has other empirically detectable properties such as being hot and smooth and of such-and-such weight and electrical conductivity.  What other options are there?

Reflecting on the data of the problem, I come to the following conclusions: The blueness is real: it is extramental and extralinguistic. It is empirically detectable; hence it cannot be an abstract object. The blueness is detectable at the cup, not at some other place. The blueness is not identical to the cup.

We can account for the data by saying say that the blueness of the cup is an ontological constituent of the cup.  Is there a better theory?    

Related articles

Properties as Parts: More on Constituent Ontology

Against Ostrich Nominalism

Defining 'Accident'

Constituent Ontology Versus Relational Ontology and an Argument Against the Latter

E. J. Lowe on the Distinction Between Constituent and Relational Ontology

Tropes

Is Socrates a Substance or a Cross-Categorical Hybrid?

Abstracta: Omnitemporal or Timeless? An Argument from McCann

Is everything in time? Or are there timeless entities?  So-called abstracta are held by many to be timeless.  Among abstracta we find numbers, (abstract as opposed to concrete) states of affairs, mathematical (as opposed to commonsense) sets, and Fregean (as opposed to Russellian) propositions, where a Fregean proposition is the sense of an indexical-free sentence in the indicative mood.  The following items are neither in space, nor causally active/passive, but some say that they exist in time at every time: 7, 7's being prime, {7}, 7 is prime.  If an item exists in time at every time, then it is omnitemporal.  If an item is 'outside' time, then it is timeless or eternal or, to be helpfully pleonastic in the manner of McCann, timelessly eternal.

Let us agree that a temporalist is one for whom everything is in time, while an eternalist is one for whom some things are not in time. 

On p. 55 of his Creation and the Sovereignty of God (Indiana University Press 2012), Hugh McCann argues that the temporalist cannot formulate his thesis without presupposing that there are timeless states of affairs, at least of the negative sort.  Here is how I see the argument. 

Part of what the temporalist says is that

1. There are no timeless states of affairs.

How is 'there are no' in (1) to be understood?  The temporalist must intend it to be taken in a way consistent with temporalism, thus:

2. There never have been, are not now, and never will be any timeless states of affairs.

Unfortunately, the eternalist will agree with the temporalist on the truth of (2).  Consider 7's being prime.  Both agree that at no time does this state of affairs exist.  The agreement is unfortunate because it shows that the bone of contention cannot be formulated in terms of (2).  The bone of contention must be formulated in terms of (1) taken tenselessly.  But then the temporalist ends up presupposing that there are timeless states of affairs.  For he presupposes that there is the timeless state of affairs, There being no timeless states of affairs.

Temporalism, when properly formulated, i.e., when formulated in a way that permits disagreement between temporalist and eternalist, refutes itself by implying its own negation.

Is this 'Mavericked-up' McCann argument a good argument or not?  Have at it, boys.

A Parallel with the Problem of Formulating Presentism

We have seen in previous posts that to avoid tautology the presentist must reach for a tenseless sense of 'exists.'  He cannot say, tautologically, that whatever exists (present-tense) exists now.  For that is not metaphysical 'news.'  It is nothing to fight over, and fight we must.  He has to say: Whatever tenselessly exists, exists now.  But then he seems to presuppose that there are times, as real as the present time, at which temporal individuals such as Socrates tenselessly exist.  The upshot is that when presentism is given a nontautological formulation, a formulation that permits disagreement beween presentist and anti-presentist, it refutes itself.  For if there are non-present times as real as the present time, then it is not the case that only present items exist. 

Addendum (10 March):  Hugh McCann Responds

On the argument from my ch. 3 about timeless states of affairs, I of course stand by it (as of this moment, at least).  But I don’t think this argument alone would suffice to show that there is a B-series.  It might be, for example, that the only timeless states of affairs that there are pertain to abstracta; things like Seven’s being prime, and so forth.  If that were so we would get no B-series, because abstracta exhibit no temporal features at all, whereas entities in a B-series share before and after relations.

BV replies:  Well, I didn't claim that McCann's argument suffices to show that there is a B-series, a series of events related by the so-called B-relations: earlier than, later than, and simultaneous with.  Perhaps my use of 'eternalist' misled him.  All I meant by it above, as I stated,  is someone who holds that some entities are timeless.  I wasn't using it in the more commonly accepted sense in which it implies a commitment to the B-series. So we agree that the above argues does not suffice to show that there is a B-series.  It could be that there are timeless entities, and entities in time, but no B-series.

As for the analogous anti-presentist argument you go on to give, I subscribe to it.  But all it shows, as far as I can see, is that we have to consider talk of tenseless states of affairs legitimate.  But to show that isn’t to show very much.  It doesn’t yet follow, for example, that we have to speak of Socrates as existing tenselessly.  Socrates is not a state of affairs, and there is nothing paradoxical about saying there neither is, was, nor will be a tenseless Socrates.  The question is just whether it is true, and there I am unsure of the answer.  Furthermore, I can imagine someone claiming that when it comes to the concrete world, tenseless states of affairs—the B-series, in effect—is just a necessary fiction, something we need in order to be able to keep proper track of our memories.  I have no knockdown argument for or against this position.  I am inclined to think, however, that it is a vast oversimplification, just as I think presentism is.

BV replies: I think what McCann is getting at here is that an adequate formulation of presentism must presuppose the meaningfulness of  talk of tenseless states of affairs, but needn't presuppose that there are tenseless states of affairs involving entities in time.  If that is what he means, then my quick little argument seems unsound, and McCann shouldn't have subscribed to it.  I'll have to think about it some more.  What a miserably difficult topic this is!

Related articles

Defining Presentism

McCann, God, and the Platonic Menagerie

Can a Thing Exist Without Existing Now?

Time and Tense: Remarks on the B-Theory

Presentism and Actualism, Tenseless Existence and Amodal Existence

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.

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Metaphysical Grounding I: True Of

Frege Meets Aquinas: A Passage from De Ente et Essentia

Here is a passage from Chapter 3 of Thomas Aquinas, On Being and Essence (tr. Robert T. Miller, emphasis added):

The nature, however, or the essence thus understood can be considered in two ways. First, we can consider it according to its proper notion, and this is to consider it absolutely. In this way, nothing is true of the essence except what pertains to it absolutely: thus everything else that may be attributed to it will be attributed falsely. For example, to man, in that which he is a man, pertains animal and rational and the other things that fall in his definition; white or black or whatever else of this kind that is not in the notion of humanity does not pertain to man in that which he is a man. Hence, if it is asked whether this nature, considered in this way, can be said to be one or many, we should concede neither alternative, for both are beyond the concept of humanity, and either may befall the conception of man. If plurality were in the concept of this nature, it could never be one, but nevertheless it is one as it exists in Socrates. Similarly, if unity were in the notion of this nature, then it would be one and the same in Socrates and Plato, and it could not be made many in the many individuals. Second, we can also consider the existence the essence has in this thing or in that: in this way something can be predicated of the essence accidentally by reason of what the essence is in, as when we say that man is white because Socrates is white, although this does not pertain to man in that which he is a man.

What intrigues me about this passage is the following argument that it contains:

1. A nature can be considered absolutely (in the abstract) or according to the being it has in this or that individual.
2. If a nature is considered absolutely, then it is not one.  For if oneness were included in the nature of humanity, e.g., then humanity could not exist in many human beings.
3. If a nature is considered absolutely, then it is not many. For if manyness were included in the nature of humanity, e.g., then humanity could not exist in one man, say, Socrates.
Therefore
4. If a nature is considered absolutely, then it is neither one nor many, neither singular nor plural.

I find this argument intriguing because I find it extremely hard to evaluate, and because I find the conclusion to be highly counterintuitive.  It seems to me obvious that a nature or essence such as humanity is one, not many, and therefore not neither one nor many!

The following is clear.  There are many instances of humanity, many human beings.  Therefore, there can be many such instances. It follows that there is nothing in the nature of humanity to preclude there being many such instances.  But there is also nothing in the nature of humanity to require that there be many instances of humanity, or even one instance.  We can express this by saying that the nature humanity neither requires nor precludes its being instantiated. This nature, considered absolutely, logically allows multiple instantiation, single instantiation, and no instantiation.  It logically allows that there be many men, just one man, or no men.

But surely it does not follow that the nature humanity is neither one nor many.  What Aquinas is doing above is confusing what Frege calls a mark (Merkmal) of a concept with a property (Eigenschaft)  of a concept.  The marks of a concept are the subconcepts which are included within it.  Thus man has animal and rational as marks.  But these are not properties of the concept man since no concept is an animal or is rational.  Being instantiated is an example of a property of man, a property that cannot be a mark of man.   In general, the marks of a concept are not properties thereof, and vice versa.  Exercise for the reader:  find a counterexample, a concept which is such that one of its marks is also a property of it.

Aquinas has an insight which can be expressed in Fregean jargon as follows.  Being singly instantiated -- one in reality --  and being multiply instantiated -- many in reality -- are not marks (Merkmale) of the nature humanity.  But because he (along with everyone else prior to 1884) confuses marks with properties (Eigenschaften), he concludes that the nature itself cannot be either one or many.

To put it another way, Aquinas confuses the 'is' of predication ('Socrates is a man') with the 'is' of subordination ('Man is an animal').  Man is predicable of Socrates, but animal is not predicable of man, pace Aristotle, Categories 3b5: no concept or nature is an animal.  Socrates falls under man; Animal falls within man.  Animal is superordinate to man while man is subordinate to animal.

For these reasons I do not find the argument from De Ente et Essentia compelling.  But perhaps there is a good Thomist response.

Nominalism and Being

Today I preach on an old text of long-time commenter and sparring partner, London Ed:

Nominalism is the doctrine that we should not multiply entities  according to the multiplicity of terms. I.e., we shouldn't  automatically assume that there is a thing corresponding to every  term. Das Seiende is a term, so we shouldnât automatically assume there is a thing corresponding to it. Further arguments are needed to show that there is or there isnât. A classic nominalist strategy is to rewrite the sentence in such a way that the term disappears.

 My first concern is whether this definition of 'nominalism' is perhaps too broad, so broad that it pulls in almost all of us. Does anyone think that every term has a referent? Don't we all hold that there can be no automatic assumption that every occurrence of a term in a stretch of discourse picks out an entity? For example, one would be hard pressed to find a philosopher who holds that 'nothing' in

   1. Nothing is in the drawer

refers to something. (Carnapian slanders aside, Heidegger does not maintain this, but this is a separate topic about which I have written a long unpublished paper.) Following Ed's excellent advice, the
apparently referential 'nothing' can be paraphrased away:

   2. It is not the case that there is something in the drawer.

This then goes into quasi-canonical notation as

   2*. ~(Ex)(x is in the drawer).

In (2*) the tilde and the particular quantifier are syncategorematic elements. On the face of it, then, there is no call to be anything other than a nominalist about 'nothing,' using 'nominalism' as per the
suggestion above.

Whether there is call to be a nominalist about 'being' is another matter. Before proceeding to it, consider the following example:

   3. Peter and Paul are blond

which could be parsed as

   3*. Peter is blond and Paul is blond.

Now I rather doubt that anyone maintains that every word in (3*) -- or rather every word in a tokening of this sentence-type whether via utterance or inscription or some other mode of encoding -- has an entity corresponding to it. This suggests a taxonomy of nominalisms:

Mad-Dog Nominalism: No word has an existing referent, not even 'Peter' and 'Paul.' (I write 'existing referent' to disallow Meinongian objects as referents. The waters are muddy enough without bringing Meinong into the picture -- please pardon the mixed metaphor.)

Extreme Nominalism: The only words that have existing referents are names like 'Peter' and Paul'; nothing in reality corresponds to such predicates as 'blond.' And a fortiori nothing corresponds to copulae and logically connective words like 'and' and 'or.'

Nominalism Proper: Particulars (unrepeatables) alone exist: there are no universals (repeatables). This view allows that something in reality corresponds to predicates such as 'blond.' It is just that what this predicate denotes is not a universal but a particular, a trope say, or an Aristotelian accident.

Methodological Nominalism: This is just Ed's suggestion that we not assume that for each word there is a corresponding entity.

I hope no one is crazy enough to be a mad-dog nominalist, and that everyone is sane enough to be a methodological nominalist. The two middle positions, however, are subject to reasonable controversy. What I am calling Extreme Nominalism has little to recommend it, but I think Nominalism Proper is quite a reasonable position.  There has to be something extralinguistic (and extramenal) corresponding to the predicate in 'Peter is blond,' but it is not obvious that it must be a universal.  

Now let's think about whether we should be nominalists with respect to words like das Seiende, that-which-is, the existent, beings, and the like. Heidegger has been known to say such things as Das Seiende ist,  or

   4. That-which-is is. (Beings are.)

Now is there anything in reality corrresponding to 'that-which-is' and 'beings'? Well of course: absolutely everything comes under 'that-which-is.' There is nothing that is named by 'Nothing.' And if I met nobody on the trail, that is not to say that I met someone named 'Nobody.' But absolutely everything falls under 'a being,' 'an existent,' ein Seiendes, das Seiende.

So I see no reason to have any nominalist scruples about the latter expressions. I don't see any problem with forming the substantive das Seiende from the present participle seiend.  But you will be forgiven if you balk at the transformation of the infinitive sein into the the substantive das Sein and take the latter to refer to Majuscule Being.

The Use and Abuse of Occam's Razor: On Multiplying Entities Beyond Necessity

Self-styled neo-Aristotelian Richard Hennessey's response to my three posts concerning his theory of accidental predication is now online. 

He graciously declines my suggestion that he make use of accidental compounds or accidental unities in his theory despite the excellent Aristotelian pedigree of these items, a pedigree amply documented in the writings of Frank Lewis and Gareth Mathews.  Following Mathews, I characterized accidental compounds as 'kooky' objects with as little pejorative intent as I found in Mathews who defends these items. Hennessey, however, apparently takes the label pejoratively:

I cannot help but agree that the seated-Socrates in question, as a being other than Socrates, is a “‘kooky’ or ‘queer’ object.” And I cannot help but wonder how anyone who rejects universals could be tempted to multiply entities and accept such a “‘kooky’ or ‘queer’ object.”

So before examing the meat of Hennessey's response to me, in a later post, we must first tackle some preliminary matters including the nature of Occam's Razor, its use and abuse, and the role of explanation and explanatory posits in philosophy.

On Brandishing the Razor

I am not historian enough to pronounce upon the relation of what is standardly called Occam's Razor to the writings of the 14th century William of Ockham. The different spellings of his name will serve as a reminder to be careful about reading contemporary concerns into the works of philosophers long dead. Setting aside historical concerns, Occam's Razor is standardly taken to be a principle of theoretical economy or  parsimony that states:

   OR. Do not multiply entities beyond necessity.

It is sometimes formulated in Latin: Entia non sunt multiplicanda praeter necessitatem. The principle is presumably to be interpreted qualitatively rather than quantitatively, thus:

   OR*. Do not multiply TYPES of entity beyond necessity.

Thus it is not individual entities that are not to be multiplied, but types or kinds or categories of entity.  To illustrate.  Some criticized David Lewis' extreme modal realism on the ground that it proliferates concreta: there are not only all the actual  concreta , there are all those merely possible ones as well.  He responded quite plausibly to the proliferation charge by pointing out that the Razor applies to categories of entity, not individual entities, and that category-wise his ontology is sparse indeed.

'Multiply' is a picturesque way of saying posit. (Obviously, there are as many categories of entity as there are, and one cannot cause them to 'multiply.')  And let's not forget the crucial qualification: beyond necessity.  That means: beyond what is needed for purposes of adequate explanation of the data that are to be explained.  Hence:

OR**  Do not posit types of entity in excess of what is needed for purposes of explanation.

So the principle enjoins us to refrain from positing more types of entity than we need to explain the phenomena that need to be explained. It is obvious that (OR**) does not tell us to prefer theory T1 over theory T2 if T1 posits fewer types of entity than T2. What it tells us is to prefer T1 over T2 if T1 posits fewer types of entity AND accounts adequately for all  the data. So there is a trade-off between positing and accounting.

Our old pal Ed over at Beyond Necessity often seems to be unaware of this.  He seems to think that simply brandishing the Razor suffices to refute a theory.  Together with this he sometimes displays a tendency to think that whole categories of entity can be as it were  shamed out of existence by labeling them 'queer.'  I picked up that word from him.  A nice, arch, donnish epithet.  But that is just name-calling, a shabby tactic best left to the ideologues. 

Hennessey is perhaps not guilty of any name-calling or entity-shaming but I note that he too seems to think that merely waving the Razor about suffices as a technique of refutation. One piece of evidence is the quotation above where he states in effect that to posit accidental compounds such as seated-Socrates is to multiply entities.  But this is to ignore the crucial question whether there is any need for the positing. 

What is offensive about Razor brandishing is the apparent ignorance on the part of some brandishers of the fact that we all agree that one ought not posit types of entity in excess of the needs of explanation. What we don't agree on, however, is whether or not a given class of entities is needed for explanatory purposes.  That is where the interesting questions and the real disagreements lie. 

Hennessey eschews universals in the theory of predication, and elsewhere.  Fine.  But he cannot justify that eschewal solely on the basis of Occam's Razor which is a purely methodological principle.  In other words, the Razor does not dictate any particular ontology.  Taken as such, and apart from its association with the nominalist Ockham, it does not favor nominalism (the view that everything is a particular) over realism (the view that there are both particulars and universals).  It does not favor any ontology over any other. 

Nor does it rule out so-called 'abstract objects' such as Fregean propositions.  I gave an argument a while back (1 August 2010 to be precise) to the conclusion that there cannot, as a matter of metaphysical necessity, be nothing at all, that there must be at least one abstract object, a proposition.  Hennessey commented on that post, Thinking about Nothing, and made the objection that I was multipying entities.  But again, the salient question is whether the entity-positing is necessary for explanatory purposes.  If my argument was a good one, then it was.  One cannot refute such an argument simply by claiming that it introduces a type of entity that is less familiar than one's favorite types.

To sum up.  Philosophy is in large part, though not entirely, an explanatory enterprise.  As such it ought to proceed according to the methodological principle formulated above as (OR**).  This principle is not controversial.  Hence it should not be presented to one's opponents as if it were controversial and denied by them.  Nor is it a principle that takes sides on the substantive questions of ontology.  Thus the following argument which is suggested by Hennessey's remarks is invalid:

1. OR**
2. Accidental compounds are a category of particular distinct from both substances and accidents.
Ergo
3. There are no accidental compounds. 

Non sequitur!  He needs a premise to the effect that the positing of accidental compounds is otiose since the explanatory job can be adequately done without them.  He needs such a premise, and of course he needs to defend it.

What I am objecting to is the idea is that by earnest asseverations of a wholly uncontroversial methodological principle one actually  advances the substantive debate.  

My Intentionality Aporia 'Ockhamized'

Edward of London proposes the following triad

O1. The proposition ‘Bill is looking for a nonexistent thing’ can be true even when there are no nonexistent things.
O2. The proposition ‘Bill is looking for a nonexistent thing’ expresses a relation between two things.
O3. Every relation is such that if it obtains, all of its relata exist.

as a nominalistic equivalent to my

W1. We sometimes think about the nonexistent.
W2. Intentionality is a relation between thinker and object of thought.
W3. Every relation R is such that, if R obtains,then all its relata exist.

Edward imposes the following contraint on aporetic polyads: "The essence of an aporetic polyad is that any proper subset of statements (including the singleton set) should be consistent on its own, and only the whole set being inconsistent."  I accept this constraint. It implies that nothing can count as an aporetic polyad if one of its limbs is self-contradictory. 

My definition runs as follows.  An aporetic polyad is a set S of n self-consistent propositions (n>1) such that (i) any n-1 members of S, taken in conjunction, entail the negation of the remaining member; (ii) each member of S has a strong claim on our acceptance.  Edward's constraint follows from this definition.  For if any member is self-inconsistent, then it cannot have a strong claim, or any claim, on our acceptance.

If I understand Edward, he is urging two points.  His first point is that my formulation of the triad is inept because (W1), unlike (O1), is self-contradictory.  If this charge sticks, then my formulation does not count as an aporetic polyad by my own definition.  His second point is that his version of the triad has a straightforward and obvious solution:  reject (O2). 

Reply to the First Point.  There is nothing self-contradictory about 'We sometimes think of the nonexistent.'  As I made clear earlier, this is a datanic, not a theoretical, claim.  On this score it contrasts with the other two limbs.  It is meant to record an obvious fact that everyone ought to grant instantly. Because the fact is obvious it is obviously self-consistent.  So if Edward denies (W1), then it is not profitable to to continue a discussion with him. 

All I can do at this point is speculate as to why Edward fails to get the point.  I suppose what he is doing is reading a theory into (W1), a theory he considers self-contradictory.    But (W1) simply records a pre-theoretical fact and is neutral with respect to such theories as Meinong's Theory of Objects.  Suppose I am imagining a winged horse.  If so, then it would be false to say that I am imagining nothing.  One cannot simply imagine, or just imagine.  It follows that I am imagining something. We are still at the level of data.  I have said nothing controversial.  One moves beyond data to theory if one interprets my imagining something that does not exist as my standing in a relation to a Meinongian nonexistent object.  That is a highly controversial but possible theory, and it is not self-contradictory contrary to what Edward implies.  But whether or not it is self-contradictory, the main point for now is that

1. BV is imagining a winged horse

Is neutral as between the following theory-laden interpretations

2. BV (or a mental act of his) stands in a dyadic relation to a Meinongian nonexistent object.

and

3. BV is imagining winged-horse-ly.

The crucial datum is that one cannot just imagine, or simply imagine.  We express this by saying that to imagine is to imagine something.  But 'imagine something' needn't be read relationally; it could be read adverbially.  Accordingly, to imagine Peter (who exists) is to imagine Peter-ly, and to imagine Polonious (who does not exist) is to imagine Polonious-ly.  I am not forced by the crucial datum to say that imagining involves a relation between subject and object; I can say that the 'object' reduces to an adverbial modification of my imagining. 

So even if the relational reading of (1) were self-contradictory -- which it isn't --  one is not bound to interpret (1) relationally.  Now (1) is just an example of (W1).  So the same goes for (W1).  (W1) is obviously true.  He who denies it is either perverse or confused.

Reply to the Second Point.  One can of course solve Edward's triad by denying (O2). But the real question is whether one can easily deny the distinct proposition  (W2).  I say no.  For one thing, the alternatives to saying that intentionality is a relation are not at all appetizing. All three of the limbs of my triad lay claim to our acceptance, and none can be easily rejected -- but they cannot all be true.  That is why there is a problem. 

A Reply to "Ockham's Nominalism"

The following is a response to "Ockham's Nominalism"  by our London sparring partner, Edward Ockham.  His words are in black, mine are in blue.  Comments are enabled.

At this stage, I should discuss Peter Lupu’s objections (mostly in the extended comment on Vallicella’s blog here) to the nominalist program.

I should first explain what I think the nominalist program is. I am taking my lead from a principle that William of Ockham neatly formulates in his Summa Logicae book I, chapter 51, where he accuses 'the moderns' of two errors, and says that the root of the second error is “to multiply entities according to the multiplicity of terms and to suppose that every term has something real (quid rei) corresponding to it”. He says grumpily that this is erroneous and leads far away from the truth. ('Radix est multiplicare entia secundum multitudinem terminorum, et quod quilibet terminus habet quid rei; quod tamen abusivum est et a veritate maxime abducens'). See also an early definition of nominalism here.

What does he mean? Well he says that it is an error. He implies it is a common one, by attributing to the moderns and by the fact he mentions it all. Thus he implies that there exist terms which do not have something real corresponding to them.

A net that snags every fish in the sea brings in too large a catch.  The trouble with the above explanation of nominalism is that it will be accepted by almost all philosophers, including plenty who would not identify themselves as nominalists.  For few if any philosophers hold that for each word in a sentence there is a corresponding referent.  Consider

1. Nobody came to the party.

No one will take 'nobody' in (1) as a name.  ("Well, I'm glad to hear that at least one person showed up.  How is Nobody doing these days?")  (1) is easily analyzed so as to remove the apparent reference of 'nobody.'  And the same goes for a long list of other synsemantic or syncategorematical expressions.  Would any philosopher say that in

2. I'm a day late and a dollar short

every word has a referent?  Edward needs to give examples of philosophers who hold that 'nobody' in (1) and 'and' in (2) have referents.  Let us hope he does not weasel out of this challenge.  Since no one assumes that every term has something real corresponding to it, the above definition of 'nominalism' is too broad to be of any use.

If Ockham is correct, the relevant distinction to draw is between queer and straight terms. Straight terms have something real corresponding to them, queer terms don’t. Furthermore, there must at least be some temptation to imagine that queer terms refer to or denote something, otherwise there would be little point in making it.

There is no need for this bizarre terminological innovation.  We already have 'autosemantic' and 'synsemantic' and equivalents.  Do not multiply terminology beyond necessity!

And let us note that synsemantic terms have useful semantic roles to play despite their not referring to anything.  There is a rather striking difference between 'I will come' and 'I will not come,' a difference that rides on the synsemantic particle 'not' which, as synsemantic, does not refer to anything.

Which brings me to the main point raised by Peter Lupu, who asks “What are ‘queer-entities’ and how do we determine whether a given entity is “queer” or “straight”? There are two parts to his question. In answer to the first, there are no such things as queer entities, if Ockham is right. There are only ‘queer terms’. These, by definition, are terms that don’t refer to or denote anything, and so by implication there are no ‘queer entities’.

In other words, synsemantic terms do not refer.  True by definition.

This is what makes any debate with realists difficult. Realists, namely those who think that queer terms refer, will persist in using the queer terms as if they did refer, and so will ask what kinds of thing are referred to, what is their ‘ontological status’ and so on. Ockhamists will naturally refuse to use these terms as if they referred, and refer the names of the terms instead, typically by using real or scare quotes.

No, realists are not those who think that queer terms refer since no one thinks that queer, i.e., nonreferring terms, refer.  Edward needs to explain the criteria for deciding whether a given term is queer or straight.  Is 'Edward' a queer term?  If not, why not?

[. . .]

That deals with Peter's first question. What are queer entities? We can't say, because there are no such things, just as we can't say what kind of things ghosts are. But we can say what 'queer terms' are. These are terms that are categorical, but which (a) have no reference or denotation and (b) appear, or are believed by many, typically on grounds of reason alone, to have a reference or denotation.

This doesn't advance the discussion at all.  First of all, we are not told what 'categorical' means.  More importantly, we have not been supplied with criteria for distinguishing queer from straight terms, to acquiesce for the nonce in this idiotic terminology. 

Peter’s second point, on how we determine whether given entity is “queer” or “straight”, I will leave for the next post, although clearly the first point applies here also. If the nominalist is right, we cannot ask this question of anything, just as we cannot ask whether a UFO came from Alpha centauri or Betelgeuse. We can only ask whether a given term is queer or straight. More to follow.

This doesn't get us anywhere.  We can ask, of a given term, whether or not it has a referent.  But then we need to be supplied with some method for answering this question.  Consider

3. Wisdom is a virtue.

Presumably, Edward will put 'wisdom' down as queer.  But on what grounds?  Is it because  he just knows (again by what method?) that everything that exists is a particular, and that if 'wisdom' has a referent then it must be a universal?  Or is there something about the word itself that tips him off that it is nonreferring? 

Is he appealing to some paraphrastic method?  Is he suggesting that what (3) expresses can be expressed salva significatione by a sentence containing no term making an apparent reference to a universal?  And in particular, would he accept the following paraphrase:

3*.  If anyone is wise, then he is virtuous?

So far, then, Londonistas 0, Phoenicians 1.

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.

 

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.

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.

Why not be a Nominalist?

0. This post is a sequel to Truthmaker Maximalism Questioned.

1. On one acceptation of the term, a nominalist is one who holds that everything that exists is a concrete  individual.  Nominalists accordingly eschew such categories of entity as: universals, whether transcendent or immanent, Fregean propositions, Castaneda's ontological operators, mathematical sets, tropes (abstract particulars, perfect particulars), and concrete states of affairs.  Nominalists of course accept that there are declarative sentences and that some of them are true.  Consider the true

1. Peter is hungry.

Nominalists cheerfully admit that the proper name 'Peter' denotes something external to language and mind, a particular man, which we can call the 'ontological correlate' of the subject term.  But, ever wary of "multiplying entities beyond necessity," nominalists fight shy of admitting an ontological correlate of  'hungry,' let alone a correlate of  'is.'   And yet, given that (1) is true, 'hungry' is true of Peter.  (In a simple case like this, the predicate is true of  the the referent of the subject term iff the sentence is true.) Now philosophers like me are wont to ask:  In virtue of what is 'hungry' true of Peter?  Since 'hungry' applies to Peter in the way in which 'leprous,' 'anorexic,' and other predicates do not, I find it reasonable to put the same question as follows:  What is the ontological ground of the correct application of 'hungry' to Peter?

2. In answering this question I introduce two posits that will enrage the nominalist and offend against his ontologcal parsimoniousness.   First of all, we need an o-correlate of 'hungry.' I admit of course that 'hungry' in our sample sentence functions differently than 'Peter.'  The latter is a name, the former is what Frege calls a concept-word (Begriffswort).  Nevertheless, there must be something in reality that corresponds to 'hungry,' and whatever it is it cannot be identical to Peter.  Why not?  Well, Peter, unlike my cat, is not hungry at every time at which he exists; and for every time t in the actual world at which  he is hungry, there is some possible world in which he is not hungry at t.  Therefore, Peter cannot be identical to the o-correlate of 'hungry.' 

We are back to our old friend (absolute numerical) identity which is an equivalence relation (reflexive, symmetrical, transitive) governed by the Indiscernibility of Identicals and the Necessity of Identity.

3. But why do we need an o-correlate of 'hungry' at all?  I asked: in virtue of what is 'hungry' true of Peter?  One sort of nominalist, the 'ostrich nominalist,' will say that there is nothing in virtue of which 'hungry' is true of Peter.  For him is is just a 'brute fact,' i.e., an inexplicable datum, that 'hungry' correctly applies to Peter.  There is no need of an ontological ground of the correctness of this application.  There is no room for a special philosophical explanation of why 'hungry' is true of Peter.  It just applies to him, and that's the end of the matter.  The ostrich nominalist of course grants that Peter's being hungry can be explained 'horizontally' in terms of antecedent and circumambient empirical causes; what he denies is that there is need for some further 'philosophical' or 'metaphysical' or 'ontological' explanation of the truth of 'Peter is hungry.'

If a nominalist says that 'hungry' is true of Peter because Peter is hungry, then I say he moves in a circle of embarrasingly short diameter.  What we want to understand are the ontological commitments involved in the true sentence, 'Peter is hungry.'  We need more than Peter.  We need something that grounds the correctness of the application of 'hungry' to him.  To say that 'hungry' is true of Peter because Peter is hungry presupposes what we are trying to understand.  Apart from this diversionary tactic, the ostrich nominalist is back to saying that there is nothing extralingusitic that grounds the correct application of 'hungry' to Peter.  He is denying the possibility of any metaphysical explanation here.  He is saying that it is just a brute fact that 'hungry' applies to Peter.

4.  As for my second posit, I would urge that introducing an o-correlate for 'hungry' such as a universal tiredness does not suffice to account for the truth of the sample sentence.  And this for the simple reason that Peter and tiredness could both exist withough Peter being tired.  What we need is a concrete state of affairs, an entity which, though it has Peter and tiredness as constituents, is distinct from each and from the mereological sum of the two. 

5.  Now one can argue plausibly against both posits.  And it must be admitted that both posits give rise to conundra that cast doubt on them.  But what is the alternative?  Faced with a problem, the ostrich sticks his head in the sand.  Out of sight, out of mind.  Similarly. the ostrich nominalist simply ignores the problem.  Or am I being unfair?

Perhaps the issue comes down to this:  Must we accept the truth of sentences like (1) as a 'brute fact,' i.e. as something insusceptible of explanation (apart, of course, from causal explanation), OR is there the possibility of a philosophical account?

6. Finally, it is worth nothing that the nominalist blunders badly  if he says that Peter is hungry in virtue of 'hungry''s applying  to him.  For that is a metaphysical theory and an absurd one to boot: it makes Peter's being hungry depend on the existence of the English predicate 'hungry.'  To avoid an incoherent, Goodmanaical, linguistic idealism, the nominalist should give no metaphysical explanation and be content to say it is just a brute fact that Peter is hungry.