Category: Logica Docens

Logical Versus Metaphysical Modality

A Pakistani reader inquires:

This is a query which I hope you can answer. Is there such a distinction as 'logical contingency' vs 'metaphysical contingency', and 'logical necessity' vs 'metaphysical necessity'? And if there is, can you explain it? Thank you.

A short answer first.  Yes, there are these distinctions.  They amount to a distinction between logical modality and metaphysical modality.  The first is also  called called narrowly logical modality while the second is also called broadly logical modality.   Both contrast with nomological modality. 

Now a long answer.  The following nine paragraphs unpack the notion of broadly logical or metaphysical modality and contrast it with narrowly logical modality.

1. There are objects and states of affairs and propositions that can be known a priori to be impossible because they violate the Law of Non-Contradiction (LNC). Thus a plane figure that is both round and not round at the same time, in the same respect, and in the same sense of 'round,' is impossible, absolutely impossible, simply in virtue of its violation of LNC. I will say that such an object is narrowly logically (NL) impossible. Hereafter, to save keystrokes, I will not mention the 'same time, same respect, same sense' qualification which will be understood to be in force.

2. But what about a plane figure that is both round and square? Is it NL-impossible? No. For by logic alone one cannot know it to be impossible. One needs a supplementary premise, the necessary truth grounded in the meanings of 'round' and 'square' that nothing that is round is square. We say, therefore, that the round square is broadly logically (BL) impossible. It is not excluded from the realm of the possible by logic alone, which is purely formal, but by logic plus a 'material' truth, namely the necessary truth just mentioned.

3. If there are BL-impossible states of affairs such as There being a round square, then there are BL-necessary states of affairs such as There being no round square. Impossibility and necessity are interdefinable: a state of affairs is necessary iff  its negation is impossible. It doesn't matter whether the modality is NL, BL, or nomological (physical). It is clear, then, that there are BL-impossible and BL-necessary states of affairs.

4. We can now introduce the term 'BL-noncontingent' to cover the BL-impossible and the BL-necessary.

5. What is not noncontingent is contingent. (Surprise!) The contingent is that which is possible but not necessary. Thus a contingent proposition is one that is possibly true but not necessarily true, and a contingent state of affairs is one that possibly obtains but does not necessarily obtain. We can also say that a contingent proposition is one that is possibly true and such that its negation is possibly true. The BL-contingent is therefore that which is BL-possible and such that its negation is BL-possible.

6. Whatever is NL or BL or nomologically impossible, is impossible period. If an object, state of affairs, or proposition is excluded from the realm of possible being, possible obtaining, or possible truth by logic alone, logic plus necessary semantic truths, or the (BL-contingent) laws of nature, then that object, state of affairs or proposition is impossible, period, or impossible simpliciter.

7. Now comes something interesting and important. The NL or BL or nomologically possible may or may not be possible, period. For example, it is NL-possible that there be a round square, but not possible, period. It is BL-possible that some man run a 2-minute mile but not possible, period. And it is nomologically possible that I run a 4-minute mile, but not possible period. (I.e., the (BL-contingent) laws of anatomy and physiology do not bar me from running a 4-minute mile; it is peculiarities not referred to by these laws that bar me. Alas, alack, there is no law of nature that names BV.)

8. What #7 implies is that NL, BL, and nomological possibility are not species or kinds of possibility. If they were kinds of possibility then every item that came under one of these heads would be possible simpliciter, which we have just seen is not the case. A linguistic way of putting the point is by saying that 'NL,' 'BL,' and 'nomological' are alienans as opposed to specifying adjectives: they shift or 'alienate' ('other') the sense of the noun they modify. From the fact that x is NL or BL or nomologically possible, it does not follow that x is possible. This contrasts with impossibility. From the fact that x is NL or BL or nomologically impossible, it does follow that x is impossible. Accordingly, 'NL,' 'BL,' and 'nomological' do not shift or alienate the sense of 'impossible.'

9. To appreciate the foregoing, you must not confuse senses and kinds. 'Sense' is a semantic term; 'kind' is ontological. From the fact that 'possible' has several senses, it does not follow that there are several species or kinds of possibility. For x to be possible it must satisfy NL, BL, and nomological constraints; but this is not to say that these terms refer to species or kinds of possibility.

Should We Abandon the Deep Problems for Problems Amenable to Solution?

UPDATE: London Ed does an excellent job of misunderstanding the following post.  Bad comments incline me to keep my ComBox closed.  But his is open.

Fred Sommers' "Intellectual Autobiography" begins as follows:

I did an undergraduate major in mathematics at Yeshiva College and went on to graduate studies in philosophy at Columbia University in the 1950s.  There I found that classical philosophical problems were studied as intellectual history and not as problems to be solved.  That was disappointing but did not strike me as unreasonable; it seemed to me that tackling something like "the problem of free will" or "the problem of knowledge" could take up one's whole life and yield little of permanent value.  I duly did a dissertation on Whitehead's process philosophy and was offered a teaching position at Columbia College.  Thereafter I was free to do philosophical research of my own choosing. My instinct was to avoid the seductive, deep problems and to focus on finite projects that looked amenable to solution. (The Old New Logic: Essays on the Philosophy of Fred Sommers, ed. Oderberg, MIT Press, 2005, p. 1)

 Sommers says something similar in the preface to his  The Logic of Natural Language (Oxford, 1982), p. xii:

My interest in Ryle's 'category mistakes' turned me away from the study of Whitehead's metaphysical writings (on which I had written a doctoral thesis at Columbia University) to the study of problems that could be arranged for possible solution.

What interests me in these two passages is the reason that Sommers gives for turning away from the big 'existential' questions of philosophy (God, freedom, immortality, and the like) to the problems of logical theory.  I cannot see that it is a good reason. (And he does seem to be giving a reason and not merely recording a turn in his career.)

The reason is that the problems of logic, but not those of metaphysics, can be "arranged for possible solution." Although I sympathize with Sommers' sentiment, he must surely have noticed that his attempt to rehabilitate pre-Fregean logical theory issues in results that are controversial, and indeed just as controversial as the claims of metaphysicians. Or do all his colleagues in logic agree with him?

The problems that Sommers tackles in his magisterial The Logic of Natural Language  are no more amenable to solution than the "deep, seductive" ones that could lead a philosopher astray for a lifetime.  The best evidence of  this is that Sommers has not convinced his MPL (modern predicate logic) colleagues. At the very most, Sommers has shown that TFL (traditional formal logic) is a defensible rival system.

If by 'pulling in our horns' and confining ourselves to problems of language and logic we were able to attain sure and incontrovertible results, then there might well be justification for setting metaphysics aside and working on problems amenable to solution. But if it turns out that logical, linguistic, phenomenological, epistemological and all other such preliminary inquiries arrive at results that are also widely and vigorously contested, then the advantage of 'pulling in our horns' is lost and we may as well concentrate on the questions that really matter, which are most assuredly not questions of logic and language — fascinating as these may be.

Given that the "deep, seductive" problems and those of logical theory are in the same boat as regards solubility, Sommer's' reason for devoting himself to logic over the big questions is not a good one.  The fact that philosophy of logic is often  more rigorous than 'big question' philosophy is not to the point.  The distinction between the rigorous and the unrigorous cuts perpendicular to that between the soluble and the insoluble.  And in any case, any philosophical problem can be tackled as rigorously as you please.

Sommers' is a rich and fascinating book. But, at the end of the day, how important is it to prove that the inference embedded in 'Some girl is loved by every boy so every boy loves a girl' really is capturable, pace the dogmatic partisans of modern predicate logic, by a refurbished traditional term logic? (See pp. 144-145) As one draws one's last breath, which is more salutary: to be worried about a silly b agatelle such as the one just mentioned, or to be contemplating God and the soul?

And shouldn't we philosophers who are still a ways from our last breaths devote our main energies to such questions as God and the soul over the trifles  of logic?

It would be nice if we could set philosophy on the "sure path of science" (Kant) by abandoning metaphysics and focusing on logic (or phenomenology or whatever one considers foundational).   But so far, this narrowing of focus and 'pulling in of one's horns' has availed nothing.  Philosophical investigation has simply become more technical, labyrinthine, and specialized.  All philosophical problems are in the same boat with respect to solubility.  A definitive answer to 'Are there atomic propositions?' (LNL, ch. 1) is no more in the offing than a definitive answer to 'Does God exist?' or 'Is the will libertarianly free?'

Ask yourself: what would be more worth knowing if it could be known?

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

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

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

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

Arguments and Proofs in Philosophy

London Ed writes:

Philosophers always refer to their arguments as 'arguments' and never as 'proofs'. This is because there is nothing in the entire, nearly three thousand year history of philosophy that would count as a proof of anything. Nothing.

This obiter dictum illustrates how, by exaggerating and saying something that is strictly false, one can still manage to convey a truth.  The truth is that there is very little in the history of philosophy that could count as a proof of anything.  But of course some philosophers do refer to their arguments as proofs.  Think of those Thomists who speak of proofs of the existence of God.  And though no Thomist accepts the ontological 'proof,' there are philosophers who refer to the ontological argument as a proof.  The Germans also regularly speak of der ontologische Gottesbeweis rather than of das ontologische Argument.  For example, Frege in a famous passage from the Philosophy of Arithmetic writes,  Weil Existenz Eigenschaft des Begriffes ist, erreicht der ontologische Beweis von der Existenz Gottes sein Ziel nicht. (sec. 53)

These quibbles aside, an argument is not the same as a proof.  'Prove' is a verb of success.  The same goes for 'disprove' and 'refute.'  But 'argue' is not.  I may argue that p without establishing that p.  But if I prove that p, then I establish that p.  Indeed, I establish it as true. 

Why has almost nothing ever been proven in the history of philosophy? 

It is because for an argument to count as a proof in philosophy — I leave aside mathematics which may not be so exacting — certain exceedingly demanding conditions must be met.  First, a proof must be deductive: no inductive argument proves its conclusion.  Second, a proof must be valid: it must be a deductive argument such that its corresponding conditional is a narrowly-logical truth, where an argument's corresponding conditional is a conditional proposition the protasis of which is the conjunction of the argument's premises, and the apodosis of which is the argument's conclusion.

Third, although a valid argument needn't have true premises, a proof must have all true premises.  In other words, a proof must be a sound argument.  Fourth, a proof cannot commit any infomal fallacy such as petitio principii.  An argument from p to p is deductive, valid, and sound.  But it is obviously no proof of anything.

Fifth, a proof must have premises that are not only true, but known to be true by the producers and the consumers of the argument.  This is because a proof is not an argument considered in abstracto but a method for generating knoweldge for some cognizer.  For example, if I do not know that I am thinking,then I cannot use that premise in a proof that I exist. 

Sixth,  a proof in philosophy must have premises all of which are known to be true in a sense of 'know' that entails absolute impossibilty  of mistake.  Why set the bar so high?  Well, if you say that you have proven the nonexistence of God, say, or that the self is but a bundle of perceptions, or that freedom of the will is an illuison, or whatever, and one of your premises is such that I can easily conceive its being false, then you haven't proven anything. You haven't rationally compelled me to accept your conclusion. You may have given a 'good' argument in the sense of a 'reasonable' argument where that is one which satisfies my first four conditions; but you haven't given me a compelling argument, an argument which is such that, were I to reject it I would brand myself as irrational.  (Of course the only compulsion here at issue is rational compulsion, not ad baculum (ab baculum?) compulsion.)

Given my exposition of the notion of proof in philosophy, I think it is clear that very little has ever been proven in philosophy. I am pretty sure that London Ed, as cantankerous and contrary as he is known to be, will agree.  But he goes further: he says that nothing has ever been proven in philosophy.

But hasn't the sophomoric relativist been refuted?  He maintains that it is absolutely true that every truth is relative.  Clearly, the sophomoric relativist contradicts himself and refutes himself.  One might object to this example by claiming that no philosopher has ever been a sophomoric relativist.  But even if that is so, it is a possible philosophical position and one that is provably mistaken. Or so say I.

Or consider a sophist like Daniel Dennet who maintains (in effect) that consciousness is an illusion.  That is easily refuted and I have done the job more than once in these pages.  But it is such a stupid thesis that it is barely worth refuting.  Its negation — that consciousness is not an illusion — is hardly a substantive thesis.  A substantive thesis would be: Consciousness is not dependent for its existence on any material things or processes.

There is also the stupidity of that fellow Krauss who thinks that nothing is something.  Refuting this nonsense hardly earns one a place in the pantheon of philosophers.

Nevertheless, I am in basic agreement with London Ed:  Nothing of any real substance has ever been proven in philosophy.  No one has ever proven that God exists, that God does not exist, that existence is a second-level property, that there is a self, that there is no self, that the will is free, that the will is not free, and so on.

Or perhaps you think you have a proof of some substantive thesis?  Then I'd like to hear it.  But it must be a proof in my exacting sense. 

Transitivity of Predication?

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

Consider these two syllogistic arguments:

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

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

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

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

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

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

Frege Meets Aquinas: A Passage from De Ente et Essentia

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

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

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

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

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

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

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

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

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

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

Closure: Some Mathematical and Philosophical Examples

A reader asks, "What is meant by 'closure' or 'closed under'? I've heard the terms used in epistemic contexts,  but I've not been able to completely understand them."

Let's start with some mathematical   examples. The natural numbers are closed under the operation of addition. This means that the result of adding any two natural numbers is a natural number. What is a natural number? On one understanding of the term, the naturals are the positive integers, the counting numbers, the members of the set {1, 2, 3, 4, 5, . . .}. On a second understanding, the naturals are the positive integers and zero: {0, 1,  2, 3, 4 . . .}. Either way, it is easy to see that adding any two   elements of either set yields an element of the same set. It is also easy to see that the naturals are also closed under multiplication. But they are not closed under subtraction. If you subtract 9 from 7,   the result (-2) is not an element of the set of natural numbers.

Now consider the squaring operation. The square of any real number is a real number. So the reals are closed under the operation of squaring. But the reals are not closed under the square root operation. The square root of -4 cannot be 2 since 2 squared is 4; it cannot be -2 either since -2 squared is 4. The square root of -2 is the complex number 2i where the imaginary number i is the square root of -1. The square  roots of negative numbers are complex; hence, the reals are not closed under the square root operation.

Generalizing, we can say that a set S is closed under a binary operation O just in case, for any elements x and y in S, xOy is an element of S. In Group Theory, a set S together with an operation O  constitutes a group only if S is closed under O.

Now for some philosophical examples. Meinongian objects (M-objects) are not closed under entailment. The M-object, the yellow brick road, although yellow is not colored even though in reality nothing can be yellow without being colored. M-objects are incomplete objects. They have all and only the properties specified in their descriptions.  So we say that the properties of M-objects are not closed under property-entailment. Property P entails property Q iff necessarily, if   anything x has P, then x has Q.

What goes for M-objects goes for intentional objects. (On my reading of Meinong, an M-object is not the same as an intentional object: there are M-objects that are not the accusatives of any actual
intending.) Suppose I am gazing out my window at the purple majesty of Superstition Mountain. The intentional object of my perception has the property of being purple, but not the properties of being colored or being extended even though in reality nothing can be purple without being both colored and extended. Phenomenologically, what is before my mind is an instance of purple, but not an instance of colored item. What I see I see as purple but not as colored.

Now consider: If S knows that p, and S knows that p entails q, then S also knows that q. If you acquiesce in the bolded thesis, then you acquiesce in the closure of 'knows' under known entailment. For what you are then committing yourself to is the proposition that a proposition q entailed by a proposition p you know — assuming you know that p entails q — is a member of the set of propositions you  know.

On the Expressibility of ‘Something Exists’

Surely this is a valid and sound argument:

1. Stromboli exists.
Ergo
2. Something exists.

Both sentences are true; both are meaningful; and the second follows from the first.  How do we translate the argument into the notation of standard first-order predicate logic with identity? Taking a cue from Quine we may formulate (1) as

1*.  For some x, x = Stromboli. In English:

1**. Stromboli is identical with something.

But how do we render (2)?  Surely not as 'For some x, x exists' since there is no first-level predicate of existence in standard logic.  And surely no ordinary predicate will do.  Not horse, mammal, animal, living thing, material thing, or any other predicate reachable by climbing the tree of Porphyry.  Existence is not a summum genus.  (Aristotle, Met. 998b22, AnPr. 92b14) What is left but self-identity?  Cf. Frege's dialog with Puenjer.

So we try,

2*. For some x, x = x.  In plain English:

2**. Something is self-identical.

So our original argument becomes:

1**. Stromboli is identical with something.
Ergo
2**. Something is self-identical.

But what (2**) says is not what (2) says.   The result is a murky travesty of the original luminous argument.

What I am getting at is that standard logic cannot state its own presuppositions.  It presupposes that everything exists (that there are no nonexistent objects) and that something exists.  But it lacks the expressive resources to state these presuppositions.  The attempt to state them results either in  nonsense — e.g. 'for some x, x' — or a proposition other than the one that needs expressing. 

It is true that something exists, and I am certain that it is true: it follows immediately from the fact that I exist.  But it cannot be said in standard predicate logic.

What should we conclude?  That standard logic is defective in its treatment of existence or that there are things that can be SHOWN but not SAID?  In April 1914. G.E. Moore travelled to Norway and paid a visit to Wittgenstein where the  latter dictated some notes to him.  Here is one:

In order that you should have a language which can express or say everything that can be said, this language must have certain properties; and when this is the case, that it has them can no longer be said in that language or any language. (Notebooks 1914-1916, p. 107)

Applied to the present example:  A language that can SAY that e.g. island volcanos exist by saying that some islands are volcanos or that Stromboli exists by saying that Stromboli is identical to something must have certain properties.  One of these is that the domain of quantification contains only existents and no Meinongian nonexistents.  But THAT the language has this property cannot be said in it or in any language.  Hence it cannot be said in the language of standard logic that the domain of quantification is a domain of existents or that something exists or that everything exists or that it is not the case that something does not exist.

Well then, so much the worse for the language of standard logic!  That's one response.  But can some other logic do better?  Or should we say, with the early Wittgenstein, that there is indeed the Inexpressible, the Unsayable, the Unspeakable, the Mystical?  And that it shows itself?

Es gibt allerdings Unaussprechliches.  Dies zeigt sich, es ist das Mystische. (Tractatus Logico-Philosphicus 6.522)

The Stromboli Puzzle

Stromboli_0607

Here is another puzzle London Ed may enjoy.  Is the following argument valid or invalid:

An island volcano exists.
Stromboli is an island volcano.
Ergo
Stromboli exists.

The argument appears valid, does it not?  But it can't be valid if it falls afoul of the dreaded quaternio terminorum, or 'four-term fallacy.'  And it looks like it does.  On the standard Frege-Russell analysis, 'exists' in the major is a second-level predicate: it predicates of the concept island volcano the property of being instantiated, of having one or more instances.  'Exists' in the conclusion, however, cannot possibly be taken as a second-level predicate: it cannot possibly be taken to predicate instantiation of  Stromboli.  "Exists' in the conclusion is a first-level predicate.  Since 'exists' is used in two different senses, the argument is invalid.  And yet it certainly appears valid.  How solve this?

(Addendum, Sunday morning: this is not a good example for reasons mentioned in the ComBox.  But my second example does the trick.)

The same problem arise with this argument:

Stromboli exists.
Stromboli is an island volcano.
Ergo
An island volcano exists.

This looks to be an instance of Existential Generalization.  How can it fail to be valid?  But how can it be valid given the equivocation on 'exists'?  Please don't say the the first premise is redundant.  If Stromboli did not exist, if it were a Meinongian nonexistent object, then Existential Generalization could not be performed, given, as Quine says, that "Existence is what existential quantification expresses."

Ockham and Induction

Ed of Beyond Necessity reports that he has translated some chapters on induction from Ockham's Summa Logicae. He goes on:

Ockham says that induction "is a progression from singulars to the universal", which is pretty much the modern understanding of the term.

That is not wrong, but it is not quite right either.  On a well-informed modern understanding induction need not involve "a progression from singulars to the universal."

Suppose that every F I have encountered thus far is a G, and that I conclude that the next F I will encounter will also be a G. This is clearly an inductive inference, but it is one that moves from a universal statement to a statement about an individual. The inference is from Every F thus far encountered is a G to The next F I will encounter will be a G.  So it is simply not the case that every inductive inference proceeds from singular cases to a universal conclusion. Some such inferences do, but not all.  This is a common misunderstanding.

It is also a mistake to think that deduction always proceeds from the universal to the singular.  See On Falsely Locating the Difference Between Deduction and Induction.

Morning Star and Evening Star

London Ed of Beyond Necessity does a good job patiently explaining the 'morning star' – 'evening star' example to one of his uncomprehending readers.  But I don't think Ed gets it exactly right.  I quibble with the following:

Summarising:
(1) The sentence “the morning star is the evening star” has informational content.
(2) The sentence “the morning star is the morning star” does not have informational content.
(3) Therefore, the term “the morning star” does not have the same informational content as “the evening star”.

One quibble is this.  Granted, the two sentences differ in cognitive value, Erkenntniswert.  (See "On Sense and Reference" first paragraph.) The one sentence expresses a truth of logic, and thus a truth knowable a priori.  The other sentence expresses a factual truth of astronomy, one knowable only a posteriori.  But note  that Frege says that they differ in cognitive value, not that the one has it while the other doesn't.  Ed says that the one has it while the other doesn't — assuming Ed is using 'informational content' to translate Erkenntniswert.  There is some annoying slippage here.

More importantly, I don't see how cognitive value/informational content can be had by such subsentential items as 'morning star' and 'evening star.'  Thus I question the validity of the inference from (1) & (2) to (3). Neither term gives us any information.  So it cannot be that they differ in the information they give.  Nor can they be contrasted in point of giving or not giving information.  Information is conveyable only by sentences or propositions.

I say this:  neither of the names Morgenstern (Phosphorus) or Abendstern (Hesperus) have cognitive value or informational content.  (The same holds, I think, if they are not proper names but definite descriptions.)  Only indicative sentences (Saetze) and the propositions (Gedanken) they express have such value or content.  As I see it, for Frege, names have sense (Sinn) and reference (Bedeutung), and they may conjure up  subjective ideas (Vorstellungen) in the minds of their  users.  But no name has cognitive value.  Sentences and propositions, however, have sense, reference, and cognitive value.  Interestingly, concept-words (Begriffswoerter)  or predicates also have sense and reference, but no cognitive value.

I also think Ed misrepresents the Compositionality Principle.  Frege is committed to compositionality of sense (Sinn),  not compositionality of informational content/cognitive value.  So adding the C. P. to his premise set will not validate the  above inference.

Composition: Formal or Informal Fallacy?

Although the fallacy of composition is standardly classified as an informal fallacy, I see  it is a formal fallacy, one rooted in logical form. Let W be any sort of whole (whether set, mereological sum, aggregate, etc.) Suppose each of the proper parts (if any) of W has some property P (or, for the nominalistically inclined, satisfies some predicate F). Does it follow that W has P or satisfies F? No it doesn't. To think otherwise is to commit the fallacy of composition: it is to argue in accordance with the  following invalid schema:
 
   1. Each member of W is F
   Therefore
   2. W is F.

To show that an argument form is invalid, it suffices to present an argment of that form having true premises and a false conclusion.  (This is because valid inference is truth-preserving: it cannot take one from true premises to a false conclusion. But it doesn't follow that invalid inference is falsehood-preserving: there are valid arguments with false premises and a true conclusion. Exercise for the reader: give examples.) Here is a counterexample that shows the invalidity of the above pattern: Each word in a given sentence is meaningful; ergo, the sentence is meaningful. (Let the sentence be 'Quadruplicity drinks procrastination.')  Since the premise is true and the conclusion false, the argument pattern is invalid. So every argument of that form is invalid, even in the case in which the premises and conclusion are both true.

Why then is Composition standardly grouped with the informal fallacies? Petitio principii is a clear  example of an informal fallacy. If I argue p, therefore p, I move in a circle of embarrassingly short diameter. But the inference is valid. (Bear in mind that 'valid' is a terminus technicus.) And if p is true, the argument is sound. Nevertheless, any argument of this form is probatively worthless: it it does not prove, but presupposes, its conclusion. Since this defect is not formal, we call it informal!

So there are clear examples of informal fallacies. But what about Equivocation? It is usually classed with the informal fallacies. Consider the syllogistic form Barbara (AAA-1):

   All M are P
   All S are M
   All S are P.

Suppose there is an equivocation on the middle term 'M.' Although this is an informal defect (in that it has not to do with logical syntax,  but with semantics) it translates into a formal defect, the dreaded quaternio terminorum or four-term fallacy, which is of course a formal fallacy: no syllogism with more than three terms is valid. (A syllogism by definition is a deductive argument having exactly two premises and exactly three terms.)

It can be shown that every equivocation on a key term in an argument induces a formal defect. So the standard classification of Equivocation as an informal fallacy cannot be taken too seriously. By  contrast, Petitio Principii is seriously informal in its probative defectiveness.

I say that Composition is like Equivocation: it is a formal fallacy in informal disguise. (And the same goes for Division, which is roughly Composition in reverse.) So I disagree with the author of a logic book who writes:

     . . . the fallacy of composition is indeed an informal fallacy. It
     cannot be discovered by a mere inspection of the form of an
     argument , that is, by the mere observation that an attribute is
     being transferred from parts onto the whole. . . . The critic must
     be certain that, given the situation, the transference of this
     particular attribute is not allowed. . . .

So the fallacy of composition is not always a fallacy, but only when it is a fallacy? That is the silliness that the author seems to be espousing. He is saying in effect the following: if you transfer an attribute from parts to whole, that is fallacious except in those cases in which it is not fallacious, i.e. those cases in which the transfer can legitimately be made.

But then what is the point of isolating a typical error in reasoning called Composition? What is the point of this label? Why not just say: there are many different part-whole relationships, and it is only be close acquaintance with the actual subject-matter that one can tell whether the attribute transfer is legitimate?

Logic is formal: it abstracts from subject-matter. So mistakes in logic are also formal. A mistake that is typical (recurrent) and sufficiently seductive to warrant a label is called a fallacy. To say or imply that the fallaciousness of a fallacy depends on the particular subject-matter of the argument is to abandon logic and  embrace confusion.

Example.  Every brick in this pile weighs more than five lbs; ergo, the pile weighs more than five lbs. This is an example of the fallacy of composition despite the fact that it is nomologically impossible that the pile not weigh more than five lbs.

Another example.  Every being in the universe is contingent; ergo, the universe is contingent.  This too is the fallacy of composition.  And this despite the fact that it is metaphysically impossible that a universe all of whose members are contingent be necessary.  

Neologisms, Paleologisms, and Grelling’s Paradox

'Neologism' is not a new word, but an old word. Hence, 'neologism' is not a neologism. 'Paleologism' is not a word at all; or at least it is not listed in the Oxford English Dictionary. But it ought to be a word, so I hereby introduce it. Who is going to stop me? Having read it and understood it, you have willy-nilly validated its introduction and are complicit with me.

Now that we have 'paleologism' on the table, and an unvast conspiracy going, we are in a position to see that 'neologism' is a paleologism, while 'paleologism' is a neologism. Since the neologism/paleologism classification is both exclusive (every word is either one or the other )and exhaustive (no word is neither), it follows that 'neologism' is not a neologism, and 'paleologism' is not a paleologism.

Such words are called heterological: they are not instances of the properties they express. 'Useless' and 'monosyllabic' are other examples of  heterological expressions in that 'useless' is not useless and 'monosyllabic' is not monosyllabic. A term that is not heterological is called autological. Examples include 'short' and 'polysyllabic.'  'Short' is short and 'polysyllabic' is polysyllabic. Autological terms are instances of the properties they express.

Now ask yourself this question: Is 'heterological' heterological? Given that the heterological/autological classification is exhaustive, 'heterological' must be either heterological or else autological. Now if the former, then 'heterological' is not an instance of the property it expresses, namely, the property of not being an instance of the property it expresses. But this implies that 'heterological' is autological. On the other hand, if 'heterological' is autological, then it is an instance of the property it expresses, namely the property of not being an instance of the property it expresses. But this implies that 'heterological' is heterological.

Therefore, 'heterological' is heterological if and only if it is not. This contradiction is known in the trade as Grelling's Paradox. It is named after Kurt Grelling, who presented it in 1908.

The ‘Is’ of Identity and the ‘Is’ of Predication

Bill Clinton may have brought the matter to national attention, but philosophers have long appreciated that much can ride on what the meaning of 'is' is. 

Edward of London 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.  If the distinction is absolute, as 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?  Or are there reasons independent of Frege's function-argument analysis of propositions for upholding the distinction between the two uses of 'is'?

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 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.  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 copula?

This is what throws me about the scholastic stuff peddled by Ed and others.  In 'Orwell is famous' they seem 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.  But even if Orwell were the only famous person, Orwell would not be identical to the only famous person.  Necessarily, Orwell is Orwell; but it is not the case that, necessarily, Orwell is the only famous person, even if it is true that Orwell is the only famous person, which he  isn't.

If you tell me that only 'Orwell' has a referent, but not 'famous,' then I will reply that that is nominalism for the crazy house.  Do you really want to say or imply that Orwell is famous because in English we apply the predicate 'famous' to him?  That's ass-backwards or bass-ackwards, one.  We correctly apply 'famous' to him because he is, in reality, famous.  (That his fame is a social fact doesn't  make it language-dependent.)  Do you really want to say or imply that, were we speaking German, Orwell would not be famous but beruehmt?  'Famous' is a word of English while beruehmt is its German equivalent.  The property, however, belongs to neither language.  If you say there are no properties, only predicates, then that smacks of the loony bin.

Suppose 'Orwell' refers to the concrete individual Orwell, and 'famous' refers to the property, being-famous.  Then you get for your trouble a different set of difficulties.  I don't deny them!  But these difficulties do not show that the scholastic view is in the clear.

This pattern repeats itself throughout philosophy.  I believe I have shown that materialism about the mind faces insuperable objections, and that only those in the grip of naturalist ideology could fail to feel their force.   But it won't do any good to say that substance dualism also faces insuperable objections.  For it could be that both are false/incoherent.  In fact, it could be that every theory proposed (and proposable by us) in solution of  every philosophical problem is false/incoherent.