Maverick Philosopher

Reader Requests Advice re: Learning Basics of Philosophical Argumentation

A New Zealand reader writes,

 

I was hoping if you are able to provide me with some guidance regarding where to begin learning the basics of philosophical arguments. I’ve been trying to understand how to evaluate political and theological debates for awhile, but despite my interest I often find them go away over my head. I found your Substack a couple of weeks ago and was delighted to find your articles not only quite easy to follow but made plenty of sense. So I thought why not give it a try and ask you for help in getting better critical thinking. It would be wonderful if you are able to help with this.

 

Many thanks,

Cameron

 

I am happy to be of assistance, Cameron. Jay F. Rosenberg's The Practice of Philosophy: A Handbook for Beginners comes to mind.

 

Your question has been put to me before. Here is a post from 2011 in which I make a few other suggestions. You will also find the comment thread to that post useful.

 

If anyone wants to help Cameron in his quest, comments are enabled below.

 

A Difference Between Plausibility and Probability

The plausibility of a conjunctive proposition is that of the least plausible of its conjuncts. Not so for the probability of a conjunctive proposition. This point is made by Nicholas Rescher in his entry 'Plausibility' in the Oxford Companion to Philosophy.

Exercise for the reader: give examples.

Ambiguity, Vagueness, Generality, Disambiguation

Top o' the Stack

Some distinctions needed for intellectual hygiene.

The Difference between Posing and Begging a Question

I found the nifty graphic below over at Flood's place.  It is a pithy and pictorial presentation of a point I have been hammering away at online for the last twenty years. Here is a Substack hammer-job. Some say we should give up the fight and let the forces of linguistic decadence obliterate the distinction between posing and begging a question. I am inclined to say that we should fight on against the anti-civilizational forces while well aware that fighting-on may be nothing more than a pointless rear-guard action.

What say you?

 

The Ersatz Eternity of the Past: Denied by Lukasiewicz!

The Pole denies the actuality of the past and in consequence thereof the ersatz eternity or accidental necessity (necessitas per accidens) of the past.

Quasi-literary Preamble:

What has been, though it needn't have been, always will have been.  What time has mothered, no future time can destroy.   What you were and that you were stand forever inscribed in the roster of being whether or not anyone  ever reads the record.  What you have done, good or bad, and what you have left undone, good or bad, cannot be erased by the passage of time. You will die, but your having lived will never die. This is so even if you and your works and days are utterly forgotten. An actual past buried in oblivion remains an actual past. The erasure of memories and memorials is not the erasure of their quondam objects. The being of what was does not depend on their being-known; it does not rest on the spotty memories, flickering and fallible, of fragile mortals or their transient monuments or recording devices.

But how paltry the ersatz eternity of time's progeny!  Time has made you and will unmake you.  In compensation, she allows your having been to rise above the reach of the flux.  Thanks a lot, bitch!  You are one mater dolorosa whose consolation is as petty as your penance is hard.

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

I posted a precursor of the above on 10 March 2010.  It elicited an astute comment from Alan Rhoda.  He wrote:

You here express the tense-logical idea that p -->FPp, that if something is the case, then it will thereafter always be the case that it has been the case. In Latin, facta infecta fieri non possunt. [The done cannot be undone.]

Believe it not, this has been denied by the famous Polish logician Lukasiewicz, no less. He seems to have accepted a version of presentism according to which (1) all (contingent) truths depend for their truth on what presently exists, and (2) what presently exists need not include anything that suffices to pick out a unique prior sequence of events as "the" actual past. Accordingly, truths about the past may cease to be true as the passage of time obliterates the traces of past events. Lukasiewicz apparently found this a comforting thought:

"There are hard moments of suffering and still harder ones of guilt in everyone’s life. We should be glad to be able to erase them not only from our memory but also from existence. We may believe that when all the effects of those fateful moments are exhausted, even should that happen only after our death, then their causes too will be effaced from the world of actuality and pass into the realm of possibility. Time calms our cares and brings us forgiveness." (Jan Lukasiewicz, "On Determinism" in  Selected Works, ed. L. Borkowski, North-Holland, Amsterdam, 1970, p.128.)

That is  to my mind an amazing passage from Lukasiewicz both because of his rejection of the tense-logical principle, p -->FPp,  and because of the consolation he derives from its rejection.

I myself find it very hard to believe that there wasn't an actual unique past. I find it impossible to believe that, with the passage of enough time, past events will somehow go from being actual to being merely possible. It seems obvious to me, a plain datum, that there is an important difference between a past event such as Kierkegaard's engagement to Regine Olsen, which actually occurred, and a merely possible (past) event such as his marriage to her which did not occur, but could have  occurred, where 'could have' is to be taken ontically and not epistemically. Now that datum tells against presentism -- unless you bring God into the picture which is what Rhoda does.  For if the present alone exists, then the wholly past does not exist, which implies that there is no difference between a merely possible past event and an actual past event.

Alan Rhoda responds:

Yes, in my paper "Presentism, Truthmakers, and God" (Pacific Philosophical Quarterly 2009). I argue that the best way for presentists to supply truthmakers for truths about the past is to appeal to divine memories.

I accept the datanic nature of your distinction between the actual and the merely possible past. I'm not clear, however, on why that distinction by itself should count against presentism. Unlike Lukasiewicz, most presentists do posit present grounds for that distinction. The live question is what sort of present facts, if any, could serve the presentist's purposes. That's where my argument for theistic presentism gets its purchase.

If only that which exists now, exists, then that which existed does not exist. If to exist = to be actual, then that which existed is not actual. Since what existed is presumably not impossible, that which existed is merely possible. It therefore looks as if one can get very quickly from the distinction I pointed out to a rejection of atheistic presentism. Atheistic presentism cannot supply the truth-makers for past-tensed truths such as 'Kierkegaard was engaged to Regine Olsen.'

Atheistic presentists need to find present facts to ground the distinction in question.  Now there are some present facts that could serve to ground some past-tensed truths. Consider 'Bill Sykes the burglar entered my house yesterday.' This contingent truth needs a truth-maker, and on presentism this truth-maker must exist today. Our presentist might plausibly say that it is Sykes' footprints outside my window, and the the broken glass, both of which exist today, that tie Sykes to the crime and make-true the contingent sentence in question.  But what makes it true that my grandfather Alphonso drank a glass of dago red on New Year's Day, 1940 and pronounced it excellent?  Suppose the red wine drunk by Alphonso came from the Gallo vineyard. What now makes it true that that particular glass of dago red came from the Gallo vineyard as opposed to the Cribari vineyard? What exists now that could serve as a truth-maker of such truths?  There are plenty of past-tensed truths that have no presently existing truth-makers.  This is why Rhoda argues that it is only present facts involving divine memories that are up to the truth-making job.

Whether recourse to God and his omniscience works to save presentism we leave for later. 

Logic Quiz: Is the Argument Below Specious or Sound?

1) What I know cannot be otherwise: if I know that p, then p cannot be false.

Therefore

2) If I know that a man is walking, then 'a man is walking' cannot be false.

Therefore

3) If  I know that a man is walking, then it is necessarily true that a man is walking.

Extra credit: explain the meaning of 'specious.'

Argumentative Circles and their Diameters: More on Presuppositionalism

The day before yesterday, re: presuppositionalism, I wrote:

We need to bear in mind  that arguments have premises and that no argument can prove its own premises. An argument of the form p therefore p is an argument valid in point of logical form in which premise and conclusion are identical, but no one will take an argument of this form as proving that p. Every circular argument of the above form is valid, and some are sound; but none are probative. By that I mean that no such argument constitutes a proof.  That ought to be perfectly obvious.

'Circularity' in respect of arguments is of course a metaphor: no argument is literally a geometrical circle. But it is a useful metaphor and I propose we extend it by speaking of the 'diameter' of a circular argument.  The logical form italicized above -- p therefore p -- has a 'diameter' than which no shorter can be conceived.  Its 'diameter' is zero. If a geometrical circle has a diameter of zero, then it is not a circle but a point.  The diameter of a circular argument of the above form is also a 'point,' figuratively speaking, the point being the one proposition that serves as both premise and conclusion.

A circular argument of zero diameter is said to be 'vicious.' Are there then 'virtuous' or if not positively virtuous then  'non-vicious' circular arguments?  Can one argue in a way that is circular but logically acceptable? Brian Bosse brought up this issue over lunch Sunday as we were discussing my longish entry on presuppositionalism. He may have had John M. Frame in mind.

Presuppositionalists such as Frame take the Word of God as set forth in the Protestant Christian Bible as their "ultimate presupposition." (Five Views on Apologetics, Zondervan 2000, 209) It is their "ultimate criterion of truth." (209)  This commitment of theirs is faith-based:

. . . for Christians, faith governs reasoning just as it governs all other human activities. Reasoning is not in some realm that is neutral between faith and unbelief. There is no such realm, since God's standards apply to all of life. (209)

What causes faith? ". . . God causes faith by his own free grace." (209) What is the rational basis of faith? ". . . the answer is that faith is based on reality, on truth. It is in accord with all the facts of God's universe and all the laws of thought that God has ordained. . . . The faith he gives us agrees with God's own perfect rationality." (209-210)

We want to know what rationally justifies faith in God and in his Word as found in the Bible. We are told that this faith is justified because it is true, agreeing as it does with all of the laws of thought that God has ordained. God himself, as the ultimate source of all things, including rationality, is the ultimate rational justification of our faith in him and his Word.  The reasoning here is plainly circular as Frame admits:

There is a kind of circularity here, but the circularity is not vicious. It sounds circular to say that faith governs reasoning and also that it is based on rationality. It is therefore important to remember that the rationality that serves as the rational basis for faith is God's own rationality. The sequence is: God's rationality -->human faith -->human reasoning. The arrows may be read "is the rational basis for." That sequence is linear, not circular. (210)

Frame's fancy footwork here is unavailing, an exercise in sophistry. He is obviously reasoning in a circle by presupposing the very thing whose existence he wants to prove. But he is loathe to admit that this is what he is doing. So he introduces a bogus distinction between vicious circles and linear circles.  But just as 'linear circle' in geometry is a contradictio in adjecto , so too is 'linear circle' in logic. 

You are either arguing in a circle or you are not. You are either presupposing what you are trying to prove or you are not. You are either begging the question or you are not. You are either committing the formal fallacy of petitio principii (hysteron proteron) or you are not. That is the long and the short of it. One or the other and no weaseling out via some bogus distinction between vicious and non-vicious circular arguments.

What Frame wants is a 'knock-down' (rationally compelling or rationally coercive) argument for the existence of the God of the Protestant Christian Bible interpreted along Calvinist lines.  He thinks he can get what wants by way of a transcendental argument,  one that issues in God "not merely as the conclusion of an argument, but as the one who makes argument possible." (220)  He wants God to play a transcendental role as the ultimate and unconditioned condition of the possibility of all our intellectual operations including reasoning, whether valid or invalid, sound or unsound. (If his God does play the transcendental role, then Frame can say that the arguments of atheists, just insofar as they are arguments, prove the existence of God!) 

Now it must be granted, as I granted to Brian over lunch, that if Frame's God exists, then he does play the transcendental role. The question, however, is whether it can be proven that nothing other than Frame's God could play the transcendental role. It can be proven that there is a transcendental condition of all our intellectual operations. (See my earlier entry.) Where Frame goes wrong is in thinking that from the fact that there is a rationally compelling argument for the existence of a transcendental condition of the possibility of all our intellectual operations (forming concepts, defining terms, making judgments, giving arguments, replying to objections offering hypotheses, etc.) it follows immediately that his God exists beyond the shadow of a rational doubt.  How does he know that his God alone could play the transcendental role? Frame may be taxed with  giving the following invalid argument:

a) If the God of the Protestant Christian Bible exists, then he plays the transcendental role;

b) It is objectively certain that something plays the transcendental role;

ergo

c) It is objectively certain that the God of the Protestant Christian Bible  plays the transcendental role. 

The premises are true, but the conclusion does not follow from them. For it is not objectively certain that nothing other than the God of the Christian Bible could play the transcendental role. This is because no non-transcendental argument -- Frame mentions the "causal argument" -- for the existence of God is rationally compelling. Hence no non-transcendental God argument can assure us that the existence of God is objectively certain. 

Here is another way to see the matter. It is rationally demonstrable that there is a total and unique way things are. (For if you assert that there is no way things are, then you are asserting that the way things are is that there is no way things are.) Now if Frame's God exists, then he is the concrete and personal metaphysical ground of the way things are. But how do we know that Frame's God exists? We cannot simply assume that the transcendental proof of the existence of the way things are is also a proof of Frame's God.  So non-transcendental arguments must be brought into to take us to Frame's God, Frame's "causal argument" for example. But these arguments are none of them rationally compelling. They do not generate objective certainty. So how do we know that something else is not the metaphysical ground of the way things are?

Retorsion Revisited: How Far Does it Reach and What Does it Prove?

Retorsion (retortion) is the philosophical procedure whereby one attempts to establish a thesis by uncovering a performative inconsistency in anyone who denies it. It is as old as Aristotle and has been put to use by philosophers as diverse as Transcendental Thomists and Ayn Rand and her followers. Retorsion is something like an ad hominem tu quoque except that the homo in question is everyman, indeed every rational being. Proofs by retorsion have the following form:

Proposition p is such that anyone who denies it falls into performative inconsistency; ergo, p is true.

Suppose a person asserts that there are no assertions.  That person falls into performative inconsistency:  the propositional content of the speech act is 'inconsistent' with the performance.  *There are no assertions* is the propositional content, or content, for short.  The speech act of asserting is in this case the performance.  The inconsistency is not strictly logical, which is why I employed scare quotes.  Strictly logical inconsistency/consistency obtains between propositions, and a performance such as asserting is not a proposition.  Performances belong to the category of events, not that of propositions. And yet it is clear that there is some sort of analog of inconsistency here, some sort or analog of 'contradiction.'  The content asserted is falsified by the act of asserting it.  The performance 'contradicts' the content.

 

Nota Notae Est Nota Rei Ipsius, Kant, and the Ontological Argument

This is a re-post, redacted and re-thought, from 22 July 2011. I dust it off because something caught my eye the other morning in the Translator's Introduction to Kant's Logic. Robert S. Hartman and Wolfgang Schwarz tell us that for Kant the principle of all inference or mediate judgment is the rule Nota notae est rei ipsius nota. (p. xlii). I'm guessing that C. S. Peirce got wind of the principle from Kant. As for Hartman, I remember hearing good things about him and his work in axiology from Hector-Neri Castañeda. I also recall Hector saying that Hartman died young. Details of Hartman's eventful life here. He died at age 63, which is young for a philosopher.  Hector died at 66.

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

"The mark of a mark is a mark of the thing itself." I found this piece of scholasticism in C. S. Peirce. (Justus Buchler, ed., Philosophical Writings of Peirce, p. 133) It is an example of what Peirce calls a   'leading principle.'

Let's say you have an enthymeme:

   Enoch was a man
   -----
   Enoch died.

Invalid as it stands, this argument can be made valid by adding a premise. (Any invalid argument can be made valid by adding a premise.) Add 'All men die' and the argument comes out valid. Peirce writes:

     The leading principle of this is nota notae est nota rei ipsius.
     Stating this as a premiss, we have the argument,

     Nota notae est nota rei ipsius
     Mortality is a mark of humanity, which is a mark of Enoch
     -----
     Mortality is a mark of Enoch.

But is it true that the mark of a mark is a mark of the thing itself? There is no doubt that mortality is a mark of humanity in the following sense: The concept humanity includes within its conceptual content the superordinate concept mortal, which implies that, necessarily, if anything is human, then it is mortal. But mortality is not a mark, but a property, of Enoch. I am invoking Gottlob Frege's distinction between a Merkmal and an Eigenschaft. Frege explains this distinction in various places, one being The Foundations of Arithmetic, sec. 53. But rather than quote Frege, I'll explain the distinction in my own way using a totally original example.

Consider the concept bachelor. This is a first-order or first-level concept in that the items that fall under it are not concepts but objects. The marks of a first-order concept are properties of the objects that fall under the concept. Now the marks of bachelor are unmarried, male, adult, and not a member of a religious order. These marks are themselves concepts, concepts one can extract from bachelor by analysis. Given that Tom falls under bachelor, he has these marks as properties. Thus unmarried, etc. are not marks of Tom, but properties of Tom, while unmarried, etc. are not properties of bachelor but marks of bachelor.

To appreciate the Merkmal (mark)-Eigenschaft (property) distinction, note that the relation between a concept and its marks is entirely different from the relation between a concept and its instances. A first-order concept includes its marks without instantiating them, while an object instantiates its properties without including them.

This is a very plausible line to take. It makes no sense to say of a concept that it is married or unmarried, so unmarried cannot be a property of the concept bachelor. Concepts don't get married or remain single. But it does make sense to say that a concept includes certain other concepts, its marks. On the other hand, it makes no sense to say of Tom that he includes certain concepts since he could do such a thing only if he were a concept, which he isn't. But it does make sense to say of Tom that he has such properties as being a bachelor, being unmarried, being an adult, etc.

Reverting to Peirce's example, mortality is a mark of humanity, but not a mark of Enoch. It is a property of Enoch. For this reason the scholastic formula is false. Nota notae NON est nota rei ipsius. The mark of a mark is not a mark of the thing itself but a property of the thing itself.

No doubt commenter Edward the Nominalist will want to wrangle with me over this slight to his scholastic lore, and I hope he does, since his objections will aid and abet our descent into the labyrinth of this fascinating cluster of problems. But for now, two quick applications.

One is to the ontological argument, or rather to the ontological argument aus lauter Begriffen as Immanuel Kant describes it, the ontological argument "from mere concepts." So we start with the concept God and analyze it. The concept God includes omniscience, etc. But 'surely' existence is also contained in the concept God. For a god who did not exist would lack a perfection, a great-making property; such a god would not be id quo maius cogitari non posse. He would not be that than which no greater can be conceived. To conceive God, then, is to conceive an existing God, whence it follows that God exists! For if you are conceiving a nonexistent God, then you are not conceiving God.

Frege refutes this version of the ontological argument -- not the only or best version I hasten to add -- in one sentence: Weil Existenz Eigenschaft des Begriffes ist, erreicht der ontologische Beweis von der Existenz Gottes sein Ziel nicht. (Grundlagen der Arithmetik, sec. 53)  "Because existence is a property of concepts, the ontological argument for the existence of God fails to attain its goal." What Frege is saying is that the ontological argument "from mere concepts" rests on the mistake of thinking of existence as a mark of concepts as opposed to a property of concepts.  No concept for Frege is such that existence is included within it. Existence is rather a property of concepts, the property of having an instance.

The other application of my rejection of the scholastic formula above is to the logical question of the correct interpretation of singular propositions. The scholastics treat singulars as if they are generals.  But if Frege is right, this is a grave logical error since it rides roughshod over the mark/property distinction. To drag this all into the full light of day would take many more posts.

Counterexamples and Outliers

An exception to a universal generalization is a counterexample that refutes the generalization. All you need is one. Generic statements cannot, however, be similarly refuted. 'Nuns don't smoke cigars' is a generic statement. If you turn up a nun who smokes cigars I won't take you to have refuted the generic statement. I'll dismiss the exception as an 'outlier.' 

Memo to self: develop this line of thinking and then apply it to 'hot button' issues such as race. Is Candace Owens representative of black females or is she an 'outlier'? And to which generic statements is she an outlier?  You won't touch this question, will you? Not with an eleven-foot pole, which is the pole you use to touch questions you won't touch  with a ten-foot pole. 

See my aptly appellated entry, Generic Statements, for more on generic statements.

Questions about a Lukasiewicz Passage

E. B. sent this:

http://www.logicmuseum.com/wiki/Logical_form_(Lukasiewicz)

“When, for instance, asserting the implication 'If all philosophers are men, then all philosophers are mortal' you would also assert as second premiss the sentence 'Every philosopher is a man', you could not get from these premisses the conclusion 'All philosophers are mortal', because you would have no guarantee that the sentence 'Every philosopher is a man' represents the same thought as the sentence 'All philosophers are men'. It would be necessary to confirm by means of a definition that 'Every A is B' means the same as 'All A's are B's'; on the ground of this definition replace the sentence 'Every philosopher is a man' by the sentence 'All philosophers are men', and only then will it be possible to get the conclusion. By this example you can easily comprehend the meaning of formalism. Formalism requires that exactly the same thought should always be expressed by means of exactly the same series of words ordered in exactly the same manner.”

My emphasis.

Suppose we compare the following two argument displays:

If all philosophers are men, then all philosophers are mortal
All philosophers are men
----
All philosophers are mortal.

If every philosopher is a man, then all philosophers are mortal
All philosophers are men
----
All philosophers are mortal.

Are they both valid, or is only the first valid? Lukasiewicz is telling us in effect that only the first is valid. No doubt the first is valid: it instantiates the valid argument form, modus ponendo ponens.  But then, by my lights, so does the second. So both arguments are valid.

But it all depends on what we take an argument to be.  I hold that  an argument is not the same as an argument display. A necessary but not sufficient condition of anything's being an argument is that it be a sequence of propositions. A proposition is not the same as a sentence in the indicative mood. Die Sonne scheint and 'The sun shines' are two different indicative sentence tokens in two different  languages. And yet they 'say the same thing' or rather can be used by the same or different speakers to  say the same thing. We accommodate this fact by introducing a species of abstract object we call propositions or thoughts, the latter word used by L. above.  The sentences cited express one and the same proposition or thought.  Similarly with 'All philosophers are men' and 'Every man is a philosopher.' They express the same proposition.

So above what we have are two different ways of displaying one and the same argument.  Since that argument instantiates a valid argument form, the argument is valid.

Consider now these two argument displays:

Omnis homo mortalis est
Sokrates homo est
-------
Sockrates mortalis est.

Every man is mortal
Socrates is a man
-----
Socrates is mortal.

How many arguments? One or two? One. One and the same argument is expressed in two different languages.  I conclude that an argument is not the same a collection of sentences. Sentences are physical (marks on paper, pixels on a screen, acoustic disturbances); propositions are not. They are not seen with the eyes or heard with the ears or felt (as in Braille) with the fingers; they are understood by the mind. 

Finally, L. speaks of  exactly the same series of words ordered in exactly the same manner.  Same words in the same order? But how do we know that the words are the same? Is it because they have the same letters in the same order?  By that criterion, 'war' in the following two sentences is the same word:

Ich war ein Soldat.
I went to war.

But the two series of letters in the same order are not the same word. 

Now consider this array:

All philosophers are men.
Philosophers are, all of them, men.
Every philosopher is a man.

These sentences 'say the same thing,' i.e., they express the same proposition or thought. I know that because I understand English.  To understand English is to understand the meanings of English words and sentences.  Meanings are understood by the mind not perceived by the sense organs.

Syntactic and Semantic Validity Again

Edward sends this interesting example:

Omnis homo est mortalis

Socrates is a man

Sokrates ist sterblich

Semantically valid, but not syntactically?

No, syntactically valid because the argument instantiates a valid argument-form, to wit:

Every F is a G
a is an F
Therefore
a is a G.

Validity is a matter of form. An argument is valid if it instantiates a valid argument-form.  It is the form that is valid or invalid in the primary senses of these terms. The argument itself is valid or invalid in secondary senses. The argument inherits its validity from the form, so to speak.  Or you could say that it is the validity of the form that is the ground of, and accounts for, the validity of the argument.

For me, and here is where Ed will disagree, a valid deductive argument such as the 'Socrates' syllogism above, is a sequence of propositions, not of sentences, that instantiates a valid argument-form.

A proposition is what a sentence in the indicative mood expresses. To be precise, a proposition is what is expressed by the tokening (whether by utterance, writing, or in some other way) of a sentence in the indicative mood.   The following three sentences, each from a different language, can be used to express one and the same proposition or Fregean Gedanke (thought) :

Sokrates mortalis est.
Sokrates ist sterblich.
Socrates is mortal.

These three numerically different sentence tokens from three different languages express the same proposition when they are used to express a proposition.  Sentences are linguistic entities. Propositions are extra-linguistic, and therefore not tied to particular languages as sentences are.  Not tied in the sense that the same proposition can be expressed in different languages.  Suppose that every English speaker is exterminated. Could it then be said that Socrates is mortal? Yes, though not in those words. One could say the same thing by uttering the corresponding German or French or Turkish  sentence. 

This is a reason to distinguish propositions from sentences.  

Now glance back at Ed's example. It is linguistically hybrid.  But logically it expresses the very same argument (sequence of propositions) that the following does:

Every man is mortal
Socrates is a man
Ergo
Socrates is mortal.

The argument expressed is syntactically valid because it is an instance of a valid argument-form.

Syntactic versus Semantic Validity

Consider the argument:
 
   Bill is a brother
   -----
   Bill is a sibling.

Is this little argument valid or invalid?  It depends on what we mean by 'valid.' Intuitively, the argument is valid in the following sense:

D1. An argument is valid if and only if it is impossible that its premise(s) be true and its conclusion false.

(D1) may be glossed by saying that there are no possible circumstances in which the premises are true and the conclusion false. Equivalently, in every possible circumstance in which the premises are true, the conclusion is true.  Since it is impossible that Bill be a brother without his being a sibling, the opening argument is valid by (D1).

(D1), though correct as far as it goes, leaves unspecified the source or ground of a valid argument's validity. This is the philosophically interesting question. What makes a valid argument valid? What is the ground of the impossibility of the premises' being true and the conclusion's being false? One answer is that the source of validity is narrowly logical or purely syntactic: the validity of a valid argument derives from its instantiation of valid argument-forms.

Now it is obvious that the validity of the above argument does not derive from its logical form. The logical form is

   Fa
   -----
   Ga

where 'a' is an arbitrary individual constant and 'F' an arbitrary predicate constant. The above argument-form is invalid since it is easy to interpret the place-holders so as to make the premise true and the conclusion false: let 'a' stand for Al, 'F' for fat and 'G' for gay.

Valid arguments are either syntactically valid or semantically valid.  The opening argument is not syntactically valid but it is semantically valid.

D2. An argument is syntactically valid iff it is narrowly-logically impossible that there be an  argument of that form having true premises and a false conclusion.

According to (D2), a valid argument inherits its validity from the validity of its form, or logical syntax. So on (D2) it is primarily argument-forms that are valid or invalid; arguments are valid or invalid only in virtue of their instantiation of valid or invalid argument-forms. (D2) is thus a specification of the generic (D1).

But there is a second specification of (D1) according to which  validity/invalidity has its source in the constituent propositions of the arguments themselves and so depends on their extra-syntactic content:

D3. An argument is extra-syntactically valid iff (i) it is impossible  that its premises be true and its conclusion false;  (ii) this impossibility is grounded neither in any contingent matter of fact nor
in formal logic proper, but in some necessary connection between the senses or the referents of the extra-logical terms of the argument.

A specification of (D3) is

D4. An argument is semantically valid iff (i) if it is impossible that its premises be true and its conclusion false; and (ii) this impossibility is grounded in the senses of the extra-logical terms of
the argument.

Thus to explain the semantic validity of the opening argument we can say that the sense of 'brother' includes the sense of 'sibling.' There is a necessary connection between the two senses, one that does not rest  on any contingent matter of fact and is also not mediated by any purely formal law of logic. Note that logic allows (does not rule out) a brother who is not a sibling. Logic would rule out a non-sibling brother only if 'x is F & x is not G' had only false substitution-instances -- which is not the case. To put it another way, a brother that is not a sibling is a narrowly-logical possibility. But it is not a broadly-logical possibility due to the necesssary connection of the two senses.

So it looks as if analytic entailments like Bill is a brother, ergo, Bill is a sibling show that subsumability under purely formal logical laws is not necessary for (generically) valid inference. Sufficient, but not necessary. Analytic   entailments appear to be counterexamples to the thesis that inferences in natural language can be validated only by subsumption under logical laws.

One might wonder  what philosophers typically have in mind when they speak of validity. I would say that most philosophers today have in mind (D1) as specified by (D2). Only a minority have in mind (D3) and its specification (D4).  I could easily be wrong about that.  Is there a sociologist of philosophers in the house?

Consider the Quineans and all who reject the analytic/synthetic distinction. They of course will have no truck with analytic  entailments and talk of semantic validity. Carnapians, on the other hand, will uphold the analytic/synthetic distinction but validate all  entailments in the standard (derivational) way by importing all analytic truths as meaning postulates into the widened category of L-truths.

Along broadly Carnapian lines one could argue that the above argument is an enthymeme which when spelled out is

   Every brother is a sibling
   Bill is a brother
   -----
   Bill is a sibling.

Since this expanded argument is syntactically valid, the original argument -- construed as an enthymeme -- is also syntactically valid. When I say that it is syntactically valid I just mean that the
conclusion can be derived from the premises using the resources of standard logic, i.e. the Frege-inspired predicate calculus one finds in logic textbooks such as I. Copi's Symbolic Logic. In the above example, one uses two inference rules, Universal Instantiation and Modus Ponens, to derive the conclusion.

If this is right, then the source of the expanded argument's validity is not in a necessary connection between the senses of the 'brother' and 'sibling' but in logical laws. The question, however, was whether the opening argument as stated is valid or invaid. I say it is semantically, but not syntactically valid.

A juicier example is the Cartesian cogito:

I think
-----

I am. 

This looks to be  semantically valid and thus valid without the need of an auxiliary premise to mediate the inferential  transition from premise to conclusion.  It is valid absent an auxiliary major premise such as 'Whatever thinks, is.'

Validity and Anaphora

The following argument appears valid:

Some deity is called 'Zeus.'
Zeus is wise.
Therefore, some deity called 'Zeus' is wise. (D. E. Buckner, Reference and Identity, 118)

Now if an argument is valid, it is valid in virtue of its logical form.  What is the logical form of the above argument? The following argument-form, Buckner correctly states, is invalid:

Ex Fx
Ga
Ex (Fx & Gx)

So if the form just depicted is the only available form of the original argument, then the validity of the argument cannot be simply a matter of logical form. And this is what Buckner concludes: "It is clearly the anaphoric connection between the premisses that makes the argument valid, but no such connection exists in the formalized version of the argument. "(119)

Buckner seems to be arguing as follows:

a) The original argument is valid. 

b) The only form it could possibly have is the one depicted above.

c) The argument-form depicted is plainly invalid.

Therefore

d) The validity of the original argument cannot be due to its logical form, but must be due to the anaphoric connection between its premises.

I do not find this argument rationally compelling. (b) is rejectable.  I suggest that the original argument is an enthymeme the logical form of which is the following:

1) For some x, x is called 'a.'
2) For any x, if x is called 'a,' then x =a.
3) a is G.
Therefore
4) For some x, (x is called 'a' and x is G).

Logical Form, Equivocation, and Propositions

A re-post with minor edits and additions from 4 September 2017.

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

Ed Buckner wants to re-fight old battles. I'm game. The following post of his, reproduced verbatim, just appeared at Dale Tuggy's site:

The concept of logical form is essential to any discussion of identity, and hence to any discussion of the Trinity. Here is a puzzle I have been discussing with the famous Bill Vallicella for many years.

(Argument 1) ‘Cicero is a Roman, therefore Cicero is a Roman’

(Argument 2) ‘Cicero is a Roman, therefore Tully is a Roman’

My puzzle [is] that the first argument is clearly not valid if the first ‘Cicero’ means the Roman, the second the American town, yet the argument seems to instantiate a valid form. Bill objects that if there is equivocation, then the argument really has the form ‘a is F, therefore b is F’, which fails to instantiate a valid form.

I then ask what is the form of. Clearly not of the sentences, since the sentences do not include the meaning or the proposition. Is it the form of the proposition expressed by the sentences? But then we have the problem of the second argument, where both ‘Cicero’ and ‘Tully’ mean the same man. Then the man is contained in both propositions, and if the form is of the proposition, the argument has the true form ‘a is F, so a is F’, which is valid. But I think no one would agree that the second argument is valid.

So logical form does not belong to the sentences, nor to the propositions expressed by them. So what is it the form of?

My answer is that the logical form of the argument is the form of the Fregean propositions expressed by the sentences that make up the argument. Let me explain.

I agree with Ed that logical form is not the form of an array of sentence-tokens. It is rather the form of an array of propositions expressed by the sentences. (To be painfully precise: it is the form of an array of propositions expressed by the assertive utterance, and thus the tokening, of a series of sentence-types by a speaker or thinker on a given occasion. A sentence-token buried in a book does not express anything by itself!)

To solve Ed's puzzle we need to distinguish three views of propositions: the Aristotelian, the Fregean, and the Russellian. This would be a good topic for an extended post. Here I will be brief.  Brevity is the soul of blog.

An Aristotelian proposition is an assertively uttered meaningful sentence in the indicative mood that expresses a complete thought.  What makes such a proposition 'Aristotelian' as opposed to 'Platonic' is that the meaning of the sentence is not something that can subsist on its own apart from the assertive tokening of the sentence.  The meaning of the sentence depends on its being expressed, whether in overt speech or in thought, by someone. And this expression must be thoughtfully done and not mindlessly like a parrot or a voice synthesizer. If there were no minds there would be no Aristotelian propositions. And if there were no languages there would be no Aristotelian propositions. In this sense, Aristotelian propositions are linguistic entities.

In brief: An Aristotelian proposition is just a declarative sentence in use together with its dependent sense or meaning. Suppose I write a declarative sentence on a piece of paper. The Aristotelian proposition is not the string of physical marks on the paper, nor it is the producing of the marks; it is the marks as produced by a minded organism on a particular occasion together with the meaning those marks embody where meaning is first in the mind and only then embodied in the marks.

A Fregean proposition is a nonlinguistic entity that subsists independently of minds and language. It is the sense (Sinn) of a declarative sentence (Satz) from which indexical elements have been extruded. For example, 'I am blogging'  does not express a Fregean proposition because of the indexical 'I' and because of the present tense of the verb phrase.  But 'BV blogs at 10:50 AM PST on 4 September 2017' expresses a Fregean proposition.

Fregean senses are extralinguistic and extramental 'abstract' or 'Platonic' items. They are not in time or space even when the objects they are about are in time and space. This is what makes Fregean propositions 'Platonic' rather than 'Aristotelian.' Fregean propositions are the primary truth-bearers; the sentences that express them are derivatively true or false.  Likewise with the judgments whose content they are.

A Russellian proposition is a blurry, hybrid entity that combines some of the features of a Fregean truth-bearer and some of the features of a truth-maker. A Russellian proposition does not reside at the level of sense (Sinn) but at the level of reference (Bedeutung).  It is out there in the (natural) world. It is what some of us call a fact or 'concrete fact' (as in my existence book) and others, e.g. D. M. Armstrong,  a state of affairs.  

Now consider a singular sentence such as 'Ed is happy.'  For present purposes, the crucial difference between a Fregean proposition and a Russellian proposition is that, on the Fregean view, the subject constituent of Ed is happy is not Ed himself with skin and hair, but an abstract surrogate that represents him in the Fregean proposition, whereas in the Russellian proposition Ed himself is a constituent of the proposition!  

We needn't consider why so many distinguished philosophers have opted for this (monstrous) view.  But this is the view that seems to have Ed in its grip and that powers his puzzle above.

If we take the relatively saner (but nonetheless problematic) view that propositions are Fregean in nature, then the puzzle is easily solved.

Ed asks: What is the logical form the form of?  He maintains, rightly, that it cannot be the form of an array of sentences. So it must be the form of an array of propositions. Right again. But then he falls into puzzlement: 

. . . ‘Cicero’ and ‘Tully’ mean the same man. Then the man is contained in both propositions, and if the form is of the proposition, the argument has the true form ‘a is F, so a is F’, which is valid.

The puzzlement disappears if we reject the Russsellian theory of propositions. A man cannot be contained in a proposition, and so it cannot be the same man in both propositions.

‘Cicero is a Roman, therefore Tully is a Roman’ is plainly invalid. Its form is: Rc, ergo Rt, which is an invalid form. If we adopt  either an Aristotelian or a Fregean view of propositions we will not be tempted to think otherwise.

‘Cicero is a Roman, therefore Cicero is a Roman’ is plainly valid. ‘Cicero is a Roman, therefore Tully is a Roman’ is plainly invalid. The logical forms are different! If, on a Russellian theory of propositions, the forms are the same, then so much the worse for a Russellian theory of propositions!

Circular Definitions, Arguments, and Explanations

In the course of our discursive operations we often encounter circularity.  Clarity will be served if we distinguish different types of circularity.  I count three types.  We could label them definitional, argumentative, and explanatory.

A.  The life of the mind often includes the framing of definitions.  Now one constraint on a good definition is that it not be circular.  A circular definition is one in which the term to be defined (the definiendum) or a cognate thereof occurs in the defining phrase (the definiens).  'A triangle is a plane figure having a triangular shape,' though plainly true, is circular.  'The extension of a term is the set of items to which the term applies' is an example of a non-circular definition. 

Ibram X. Kendi, the race 'theorist' currently much-loved by the 'woke,' was recently asked to define 'racism.' He came out with this brilliancy:  “A collection of racist policies that lead to racial inequity that are substantiated by racist ideas." Video here.

B.  Sometimes we argue.  We attempt to support a proposition p by adducing other propositions as reasons for accepting p.  Now one constraint on a good argument is that it not be circular.  A circular argument in is one in which the conclusion appears among the premises, sometimes nakedly, other times clothed for decency's sake  in different verbal dress.  Supply your own examples.

C.  Sometimes we explain.  What is it for an individual x to exist?  Suppose you say that for x to exist is for some property to be instantiated.  One variation on this theme is to say that for Socrates to exist is for the haecceity property Socrateity to be instantiated.  This counts as a metaphysical explanation, and a circular one to boot.  For if Socrateity is instantiated, then it is is instantiated by Socrates who must exist to stand in the instantiation relation.  The account moves in a circle, an explanatory circle of embarrassingly short diameter.

Suppose someone says that for x to exist is for x to be identical to something or other.  They could mean this merely as an equivalence, in which case I have no objection.  But if they are shooting for a explanation of existence in terms of identity-with-something-or-other, then they move in an explanatory circle. For if x exists in virtue of its identity with some y, then y must exist, and you have moved in an explanatory circle.

Some philosophers argue that philosophers ought not be in the business of explanation.  I beg to differ.  But that is a large metaphilosophical topic unto itself.

A Reader Asks about Existence and Instantiation

My responses are in blue.

Hello, Dr. Vallicella. I am a reader of your blog. I just read your article "Existence: Two Dogmas of Analysis" in Neo-Aristotelian Perspectives in Metaphysics (eds. Novotny and Novak, Routledge, 2014, pp. 45-75 , and I thought it was fantastic. I will have to read it again at some point. There were some parts in it that I found very interesting, and I was hoping I could ask you about. I want to focus on what you said in section 6.6, page 57. You write: 

 

"It is clear that “Unicorns do not exist” cannot be about unicorns: There are none. So it is reasonably analysed in terms of “ The concept unicorn is not instantiated”. But then the concept must exist, and its existence cannot be its being instantiated." 

 

The question I wanted to ask you was specifically about the final part, "But then the concept must exist, and its existence cannot be its being instantiated". I will try to keep the questions as brief as possible, 

 

The thin theorist might not identify the existence of the concept of a unicorn with its being instantiated, but with the concept of the concept of the unicorn being instantiated, and so on . . .

 

1) If it were possible that there be an infinite number of concepts, would there be any problem with this view?

 

BV:  An infinite regress would arise.

 

2) Clearly, we have a regress here, but is it vicious?

 

BV: Yes, because there would be no explanation of  the existence of the first concept in the infinite series. You might reply by saying that the series is actually, as opposed to potentially, infinite.  If so, then every concept in the series would have an explanation of its existence.  To which my response would be:   what explains the existence of the entire actually infinite series of concepts?

 

(An analogous situation. Suppose the universe is a beginningless actual infinity of continuum-many states with each state caused by earlier ones. If so, every state would have a causal explanation. But if every state of the universe has a causal explanation, then one might plausibly suppose that the universe has a causal explanation, one that is internal to it. Some people have maintained this with an eye toward ruling out the need for a transcendent explainer such as God. "There is no need for God because a universe with an actually infinite past has the resources to explain itself."  My objection would be that this account leaves us with no explanation of why the entire series of states exists in the first place.  Given that the entire series is modally contingent, and thus possibly such as not to exist at all, then any explanation of it, assuming that there is an explanation of it, could only be external or transcendent. Now back to the main thread.)

 

One might also question whether the concept regress could even get started. You want to say that the concept unicorn exists in virtue of its being an instance of the concept concept unicorn. But these two concepts have exactly the same content. How then do they differ? The concept unicorn is an instance of the concept concept, but I fail to see any difference between the concept unicorn and the concept concept unicorn.

 

3) The overall worry is that if we define x's existence in terms of instantiation, and then ask 'what are "x's"', we say things in existence, and, this is circular, but, since we are simply dealing with the analysis of terms, aren't we only dealing with semantic circularity? I am not sure that there is any problem with this sort of circularity (if there is a problem, it would be with the informativeness with the analysis rather than the accuracy).

 

BV: But we are not merely dealing with the analysis of terms; we are seeking to understand what it is for an individual to exist, given that the existence of a thing is extra-linguistic.   Let's keep in mind what the question is.  The question is whether an adequate theory of existence could treat '. . . exist(s)' as a second-level or second-order predicate only, that is, a predicate of concepts, properties, propositional functions,  descriptions (definite or indefinite), or cognate items. That is the Frege-Russell theory that I have in my sights in the portion of text to which my reader refers.

 

Granted, it is  true that Fs exist iff the concept F is instantiated.  For example, it is  true that cats exist iff the concept cat is instantiated. (This assumes that there is the concept cat, which is certainly true in our world if not in all possible worlds: it depends on what we take concepts to be.) But the right-hand-side (RHS) of the biconditional merely specifies a truth-condition on the semantic plane: it does not take us beyond or beneath that plane to the plane of extra-linguistic reality.  The truth of the LHS requires an ontological ground, a truth-maker, not a truth-condition. For consider: if the concept cat is instantiated, then, since it is a first-order concept, and relational as opposed to monadic, it is instantiated by one or more individuals. Individuals by definition are impredicable and uninstantiable. My cat Max Black, for example, is categorially unfit to have any instances, and you can't predicate him of anything. The little rascal is unrepeatable and impredicable.

 

Now either the instantiating individuals exist or they do not. If they do not, then the truth of the biconditional above is not preserved. But if they do exist, then the sense in which the instances exist is toto caelo different from the sense specified by 'is instantiated.' To repeat, by definition, individuals cannot be instantiated; therefore, the existence of an individual --call it singular existence --  cannot be explicated in terms of instantiation.

 

The instantiation account of existence either changes the subject from singular existence to general existence (instantiation) or else it moves in a circle of embarrassingly short diameter.  We want to know what it is for individuals to exist, and we are told that for individuals to exist is for first-level concepts to be instantiated; but for these concepts to be instantiated, their instances must exist singularly and thus in a sense that cannot be explicated in terms of instantiation. To put it another way: the account presupposes what it is trying to get rid of. It wants to reduce singular existence to general existence, thereby eliminating singular existence, but it ends up presupposing singular existence. If you tell me that the instances neither exist nor do not exist and that this contrast first arises at the level of concepts , then I will point out that you are thereby committed to Meinongian objects, to pure Sosein without Dasein.

 

The circularity I allege is the circularity of ontological/metaphysical explanation.  Is 'Tom exists' true because Tom exists, or does Tom exist because 'Tom exists' is true?  If this question makes sense to you and you respond by opting for  the former, then you understand metaphysical explanation.  It is an explanation that is neither empirical nor narrowly logical. Somewhat murky it might be, but nonetheless indispensable for metaphysics.  Similarly with the question: does Tom exist because some concept C is instantiated, or is C instantiated because Tom exists? The question makes sense and the answer is the latter.

 

I want to note that these are questions someone asked me about this view, and I wasn't sure how to respond, even though I ultimately do agree with your analysis of the thin theory. For the third problem, I would have said that that sort of response would merely ignore the fact that the question 'what is existence?' has ontological consequences, and is not merely a question of semantics. [Right!] If that is all we are concerned with (semantics), then we are concerned with something different than what most classical philosophers are concerned with when they are talking about the question 'what is existence?', which is the ontological aspect of that question, and as such, the circularity issue is a real problem. [You got it!]

 

BV: The problem with Frege, Russell, Quine, van Inwagen, and the rest of the 'thin  crew' is that they try to reduce existence to a merely logical topic. An opposite or at least different mistake is made by the phenomenologists who (most of them, not all of them) try to reduce existence to a phenomenological topic.  Heidegger, near the beginning of Sein und Zeit, opines that "Ontology is only possible as phenomenology." 

 

So I got me a two-front war on my hands: against the nuts-and-bolts analysts to the West and against the febrile phenomenologists to the East.

 

Another Thought on Psychologism in Logic

Logic is prescriptive and proscriptive.  Logic prescribes how we ought to think if we would arrive at truth. It also proscribes those ways of thinking that lead to error.  But 'ought' implies 'can.' How we ought to think must be really possible, indeed really possible for us, where what is really possible for us is grounded in how we actually and contingently are. A real possibility of thinking this way or that must be based in actual abilities, actual abilities of real minds in the real order.  The logically normative must be psychologically implementable.  The ideal patterns residing in the ὑπερουράνιος τόπος of Plato must be realizable in enmattered minds.

There look to be the makings here of an argument for a defensible psychologism.  (Logic cannot be a part of empirical psychology, but how could it have nothing to do with the latter?)

The above train of thought is from a couple of years ago.  (Journal vol. XXXIII, pp. 22-23, entry of 4 January 2019) Now I find the following in the Martin Kusch SEP article on psychologism, referenced in the immediately preceding entry:

1. Normative-prescriptive disciplines — disciplines that tell us what we ought to do — must be based upon descriptive-explanatory sciences.
2. Logic is a normative-prescriptive discipline concerning human thinking.
3. There is only one science which qualifies as constituting the descriptive-explanatory foundation for logic: empirical psychology.
Ergo, logic must be based upon psychology.

The above is the second of five patterns of psychologistic reasoning that Kusch distinguishes.  He attributes it to Wilhelm Wundt.  My thought above runs along parallel rails.

Logic, prescribing as it does how we OUGHT to think, by the same stroke prescribes how we ought to THINK. The abstract patterns definitive of the oughts and ought nots of inference may reside in Plato's timeless heaven, but thinking and thus judging is in time and takes time.  Inference, in particular, takes time. Its analog up yonder is implication. And so the abstractly logical must touch ground in the matter of minds in time.  An abstract entity can't think.

But a concrete hunk of intracranial meat can't think either. And meat can't mean. Minds mean. If we were just meatheads we couldn't think or mean. Thinking is a psychic function.  Arguably, though, it is not the psyche as objectified and manifest to inner sense that thinks but the psyche as subject, the psyche as pre-objective, pre-mundane, and thus transcendental.  But from Descartes on it has proven to be a bear of a task to get a good solid grip on the transcendental. Husserl struggled with it life-long and  yet couldn't drag it out of the dreck into the clear light of day. And where the great Husserl failed we lesser luminaries and flickering lights are even less likely to succeed.

Must we regress to the spiritual? But how can we get a grip on it without objectifying it?  We cannot help but reify, but the Cogitans is not a res, not  spiritual substance.

The noetic as such embraces the logical, the psychological, the transcendental and the spiritual. 

On that gnomic note I end this meditation.

Related: Martin Kusch, Psychologism (from Ralph Dumain's Autodidact Project)

Has Any Philosophical Problem Been Solved? The case of psychologism in logic.

For Cyrus

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

A reader is skeptical of my solubility skepticism. He adduces the problem of psychologism in logic which, he suggests, has been definitively settled in favor of the anti-psychologizers.  Here, then, is a problem that supposedly has been solved. There is progress in philosophy after all. My reader is joined by Robert Spaemann who, in his Persons, tr. O'Donovan, Oxford 2006, writes:

The refutation of psychologism in logic, with which Husserl and Frege are associated, is among the very few philosophical achievements that have brought an existing debate to a decisive close. (54)

Would that it were so! But alas it is not.  The existing debate rages on. Having been brought up on Husserl, and influenced by Frege, I was for a long time an opponent of psychologism in logic, and thought the issue resolved. Time to revaluate! Here is a post from August 2004 from my first blog:

ARE THE LAWS OF LOGIC EMPIRICAL GENERALIZATIONS?

Someone on a discussion list recently resurrected the old idea of John Stuart Mill and others that the laws of logic are empirical generalizations from what we do and do not perceive. Thus we never perceive rain and its absence in the same place and at the same time. The temptation is to construe such logic laws as the Law of Non-Contradiction -- ~(p & ~p) -- as generalizations from psychological facts like these. If this is right, then logical laws lack the a priori character and epistemic ‘dignity’ that some of us are wont to see in them. They rest on psychological facts that might have been otherwise.

But now consider this reductio ad absurdum:

1. The laws of logic are empirical generalizations. (Assumption for reductio)
2. Empirical generalizations, if true, are merely contingently true. (By definition of ‘empirical generalization’: empirical generalizations record what happens to be the case, but might not have been the case.) Therefore,
3. The laws of logic, if true, are merely contingently true. (From 1 and 2)
4. If proposition p is contingently true, then it is possible that p be false. (Def. of ‘contingently true.’)Therefore,
5. The laws of logic, if true, are possibly false. (From 3 and 4)Therefore,
6. LNC is possibly false: there are logically possible worlds in which ‘p&~p’ is true. (From 5 and the fact that LNC is a law of logic.)
7. But (6) is absurd (self-contradictory): it amounts to saying that it is logically possible that the very criterion of logical possibility, namely LNC, be false. Corollary: if laws of logic were empirical generalizations, we would be incapable of defining ‘empirical generalization’: this definition requires the notion of what is the case but (logically) might not have been the case.

The above is a good, but not a compelling, argument. For it presupposes the distinction between necessary and contingent propositions.  Is that distinction objectively self-evident? Martin Kusch, Psychologism, Stanford Encyclopedia of Philosophy:

Massey also invokes the stronger form of the claim that logical truths are not necessary (1991, 188). According to this criticism, the very notion of necessity which is presupposed in calling logical laws ‘necessary truths’, is beset with difficulties. The argument leading to this conclusion was developed in a series of well-known papers by Quine. Quine argued that the notions of analyticity, necessity and aprioricity stand or fall together and that the traditional distinction between analytic and synthetic truths is relative rather than absolute. But once this distinction becomes relative, necessity and aprioricity go by the board (Quine 1951, Engel 1991, 268–70). Massey summarises the implications of Quine’s arguments succinctly:

If we reject the concept of necessity … we also forego the concept of contingency. If it makes no sense to say that the truths of mathematics are necessary, it makes no better sense to say that those of psychology or any other so-called empirical science are contingent. But if we may not employ necessity and contingency to demarcate the deliverances of the empirical sciences from those of the formal sciences, how are we to distinguish them in any philosophically interesting way? (1991, 188).

Now I don't much cotton to Quine, but he is no slouch of a logician!  And he is certainly a looming presence in 20th century American philosophy.  So on the basis of his dissent alone, we ought to agree that the psychologism problem has not been solved.   I am assuming that a problem hasn't been solved unless it has been solved to the satisfaction of all competent practitioners.  It hasn't been solved until the debate about it has been brought to a decisive close. Kusch gives several reasons in addition to the one cited above why this is not the case with respect to the psychologism debate. 

First and Second Intentions: Buckner on Zabarella, Kant, Frege, and Wittgenstein

The following two quotations are from the Facebook Medieval Logic forum.

 

Giacomo Zabarella (1533 – 1589). “Now first intentions are names immediately signifying realities by means of a concept in the soul, for instance, animal and human being, or those concepts of which these names are signs. But second intentions are other names imposed on these names, for instance, genus, species, name, verb, proposition, syllogism, and others of that sort, or the concepts themselves that are signified through these names.”

Edward Buckner comments:

 

The distinction [between first and second intentions] is rediscovered in various ways by subsequent philosophers. I see something like it in Kant’s distinction between concepts which are ‘pure’, and concepts which are not, in Frege’s distinction between concept and object words, and possibly in Wittgenstein, who viewed logic as a sort of scaffolding through which we conceive the world, a scaffolding which cannot be described in words. (4121 “Propositions cannot represent logical form: it is mirrored in them”). If I understand Wittgenstein, it is that there can be no science of second intentions in Zabarella’s sense, for such a science would be a futile attempt to represent logical form. The Tractatus of course is such an attempt, which is why he says (654) his propositions, while nonsensical, can be used as steps [in a ladder] to climb up beyond them, then throw away the ladder.

 

Kant

 

I think Ed is wrong above about Kant.  For Kant, the pure is the opposite of the empirical. Every concept is either pure or empirical and no concept is both. A pure concept is one that is not drawn from experience, ein solcher der nicht von der Erfahrung abgezogen ist, but originates from the understanding in respect of both form and content, sondern auch dem Inhalte nach aus dem Verstande entspringt. The form of all concepts, including pure concepts, arises from reflexion Reflexion, and thus from the understanding. Empirical concepts arise from the senses, entspringen aus den Sinnen,  by comparison of the objects of experience. Their content comes from the senses, and their form of universality, Form der Allgemeinheit, alone from the understanding.

 

If Buckner is telling us that Kant's pure-empirical distinction runs parallel to Zabarella's first intention-second intention distinction, then that can't be right. For Zabarella's animal and human being, which are first intentions for him, count as empirical concepts for Kant. 

 

Any comparison of Zabarella (1533-1589) the Aristotelian and Kant is bound to be fraught with difficulty because of the transcendental-subjective turn of modern philosophy commencing with Descartes (1596-1650).  For Aristotle, the categories are categories of a real world independent of  our understanding; for Kant, the categories are precisely categories of the understanding (Verstandeskategorien) grounded in the understanding both in their form and in their content.  The categories of Aristotle are thus objective, categories belonging to a world to be understood, and not subjective, categories whereby a mind understands the world.

 

Pure Concepts of Reason as Limit Concepts

 

Kant also speaks in his Logic and elsewhere of Ideas which are pure concepts of reason, Vernunft, and not of understanding, Verstand. Die Idee ist ein Vernunftbegriff deren Gegenstand gar nicht in der Erfahrug kann angetroffen werden. (Logik, sec. 3)  The objects of these pure concepts of reason cannot be known by us because our form of intuition, Anschauung, is sensible, not intellectual. We can know only phenomena, not noumena. Among these Ideas, which are plainly limit concepts, are God, the soul, the world-whole, and freedom. And they are not merely negative limit concepts. Free will, for example, is objectively real despite its not being obejctively knowable. But more on this later.

 

Frege

 

I also think Ed is wrong about Frege.  But I'll leave that for later. Wifey wants to go out to dinner. Philosophy before bread, but happy wife, happy life!

 

As for Wittgenstein, I think Ed is on the right track. 

 

 

How Much Logic Do I Need?

A reader who reports that his main interest is in contemporary metaphysics inquires:

Should I learn as much logic as humanly possible during my PhD? Or should I learn only what I need along the way? I have a basic grasp of symbolic and predicate logic, but little meta-logic.

First of all, it makes no sense to oppose symbolic to predicate logic.  Modern symbolic logic includes both propositional logic and predicate logic.

Second, learn what you need as you go along.  For example, existence is one of the central topics in metaphysica generalis. To work on this topic in an informed way you have to understand the modern quantificational treatment of existence in mathematical logic. 

Here is the minimum required for doing metaphysics. First, a thorough grounding in traditional formal logic including the Aristotelian syllogistic. Second, modern symbolic logic including the propositional calculus and first-order predicate logic with identity.  Third, some familiarity with axiomatics and the concepts of metalogic including consistency and completeness of axiom systems.  Fourth, axiomatic set theory. Fifth, some (alethic) modal logic both propositional and quantified.

The best way to master these subjects, or at least the first two mentioned, is by teaching them to undergraduates.  

Truth and Falsity from a Deflationary Point of View

The following equivalence is taken by many to support the deflationary thesis that truth has no substantive nature, a nature that could justify a substantive theory along correspondentist, or coherentist, or pragmatic,  or other lines.  For example, someone who maintains that truth is rational acceptability at the ideal (Peircean) limit of inquiry is advancing a substantive theory of truth that purports to nail down the nature of truth.  Here is the equivalence:

1)  <p> is true iff p.

The angle brackets surrounding a declarative sentence make of it a name of the proposition the sentence expresses. For example, <snow is white> --  the proposition that snow is white -- is true iff snow is white. (1) suggests that the predicate ' ___ is true' does not express a substantive property.  We can dispense with the predicate and say what we want without it. It suggests that there is no such legitimate metaphysical question as: What is the nature of truth?  Having gotten rid of truth, can we get rid of falsity as well?

A false proposition is one that is not true.  This suggests that 'false,' as a predicate applicable to propositions and truth-bearers generally, is definable in terms of 'true' and 'not.' Perhaps as follows:

2) <p> is false iff <p> is not true.

From (2) we may infer

2*) <p> is false iff ~(<p> is true)

and then, given (1),

2**) <p> is false iff ~p.

This suggests that if we are given the notions of 'proposition' and 'negation,' we can dispense with the supposed properties of truth and falsity. (1) shows us how to dispense with 'true' and (2**) show us how to dispense with 'false.'

But we hit a snag when we ask what 'not' means.  Now the standard way to explain the logical constants employs truth tables. Here is the truth table for the logician's 'not' which is symbolized by the tilde, '~'.

But now we see that our explanation is circular. We set out to explain the meaning of 'false' in terms of 'not' only to find that 'not' cannot be explained except in terms of 'false.' We have moved in a circle.

The Ostrich has a response to this:

. . . we can define negation without reaching for the notions of truth and falsity. Assume that the notion of ‘all possible situations’ is coherent, and suppose it is coherent for any proposition ‘p’ to map onto a subset of that set. Then ‘not p’ maps onto the complement. The question is whether the very idea of a complement of a subset covertly appeals to the concept of negation. But then that suggests that negation is a primitive indefinable concept, rather than what you are claiming (namely that it is truth and falsity which are primitive).

So let's assume that there is a set S of possible worlds,and that every proposition (except impossible propositions)  maps onto to an improper or a proper subset of S. The necessary propositions map onto the improper subset of S, namely S itself. Each contingent proposition p maps onto a proper subset of S, but a different proper subset for different propositions. If so, ~p maps onto the complement of the proper subset that p maps onto.  And let's assume that negation can be understood in terms of complementation.

The most obvious problem with the Ostrich response is that it relies on the notion of a proposition. But this notion cannot be understood apart from the notions of truth and falsity.  Propositions are standardly introduced as the primary vehicles of the truth-values. They alone are the items appropriately characterizable as either true or false. Therefore, to understand what a proposition is one must have an antecedent grasp of the difference between truth and falsity. 

To understand the operation of negation we have to understand that upon which negation operates, namely, propositions, and to understand propositions, we need to understand truth and falsity.

A second problem is this. Suppose contingent p maps onto proper subset T of S.  Why that mapping rather than some other? Because T is the set of situations or worlds in which p is true . . . . The circularity again rears its ugly head.

The Ostrich, being a nominalist, might try to dispense with propositions in favor of declarative sentences. But when we learned our grammar back in grammar school we learned that a declarative sentence is one that expresses a complete thought, and a complete thought is -- wait for it -- a proposition or what Frege calls ein Gedanke: not a thinking, but the accusative of a thinking. 

Truth and falsity resist elimination.

Excluded Middle, Presentism, Truth-Maker: An Aporetic Triad

Suppose we acquiesce in the conflation of Excluded Middle and Bivalence.  The conflation is not unreasonable.  Now try this trio on for size:

Excluded Middle: Every proposition is either true, or if not true, then false.
Presentism: Only what exists at present, exists.
Truth-Maker: Every contingent truth has a truth-maker.

The limbs of the triad are individually plausible but collectively inconsistent. Why inconsistent?

I will die. This future-tensed sentence is true now. It is true that I will die. Is there something existing at present that could serve as truth-maker? Arguably yes, my being mortal. I am now mortal, and my present mortality suffices for the truth of 'I will die.' Something similar holds for my coat. It is true now that it will cease to exist.  While it is inevitable that I will die and that my coat will cease to exist, it is not inevitable that my coat will be burnt up (wholly consumed by fire).  For there are other ways for it to cease to exist, by being cut to pieces, for example, or by just wearing out.

By 'future contingent,' I mean a presently true future-tensed contingent proposition.  The following seems to be a clear example: BV's coat will sometime in the future cease to exist by being wholly consumed in a fire. To save keystrokes: My coat will be burnt up.

By Excluded Middle, either my coat will be burnt up or my coat will not be burnt up. One of these propositions must be true, and whichever one it is, it is true now. Suppose it is true now that my  coat will be burnt up. There  is nothing existing at present that could serve as truth-maker for this contingent truth.  And given Presentism, there is nothing existing at all that could serve as truth-maker.  For on Presentism, only what exists now, exists full stop.  The first two limbs, taken in conjunction, entail the negation of the third, Truth-Maker.  The triad is therefore inconsistent.

So one of the limbs must be rejected. Which one?

An Objection

You say that nothing that now exists could serve as the truth-maker of the presently true future-tensed  contingent proposition BV's coat will be burnt up. I disagree.  If determinism is true, then the present state of the world together with the laws of nature necessitates every later state.   Assuming the truth of the proposition in question, there is a later state of the world in which your shabby coat is burnt up. The truth-maker of the future contingent proposition would then be the present state of the world plus the laws of nature.  So if determinism is true, your triad is consistent, contrary to what you maintain, and we will not be forced to give up one of the very plausible constituent propositions.

Question: Is there a plausible reply to this objection? No. I'll explain why later.

Excluded Middle, Bivalence, and Disquotation

LEM: For every  p, p v ~p.

BV: Every proposition is either true or false.

These principles are obviously not identical.  Excluded Middle is syntactic principle, a law of logic, whereas Bivalence is a semantic principle. The first says nothing about truth or falsity. The second does. (See Michael Dummett, Truth and Other Enigmas, Harvard UP, 2nd ed. , 1980, p. xix; Paul Horwich, Truth, Oxford UP, 2nd ed., 1998, p. 79) Though not identical they might nonetheless be logically equivalent.  Two propositions are logically equivalent iff each entails the other.  Entailment is the necessitation of material implication. Can it be shown that (LEM) and (BV)  entail each other? Let's see.

The logical equivalence of the two principles can be demonstrated if we assume the disquotational schema:

DS: p is true iff p.

For example, snow is white is true iff snow is white. Or, if you insist, 'snow is white' is true iff snow is white. In the latter forrmulation, which does not involve reference to propositions, the truth predicate  -- 'is true' -- is merely a device of disquotation or of semantic descent. On either formulation, 'is true' adds no sentential/propositional content:  the sentential/propositional content is the same on both sides of the biconditional.  The content of my assertion is exactly the same whether I assert that snow is white or I assert that snow is white is true.  But if (DS) is granted, then so is:

DS-F: p is false iff ~p.

For example, snow is white is false iff ~(snow is white).    

Now if the disquotational schemata exhaust what it is to be true and what it is to be false, then (LEM) and (BV) are logically equivalent.

Given (DS) and (DS-F), we can rewrite (LEM) as

LEM-T: For every p, p is true v p is false.

Now (LEM-T) is simply a restatement of (BV). The principles are therefore logically equivalent given the disquotational schemata. 

But this works only if falsehood can be adequately explained in terms of the merely logical operation of negation.  This will NOT work if negation can only be explained in terms of falsehood.  For then we would enter  an explanatory circle of embarrassingly short diameter. 

Ask yourself: when is one proposition the negation of another? The negation of p is the proposition that is true iff p is false and false iff p is true.  To explain the logico-syntactic notion of negation we have to reach for the semantic notions of truth and falsehood.  But then falsehood cannot be exhaustively understood or reduced to negation.

It is telling that to explain negation and the other logical connectives we use TRUTH tables.  Such explanation is satisfactory.  But it would not be if the redundancy or disappearance or disquotational schemata gave the whole meaning of 'true' and 'false.'  (The point is made by M. Dummett, Truth and Other Enigmas, p. 7)

I take this explanatory circle to show that there is more to truth and falsehood than is captured in the above disquotational schemata.

Conclusion: if one's reason for accepting the logical equivalence of (LEM) and (BV) is (DS) then that is a bad reason.

Are there counterexamples to (DS)?  It seems to fail right-to-left if 'Sherlock Holmes is a detective' is plugged in for 'p' on the RHS of (DS).  Arguably, Holmes is a detective, but it is not true that Holmes is a detective.  For it to be true that Holmes is a detective, 'Holmes' would have to refer to something that exists.  But this requirement is not satisfied in the case of purely fictional items.  I am assuming that veritas sequitur esse, that truth 'follows' or supervenes upon being (existence):

VSE:  There are no true predications about what does not exist.

Since Holmes does not exist, 'Holmes is a detective' appears to express a proposition that is neither true nor false. Likewise for its negation, 'Holmes is not a detective.'  (LEM) is not violated since either Holmes is a detective or Holmes is not a detective. But (BV) is violated since the two Holmes propositions are neither true nor false.

It is worth noting that from 'Only propositions have truth-values' one cannot validly infer 'All propositions have truth-values.'  

Excluded Middle, Bivalence, and Tertium Non Datur

Dave Gudeman comments:

I was surprised to see you distinguishing between bivalence and the LEM. As far as I can tell, in the traditional and most common formulations, they are identical.

Here is the way I understand it.  They are not identical.  Excluded Middle is a law of logic, whereas Bivalence is a semantic principle. (See Michael Dummett, Truth and Other Enigmas, Harvard UP, 2nd ed. , 1980, p. xix; Paul Horwich, Truth, Oxford UP, 2nd ed., 1998, p. 79) If 'p' is a place-holder for a proposition, any proposition, then Excluded Middle is:

LEM. p v ~p.

If 'p' is a propositional variable, and we quantify over propositions, then we have the universal quantification

LEM*. For all p, p v ~p.

It is understood that the wedge in the above formulae signifies exclusive disjunction. Why is that understood? Because both p and not-p is excluded by the Law of Non-Contradiction:

LNC. ~(p & ~p).  

If I may be permitted parenthetically to wax poetic in these aseptic precincts, (LNC) possesses a 'dignity' in excess of that possessed by (LEM). What I mean is that there are some fairly plausible counterexamples to (LEM), but none that are very plausible to (LNC).  Few philosophers are dialetheists; many more accept truth-value gaps.

The laws of logic are purely formal: they abstract from content or meaning. They are syntactic principles. Bivalence, by contrast, is a semantic principle. It goes like this:

BV. Every proposition is either true or false.

Tertium non datur means that a third is not given: there is no third truth value.  (TND) is also a semantic principle:

TND. No proposition is neither true nor false.

So the difference between (LEM) and (BV) is that the first is a syntactic principle and the second a semantic principle. But is this a difference that makes a difference? Is there a conceivable case where (LEM) is true but (BV) false?  I don't know the answers to these questions. Either that or I forgot them.

But if you conflate the two principles,  then you are in good company. W. V. O. Quine, Mathematical Logic, Harvard UP, 8th ed., 1976, p. 51: ". . . the law of excluded middle, which is commonly phrased as saying that every statement is either true or false . . . ."

Atomic Sentences and Syncategorematic Elements

The Ostrich tells me that Frege has no copula. That's not wrong, but there is a nuance that muddies the waters. Suppose Al is fat. The symbolization as Fa suggests the absence of a copula and thus the absence of a syncategorematic element. There appears to be only two categorematic elements, a and F. Well, let's see.

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

According to Fred Sommers (The Logic of Natural Language, Oxford UP, 1982, 166), ". . . one way of saying what an atomic sentence is is to say that it is the kind of sentence that contains only categorematic expressions." Earlier in the same book, Sommers says this:

In Frege, the distinction between subjects and predicates is not due to any difference of syncategorematic elements since the basic subject-predicate propositions are devoid of such elements.  In Frege, the difference between subject and predicate is a primitive difference between two kinds of categorematic expressions. (p. 17)

Examples of categorematic (non-logical) expressions are 'Socrates' and 'mammal.'  Examples of syncategorematic (logical) expressions are 'not,' 'every,' and  'and.'  As 'syn' suggests, the latter expressions are not semantic stand-alones, but have their meaning only together with categorematic expressions.  Sommers puts it this way: "Categorematic expressions apply to things and states of affairs; syncategorematic expressions do not." (164) 

At first I found it perfectly obvious that atomic sentences have only categorematic elements, but now I have doubts.  Consider the atomic sentence  'Al is fat.' It is symbolized thusly: Fa.  'F' is a predicate expression the reference (Bedeutung) of which is a Fregean concept (Begriff) while 'a' is a subject-expression or name the reference of which is a Fregean object (Gegenstand).  Both expressions are categorematic or 'non-logical.'  Neither is syncategorematic.  And there are supposed to be no syncategorematic elements in the sentence:  there is just 'F' and 'a.'

But wait a minute!  What about the immediate juxtaposition of 'F' and 'a' in that order? That juxtaposition is not nothing.  It conveys something.  It conveys that the referent of 'a' falls under the referent of 'F'.  It conveys that the object a instantiates the concept F. I suggest that the juxtaposition of the two signs is a syncategorematic element.  If this is right, then it is false that atomic sentences lack all syncategorematic elements.

Of course, there is no special sign for the immediate juxtaposition of 'F' and 'a' in 'Fa.'  So I grant that there is no syncategorematic element if such an element must have its own separate and isolable sign. But there is no need for a separate sign; the immediate juxtaposition does the trick.  The syncategorematic element is precisely the juxtaposition.

Please note that if there were no syncategorematic element in 'Fa' there would not be any sentence at all.  A sentence is not a list.  The sentence 'Fa' is not the list 'F, a.'  A (declarative) sentence expresses a thought (Gedanke) which is its sense (Sinn).  And it has a reference (Bedeutung), namely a truth value (Wahrheitswert).  No list of words (or of anything else) expresses a thought or has a truth value.  So a sentence is not a list of its constituent words.  A sentence depends on its constituent words, but it is more than them.  It is their unity. 

We here touch upon the ancient problem of the unity of the proposition first descried by the immortal Plato.

So I say there must be a syncategorematic element in 'Fa' if it is to be a sentence.  There is need of a copulative element to tie together subject and predicate.  It follows that, pace Sommers, it is false that atomic sentences are devoid of syntagorematic elements.

Note what I am NOT saying.  I am not saying that the copulative element in a sentence must be a separate sign such as 'is.'  There is no need for the copulative  'is.'  In standard English we say 'The sea is blue' not 'The sea blue.' But in Turkish one can say Deniz mavi and it is correct and intelligible.  My point is not that we need the copulative 'is' as a separate sign but that we need a copulative element which, though it does not refer to anything, yet ties together subject and predicate.  There must be some feature of the atomic sentence that functions as the copulative element, if not immediate juxtaposition then something else such as a font difference or color difference.

At his point I will be reminded that Frege's concepts (Begriffe) are unsaturated (ungesaettigt).  They are 'gappy' or incomplete unlike objects.  The incompleteness of concepts is reflected in the incompleteness of predicate expressions.  Thus '. . . is fat' has a gap in it, a gap fit to accept a name such as 'Al' which has no gap.  We can thus say that for Frege the copula is imported into the predicate.  It might be thought that the gappiness of concepts and predicate expressions obviates the need for a copulative element in the sentence and in the corresponding Thought (Gedanke) or proposition.

But this would be a mistake.  For even if predicate expressions and concepts are unsaturated, there is still a difference between a list and a sentence.  The unsaturatedness of a concept merely means that it combines with an object without the need of a tertium quid.  (If there were a third thing, then Bradley's regress would be up and running.)  But to express that a concept is in fact instantiated by an object requires more than a listing of a concept-word (Begriffswort) and a name.  There is need of a syncategorematical element in the sentence.

So I conclude that if there are any atomic sentences, then they cannot contain only categorematic expressions.

The Ostrich tells me that Frege has no copula. That's not wrong, but there is a nuance that muddies the waters. Suppose Al is fat. The symbolization as Fa suggests the absence of a copula and thus the absence of a syncategorematic element. There appears to be only two categorematic elements, a and F. Well, let's see.

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

According to Fred Sommers (The Logic of Natural Language, Oxford UP, 1982, 166), ". . . one way of saying what an atomic sentence is is to say that it is the kind of sentence that contains only categorematic expressions." Earlier in the same book, Sommers says this:

In Frege, the distinction between subjects and predicates is not due to any difference of syncategorematic elements since the basic subject-predicate propositions are devoid of such elements.  In Frege, the difference between subject and predicate is a primitive difference between two kinds of categorematic expressions. (p. 17)

Examples of categorematic (non-logical) expressions are 'Socrates' and 'mammal.'  Examples of syncategorematic (logical) expressions are 'not,' 'every,' and  'and.'  As 'syn' suggests, the latter expressions are not semantic stand-alones, but have their meaning only together with categorematic expressions.  Sommers puts it this way: "Categorematic expressions apply to things and states of affairs; syncategorematic expressions do not." (164) 

At first I found it perfectly obvious that atomic sentences have only categorematic elements, but now I have doubts.  Consider the atomic sentence  'Al is fat.' It is symbolized thusly: Fa.  'F' is a predicate expression the reference (Bedeutung) of which is a Fregean concept (Begriff) while 'a' is a subject-expression or name the reference of which is a Fregean object (Gegenstand).  Both expressions are categorematic or 'non-logical.'  Neither is syncategorematic.  And there are supposed to be no syncategorematic elements in the sentence:  there is just 'F' and 'a.'

But wait a minute!  What about the immediate juxtaposition of 'F' and 'a' in that order? That juxtaposition is not nothing.  It conveys something.  It conveys that the referent of 'a' falls under the referent of 'F'.  It conveys that the object a instantiates the concept F. I suggest that the juxtaposition of the two signs is a syncategorematic element.  If this is right, then it is false that atomic sentences lack all syncategorematic elements.

Of course, there is no special sign for the immediate juxtaposition of 'F' and 'a' in 'Fa.'  So I grant that there is no syncategorematic element if such an element must have its own separate and isolable sign. But there is no need for a separate sign; the immediate juxtaposition does the trick.  The syncategorematic element is precisely the juxtaposition.

Please note that if there were no syncategorematic element in 'Fa' there would not be any sentence at all.  A sentence is not a list.  The sentence 'Fa' is not the list 'F, a.'  A (declarative) sentence expresses a thought (Gedanke) which is its sense (Sinn).  And it has a reference (Bedeutung), namely a truth value (Wahrheitswert).  No list of words (or of anything else) expresses a thought or has a truth value.  So a sentence is not a list of its constituent words.  A sentence depends on its constituent words, but it is more than them.  It is their unity. 

We here touch upon the ancient problem of the unity of the proposition first descried by the immortal Plato.

So I say there must be a syncategorematic element in 'Fa' if it is to be a sentence.  There is need of a copulative element to tie together subject and predicate.  It follows that, pace Sommers, it is false that atomic sentences are devoid of syntagorematic elements.

Note what I am NOT saying.  I am not saying that the copulative element in a sentence must be a separate sign such as 'is.'  There is no need for the copulative  'is.'  In standard English we say 'The sea is blue' not 'The sea blue.' But in Turkish one can say Deniz mavi and it is correct and intelligible.  My point is not that we need the copulative 'is' as a separate sign but that we need a copulative element which, though it does not refer to anything, yet ties together subject and predicate.  There must be some feature of the atomic sentence that functions as the copulative element, if not immediate juxtaposition then something else such as a font difference or color difference.

At his point I will be reminded that Frege's concepts (Begriffe) are unsaturated (ungesaettigt).  They are 'gappy' or incomplete unlike objects.  The incompleteness of concepts is reflected in the incompleteness of predicate expressions.  Thus '. . . is fat' has a gap in it, a gap fit to accept a name such as 'Al' which has no gap.  We can thus say that for Frege the copula is imported into the predicate.  It might be thought that the gappiness of concepts and predicate expressions obviates the need for a copulative element in the sentence and in the corresponding Thought (Gedanke) or proposition.

But this would be a mistake.  For even if predicate expressions and concepts are unsaturated, there is still a difference between a list and a sentence.  The unsaturatedness of a concept merely means that it combines with an object without the need of a tertium quid.  (If there were a third thing, then Bradley's regress would be up and running.)  But to express that a concept is in fact instantiated by an object requires more than a listing of a concept-word (Begriffswort) and a name.  There is need of a syncategorematical element in the sentence.

So I conclude that if there are any atomic sentences, then they cannot contain only categorematic expressions.

Presupposition and Excluded Middle

If Socrates dies at time t, then Socrates was alive prior to t. If Socrates does not die at t, then Socrates was alive prior to t.  Since both 'Socrates dies at t' and 'Socrates does not die at t' entail 'Socrates was alive prior t,' we say that the latter is a semantic presupposition of 'Socrates dies at t.'

But wait a minute! Doesn't what I have written generate an inconsistent tetrad?

1) p entails q

2) Not-p entails q

3) Necessarily, for any p, either p or not-p (Law of Excluded Middle)

4) q is contingent.

The conjunction of the first three limbs entails the negation of the fourth. So something has to give.

It is a datum that q -- 'Socrates was alive prior to t' -- is contingent: true in some but not all possible worlds. So we either reject semantic presupposition (which requires the truth of both (1) and (2) ) or we reject Excluded Middle.

Why not reject Excluded Middle? Socrates dies at t and Socrates does not die at t are contradictories: each is the negation of the other.  There is no possible world in which both are true.  And yet there are possible worlds in which neither is true. Those are the worlds in which Socrates does not exist.

Is Assertion Closed Under Entailment? Assertion and Presupposition

Suppose a person asserts that p. Suppose also that p entails q. Does it follow that the person asserting that p thereby asserts that q?  If so, and if p and q are any propositions you like, then assertion is closed under entailment.  If assertion is not closed under entailment, then there will be examples in which a person asserts that p, p entails q, but the person does not assert that q.

By 'entailment' I understand a relation between propositions. P entails q iff it is impossible for p to be true, and q false. By 'assertion' I mean a speech act, an act of asserting, a concrete, datable, linguistic performance, not a proposition.  By 'the content of an assertion' I mean the proposition expressed  when a person makes an assertion. A proposition is not the same as a sentence. 'The war has come to an end' is a sentence in English. 'Der Krieg hat zu Ende gekommen' is a sentence in German.  The sentences are different, both at the type level and at the token level. And yet they can both be used to express one and the same thought. That same thought is the proposition.  By 'thought' here I do not mean an occurrent episode of thinking, but the accusative (direct object) of such an act of thinking. You could also call it a 'content' although that term is ambiguous for reasons I won't go into now.

Preliminaries aside, back to our question.

That James no longer works for Amazon has among its entailments that James worked for Amazon, that someone named 'James' worked for Amazon, and that someone no longer works for Amazon.

Now suppose I assert that James no longer works for Amazon.  Do I thereby assert that James worked for Amazon?  I say No.

Here is a more striking example. Sophomore Sam asserts that there are no truths.  The content of his act of assertion, namely, the proposition that there are no truths, entails that the content of his assertion is not true.  But surely the latter is no part of what Sam asserts. 

So assertion is not closed under entailment.

Suppose that Tom asserts that he is glad that Trump beat Hillary.  The content of the assertion entails that Trump beat Hillary. But that Trump beat Hillary is not what Tom asserts.  We can say that Tom's act of assertion presupposes that Trump beat Hillary.  But neither Tom nor his act of assertion is a proposition. So if Tom's act of assertion presupposes that Trump beat Hillary, then presupposition is not a relation between propositions, but a relation between a non-proposition (a person or his speech act) and a proposition.

On the other hand, that Tom is glad that Trump beat Hillary entails that Trump beat Hillary. This is a relation between propositions and it makes some sense to say that the first presupposes the second.

This raises a question. Is presupposition primarily something that people do, or is it primarily a relation between propositions?

Paradox and Contradiction

A form of words can be paradoxical but not contradictory, e.g., "Most people want to become old, but few want to be old."

The expression is paradoxical, and therein lies its literary charm, but the thought is non-contradictory. The thought, expressed non-paradoxically, is: Most want to live a long time, but few if any want to suffer the decrepitude attendant upon living a long time.

One logic lesson to be drawn is that a paradox is not the same as a contradiction.

It is therefore a mistake to refer to Russell's Antinomy as 'Russell's Paradox.'

Thus spoke the Language Nazi.

Is Assertion External or Internal to Logic? A Note on Irad Kimhi

The main point of Peter Geach's paper, "Assertion" (Logic Matters, Basil Blackwell, 1972, pp. 254-269) is what he calls the Frege point: A thought may have just the same content whether you assent to its truth or not; a proposition may occur in discourse now asserted, now unasserted, and yet be recognizably the same proposition. This seems unassailably correct. One will fail to get the Frege point, however, if one confuses statements and propositions. An unstated statement is a contradiction in terms, but an unasserted proposition is not. The need for unasserted propositions can be seen from the fact that many of our compound assertions (a compound assertion being one whose content is propositionally compound) have components that are unasserted.

To assert a conditional, for example, is not to assert its antecedent or its consequent. If I assert that if Tom is drunk, then he is unfit to drive, I do not thereby assert that he is drunk, nor do I assert that he is unfit to drive.  I assert a compound proposition the components of which I do not assert. I assert a relation between two propositions without asserting either of them.

The same goes for disjunctive propositions. To assert a disjunction is not to assert its disjuncts. Neither propositional component of Either Tom is sober or he is unfit to drive is asserted by one who merely asserts the compound disjunctive proposition.

On one view of logic, it studies propositions and the relations between them  such as entailment, consistency, and inconsistency in abstraction from the concrete mental acts in which the propositions are accepted, rejected, or merely entertained. Logic is thus kept apart from psychology. If so, then assertion, as a speech act founded in the mental act of acceptance, is external to logic.  If this were not the case, then how would one account for the validity of the following obviously valid argument?

a) If Tom is drunk, then Tom is unfit to drive
b) Tom is drunk
Therefore
c) Tom is unfit to drive.

For the argument to be an instance of the valid argument form modus ponendo ponens, the protasis of (a) must be the same proposition as is expressed by (b). But then the assertoric force that (b) carries when the argument is given by someone cannot be part of the proposition. For the assertoric force  is no part of the proposition that is the protasis of (a).

So if formal logic studies propositions in abstraction from the concrete episodes of thinking in which they are brought before minds, then assertion is external to formal logic.

But according to the NYT, a philosopher with a cult following among the cognoscenti rejects the above view:

[Irad] Kimhi argues that this view is wrong, and that the distinction between psychology and logic has led our understanding of thinking astray. Consider that the following statement does not, according to the standard view, constitute a logical contradiction: “It’s raining, but I don’t believe it’s raining.” Why? Because the first part of the sentence concerns a state of affairs in the world (“it’s raining”), whereas the second part concerns someone’s state of mind (“I don’t believe it’s raining”).

Kimhi wants to rescue the intuition that it is a logical contradiction to say, “It’s raining, but I don’t believe it’s raining.” But to do this, he has to reject the idea that when you assert a proposition, what you are doing is adding psychological force (“I think … ”) to abstract content (“it’s raining”). Instead, Kimhi argues that a self-conscious, first-person perspective — an “I” — is internal to logic. For him, to judge that “it’s raining” is the same as judging “I believe it’s raining,” which is the same as judging “it’s false that it’s not raining.” All are facets of a single act of mind.

I haven't read Kimhi's book, and I am not sure I should trust the NYT account, but Kimhi seems to be recycling Kant in a confused way. At B 132 of Critique of Pure Reason, Kant writes, "It must be possible for the 'I think' to accompany all my representations; for otherwise something would be represented in me which could not be thought at all, and that is equivalent to saying that the representation would be impossible, or at least would be nothing to me." (NKS tr.)

Consider a propositional representation.  One's awareness that it is raining need not be accompanied by an explicit act of reflection, the one expressed by 'I think that it is raining,' but it must be possible that this reflection occur. Thus there is a necessary connection between the propositional representation 'It is raining' and Kant's  transcendental unity of apperception. The latter could be described as " a self-conscious, first-person perspective — an “I” — [that] is internal to logic." But it is a transcendental I, one common to all cognitive subjects, and not the psychological I of a particular cognitive subject. Kimhi seems to be speaking of the latter.

Kant's Ich denke points us back to Descartes' cogito. The Frenchman discovers that while he can doubt many things, he cannot doubt that he is doubting these things. He can doubt the existence of the cat he 'sees' -- using 'see' in a strictly phenomenological way -- but he cannot doubt the existence of his 'seeing' as a mental act or cogitatio. His doubting is a thinking, but it is not a believing.  The Dubito ergo sum is but a special case of the generic Cogito ergo sum.  His doubting that he has a body is not a believing that he has a body but it is a thinking in the broad Cartesian sense that subsumes all intentional states or mental acts.

Accordingly, the 'I think' that must be able to accompany all my representations does not have the specific sense of 'I believe.' Belief is one type of mental act among many. One who believes does not doubt, and conversely. But both think. The 'I think' expresses an explicit reflection on the occurrent intentional state one is in, whether one is doubting, believing, wishing, hoping remembering, etc.

So there is a defensible sense in which there is an I internal to logic, but this is the transcendental I of the original synthetic unity of apperception, not the I of the psychophysical subject in nature.   If there is an I internal to logic, it is the I of the transcendental prefix,  the 'I think ___' which must be able to accompany all my representation.  But this 'I think ___' of the transcendental prefix does not have the sense of the ordinary language 'I think so' which means 'I believe so.' 

One consequence of Kimhi’s view is that “It’s raining, but I don’t believe it’s raining” becomes a logical contradiction. Another consequence is that a contradiction becomes something that you cannot believe, as opposed to something that you psychologically can but logically ought not to believe (as the traditional cleavage between psychology and logic might suggest). A final consequence is that thinking is not just a cognitive psychological act, but also one that is governed by logical law.

In other words, the distinction between psychology and logic collapses. Logic is not a set of rules for how to think; it is how we think, just not in a way that can be captured in conventional scientific terms. Thinking emerges as a unique and peculiar activity, something that is part of the natural world, but which cannot be understood in the manner of other events in the natural world. Indeed, Kimhi sees his book, in large part, as lamenting “the different ways in which philosophers have failed to acknowledge — or even denied — the uniqueness of thinking.”

The above strikes me as based on a confusion of the transcendental 'I think' with the psychological 'I believe.'  It seems to me that one can have a reflective awareness as of rain falling without believing that rain is falling. What is impossible, and contradictory, is to have a reflective awareness as of rain falling without thinking (in the broad Cartesian sense that subsumes specific types of mental act) that rain is falling. 

The transcendental I's thinking is governed by logical law, but not the thinking of the empirical I in nature. So the distinction between psychology and logic does not collapse. To the extent that I can make sense of what Kimhi is saying on the basis of the NYT article he seems to be trying to naturalizer Kant's transcendental ego.  Good luck with that.

Perhaps talk of a transcendental I is nonsense if it is supposed to be a real entity that thinks; but only a transcendental I could be internal to formal logic.

If anyone has read Kimhi's book, his comments would be appreciated. 

Does the Validity of an Argument Depend on the Order of its Premises?

Suppose you have a valid argument. Can you render the argument invalid by changing the display order of the premises?

I should think never. The Dark Ostrich, however, offers the following putative counterexample. He says he got it from Sainsbury; I should like to see a reference.  And if there is a literature on this, I should like to see a bibliography.

(A) Some Greek is called ‘Mark’, Mark is an evangelist, therefore some Greek is an evangelist. (VALID)

(B) Mark is an evangelist, some Greek is called ‘Mark’, therefore some Greek is an evangelist. (NOT VALID)

(A) is valid and (B) is not. But this is not evidence that premise order affects validity. For while the sentences are the same, the premises of the two arguments are not the same.  Made explicit, (A) becomes

(A*) Some Greek is called 'Mark', this same individual called 'Mark is an evangelist, therefore some Greek is an evangelist.

Clearly, (A*) and (B) have different premises. So it is not the different order of the premises in (B) that causes it to be invalid.

The Two Opposites of 'Nothing' and the Logical Irreducibility of Being (2018 Version)

This entry is part of the ongoing debate with the Opponent a. k. a. the Dark Ostrich.

It is interesting  that 'nothing' has two opposites.  One is 'something.'  Call it the logical opposite.  The other is 'being.'  Call it the ontological opposite.  Logically, 'nothing' and 'something' are interdefinable quantifiers:

D1. Nothing is F =_df it is not the case that something is F.

D2. Something is F =_df it is not the case that nothing is F.

These definitions, which are part of the articulation of the Discursive Framework (DF), give us no reason to think of one term as more basic than the other.  Logically, 'nothing' and 'something'  are on a par.  Logically, they are polar opposites.  Anything you can say with the one you can say with the other, and vice versa.

We also note that as quantifiers, as terms expressing logical quantity, 'nothing' and 'something' are not names or referring expressions.

So far I have said nothing controversial.

Ontologically, however, being and nothing are not on a par.  They are not polar opposites.  Being is primary, and nothing is derivative.  (Note the ambiguity of 'Nothing is derivative' as between 'It is not the case that something is derivative' and 'Nothingness is derivative.'  The second is meant.)

Now we enter the arena of controversy. For it might be maintained that there are no ontological uses of 'being,' and 'nothing,' that talk of being and nothing  is replaceable without remainder by use of the quantifiers defined in (D1) and (D2).

Quine said that "Existence is what existential quantification expresses."  (Ontological Relativity and Other Essays, p. 97)I deny it:  there is more to existence than what the existential quantifier expresses.  Quine's is a thin theory of existence; mine is a thick theory.  Metaphorically, existence possesses an ontological thickness.  This is very important for metaphysics if true.

I won't be able to prove my point because nothing in philosophy can be proven.  But I can argue for my point in a fallacy-free manner.  I am justified in holding my view so long as no one can convict me of a clear-cut error. 

Suppose we try to define the existential 'is' in terms of the misnamed because question-begging 'existential' quantifier.  (The proper moniker is 'particular quantifier.')  This is standardly done as follows.

D3. y is/exists =_df for some x, y = x.

In plain English, for y to be or exist is for y to be identical to something. For Quine to be or exist is for Quine to be identical to something.  In general, to be is to be identical to something, not some one thing of course, but something or other.   This thing, however, must exist, and in a sense not captured by (D3).  Thus

Quine exists =_df Quine is identical to something that exists

and

Pegasus does not exist =_df nothing that exists is such that Pegasus is identical to it

or

Pegasus is diverse from everything that exists.

The point, which many find elusive, is that the items in the domain of quantification  must be there to be quantified over, where 'there' has not a locative but an existential sense.  For if the domain includes nonexistent objects, then, contrary to fact, Pegasus would exist in virtue of being identical to an item in this widened domain, namely, Pegasus.

The conclusion is (to me!) obvious: one cannot explicate the existential 'is' in terms of the particular quantifier without circularity, without presupposing that things exist in a sense of 'exist' that is not captured by (D3).

Mere logicians won't accept or perhaps even understand this since existence is "odious to the logician" as George Santayana observes. (Scepticism and Animal Faith, Dover, 1955, p. 48, orig. publ. 1923.) You have to have metaphysical aptitude to understand it. (But now I am tending toward the tendentious.)

Intellectual honesty requires that I admit that I am basing myself on an intuition, what J. Maritain calls the intuition of Being.  I find it self-evident that the existence of a concrete individual is an intrinsic determination that makes it be as opposed to not be. This implies a real distinction between x and the existence of x. Accordingly, the existence of an individual cannot be reduced to its self-identity: the existence of Quine does not reduce to Quine's being (identical to) Quine, as on the thin theory.  And the nonexistence of Pegasus does not reduce to its being diverse from everything.  (If to be is to be identical to something, then not to be is to be diverse from everything.)

The Opponent does not share my intuition.  In the past I have berated him for being 'existence-blind' but he might plausibly return the 'compliment' by accusing me of double vision:  I see Socrates but I also 'see' the existence of Socrates when there is no such 'thing.' 

So far, not good:  I can't refute the Opponent but he can't refute me.  Stand-off.  Impasse, a-poria.

Let me try a different tack.  Does the Opponent accept 

ENN. Ex nihilo nihil fit?

Out of nothing nothing comes.  Note that 'nothing' is used here in two different ways, ontologically and logically/quantificationally. For what the hallowed dictum states is that it is not the case that something arises from nothing/Nothingness.  

Now if the Opponent accepts the truth or even just the meaningfulness of (ENN), then he must (!) admit that there are two senses of 'nothing,' the logical and the ontological, and correspondingly, two senses of 'something.'  If so, then being and nothing cannot be exhaustively understood in terms of logical quantifiers and propositional negation, and then the thin theory bites the dust.

But if the thin theory succumbs, then there is more to existence than can be captured within the Discursive Framework.

Related articles

Maverick Philosopher: Singular Existence and Quantification

The Riddle of Evil and the Pyrrhonian 'Don't Care'

A Defense of David Benatar Against a Scurrilous <i>New Criterion</i> Attack

Singular Existence and Quantification

For Tim M. who wants to discuss this topic with me. ComBox open.

......................... 

Singular existence is the existence of particular individuals.  It is the existence attributed by a use of a singular sentence such as 'Max exists,' where 'Max' is a proper name.  

A standard way to conceptualize singular existence, deriving from Quine and endorsed by Peter van Inwagen, is in terms of the 'existential' -- I prefer to say 'particular' -- quantifier of standard predicate logic. Thus,

Max exists =_df for some x, x = Max. 

In general,

x exists =_df for some y, x = y.

In the standard notation of modern predicate logic with identity, 

x exists =_df (∃y)(x = y).

What the latter two formulae express is that an individual exists if and only if it is identical to something. Assuming that there are no nonexistent objects in the domain of quantification, these biconditionals are undoubtedly true, and indeed necessarily true.  Meinongians reject the assumption but it is quite reasonable, so let it stand. Even so, I cannot see that the biconditionals  just listed sanction the reduction of existence to identity-to-something.  

Those of a deflationary bent would welcome such a reduction. For it would allow the elimination of existence as a topic of metaphysical investigation in favor of the sober logic of 'exists.'  You will notice that on the left-hand side of the biconditionals there is the apparently non-logical, content-rich word 'exists' whereas on the right-hand side all the symbols are logical.  If we can get rid of the word 'exists,' then perhaps we can get rid of the temptation to ask about Existence and Being. Aquinas, for example, tells us that God is not an ens among entia, but esse, Being or To Be: Deus est ipsum esse subsistens.  This presupposes that there is such a 'thing' as Being.  If the deflationary account is correct, there isn't.

So my question is this: is the deflationary account adequate? Or is there more to existence than can be captured by the so-called 'existential' quantifier of modern predicate logic?

An Argument Against Reduction

If Max is identical to something, then this thing can only be Max. The upshot is that the existence of Max is his self-identity.  But note that whereas my cat Max, being a contingent being, might not have existed, it is not the case that Max might not have been self-identical. It is true that Max might not have existed, but it is false that Max might not have been Max.  So existence cannot be reduced to self-identity. This holds for all contingent beings. Only a necessary being such as God could be such that existence and self-identity are one and the same. The argument, then, is this:

P1. Every contingent existent is possibly nonexistent
P2. No contingent existent is possibly non-self-identical
------------
C1. No contingent existent is such that its possible nonexistence = its possible non-self-identity
------------
C2. No contingent existent is such that its existence = its self-identity.

It follows that there is more to existence than what is captured by our Quinean biconditionals.  

An Objection

Is the above argument decisive? A Quinean might respond by denying (P2) and running the argument in reverse.  Insisting that to exist = to be self-identical, he argues that if a thing is contingent (possibly nonexistent), then it is possibly non-self-identical. If Max is contingent, then there is a possible world W in which he doesn't exist. Since Max does not exist in W, he has no properties there. Hence he is neither self-identical nor non-self-identical in W.

Is this objection any good?  

Ambiguity, Vagueness, Generality, Disambiguation

Ambiguity. A property of linguistic expressions, primarily. An expression is ambiguous if it has two or more distinct meanings. Back in the day a guy asked me, "Where's your head, man?" I thought he was inquiring into my psychological state, but he merely needed to relieve himself. 'Head' is ambiguous. In its nautical use it refers to a toilet. Ambiguity is either syntactic or semantic. The example lately offered is semantic.

Amphiboly. An amphiboly is a syntactic ambiguity. Scope ambiguity is one subspecies. Consider 'Whatever happens must happen.' On an innocuous parsing with the modal operator operating on the whole sentence, it comes out a trivial logical truth:

Necessarily, whatever happens, happens.

But if the modal operator is imported into the sentence and attached to the consequent of the conditional, we get a probably false piece of fatalist metaphysics:

Whatever happens, necessarily happens.

Equivocation. An equivocation is a semantic ambiguity.  Consider this abortion argument:

The fetus is a part of a woman's body.
A woman has the right to do whatever she wants with any part of her body.
Therefore
A woman has the right to do whatever she wants with the fetus, including having it killed.

Is 'part' being used in the same sense in the first and second premises? If not, the argument succumbs to the fallacy of equivocation. I would say that the argument does so succumb. For the minor to be uncontroversially true, the term 'part' must be given a narrow reading that exclude the fetus. But for the major to be true, 'part' must be construed broadly so as to include it. Ergo, etc.

Vagueness. If an ambiguous expression harbors a multiplicity of distinct meanings, a vague expression lacks a definite meaning. Ambiguity and vagueness should therefore not be confused.  To have multiple definite meanings is not the same as to have no one definite meaning.

Generality. Statements divide into the singular and the general.  General statements divide into the universal, the particular, and the generic. 'Socrates is a man' is singular. 'All men are mortal' and 'Some mortals are men' are universal and particular respectively. 'Germans are industrious' is generic. For more on generics see Generic Statements.

Please avoid the phrase 'vague generalities.' Just as you shouldn't confuse ambiguity with vagueness, you shouldn't confuse vagueness with generality.  Most generalizations have a definite meaning.

Disambiguation. If an expression is ambiguous, then it cries out for disambiguation.  To disambiguate is to remove ambiguity by listing the different meanings of a word or phrase or sentence.

Class dismissed.

The Function-Argument Schema in the Analysis of Propositions, Part II

A second installment from the Ostrich of London. 

Another difficulty with the function-argument theory is staring us in the face, but generally unappreciated for what it is. As Geach says, the theory presupposes an absolute category-difference between names and predicables, which comes out in the choice of ‘fount’ [font] for the schematic letters corresponding to name and predicable. For example ‘Fa’, where the upper case ‘F’ represents the predicable, as Geach calls it, and lower case ‘a’ the name. As a direct result, there is only one negation of the proposition, i.e. ‘~Fa’, where the tilde negates whatever is expressed by ‘Fa’. But ‘F’ is a function mapping the referent of ‘a’ onto the True or the False, so ‘~Fa’ says that a does not map onto the True. The object a is there all right, but maps to a different truth-value. Thus ‘Fa’ implies ExFx, ‘~Fa’ implies Ex~Fx, and excluded middle (Fa or ~Fa) implies that something, i.e. a, does or does not satisfy F. The function-argument account has the bizarre consequence that the name always has a referent, which either does or does not satisfy the predicable. There is no room for the name not being satisfied. Indeed, the whole point of the function theory is to distinguish the idea of satisfaction, which only applies to predicables, from reference, which is a feature of proper names only. As Frege points out here:

The word 'common name' is confusing .. for it makes it look as though the common name stood under the same, or much the same relation to the objects that fall under the concept as the proper name does to a single object. Nothing could be more false! In this case it must, of course, appear as though a common name that belongs to an empty concept were as illegitimate as a proper name that designates [bezeichnet] nothing.

The scholastic two-term account, by contrast, allows for the non-satisfaction of the proper name. ‘Frodo is a hobbit’ is true if and only if something satisfies both ‘hobbit’ and ‘Frodo’. It is essential to Aristotle’s theory of the syllogism, as Geach notes, that the middle term (the one which appears in both premisses) can be subject in one premiss, predicate in another. The notion of ‘satisfaction’ or ‘supposition’ applies to both subject and predicate, even if the subject is a proper name like ‘Frodo’. Thus the negation of ‘Frodo is a hobbit’ can be true in two ways. Either some individual satisfies ‘Frodo’ but does not satisfy ‘hobbit’. We express this in English by so-called predicate negation ‘Frodo is not a hobbit’, where the negative is placed after the copula. Or no individual satisfies ‘Frodo’, which we can express by placing the negation before the whole proposition, ‘it is not the case that Frodo is a hobbit’. So the scholastic theory neatly accounts for empty proper names. Not so for the function-argument theory, a difficulty which was recognised early on. Frege developed a complex and (in my view) ultimately incoherent theory of sense and reference. Russell thought that proper names were really disguised descriptions, which is actually a nod to the scholastic theory.

Of course there is a separate problem for the two term theory, of making sense of a proper name not being ‘satisfied’. What concept is expressed by the proper name that is satisfied or not satisfied, and which continues to exist as a concept even if the individual ceases to exist? Bill and I have discussed this many times, probably too many times for his liking.

BV: What is particularly interesting here is the claim that Russell's theory of proper names is a nod to to the scholastic theory.  This sounds right, although we need to bear in mind that Russell's description theory is a theory of ordinary proper names. Russell also allows for logically proper names, which are not definite descriptions in disguise.  The Ostrich rightly points out that that for Frege there there is an absolute categorial difference between names and predicables.  I add that this is the linguistic mirror of the absolute categorial difference in Frege between objects and concepts (functions). No object is a concept, and no concept is an object.  No object can be predicated, and no concept can be named. This leads directly to the Paradox of the Horse:  The concept horse is not a concept. Why not? Because 'the concept horse' is a name, and whatever you name is an object. 

This is paradoxical and disturbing because it imports ineffability into concepts and thus into logic. If concepts cannot be named and objectified, then they are not wholly graspable.  This is connected with the murky notion of the unsaturatedness of concepts. The idea is not that concepts cannot exist uninstantiated; the idea is that concepts have a 'gappy' nature that allows them to combine with objects without the need for a tertium quid to tie them together.   Alles klar?

Now it seems to me that Russell maintains the absolute categorial difference between logically proper names and predicates/predicables. ('Predicable' is a Geachian term and it would be nice to hear how the Ostrich defines it.) Correct me if I am wrong, but this presupposition of an absolute categorial difference between logically proper names and predicates/predicables is a presupposition of all standard modern logic.  It is 1-1 with the assumption that there are atomic propositions.

Here is one problem.  On the Russellian and presumably also on the scholastic theory, an ordinary proper name stands to its nominatum in the same relation as a predicate to the items that satisfy it.  Call this relation 'satisfaction.'  Socrates satisfies 'Socrates' just as he and Plato et al. satisfy 'philosopher.' Now if an item satisfies a term, then it instantiates the concept expressed by the term. But what is the concept that 'Socrates' expresses?  One candidate is: the unique x such that x is the teacher of Plato. Another is: the greatest philosopher who published nothing. 

Notice, however, that on this approach singularity goes right out the window. 'Socrates' is a singular term. But 'the greatest philosopher who published nothing' is a general term despite the fact that the latter term, if satisfied, can be satisfied by only one individual in the world that happens to be actual. It is general because it is satisfied by different individuals in different possible worlds. Without prejudice to his identity, Socrates might not have been the greatest philosopher to publish nothing.  He might not have been a philosopher at all. So a description theory of names cannot do justice to the haecceity of Socrates. What makes Socrates precisely this individual cannot be some feature accidental to him. Surely the identity of an individual is essential to it.

If we try to frame a concept that captures Socrates' haecceity, we hit a brick wall.  Concepts are effable; an individual's haeceity or thisness is ineffable.  Aristotle says it somewhere, though not in Latin: Individuum ineffabile est.  The individual as such is ineffable. There is no science of the particular qua particular.  There is no conceptual understanding of the particular qua particular because the only concepts we can grasp are general in the broad way I am using 'general.'  And of course all understanding is conceptual involving as it does the subsumption of particular under concepts.

Some will try the following move.  They will say that 'Socrates' expresses the concept, Socrateity, the concept of being Socrates, or being identical to Socrates. But this haecceity concept is a pseudo-concept.  For we had to bring in the non-concept Socrates to give it content.

There are no haecceity concepts. As the Ostrich appreciates, this causes trouble for the scholastic two-name theory of predication according to which 'Socrates' and 'wise' are both names, and the naming relation is that of satisfaction.  It makes sense to say that the concept wise person is uninstantiated. But it makes no sense to say that the concept Frodoity is uninstantiated for the simple reason that there cannot be any such concept.

It looks like we are at an impasse. We get into serious trouble if we go the Fregean route and hold that names and predicates/predicables are radically disjoint and that the naming/referring relation is toto caelo different from the satisfaction relation.  But if we regress to the scholastic two-name theory, then we have a problem with empty names. 

Related articles

The Function-Argument Schema in the Analysis of Propositions

The Function-Argument Schema in the Analysis of Propositions

The Ostrich of London sends the following to which I add some comments in blue.

Vallicella: ‘One of Frege's great innovations was to employ the function-argument schema of mathematics in the analysis of propositions’.  

Peter Geach (‘History of the Corruptions of Logic’, in Logic Matters 1972, 44-61) thinks it actually originated with Aristotle, who suggests (Perihermenias 16b6) that a sentence is composed of a noun (ὄνομα) and a verb (ῥῆμα), and the verb is a sign of something predicated of something else. According to Geach, Aristotle dropped this name-predicate theory of the proposition later in the Analytics, an epic disaster ‘comparable only to the fall of Adam’, so that logic had to wait more than two thousand years before the ‘restitution of genuine logic’ ushered in by Frege and Russell. By ‘genuine logic’ he means modern predicate logic, which splits a simple proposition into two parts, a function expression, roughly corresponding to a verb, and an argument expression, roughly corresponding to a noun. ‘To Frege we owe it that modern logicians almost universally accept an absolute category-difference between names and predicables; this comes out graphically in the choice of letters from different founts [fonts] of type for the schematic letters of variables answering to these two categories’.

The Fregean theory of the proposition has never seemed coherent to me. Frege began his studies (Jena and Göttinge, 1869–74) as a mathematician. Mathematicians naturally think in terms of ‘functions’ expressing a relation between one number and another. Thus

            f(3)  =  9

where ‘3’ designates the argument or input to the function, corresponding to Aristotle’s ὄνομα, ‘f()’ the function, here y=x², corresponding to Aristotle’s ῥῆμα, and ‘9’ the value of the function. The problem is the last part. There is nothing in the linguistic form of the proposition which corresponds to the value in the linguistic form of the mathematical function. It is invisible. Now Frege thinks that every propositional function or ‘concept’ maps the argument to one of two values, either the True or the False. OK, but this is a mapping which, unlike the mathematical mapping, cannot be expressed in language. We can of course write

            ___ is wise(Socrates) = TRUE

but then we have to ask whether that equality is true or false, i.e. whether the function ‘is_wise(--) = TRUE’ itself maps Socrates onto the true or the false. The nature of the value (the ‘truth value’) always eludes us. There is a sort of veil beyond which we cannot reach, as though language were a dark film over the surface of the still water, obscuring our view of the Deep.

BV: First a quibble. There is no need for the copula 'is' in the last formula since, for Frege, concepts (which are functions) are 'unsaturated' (ungesaettigt) or incomplete.  What exactly this means, of course, is  a separate problem.  The following suffices:

___wise(Socrates) = TRUE.

The line segment '___' represents the gappiness or unsaturatedness of the concept expressed by the concept-word (Begriffswort).

Quibbling aside, the Ostrich makes two correct interrelated points, the first negative, the second positive.

The first is that while 'f(3) = 9' displays the value of the function for the argument 3, namely 9, a sentence that expresses a (contingent) proposition does NOT display its truth-value. The truth-value remains invisible. I would add that this is so whether I am staring at a physical sententional inscription or whether I am contemplating a proposition with the eye of the mind.  The truth or falsity of a contingent proposition is external to it.  No doubt, 'Al is fat' is true iff Al is fat.' But this leaves open the question whether Al is fat.  After all the biconditional is true whether or not our man is, in fact, obese.

The second point is that there has to be something external to a contingent proposition (such as the one expressed by 'Socrates is wise') that is involved in its being true, but this 'thing,' -- for Frege the truth-value -- is ineffable.  Its nature eludes us as the Ostrich correctly states.  I used the somewhat vague phrase 'involved in its being true' to cover two possibilities. One is the Fregean idea that declarative sentences have both sense and reference and that the referent (Bedeutung) of a whole declarative sentence is a truth-value.  The other idea, which makes a lot more sense to me, is that a sentence such as 'Socrates is wise' has a referent, but the referent is a truth-making fact or state of affairs, the fact of Socrates' being wise.

Now both of these approaches have their difficulties.  But they have something sound in common, namely, the idea that there has to be something external to the contingent declarative sentence/proposition involved in its being true rather than false.  There has to be more to a true proposition than its sense.  It has to correspond to reality.  But what does this correspondence really come to? Therein lies a major difficulty.  

How will the Ostrich solve it? My impression is that he eliminates the difficulty by eliminating reference to the extralinguistic entirely. 

Related articles

Maverick Philosopher: God, Truth, Reality Denial: A Response to Some Questions

Logical Form, Equivocation, and Propositions

Ed Buckner wants to re-fight old battles. I'm game. The following post of his, reproduced verbatim, just appeared at Dale Tuggy's site:

The concept of logical form is essential to any discussion of identity, and hence to any discussion of the Trinity. Here is a puzzle I have been discussing with the famous Bill Vallicella for many years.

(Argument 1) ‘Cicero is a Roman, therefore Cicero is a Roman’

(Argument 2) ‘Cicero is a Roman, therefore Tully is a Roman’

My puzzle [is] that the first argument is clearly not valid if the first ‘Cicero’ means the Roman, the second the American town, yet the argument seems to instantiate a valid form. Bill objects that if there is equivocation, then the argument really has the form ‘a is F, therefore b is F’, which fails to instantiate a valid form.

I then ask what is the form of. Clearly not of the sentences, since the sentences do not include the meaning or the proposition. Is it the form of the proposition expressed by the sentences? But then we have the problem of the second argument, where both ‘Cicero’ and ‘Tully’ mean the same man. Then the man is contained in both propositions, and if the form is of the proposition, the argument has the true form ‘a is F, so a is F’, which is valid. But I think no one would agree that the second argument is valid.

So logical form does not belong to the sentences, nor to the propositions expressed by them. So what is it the form of?

My answer is that the logical form of the argument is the form of the Fregean propositions expressed by the sentences that make up the argument. Let me explain.

I agree with Ed that logical form is not the form of an array of sentence-tokens. It is rather the form of an array of propositions expressed by the sentences. (To be painfully precise: it is the form of an array of propositions expressed by the assertive utterance, and thus the tokening, of a series of sentence-types by a speaker or thinker on a given occasion. A sentence-token buried in a book does not express anything by itself!)

To solve Ed's puzzle we need to distinguish three views of propositions: the Aristotelian, the Fregean, and the Russellian. This would be a good topic for an extended post. Here I will be brief.  Brevity is the soul of blog.

An Aristotelian proposition is an assertively uttered meaningful sentence in the indicative mood that expresses a complete thought.  What makes such a proposition 'Aristotelian' as opposed to 'Platonic' is that the meaning of the sentence is not something that can subsist on its own apart from the assertive tokening of the sentence.  The meaning of the sentence depends on its being expressed, whether in overt speech or in thought, by someone. If there were no minds there would be no Aristotelian propositions. And if there were no languages there would be no Aristotelian propositions. In this sense, Aristotelian propositions are linguistic entities.

In brief: An Aristotelian proposition is just a declarative sentence in use together with its dependent sense or meaning. Suppose I write a declarative sentence on a piece of paper. The Aristotelian proposition is not the string of physical marks on the paper, nor it is the producing of the marks; it is the marks as produced by a minded organism on a particular occasion together with the meaning those marks embody.

A Fregean proposition is a nonlinguistic entity that subsists independently of minds and language. It is the sense (Sinn) of a declarative sentence from which indexical elements have been extruded. For example, 'I am blogging'  does not express a Fregean proposition because of the indexical 'I' and because of the present tense of the verb phrase.  But 'BV blogs at 10:50 AM PST on 4 September 2017' expresses a Fregean proposition.

Fregean senses are extralinguistic and extramental 'abstract' or 'Platonic' items.  They are not in time or space even when the objects they are about are in time and space. This is what makes Fregean propositions 'Platonic' rather than 'Aristotelian.' Fregean propositions are the primary truth-bearers; the sentences that express them are derivatively true or false.

A Russellian proposition is a blurry, hybrid entity that combines some of the features of a Fregean truth-bearer and some of the features of a truth-maker. A Russellian proposition does not reside at the level of sense (Sinn) but at the level of reference (Bedeutung).  It is out there in the (natural) world. It is what some of us call a fact or 'concrete fact' (as in my existence book) and others a state of affairs.  

Now consider a singular sentence such as 'Ed is happy.'  For present purposes, the crucial difference between a Fregean proposition and a Russellian proposition is that, on the Fregean view, the subject constituent of Ed is happy is not Ed himself with skin and hair, but an abstract surrogate that represents him in the Fregean proposition, whereas in the Russellian proposition Ed himself is a constituent of the proposition!

We needn't consider why so many distinguished philosophers have opted for this (monstrous) view.  But this is the view that seems to have Ed in its grip and that powers his puzzle above.

If we take the relatively saner (but nonetheless problematic) view that propositions are Fregean in nature, then the puzzle is easily solved.

Ed asks: What is the logical form the form of?  He maintains, rightly, that it cannot be the form of an array of sentences. So it must be the form of an array of propositions. Right again. But then he falls into puzzlement: 

. . . ‘Cicero’ and ‘Tully’ mean the same man. Then the man is contained in both propositions, and if the form is of the proposition, the argument has the true form ‘a is F, so a is F’, which is valid.

The puzzlement disappears if we reject the Russsellian theory of propositions. A man cannot be contained in a proposition. and so it cannot be the same man in both propositions.

‘Cicero is a Roman, therefore Tully is a Roman’ is plainly invalid. Its form is: Rc, ergo Rt, which is an invalid form. If we adopt  either an Aristotelian or a Fregean view of propositions we will not be tempted to think otherwise.

‘Cicero is a Roman, therefore Cicero is a Roman’ is plainly valid. ‘Cicero is a Roman, therefore Tully is a Roman’ is plainly invalid. The logical forms are different! If, on a Russellian theory of propositions, the forms are the same, then so much the worse for a Russellian theory of propositions!

Why Be Consistent? Three Types of Consistency

A reader inquires:

This idea of the necessity to be consistent seems to be the logician's "absolute," as though being inconsistent was the most painful accusation one could endure. [. . .] What rule of life says that one must be absolutely consistent in how one evaluates truth? It is good to argue from first principles but it can also lead one down a rat hole.

Before we can discuss whether one ought to be consistent, we need to know which type of consistency is at issue. There are at least three types of consistency that people often confuse and that need to be kept distinct. I'll call them 'logical,' 'pragmatic,' and 'diachronic.' But it doesn't matter how we label them as long as we keep them separate.

 1. Logical or Propositional Consistency. To say of two propositions that they are consistent is to to say that they can both be true, where 'can' expresses logical or broadly logical possibility. To say of two propositions that they are inconsistent is to say that they cannot both be true, where 'cannot' expresses logical or broadly logical impossibility.

I am blogging but not wearing a hat. My blogging is obviously consistent with my not wearing a hat since both propositions are true. But my blogging is also consistent with my wearing a hat since it is possible that I both be blogging and wearing a hat. But I am blogging now and I am not writing now are inconsistent since they cannot both be true. The first proposition entails the second, which implies the impossibility of the first being true and the second false.

Liberals often say that support for fetal rights is 'inconsistent' with support for the death penalty. But surely the following propositions are not logically inconsistent:

P1. Human fetuses have a right to life which cannot be overridden except in rare cases (e.g. threat to the life of the mother).

P2. Capital punishment for certain offences is morally justified.

Where is the inconsistency? I see none. Indeed, they are plainly logically consistent. Suppose that the right to life is grounded in the potentiality to develop into something to which one accords person-status. This is a possible view, and indeed one actually held by many. Any Aristotelian worth his salt will be able to spell it out coherently and perhaps even persuasively. Suppose also that a similarly coherent case is made for P2. One will then have made a case for the possibility of each. Joint possibility does not straightaway follow from the possibility of each, but if there is no reason to think of them as jointly impossible, then we should consider them jointly possible. On the face of it, P1 and P2 are logically consistent.  They can both be true.

2. Pragmatic Consistency. By this I mean consistency in the application of a principle. Consistency in this sense is not a relation between or among propositions, but involves a relation among a person,  a principle,  and cases to which the person applies the principle.

To apply a principle consistently is to apply it to all like cases in a like manner. So if the principle is to cherish, value, and uphold human life, then perhaps the thought of those who see inconsistency in support of both fetal rights and capital punishment is that to apply this principle to the unborn but not to certain criminals is to apply it inconsistently. "How can you oppose the killing of the unborn, when you favor the killing of certain criminals? Be consistent!"

The answer to this should be obvious. The cases are dissimilar. The unborn are innocent while criminals are not. This is a difference that makes a moral difference; it is a difference that justifies a difference in treatment. No doubt principles should be applied to like cases in a like manner. But there is no inconsistency in refusing to apply a principle to cases that are relevantly dissimilar.

Principles obviously allow of exceptions. A person who fancies himself 'consistent' in opposing both abortion and capital punishment on the ground that all human life is worthy of respect will in almost all cases make an exception when it comes to killing in self-defense or killing in a just war. Now wouldn't it be churlish and absurd to accuse such a person of being 'inconsistent'? "If you were consistent in your valuing of human life, you would value the life of the jihadi who has come to decapitate you and your family, and you would not lift a finger against him."

3. Diachronic or 'Emersonian' Consistency. Here is a famous passage from Ralph Waldo Emerson's "Self-Reliance" rarely quoted in full:

A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words and tomorrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day.(Ziff, 183)

People routinely rip the initial clause of this passage out of its context and take Emerson to be attacking logical consistency. But he is doing no such thing. It should be clear that Emerson’s dictum has nothing to do with logical consistency and everything to do with consistency of beliefs over time. The consistency in question is diachronic rather than synchronic. A “little mind” is “foolishly consistent” if it refuses to changes its beliefs when change is needed due to changing circumstances, further experience, or clearer thinking.

It should be clear that if I believe that p at time t, but believe that ~p at later time t*, it does not follow that I hold logically inconsistent beliefs. Doxastic alteration, like alteration in general, is non-contradictory for the simple reason that properties which are contradictory when taken in abstracto are had at different times. My coffee changes from hot to non-hot, and thus has contradictory attributes when we abstract from the time of their instantiation. But since the coffee instantiates them at different times, there is no contradiction such as would cause us to join Parmenides in denying the reality of the changeful world.

Belief change is just a special case of this. Suppose a politician changes her position for some good reason. There is not only nothing wrong with this, it shows an admirable openness. She goes from believing in a progressive tax scheme to believing in a flat tax, say. Surely there is no logical contradiction involved, and for two reasons. First, the property of believing that a progressive tax is warranted is not the contradictory, but merely the contrary, of the property of believing that a flat tax is warranted. (They cannot both be instantiated at the same time, but it is possible that neither be instantiated.) Second, the properties are had at different times. A logical contradiction ensues only when one simultaneously maintains both that p and that ~p.

Emerson’s sound point, then, is that one should not make a fetish out of doxastic stasis: there is nothing wrong with being ‘inconsistent’ in the sense of changing one’s beliefs when circumstances change and as one gains in experience and insight. But this is not to say that one should adopt the antics of a John Kerry or a Hillary Clinton.  Relative stability of views over time is an indicator of character.

Before leaving this topic, let's consider what Walt Whitman has to say in the penultimate section 51 of “Song of Myself” in Leaves of Grass:

Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)

Here it appears that Whitman is thumbing his nose at logical consistency. If so, the Emersonic and Whitmanic dicta ought not be confused.

4. Why be consistent? Ought one be consistent in any of these three senses? I should say it is self-evident that one ought to strive to be logically consistent. For if one's beliefs are inconsistent, then they cannot all be true, which implies that one or more of them are false. The ideal doxastic set would consist of beliefs that are both true and consistent. Logical consistency by itself is not enough since false beliefs can be consistent. But consistency is necessary for doxastic perfection and thus a goal worthy of pursuit.

As for pragmatic consistency, consistency in the application of principles to like cases, this too seems to be a goal that ought to be pursued, although I don't know how I would argue for it. More on this later.

Diachronic (Emersonian) consistency, however, is not an epistemic desideratum. On the contrary, one ought to change one's beliefs when new facts and arguments so warrant.

A reader inquires:

This idea of the necessity to be consistent seems to be the logician's "absolute," as though being inconsistent was the most painful accusation one could endure. [. . .] What rule of life says that one must be absolutely consistent in how one evaluates truth? It is good to argue from first principles but it can also lead one down a rat hole.

Before we can discuss whether one ought to be consistent, we need to know which type of consistency is at issue. There are at least three types of consistency that people often confuse and that need to be kept distinct. I'll call them 'logical,' 'pragmatic,' and 'diachronic.' But it doesn't matter how we label them as long as we keep them separate.

 1. Logical or Propositional Consistency. To say of two propositions that they are consistent is to to say that they can both be true, where 'can' expresses logical or broadly logical possibility. To say of two propositions that they are inconsistent is to say that they cannot both be true, where 'cannot' expresses logical or broadly logical impossibility.

I am blogging but not wearing a hat. My blogging is obviously consistent with my not wearing a hat since both propositions are true. But my blogging is also consistent with my wearing a hat since it is possible that I both be blogging and wearing a hat. But I am blogging now and I am not writing now are inconsistent since they cannot both be true. The first proposition entails the second, which implies the impossibility of the first being true and the second false.

Liberals often say that support for fetal rights is 'inconsistent' with support for the death penalty. But surely the following propositions are not logically inconsistent:

P1. Human fetuses have a right to life which cannot be overridden except in rare cases (e.g. threat to the life of the mother).

P2. Capital punishment for certain offences is morally justified.

Where is the inconsistency? I see none. Indeed, they are plainly logically consistent. Suppose that the right to life is grounded in the potentiality to develop into something to which one accords person-status. This is a possible view, and indeed one actually held by many. Any Aristotelian worth his salt will be able to spell it out coherently and perhaps even persuasively. Suppose also that a similarly coherent case is made for P2. One will then have made a case for the possibility of each. Joint possibility does not straightaway follow from the possibility of each, but if there is no reason to think of them as jointly impossible, then we should consider them jointly possible. On the face of it, P1 and P2 are logically consistent.  They can both be true.

2. Pragmatic Consistency. By this I mean consistency in the application of a principle. Consistency in this sense is not a relation between or among propositions, but involves a relation among a person,  a principle,  and cases to which the person applies the principle.

To apply a principle consistently is to apply it to all like cases in a like manner. So if the principle is to cherish, value, and uphold human life, then perhaps the thought of those who see inconsistency in support of both fetal rights and capital punishment is that to apply this principle to the unborn but not to certain criminals is to apply it inconsistently. "How can you oppose the killing of the unborn, when you favor the killing of certain criminals? Be consistent!"

The answer to this should be obvious. The cases are dissimilar. The unborn are innocent while criminals are not. This is a difference that makes a moral difference; it is a difference that justifies a difference in treatment. No doubt principles should be applied to like cases in a like manner. But there is no inconsistency in refusing to apply a principle to cases that are relevantly dissimilar.

Principles obviously allow of exceptions. A person who fancies himself 'consistent' in opposing both abortion and capital punishment on the ground that all human life is worthy of respect will in almost all cases make an exception when it comes to killing in self-defense or killing in a just war. Now wouldn't it be churlish and absurd to accuse such a person of being 'inconsistent'? "If you were consistent in your valuing of human life, you would value the life of the jihadi who has come to decapitate you and your family, and you would not lift a finger against him."

3. Diachronic or 'Emersonian' Consistency. Here is a famous passage from Ralph Waldo Emerson's "Self-Reliance" rarely quoted in full:

A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words and tomorrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day.(Ziff, 183)

People routinely rip the initial clause of this passage out of its context and take Emerson to be attacking logical consistency. But he is doing no such thing. It should be clear that Emerson’s dictum has nothing to do with logical consistency and everything to do with consistency of beliefs over time. The consistency in question is diachronic rather than synchronic. A “little mind” is “foolishly consistent” if it refuses to changes its beliefs when change is needed due to changing circumstances, further experience, or clearer thinking.

It should be clear that if I believe that p at time t, but believe that ~p at later time t*, it does not follow that I hold logically inconsistent beliefs. Doxastic alteration, like alteration in general, is non-contradictory for the simple reason that properties which are contradictory when taken in abstracto are had at different times. My coffee changes from hot to non-hot, and thus has contradictory attributes when we abstract from the time of their instantiation. But since the coffee instantiates them at different times, there is no contradiction such as would cause us to join Parmenides in denying the reality of the changeful world.

Belief change is just a special case of this. Suppose a politician changes her position for some good reason. There is not only nothing wrong with this, it shows an admirable openness. She goes from believing in a progressive tax scheme to believing in a flat tax, say. Surely there is no logical contradiction involved, and for two reasons. First, the property of believing that a progressive tax is warranted is not the contradictory, but merely the contrary, of the property of believing that a flat tax is warranted. (They cannot both be instantiated at the same time, but it is possible that neither be instantiated.) Second, the properties are had at different times. A logical contradiction ensues only when one simultaneously maintains both that p and that ~p.

Emerson’s sound point, then, is that one should not make a fetish out of doxastic stasis: there is nothing wrong with being ‘inconsistent’ in the sense of changing one’s beliefs when circumstances change and as one gains in experience and insight. But this is not to say that one should adopt the antics of a John Kerry or a Hillary Clinton.  Relative stability of views over time is an indicator of character.

Before leaving this topic, let's consider what Walt Whitman has to say in the penultimate section 51 of “Song of Myself” in Leaves of Grass:

Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)

Here it appears that Whitman is thumbing his nose at logical consistency. If so, the Emersonic and Whitmanic dicta ought not be confused.

4. Why be consistent? Ought one be consistent in any of these three senses? I should say it is self-evident that one ought to strive to be logically consistent. For if one's beliefs are inconsistent, then they cannot all be true, which implies that one or more of them are false. The ideal doxastic set would consist of beliefs that are both true and consistent. Logical consistency by itself is not enough since false beliefs can be consistent. But consistency is necessary for doxastic perfection and thus a goal worthy of pursuit.

As for pragmatic consistency, consistency in the application of principles to like cases, this too seems to be a goal that ought to be pursued, although I don't know how I would argue for it. More on this later.

Diachronic (Emersonian) consistency, however, is not an epistemic desideratum. On the contrary, one ought to change one's beliefs when new facts and arguments so warrant.

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

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

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

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

To illustrate the putative distinction, consider

1. George Orwell is Eric Blair

and

2. George Orwell is famous.

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

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

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

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

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

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

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

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

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

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

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

Generic Statements

Statements divide into the singular and the general.  General statements divide into the universal, the particular, and the generic. Generic statements are interesting not only to the logician and linguist and philosopher but also to critics of ideology and conservative critics of leftist ideology critique.  For example, leftists will find something 'ideological' about the generic  'Women are nurturing' whereas conservatives will hold that the sentence expresses the plain truth and that some sort of obfuscation and chicanery is involved when  leftists deny this plain biologically-based  truth and try to tie its very meaning to the legitimation and preservation of existing power relations in society.

In this entry, perhaps the first in a series, I confine myself to presenting examples of generic statements and to giving a preliminary exegesis of the linguistic data, noting some features of generic generalizations, and some philosophical questions that arise.

Examples of Generic Statements

Some of the examples are my own, some are culled from the literature. Some of the following are true, some false, and some politically incorrect.  Trigger Warning!  All girly girls and pajama boys out of the seminar room and into their safe spaces! Uncle Bill will visit you later with milk and cookies and cuddly animals.

• Dutchmen are good sailors. (Arnauld)
• Germans are industrious.
• Jews are very intelligent.
• Birds fly. 
• Chickens lay eggs.
• Germans make better soldiers than Italians.
• Cigars are what Bill smokes these days.
• Men are taller than women.
• Blacks are more criminally prone than whites.
• Priests don't ride motorcycles.
• Reducing taxes leads to increased economic growth.
• Turks are hospitable.
• Turks are very bad drivers.
• Analytic philosophers do not know the history of philosophy very well.
• Humanities departments are lousy with leftists.
• The dodo is extinct.
• Schockley invented the transistor.
• The lion has a mane.
• Blacks are not good at deferring gratification.
• Conservatives are racists.
• Women are nurturing and better with children.
• Fred drinks wine with dinner.
• The potato is highly digestible.

Some Features of Generic Statements

One obvious feature of generic statements is that they are not replaceable either salva veritate or salva significatione by either universal or particular quantified statements.  It is true that Germans are industrious, but false that all are.  That some are is true, but 'Some Germans are industrious' does not convey the sense of 'Germans are industrious.'  The generic and the particular generalization agree in truth value but differ in sense.

In a vast number of cases, if I assert that the Fs are Gs I do not mean to endorse the corresponding universal generalization.  No doubt birds fly, but it is false that all birds fly: the penguin is a bird, but it doesn't fly.  And I know that.  So if I say that birds fly, you can't refute me by bringing up the penguin.  And if I say that Italians and those of Italian extraction are frugal and masters of personal finance, which is manifestly true, you cannot refute me by bringing up your cousin Vinny, the spendthrift of Hoboken.  The same goes for 'Humanities departments are lousy with leftists.'   'Chickens lay eggs' has the interesting property that all the roosters strutting around in the world's barnyards cannot counterexample it into falsehood.

It is interesting to note  that one can make a generic statement (express a generic proposition) using a sentence with 'all' or 'every.' My example:  Omnis homo mendax.  'Every man is a liar.'  An assertive utterance of this sentence in normal contexts expresses the proposition that people lie, not the proposition that all people lie.  Or if someone says, unguardedly, or Trumpianly, 'All politicians are crooks,' he won't be fazed if you point out that the late Patrick Daniel Moynihan was no crook.  The speaker may have engaged in a hasty generalization, but then again he may have intended a generic statement.

On the other hand, we sometimes omit the universal quantifier even though the proposition we intend to express is a universal quantification.  An assertive utterance of 'Arguments have premises'  intends Every argument has premises. The possibility of counterexamples is not countenanced.  Contrast this with the generic 'Chickens lay eggs' which is plainly true even though only  hens lay eggs.

'Arguments have premises' is non-generic and elliptical for 'All arguments have premises.'    But what about 'Men are mortal'?  Is it replaceable salva significatione with 'All men are mortal'?  Perhaps not, perhaps it is a generic statement that admits of exceptions, as generics typically do.  After all, Christ was a man but he was not mortal inasmuch as he was also God. 

A clearer example is 'Man is bipedal.'  This cannot be replaced salva veritate by 'All men are bipedal' since the latter is false.  Nor can it be replaced salva significatione by 'Some man is bipedal, which, though plainly true, is not what 'Man is bipedal' means.  And the same holds for translations using the quantifiers 'many' and 'most'  and 'almost all.'

We are tempted to say that 'Man is bipedal' by its very sense cannot be about individual humans, whether all of them, most of them, many of them, or some of them,  but must be about a common generic essence that normal, non-defective humans instantiate.  But how could this be?  No generic essence has two feet.  It is always only an individual man that has or lacks two feet.  Here, then, is one of the philosophical puzzles that arise when we think about generic statements.  It is the problem of what generic statements are about, which is not to be confused with the question whether they have truth makers.

And then there is 'Man is a rational animal.'  Let us agree that to be rational is either to possess the capacity to reason or to possess the second-order capacity to develop this first-order capacity.  Aristotle's dictum is true, while 'All humans are rational animals' is false.  So Aristotle's dictum is a generic sentence that cannot be replaced by a quantified sentence. It is false that all humans are rational animals because an anencephalic human fetus, while obviously human (not bovine, canine, etc.), having as it does human parents, is not rational in the sense defined.

And of course we cannot replace 'Man is a rational animal' with 'Most men are rational animals.'  For the dictum plainly intends something like: it the nature or essence of man to be rational.  What then is the dictum about?  If you tell me that it is about the generic essence man, then I will point out the obvious: no abstract object reasons, is capable of reasoning, or has the potentiality to acquire the power to reason.  

Some philosophers hold that every truth has a truth-maker.  What then are the truth-makers for the vast class of true generics?  Do they have any? 

REFERENCE

Panayot Butchvarov, Anthropocentrism in Philosophy: Realism, Antirealism, Semirealism, de Gruyter, 2015, Chapter 8, "Generic Statements," pp. 151-168.

'Women are Better at Looking After Children'

The Opponent supplies the above-captioned sentence  for analysis.  He reports that a female family member was widely defriended (unfriended?) on Facebook for agreeing that it is true.  Of course the sentence is true as anyone with common sense and experience of life knows.

It is an example of a generic statement or generic generalization.  It obviously does not mean that all women are better at looking after children.  The Opponent writes,

I think the PC brigade would claim that any utterance whatsoever of ‘women are better at looking after children’ has a separate implicature, i.e. ‘what is suggested in an utterance, even though neither expressed nor strictly implied.’ Something like ‘women belong in the home’, i.e. the normative 'women ought to be at home looking after the children.'

No?

The Opponent and I agree that the sentence under analysis is true.  This leaves three questions.  

First, does the non-normative sentence conventionally imply the normative one?  Is there conventional implicature here?  We of course agree that we are not in the presence of logical implication or entailment. 

Second, is there conversational implicature here?

Third, is the normative sentence true?

As for the first question,I find no conventional implicature.  A conventional implicature is a non-logical implication that is not context-sensitive but depends solely on the conventional meanings of the words in the relevant sentences.  For example, 'Tom is poor but happy' implies that poverty and happiness are not usually found together.  This is not a logical implication; it is a case of conventional implicature.  Same with 'Mary had a baby and got married.'  This is logically consistent with the birth's coming before the marriage and the marriage's coming before the birth.  But it conventionally implies that Mary had a baby and then got married. This implicature is not sensitive to context of use but is inscribed in (as a Continental philosopher might say) the language system itself.  

What about conversational implicature?  This varies from context of use to context of use.  Consider my kind of conservative, the traditional conservative that rejects both the conservatism of the neo-cons and the white-race-based identity-political conservatism of the Alternative Right.  My brand of conservatism embraces certain classical liberal commitments, including: universal suffrage, the right of women to own property in their own names, and the right of women to pursue careers outside the home.

So if conservatives of my type are conversing and one says, 'Women are better at looking after children,' then this does not conversationally imply that women ought to be at home looking after the children.  But among a different type of conservative, an ultra-traditional conservative who holds that woman's place is in the home, then we are in the presence of a conversational implicature.

Finally, is it true that women ought to be at home looking after children?  I would say No in keeping with my brand of conservatism, which I warmly recommend as the best type there is, avoiding as it does the extremism of the ultra-traditional throne-and-altar, women-tied-to-the-stove conservatism (men are better cooks in any case), the namby-pamby libertarian-conservative fusionism of the Wall Streer Journal types, and the race-based identity-political extremism of the 'alties' and the neo-reactionaries.

Now if this were part of a journal article, I would not preen like this.  But this ain't no journal article.  This here's a blog post, bashed out quickly.  

Blogging's a 'sport' like speed chess.   

Your move, Opponent.

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The Two Opposites of 'Nothing' and the Logical Irreducibility of Being

This entry is part of the ongoing debate with the Opponent.

It is interesting  that 'nothing' has two opposites.  One is 'something.'  Call it the logical opposite.  The other is 'being.'  Call it the ontological opposite.  Logically, 'nothing' and 'something' are interdefinable quantifiers:

D1. Nothing is F =_df It is not the case that something is F.

D2. Something is F =_df it is not the case that nothing is F.

These definitions, which are part of the articulation of the Discursive Framework (DF), give us no reason to think of one term as more basic than the other.  Logically, 'nothing' and 'something'  are on a par.  Logically, they are polar opposites.  Anything you can say with the one you can say with the other, and vice versa.

We also note that as quantifiers, as terms expressing logical quantity, 'nothing' and 'something' are not names or referring expressions.

So far I have said nothing controversial.

Ontologically, however, being and nothing are not on a par.  They are not polar opposites.  Being is primary, and nothing is derivative.  (Note the ambiguity of 'Nothing is derivative' as between 'It is not the case that something is derivative' and 'Nothingness is derivative.'  The second is meant.)

Now we enter the arena of controversy. For it might be maintained that there are no ontological uses of 'being,' and 'nothing,' that talk of being and nothing  is replaceable without remainder by use of the quantifiers defined in (D1) and (D2).

Quine said that "Existence is what existential quantification expresses."  I deny it:  there is more to existence than what the existential quantifier expresses.  Quine's is a thin theory of existence; mine is a thick theory.  Metaphorically, existence possesses an ontological thickness.  This is very important for metaphysics if true.

I won't be able to prove my point because nothing in philosophy can be proven.  But I can argue for my point in a fallacy-free manner.

Suppose we try to define the existential 'is' in terms of the misnamed because question-begging 'existential' quantifier.  (The proper moniker is 'particular quantifier.')  This is standardly done as follows.

D3. y is/exists =_df for some x, y = x.

In plain English, for y to be or exist is for y to be identical to something. For Quine to be or exist is for Quine to be identical to something.  In general, to be is to be identical to something, not some one thing of course, but something or other.   This thing, however, must exist, and in a sense not captured by (D3).  Thus

Quine exists =_df Quine is identical to something that exists

and

Pegasus does not exist =_df nothing that exists is such that Pegasus is identical to it

or

Pegasus is diverse from everything that exists.

The point, which many find elusive, is that the items in the domain of quantification  must be there to be quantified over, where 'there' has not a locative but an existential sense.  For if the domain includes nonexistent objects, then, contrary to fact, Pegasus would exist in virtue of being identical to an item in this widened domain.

The conclusion is obvious: one cannot explicate the existential 'is' in terms of the particular quantifier without circularity, without presupposing that things exist in a sense of 'exist' that is not captured by (D3).

Mere logicians won't accept or perhaps even understand this since existence is "odious to the logician" as George Santayana observes. (Scepticism and Animal Faith, Dover, 1955, p. 48, orig. publ. 1923.) You have to have metaphysical aptitude to understand it. (But now I am tending toward the tendentious.)

Intellectual honesty requires that I admit that I am basing myself on an intuition, what J. Maritain calls the intuition of Being.  I find it self-evident that the existence of a concrete individual is an intrinsic determination that makes it be as opposed to not be. This implies a real distinction between x and the existence of x. Accordingly, the existence of an individual cannot be reduced to its self-identity: the existence of Quine does not reduce to Quine's being (identical to) Quine, as on the thin theory.  And the nonexistence of Pegasus does not reduce to its being diverse from everything.  (If to be is to be identical to something, then not to be is to be diverse from everything.)

The Opponent does not share my intuition.  In the past I have berated him for being 'existence-blind' but he might plausibly return the 'compliment' by accusing me of double vision:  I see Socrates but I also 'see' the existence of Socrates when there is no such 'thing.' 

So far, not good:  I can't refute the Opponent but he can't refute me.  Stand-off.  Impasse, a-poria.

Let me try a different tack.  Does the Opponent accept 

ENN. Ex nihilo nihil fit?

Out of nothing nothing comes.  Note that 'nothing' is used here in two different ways, ontologically and logically/quantificationally. For what the hallowed dictum states is that it is not the case that something arises from nothing/Nothingness.  

Now if the Opponent accepts the truth or even just the meaningfulness of (ENN), then he must admit that there are two senses of 'nothing,' the logical and the ontological, and correspondingly, two senses of 'something.'  If so, then being and nothing cannot be exhaustively understood in terms of logical quantifiers and propsitional negation, and then the thin theory bites the dust.

But if the thin theory succumbs, then there is more to existence than can be captured within the Discursive Framework.

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The Discursive Framework, Logic, and Whether the Via Negativa is the Path to Nowhere

The Historian of Logic comments:

It seems to me that what you call the ‘Discursive Framework’ is what I and others call ‘logic’, and that it reflects a Kantian view of logic that prevailed before Russell and Frege, namely that logic reflects the ‘laws of thought’ only. Are you mooting the possibility of beings which defy conception under these laws, or realms where the laws do not apply?

I was re-reading Kant’s Logic last week and it is full of this stuff.

Logic.  I would define logic as the normative science of inference. Science: scientia, study of.  Inference:  the mental process of deriving a proposition (the conclusion) from one or more  propositions (the premises).  Normative: logic is not concerned with how people think as a matter of fact, which is a concern of psychology, but with how they ought to think if they are to arrive at truth and move from known truths to further truths.   The task of logic is to set forth the criteria whereby correct inferences may be distinguished from incorrect inferences. 

The above definition is neutral with respect to any number of ontological questions.  Thus I used 'proposition' above innocuously without presupposing any theory as to what propositions are.  I spoke of inference as a mental process, but this too is innocuous inasmuch as one could be a mind-brain identity theorist and agree with me about logic.  (But if you are an eliminativist about the mental, then you 'get the boot':  it is a Moorean fact that there are inferences.)

Discursive Framework.  This is not the same as logic, pace the Historian, even though it does contain such logical principles as LNC and LEM, and indeed the whole of standard logic.  (We can argue about 'standard' in the ComBox.)  The DF also contains principles that are not strictly logical -- they are not logical truths -- but are better classifiable as metaphysical, as propositions of metaphysica generalis.  Examples:

a. Everything exists: There are no nonexistent items.  Pace van Inwagen, the negation of this is not a logical contradiction.

b. Everything has properties.  (Partisans of bare or thin particulars do not deny this.)

c. Nothing has a property P by being identical to P.   (The 'is' of predication is not assimilable to the 'is' if formal identity.)

d. Principles of logic, such as For any x, x = x, are not just true of objects of thought qua objects of thought, but are also true  of mind-independentally real items.   Thus the principles of logic are not merely principles of thought but principles of reality as well. Not merely logical, they are also ontological.  There is a jump here, from the logical to the ontological, that Aristotle was aware of.  With that jump comes the problem of justifying it.

e. The thinking of ectypal intellects such as ourselves is necessarily such as to involve a distinction between subject and predicate. There are no simple thoughts/propositions if by that we mean thoughts/proposition lacking sub-propositional structure.  Every proposition is internally structured, e.g. Fa, Rab, (x)Fx, etc.  

Laws of Thought but No Psychologism.  Kant, Husserl, and Frege all rejected psychologism in logic.  Are the laws of logic laws of thought?  Yes, of course.  What else would they be?  But this is not to say that they are laws of human psychology.  They are laws that govern the thinking of any actual or possible ectypal intellect.  They might also be laws of reality, all reality, with no exceptions. But surely it would be uncritical simply to assume this.  It wants proof, or at least argument.  As I said, Aristotle had already seen the problem.

Are you mooting the possibility of beings which defy conception under these laws, or realms where the laws do not apply?

Yes, that is what I am doing, although I wouldn't speak of beings.  That's plural, and the singular-plural distinction is part and parcel of the Discursive Framework.  My aim is to make philosophy safe for mysticism.    My aim is to show that while remaining in philosophy, in the DF, one can come to descry the 'possibility' of a, or rather, THE transdiscursive realm.  I deny that the via negativa is the road to nowheresville or u-topia.

I am not attempting anything new; the novelty is merely in the way I go about it.  And there is nothing illogical about it.  Or can you find non sequiturs or other strictly logical mistakes in the above or in recent cognate posts?  If there is a suprarational realm would it not be sloppy thinking, and thus 'illogical,' to assume that it must be infrarational?

Nothing new:  we have seen this sort of thing in the Far East in Buddhist schools like that of Nagarjuna and in Taoism; in the ancient and medieval Western world, e.g., Pseudo-Dionysus the Areopagite, and in the modern period with Kant and then again in the early Wittgenstein.

The Doctrine of Divine Simplicity (DDS) Helps Focus The Issue.  Duality is unavoidable on the discursive plane.  To think is to judge, and to judge at the most basic level  is to judge of a that it is or is not F.  At a bare minimum, then, there is the duality of subject and property.  (Brentano transformations of  predications into existential sentences avail nothing: the duality of existence-nonexistence remains.) As I said above, no thought/proposition, no content of an act of thinking, is simple.  But God is simple according to DDS.  He is identical to his attributes, which implies that each attribute is identical to every other one.  If he weren't then he would be dependent on his attributes for his nature, and he would not be the absolute reality.  He could not possess aseity. He could not be uniquely unique. If God were unique only in the sense that he is necessarily one of a kind, then he would one of a class of such beings, and a greater could be conceived, namely, a being uniquely unique, i.e., unique in the sense of transcending the very distinction between instance and kind.

Now if God is simple, then how can our talk and thought, which is necessarily discursive, be literally true of him?  One response is that God talk is literal but analogical.  This needs exploring in a separate post.  But if we cannot accept the doctrine of analogy, then the simple God lies entirely beyond the DF. 

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a

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Language and Reality

Circular Definitions, Arguments, and Explanations

In the course of our discursive operations we often encounter circularity.  Clarity will be served if we distinguish different types of circularity.  I count three types.  We could label them definitional, argumentative, and explanatory.

A.  The life of the mind often includes the framing of definitions.  Now one constraint on a good definition is that it not be circular.  A circular definition is one in which the term to be defined (the definiendum) or a cognate thereof occurs in the defining term (the definiens).  'A triangle is a plane figure having a triangular shape,' though plainly true, is circular.  'The extension of a term is the set of items to which the term applies' is an example of a non-circular definition. 

B.  Sometimes we argue.  We attempt to support a proposition p by adducing other propositions as reasons for accepting p.  Now one constraint on a good argument is that it not be circular.  A circular argument in is one in which the conclusion appears among the premises, sometimes nakedly, other times clothed for decency's sake  in different verbal dress.  Supply your own examples.

C.  Sometimes we explain.  What is it for an individual x to exist?  Suppose you say that for x to exist is for some property to be instantiated.  One variation on this theme is to say that for Socrates to exist is for the haecceity property Socrateity to be instantiated.  This counts as a metaphysical explanation, and a circular one to boot.  For if Socrateity is instantiated, then it is is instantiated by Socrates who must exist to stand in the instantiation relation.  The account moves in a circle, an explanatory circle of embarrassingly short diameter.

Suppose someone says that for x to exist is for x to be identical to something or other.  They could mean this merely as an equivalence, in which case I have no objection.  But if they are shooting for a explanation of existence in terms of identity-with-something-or-other, then they move in an explanatory circle. For if x exists in virtue of its identity with some y, then y must exist, and you have moved in an explanatory circle.

Some philosophers argue that philosophers ought not be in the business of explanation.  I beg to differ.  But that is a large metaphilosophical topic unto itself.

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Neither the Existence Nor the Nonexistence of God is Provable

A post of mine ends like this:

To theists, I say: go on being theists.  You are better off being a theist than not being one.  Your position is rationally defensible and the alternatives are rationally rejectable.  But don't fancy that you can prove the existence of God or the opposite.  In the end you must decide how you will live and what you will believe.

About "Don't fancy that you can prove the existence of God or the opposite," Owen Anderson asks:

How would we know if that claim is itself true?  Isn't it is possible that one or the other can indeed be proven?

To formulate my point in the declarative rather than the exhortative mood:  

 

    P. Neither the existence nor the nonexistence of God is provable.

 

How do I know (P) to be true?  By reflection on the nature of proof.  An argument is a proof if and only if it satisfies all of the following six requirements: it is deductive; valid in point of logical form; free of such informal fallacies as petitio principii; possesses a conclusion that is relevant to the premises; has premises each of which is true; has premises each of which is known to be true.

 

I say that an argument is a proof if and only it is rationally compelling, or rationally coercive.  But an argument needn't be rationally compelling to be a more or less 'good argument,' one that renders its conclusion more or less rationally acceptable.

 

Now if my definition above gives what we ought to mean by 'proof,' then it is clear that neither the existence nor the nonexistence of God can be proven. Suppose you present a theistic or anti-theistic argument that satisfies the first five requirements.  I will then ask how you know that the premises are true.  Suppose one of your premises is that change is the conversion of potency into act. That is a plausible thing to maintain, but how do you know that it is true?  How do you know that the general-ontological framework within which the proposition acquires its very sense, namely, Aristotelian metaphysics, is tenable?  After all, there are alternative ways of understanding change.  That there is change is a datum, a Moorean fact, but it would be an obvious mistake to confuse this datum with some theory about it, even if the theory is true.  Suppose the theory is true.  This still leaves us with the question of how we know it is.   Besides, the notions of potency and act, substance and accident, form and matter,  and all the rest of the Aristotelian conceptuality are murky and open to question.  (For example, the notion of prime matter is a necessary ingredient in an Aristotelian understanding of substantial change, but the notion of materia prima is either incoherent or else not provably coherent.)

 

To take a second example, suppose I give a cosmological argument the starting point of which is the seemingly innocuous proposition that there are are contingent beings, and go on to argument that this starting point together with some auxiliary premises, entails the existence of God.  How do I know that existnece can be predicated of concrete individuals?  Great philosophers have denied it.  Frege and Russell fanmously held that existence vannot be meaningfully predicated of individuals but only of cncepts and propositional functions.  I have rather less famoulsy argued that the 'GFressellina' view' is mstaken, but this is a point of controversy.  Furtrhertmore, if existence cannot be meaningfully predicated of individuals, how can individuals be said to exist contingently?

 

The Appeal to Further Arguments 

 

If you tell me that the premises of your favorite argument can be known to be true on the basis of further arguments that take those premises as their conclusions, then I simply iterate my critical procedure: I run the first five tests above and if your arguments pass those, then I ask how you know that their premises are true.  If you appeal to still further arguments, then you embark upon a vicious infinite regress.

 

The Appeal to Self-Evidence

 

If you tell me that the premises of your argument are self-evident, then I will point out that your and my subjective self-evidence is unavailing.  It is self-evident to me that capital punishment is precisely what justice demands in certain cases.  I'll die in the ditch for that one, and pronounce you morally obtuse to boot for not seeing it.  But there are some who are intelligent, well-meaning, and sophisticated to whom this is not self-evident.  They will charge with with moral obtuseness.  Examples are easily multiplied. What is needed is objective, discussion-stopping, self-evidence.  But then, how, in a given case, do you know that your evidence is indeed objective?  All you can go on is how things seem to you.  If it seems to you that it is is objectively the case that p, that boils down to: it seems to you that, etc., in which case your self-evidence is again merely subjective.

 

The Appeal to Authority

 

You may attempt to support the premises of your argument by an appeal to authority.  Now many such appeals  are justified. We rightly appeal to the authority of gunsmiths, orthopaedic surgeons, actuaries and other experts all the time, and quite sensibly. But such appeals are useless when it comes to PROOF.  How do you know that your putative authority really is one, and even if he is, how do you know that he is eight in the present case?  How do you know he is not lying to you well he tells you you need a new sere in your  semi-auto pistol?

 

The Appeal to Revelation

 

This is the ultimate appeal to authority.  Necessarily, if God reveals that p, then p!  Again, useless for purposes of proof.  See Josiah Royce and the Paradox of Revelation.

 

Move in a Circle?

 

If your argument falls afoul of petitio principii, that condemns it, and the diameter of the circle doesn't matter.  A circle is a circle no matter its diameter.

 

Am I Setting the Bar Too High?

 

It seems to me I am setting it exactly where it belongs.  After all we are talking about PROOF here and surely only arguments that generate knowledge count as proofs.  But if an argument is to generate a known proposition, then its premises must be known, and not merely believed, or believed on good evidence, or assumed, etc.  

 

"But aren't you assuming that knowledge entails certainty, or (if this is different) impossibility of mistake?"  Yes I am assuming that.  Argument here.  

 

 Can I Consistently Claim to Know that (P) is true?

 

Owen Anderson asked me how I know that (P) is true.   I said I know it by reflection on the concept of proof.  But that was too quick. Obviously I cannot consistently claim to know that (P) if knowledge entails certainty.  For how do I know that my definition captures the essence of proof?  How do I know that there is an essence of proof, or any essence of anything?   What I want to say, of course, is that it is very reasonable to define 'proof' as I define it -- absent some better definition -- and that if one does so define it then it is clear that there are very few proofs, and, in particular, that there are no proofs of God or of the opposite.

 

"But then isn't it is possible that one or the other can indeed be proven?"

 

Yes, if one operates with a different, less rigorous, definition of 'proof.'  But in philosophy we have and maintain high standards.  So I say proof is PROOF (a tautological form of words that expresses a non-tautological proposition) and that we shouldn't use the word to refer to arguments that merely render their conclusions rationally acceptable.  

 

Note also that if we retreat from the rationally compelling to the rationally acceptable, then both theism and atheism are rationally acceptable.  I suspect that what Owen wants is a knock-down argument for the existence of God.  But if that is what he wants, then he wants a proof in my sense of the world.  If I am right, that is something very unreasonable to expect.

 

There is no getting around the need for a decision.  In the end, after all the considerations pro et contra, you must decide what you will believe and how you will live.

 

Life is a venture and an adventure.  You cannot live without risk.  This is true not only in the material sphere, but also in the realm of ideas.

 

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An Insufficient Argument Against Sufficient Reason

Generic and Specific Problems of Evil: The Nature and Tractability of the Problem Depends on the Type of Theism Espoused

Josiah Royce and the Paradox of Revelation

Kripke, Belief, Irrationality, and Contradiction

London Ed comments:

I also note a confusion that has been running through this discussion, about the meaning of ‘contradiction’. I do not mean to appeal to etymology or authority, but it’s important we agree on what we mean by it. On my understanding, a contradiction is not ‘the tallest girl in the class is 18’ and ‘the cleverest girl in the class is not 18’, even when the tallest girl is also the cleverest. Someone could easily believe both, without being irrational. The point of the Kripke puzzle is that Pierre seems to end up with an irrational belief. So it’s essential, as Kripke specifies, that he must correctly understand all the terms in both utterances, and that both utterances are logically contradictory, as in ‘Susan is 18’ and ‘Susan is not 18’.

Do we agree?

Well, let's see.  The Maverick method enjoins the exposure of any inconsistent polyads that may be lurking in the vicinity.  Sure enough, there is one:

An Inconsistent Triad

a. The tallest girl in the class is the cleverest girl in the class.
b. The tallest girl in the class is 18.
c. The cleverest girl in the class is not 18.

This trio is logically inconsistent in the sense that it is not logically possible that all three propositions be true.  But if we consider only the second two limbs, there is no logical inconsistency:  it is possible that (b) and (c) both be true.  And so someone, Tom for example, who believes that (b) and also believes that (c) cannot be convicted of irrationality, at least not on this score.  For all Tom knows  -- assuming that he does not know that (a) -- they could both be true:  it is epistemically possible that both be true.  This is the case even if in fact (a) is true.  But we can say more: it is metaphysically possible that both be true.  For (a), if true, is contingently true, which implies that it is is possible that it be false.

By contrast, if Tom entertains together, in the synthetic unity of one consciousness, the propositions expressed by 'Susan is 18 years old' and 'Susan is not 18 years old,' and if Tom is rational, then he will see that the two propositions are logical contradictories of each other, and it will not be epistemically possible for him that both be true.  If he nonetheless accepts both, then we have a good reason to convict him of being irrational, in this instance at least.

Given the truth of (a), (b) and (c) cannot both be true and cannot both be false.  This suggests  that the pair consisting of (b) and (c) is a pair of logical contradictories.  But then we would have to say that the contradictoriness of the pair rests on a contingent presupposition, namely, the truth of (a).  London Ed will presumably reject this.  I expect he would say that the logical contradictoriness of a pair of propositions cannot rest on any contingent presupposition, or on any presupposition at all.  Thus

d. Susan is 18

and

e. Susan is not 18

form a contradictory pair the contradictoriness of which rests on their internal logical form -- Fa, ~Fa -- and not on anything external to the propositions in question.

 So what should we say?  If Tom believes both (b) and (c), does he have contradictory beliefs?  Or not? 

The London answer is No!  The belief-contents are not formally contradictory even though, given the truth of (a), the contents are such that they cannot both be true and cannot both be false.  And because the belief-contents are not formally contradictory, the beliefs themselves -- where a belief involves both an occurrent or dispositional state of a person and a belief-content towards which the person takes up a propositional attitude -- are in no theoretically useful sense logically contradictory.

The Phoenix answer suggestion is that, because we are dealing with the beliefs of a concrete believer embedded in the actual world, there is sense to the notion that Tom's beliefs are contradictory in the sense that their contents are logically contradictory given the actual-world truth of (a).  After all, if Susan is the tallest and cleverest girl, and the beliefs in question are irreducibly  de re, then Tom believes, of Susan, that she is both 18 and not 18, even if Tom can gain epistemic access to her only via definition descriptions.   That belief is de re, irreducibly, is entailed  by (SUB), to which  Kripke apparently subscribes:

SUB:  Proper names are everywhere intersubstitutable salva veritate.

A Second  Question

If, at the same time,  Peter believes that Paderewski is musical and Peter believes that Paderewski is not musical, does it follow that Peter believes that (Paderewski is musical and Paderewski is not musical)?  Could this conceivably be a non sequitur? Compare the following modal principle:

MP:  If possibly p and possibly ~p, it does not follow that possibly (p & ~p).

For example, I am now seated, so it is possible that I now be seated; but it is also possible that I now  not be seated, where all three occurrences/tokens of 'now' rigidly designate the same time.  But surely it doesn't follow that it is possible that (I am now seated and I am now not seated).  Is it perhaps conceivable that

BP:  If it is believed by S that p and it is believed by S that ~p, it does not follow that it is believed by S that (p & ~p)?

Has anybody ever discussed this suggestion, even if only to dismiss it?

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In What Sense Does an Indefinite Noun Phrase Refer?

London Ed propounds a difficulty for our delectation and possible solution:

Clearly the difficulty with the intralinguistic theory is its apparent absurdity, but I am trying to turn this around. What can we say about extralinguistic reference?  What actually is the extralinguistic theory? You argue that the pronoun ‘he’ inherits a reference from its antecedent, so that the pronoun does refer extralinguistically, but only per alium, not per se.

Mark 14:51 And there followed him [Jesus] a certain young man (νεανίσκος τις) , having a linen cloth (σινδόνα) cast about his naked body; and the young men laid hold on him.  14:52 And he left the linen cloth, and fled from them naked.

So the pronoun ‘he’ inherits its reference through its antecedent. But the antecedent is the noun phrase ‘a certain young man’. On your theory, does this refer extralinguistically?  That’s a problem, because indefinite noun phrases traditionally do not refer, indeed that’s the whole point of them. ‘a certain young man’ translates the Latin ‘adulescens quidam’ which in turn translates the Greek ‘νεανίσκος τις’. Here ‘certain’ (Latin quidam, Greek τις) signifies that the speaker knows who he is talking about, but declines to tell the audience who this is. Many commentators have speculated that the man was Mark himself, the author of the gospel, which if true means that ‘a certain young man’ and the pronouns, could be replaced with ‘I’, salva veritate.  But Mark deliberately does not tell us.

So, question 1, in what sense does the indefinite noun phrase refer, given that, on the extralinguistic theory, it has to be the primary referring phrase, from which all subsequent back-reference inherits its reference?

A. First of all, it is not clear why Ed says, ". . . indefinite noun phrases traditionally do not refer, indeed that’s the whole point of them."  Following Fred Sommers, in traditional formal logic (TFL) as opposed to modern predicate logic (MPL), indefinite noun phrases do refer. (See Chapter 3, "Indefinite Reference" of The Logic of Natural Language.) Thus the subject terms in 'Some senator is a physician' and 'A physician is running for president' refer, traditionally, to some senator and to a physician.  This may be logically objectionable by Fregean lights but it is surely traditional.  That's one quibble.  A second is that it is not clear why Ed says "that's the whole point of them."

So the whole point of a tokening of 'a certain young man' is to avoid making an extralinguistic reference?  I don't understand.

B.  Ed says there is a problem on my view.  A lover of aporetic polyads, I shall try to massage it into one.  I submit for your solution the following inconsistent pentad:

a. There are only two kinds of extralinguistic reference: via logically proper names, including demonstratives and indexicals, and via definite descriptions.
b. The extralinguistic reference of a grammatical pronoun used pronominally (as opposed to quantificationally or indexically) piggy-backs on the extralinguistic reference of its antecedent. It is per alium not per se.
c. 'His,' 'him,' and 'he' in the verse from Mark are pronouns used pronominally the antecedent of which is 'a certain young man.'
d.  'A certain young man' in the verse from Mark is neither a logically proper name nor a definite description.
e.  'A certain young man' in the verse from Mark refers extralinguistically on pain of the sentence of which it is a part being not true.

The pentad is inconsistent.

The middle three limbs strike me as datanic.  So there are two possible solutions.

One is (a)-rejection.  Maintain as Sommers does that indefinite descriptions can refer.  This 'solution' bangs up against the critique of Peter Geach and other Fregeans.

The other is (e)-rejection.  Deny that there is any extralinguistic reference at all.  This, I think, is Ed's line.  Makes no sense to me, though.

I wonder: could Ed be toying with the idea of using the first four limbs as premises in an argument to the conclusion that all reference is intralinguistic?  I hope not.

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Like a Moth to the Flame

Jean van Heijenoort was drawn to Anne-Marie Zamora like a moth to the flame. He firmly believed she wanted to kill him and yet he travelled thousands of miles to Mexico City to visit her where kill him she did by pumping three rounds from her Colt .38 Special into his head while he slept.  She then turned the gun on herself.  There is no little irony in the fact that van Heijenoort met his end in the same city as Lev Davidovich Bronstein, better known as Leon Trotsky.  For van Heijenoort was Trotsky's secretary, body guard, and translator from 1932 to 1939.

The former 'Comrade Van' was a super-sharp logician but a romantic fool nonetheless.  He is known mainly for his contribution to the history of mathematical logic.  He edited From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931 (Harvard University Press 1967) and translated some of the papers.  The source book is a work of meticulous scholarship that has earned almost universally high praise from experts in the field.  

One lesson is the folly of seeking happiness in another human being.  The happiness we seek, whether we know it or not, no man or woman can provide. And then there is the mystery of self-destruction. Here is a brilliant, productive, and well-respected man.  He knows that 'the flame' will destroy him, but he enters it anyway.  And if you believe that this material life is the only life you will ever have, why throw it away for an unstable, pistol-packing female?  

One might conclude to the uselessness of logic for life.  If the heart has its reasons (Pascal) they apparently are not subject to the discipline of mathematical logic.    All that logic and you still behave irrationally about the most important matters of self-interest?  So what good is it?  Apparently, van Heijenoort never learned to control his sexual and emotional nature.  Does it make sense to be ever so scrupulous about what you allow yourself to believe, but not about what you allow yourself to love?

SOURCES (The following are extremely enjoyable books.  I've read both twice.)

Anita Burdman Feferman, Politics, Logic, and Love: The Life of Jean van Heijenoort, Boston: Jones and Bartlett Publishers, 1993.

Jean van Hejenoort, With Trotsky in Exile: From Prinkipo to Coyoacan, Harvard UP, 1978.

Related:  Trotsky's Faith

The Last Words of Leon Trotsky

 

Trotsky, Frida Kahlo, with van Heijenoort standing behind Frida.

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God, Proof, and Desire

From a reader:

. . . I’m confused by some of your epistemic terms. You reject [in the first article referenced below] the view that we can “rigorously prove” the existence of God, and several times say that theistic arguments are not rationally compelling, by which you mean that there are no arguments “that will force every competent philosophical practitioner to accept their conclusions on pain of being irrational if he does not.“

Okay, so far I’m tracking with you. But then you go on to say that “[t]here are all kinds of evidence” for theism (not just non-naturalism), while the atheist “fails to account for obvious facts (consciousness, self-consciousness, conscience, intentionality, purposiveness, etc.) if he assumes that all that exists is in the space-time world. I will expose and question all his assumptions.  I will vigorously and rigorously drive him to dogmatism.  Having had all his arguments neutralized, if not refuted, he will be left with nothing better than the dogmatic assertion of his position."

So how is the atheist not irrational on your view, assuming he is apprised of your arguments? Perhaps the positive case for theism and the negative case against naturalism don’t count as demonstrations in a mathematical sense, but I’m not sure why they’re not supposed to be compelling according to your gloss on the term.

The term 'mathematical' muddies the waters  since it could lead to a side-wrangle over what mathematicians are doing when they construct proofs.  Let's not muddy the waters.  My claim is that we have no demonstrative knowledge of the truth of theism or of the falsity of naturalism.  Demonstrative knowledge is knowledge produced by a demonstration.  A demonstration in this context is an argument that satisfies all of the following conditions:

1. It is deductive
2. It is valid in point of logical form
3. It is free of such informal fallacies as petitio principii
4. It is such that all its premises are true
5. It is such that all its premises are known to be true
6. It is such that its conclusion is relevant to its premises.

To illustrate (6).  The following argument satisfies all of the conditions except the last and is therefore probatively worthless:

Snow is white
ergo
Either Obama is president or he is not.

On my use of terms, a demonstrative argument = a probative argument = a proof = a rationally compelling argument.  Now clearly there are good arguments (of different sorts) that are not demonstrative, probative, rationally compelling.  One type is the strong inductive argument. By definition, no such argument satisfies (1) or (2).  A second type is the argument that satisfies all the conditions except (5). 

Can one prove the existence of God?  That is, can one produce a proof (as above defined) of the existence of God?   I don't think so.  For how will you satisfy condition (5)?  Suppose you give argument A for the existence of God.  How do you know that the premises of A are true?  By argument?  Suppose A has premises P1, P2, P3.  Will you give arguments for these premises?  Then you need three more arguments, one for each of P1, P2, P3, each of which has its own premises.  A vicious infinite regress is in the offing.  Needless to say, moving in an argumentative circle is no better.

At some point you will have to invoke self-evidence.   You will have to say that, e.g., it is just self-evident that every event has a cause.  And you will have to mean objectively self-evident, not just subjectively self-evident.  But how can you prove, to yourself or anyone else, that what is subjectively self-evident is objectively self-evident?  You can't, at least not with respect to states of affairs transcending your consciousness. 

I conclude that no one can prove the existence of God.  But one can reasonably believe that God exists.  The same holds for the nonexistence of God.  No one can prove the nonexistence of God.  But one can reasonably believe that there is no God.

The same goes for naturalism.  I cannot prove that there is more to reality than the space-time system and its contents.  But I can reasonably believe it.  For I have a battery of arguments each of which satisfies conditions (1), (2), (3) and (6) and may even, as far as far as I know, satisfy  (4).

"So how is the atheist not irrational on your view, assuming he is apprised of your arguments?"

He is not irrational because none of my arguments are rationally compelling in the sense I supplied, namely, they are not such as to force every competent philosophical practitioner to accept their conclusions on pain of being irrational if he does not.  To illustrate, consider the following argument from Peter Kreeft (based on C. S. Lewis), an argument I consider good, but not rationally compelling.  I will argue (though I will not prove!) that one who rejects this argument is not irrational.

The Argument From Desire

• Premise 1: Every natural, innate desire in us corresponds to some real object that can satisfy that desire.
• Premise 2: But there exists in us a desire which nothing in time, nothing on earth, no creature can satisfy.
• Conclusion: Therefore there must exist something more than time, earth and creatures, which can satisfy this desire.

This something is what people call "God" and "life with God forever."

This is surely not a compelling argument.  In fact, as it stands, it is not even valid.  But it is easily repaired.  There is need of an additional premise, one to the effect that the desire that nothing in time can satisfy is a natural desire.  This supplementary  premise is needed for validity, but it is not obviously true.  For it might be -- it is epistemically possible that -- this desire that nothing in time can satisfy is artificially induced by one's religious upbringing or some other factor or factors.

Furthermore, is premise (1) true?  Not as it stands.  Suppose I am dying of thirst in the desert.  Does that  desire in me correspond to some real object that can satisfy it?  Does the existence of my token desire entail the existence of a token satisfier?  No!  For it may be that there is no potable water in the vicinity, when  only potable water in the immediate vicinity can satisfy my particular thirst.  At most, what the natural desire for water shows is  that water had to have existed at some time.  It doesn't even show that water exists now.  Suppose all the water on earth is suddenly rendered undrinkable.  That is consistent with the continuing existence of the natural desire/need for water.

But this is not a decisive objection since repairs can be made.  One could reformulate:

1* Every type of natural, innate desire in us corresponds to some real object that can satisfy some tokens of that type of desire.

But is (1*) obviously true?  It could be that our spiritual desires are not artificial, like the desire to play chess, but lacking in real objects nonetheless.  It could be that their objects are merely intentional.  Suppose our mental life (sentience, intentionality, self-awareness, the spiritual desires for meaning, for love, for lasting happiness, for an end to ignorance and delusion and enslavement to base desires) is just an evolutionary fluke.  Our spiritual desires would then be natural as opposed to artificial, but lacking in real objects. 

Why do we naturally desire, water, air, sunlight?  Because without them we wouldn't have come into material existence in the first place.  Speaking loosely, Nature implanted these desires in us.  This is what allows us to infer the reality of the object of the desire from the desire.  Now if God created us and implanted in us a desire for fellowship with him, then we could reliably infer the reality of God from the desire.  But we don't know whether God exists; so it may be that the natural desire for God lacks a real object.

Obviously, one cannot define 'natural desire' as a desire that has a real and not merely intentional object, and then take the non-artificiality of a desire as proof that it is natural.  That would be question-begging.

My point is that  (1) or (1*) is not known to be true and is therefore rationally rejectable.  The argument from desire, then, is not rationally compelling.

 As for premise (2), how do we know that it is true? Granting that it is true hitherto, how do we know that it will be true in the future?  The utopian dream of the progressives is precisely that we can achieve here on earth final satisfaction of our deepest desires.  Now I don't believe this for a second.  But I don't think one can reasonably claim to know that (2) is false.  What supports it is a very reasonable induction.  But inductive arguments don't prove anything.

In sum, the argument from desire, suitably deployed and rigorously articulated, helps render theistic belief rationally acceptable.  But it is not a rationally compelling argument.

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Denying the Antecedent?

While traipsing through the Superstition foothills Sunday morning in search of further footnotes to Plato, I happened to think of James Madison and Federalist #51 wherein we read, "If men were angels, no government would be necessary."  My next thought was: "Men are not angels."  But I realized it could be the formal fallacy of Denying the Antecedent were I to conclude to the truth, "Some government is necessary." (I hope you agree with me that that is a truth.)

The first premise is a counterfactual conditional, indeed, what I call a per impossibile counterfactual.  To keep things simple, however, we trade the subjunctive in for the indicative.  Let this be the argument under consideration:

1. If men are angels, then no government is necessary.
2. Men are not angels.
ergo
3. Some government is necessary.

A prima vista, we have here an instance of the invalid argument-form, Denying the Antecedent:

If p, then q
~p
ergo
~q.

But I am loath to say that the argument (as opposed to the just-depicted argument-form) is invalid. It strikes me as valid.  But how could it be valid?

Approach One

One could take the (1)-(3) argument to be an enthymeme where the following is the tacit premise:

1.5 If no government is necessary, then men are angels.

Add (1.5) to the premises of the original argument and the conclusion follows by modus tollendo tollens. 

Approach Two

Might it be that 'if ___ then ___' sentences in English sometimes express biconditional propositions?  Clearly, if we replace (1) with

1* Men are angels if and only if no government is necessary

the resulting argument is valid.

Approach Three

One might take the (1)-(3) argument as inductive.  Now every inductive argument is invalid in the technical sense of 'invalid' in play here.  So if there are good inductive arguments, then there are good invalid arguments.  Right?  If the (1)-(3) argument is inductive, then I think we should say it is a very strong inductive argument.  It would then be right churlish and cyberpunkish to snort, "You're denying the antecedent!"

The question arises: are there any good examples from real argumentative life (as opposed to logic text books) of Denying the Antecedent?  I mean, nobody or hardly anybody argues like this:

If Jack ran a red light, then Jack deserves a traffic citation.
Jack did not run a red light.
ergo
Jack does not deserve a traffic citation.

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