Existence – Page 14 – Maverick Philosopher

Singular Concepts and Singular Negative Existentials

London Ed seems to be suggesting that we need irreducibly singular concepts (properties, propositional functions) if we are properly to analyze grammatically singular negative existence statements such as

1. Vulcan does not exist.

But why do we need to take 'Vulcan' to express a singular concept or haecceity property? Why isn't the following an adequate analysis:

1A. The concept Small, intra-Mercurial planet whose existence explains the peculiarities of Mercury's orbit is not instantiated.

Note that the concept picked out by the italicized phrase is general not singular. It is general even though only one individual instantiates it if any does. The fact that different individuals instantiate it at different possible worlds suffices to make the concept general, not irreducibly singular.

More on Translating ‘Something Exists’ and a Response to Brightly

I issued the following challenge: translate 'Something exists' into standard first-order predicate logic with identity. This is the logic whose sources are Frege and Russell. So I call it Frege-Russell logic, or, to be cute, 'Fressellian' logic. My esteemed commenters don''t see much of a problem here. So let me first try to explain why I see a problem. I then consider David Brightly's proposal.

1. First of all, 'Something exists' cannot be rendered as 'For some x, x exists.' This is because 'exist(s)' is not an admissible first-level predicate in Frege-Russell logic. The whole point of the Fressellian approach is to make 'exist(s)' disappear into the machinery of quantification. There is no such propositional function as 'x exists.' 'For some x, x exists' is gibberish, syntactic nonsense in Frege-Russell logic.

2. But the following is not gibberish: 'For some x, x = x.' So one will be tempted to say that 'Something exists' can be rendered as 'For some x, x = x,' ('Something is self-identical') and 'Everything exists' as 'For all x, x = x' ('Everything is self-identical').

But this won't work either. It is true that everything that exists is self-identical, and vice versa. But it doesn't follow, nor is it true, that existence is self-identity. Here is one consideration. When I say of Tom that he exists, I am not saying that he is self-identical. Suppose I hear a false rumour to the effect that Tom is no more. But then I encounter him in the flesh. I exclaim, "You still exist!" Clearly, "You are still self-identical" does not mean the same. If I said that, Tom might retort, "What the hell, man, were you worried that I had become legion?" In some circumstances, that a man should continue in existence is surprising. But we are never surprised by a man's continuing in self-identity.

Furthermore, when Tom ceases to exist, he does not become self-diverse. Loss of existence is not loss of self-identity. To put the point in formal mode, after his demise 'Tom' continues to refer to one and the same individual, Tom. The bearer of the name is gone, but not the reference. Otherwise it could not be true that Tom is gone. There is also a modal consideration. Tom is a contingent being: he exists but he might not have existed. If existence is self-identity, then Tom's possible nonexistence is Tom's possible self-diversity — which is absurd. It makes prima facie sense to say of an individual that it might not have existed or that it no longer exists; but it make no sense at all to say of an individual that it might not have been self-identical or that it is no longer self-identical. If Tom might not have existed, then it is Tom who might not have existed. But if Tom might not have been self-identical, then it is not Tom who might not have been self-identical.

So, even if everything that exists is self-identical and conversely, existence is not self-identity. When we say that something exists we are not saying that something is self-identical, and when we say that everything exists we are not saying that everything is self-identical. I conclude that 'Something exists' is not expressible in the terms of the Frege-Russell system. As for 'Everything exists,' it is surely a presupposition of the whole Frege-Russell approach: the approach presupposes that Meinong was wrong to speak of nonexistent objects. But this presupposition cannot be expressed, cannot be 'said,' in Fressellian terms.

We are in the following curious predicament. Something that must be true if if the Fresselian system is to be tenable — that everything exists, that there are no nonexistent objects — is not expressible within the system.

3. David Brightly accepts my challenge to give a Frege-Russell translation of 'Something exists.' He writes:

And as a Fressellian I accept the challenge. That property is Individual aka Object, the concept at the root of the Porphyrean tree. We can say 'Something exists' with ∃x.Object(x), ie, there is at least one object. Likewise ∀x.Object(x) (which is always true, even when the box is empty) says 'Everything exists' and its negation (which is always false) says 'Some thing is not an object'. But both these last are unenlightening—because always true and always false, respectively, they convey no information, make no distinction, are powerless to change us.

I asked: which property is it whose instantiation is the existence of something? David's answer is that it is the property or concept Individual or Object. And so I take David to be saying something like the following. "Just as the existence of cats is the being-instantiated of the concept cat, the existence of something is the being-instantiated of the concept Object."

David mentions the tree of Porphyry:

David speaks of the 'root' of the tree where I speak of its apex. No matter. However we visualize it, upside down or right side up, David's suggestion is that Object or Substance (as above) is a summum genus, a supreme genus. It is a concept superordinate to every concept, a concept under which everything falls.

Operating with a scheme like this, we can, in the spirit of Frege's dialogue with the illustrious Puenjer, reduce every existential proposition (or at least every general existential proposition) to a predication by climbing Porphyry's tree. Thus:

Cats exist –> Some mammal is a cat
Mammals exist –> Some animal is a mammal
Animals exist –> Some living thing is an animal
Living things exist –> Some body is a living thing
Bodies exist –> Some substance is a body
Substances exist –> Some Objects are substances.

The point of these translations is to dispense with 'existst(s)' by showing how propositions of the form Fs exist can be replaced salva veritate with propositions of the form Some G is a F, where G is superordinate to F. This amounts to the elimination of existence in favor of the logical quantity, someness.

We have now climbed to the tippy-top of the tree of Porphyry. We have ascended to a concept superordinate to every concept (except itself) a genus generalissimum, a most general genus. And what concept might that be? Such a concept must have maximal extension and so will have minimal intension. It will be devoid of all content, abstracting as it does from all differences. Frege in his dialog with Puenjer suggests something identical with itself as the maximally superordinate concept. 'There are men' and 'Men exist' thus get rendered as 'Something identical with itself is a man.' (63) Something identical with itself is equivalent to Brightly's Object.

4. Now why can't I accept the Frege-Brightly view? Well, I've already shown that 'Everything exists' cannot be translated as 'Everything is self-identical.' But this is tantamount to having established that the concept whose instantiation is the existence of everything cannot be the concept self-identical something or the concept Object.

Another way to see this is by considering two individuals at the very bottom of the Porphyrean tree. So consider my cats, Max and Manny. In respect of being cats, mammals, beasts, animals, living things, material substances, and self-identical somethings, they do not differ. They do not differ quidditatively. But they do differ: they differ in their very existence. Each has his own existence. Max is not Manny, and Manny is not Max. That is not a mere numerical difference; it is a numerical-existential difference. Since each cat has its own existence, the existence of either cannot be the being-instantiated of any quidditative concept. All such concepts abstract from existence. The same goes for all individuals. Individuals exist. But the existence of individuals is not the being-instantiated of any concept. If you want, you can think of existent (self-identical something) as a highest genus, but Existence — that in virtue of which things exist and are not nothing — is not a highest genus. And it is Existence that is the topic. There are no instances of Existence. Existing things are not a kind of thing.

The Frege-Russell theory fails utterly as a theory of Existence.

As sure as I am sitting here, I am sure that I will not convince the Londonistas. That fact is more grist for the (meta)philosophical mill.

On Translating ‘Some Individual Exists’ Fressellianly

An astute reader comments:

You write:

2. But can this presupposition be expressed (said) in this logic? Here is a little challenge for you Fressellians: translate 'Something exists' into standard logical notion. You will discover that it cannot be done. Briefly, if existence is instantiation, which property is it whose instantiation is the existence of something? Same problem with 'Nothing exists.' If existence is instantiation, which property is it whose non-instantiation is the nonexistence of anything? Similarly with 'Everthing exists' and 'Something does not exist.'

But couldn't we translate those expressions this way (assuming we have only two properties: a, b)?
1. "something exists" -> "there is an x that instantiates either a or b or ab"
2. "everything exists" -> "there is an x that instantiates a and there is a y that instantiates b and there is a z that instantiates ab"
3. "nothing exists" -> 1 is false
4. "something doesn't exist" -> 2 is false

I am afraid that doesn't work. We need focus only on on 'Some individual exists.' The reader's proposal could be put as follows. Given the properties F-ness and G-ness,

What 'Some individual exists' says is exactly what 'Either F-ness is instantiated or G-ness is instantiated' says.

I would insist however that they do not say the same thing, i.e., do not have the same meaning. The expression on the left says that some individual or other, nature unspecified, exists. The expression on the right, however, makes specific reference to the 'natures' F-ness and G-ness. Surely, 'Some individual exists' could be true even if there are are no individuals that are either Fs or Gs.

Note that it is not a matter of logic what properties there are. This is an extralogical question.

On the Frege-Russell treatment of existence, 'exist(s)' is a second-level predicate, a predicate of concepts, properties, propositional functions and cognate items. It is never an admissible predicate of individuals. Thus in this logic every affirmation of existence must say of some specified concept or property that it is instantiated, and every denial of existence must say of some specified concept or property that it fails of instantiation.

This approach runs into trouble when it comes to the perfectly meaningful and true 'Something exists' and 'Some individual exists.' For in these instances no concept or property can be specified whose instantiation is the existence of things or the existence of individuals. To head off an objection: self-identity won't work.

That there are individuals is a necessary presupposition of the Frege-Russell logic in that without it one cannot validly move from 'F-ness is instantiated' to 'Fs exist.' But it is a necessary presupposition that cannot be stated in the terms of the system. This fact, I believe, is one of the motivations for Wittgenstein's distinction between the sayable and the showable. What cannot be said, e.g., that there are individuals, is shown by the use of such individual variables as 'x.'

The paradox, I take it, is obvious. One cannot say that 'There are individuals' is inexpressible without saying 'There are individuals.' When Wittgenstein assures us that there is the Inexpressible, das Unaussprechliche, he leaves himself open to the retort: What is inexpressible? If he replies, 'That there are individuals,' then he is hoist by his own petard.

Surely it is true that there are individuals and therefore expressible, because just now expressed.

"The suicide of a thesis," says Peter Geach (Logic Matters, p. 265), "might be called Ludwig's self-mate . . . . " Here we may have an instance of it.

Wittgenstein and Rejectionism

I characterized Rejectionism with respect to the question why there is anything at all as follows: "The rejectionist rejects the question as ill-formed, as senseless." London Ed suggests that Wittgenstein may be lumped in with the rejectionists. He has a point, though I do insist on the distinction between taking 'Why is there anything at all?' as an explanation-seeking why-question and taking it as a mere expression of wonder at the sheer existence of things. We know that Wittgenstein was struck with wonder at the sheer existence of things. What is now to be discussed is whether Wittgenstein can be read as making a rejectionist response to the ultimate explanation-seeking why-question.

Ed quotes from Anthony Kenny's book, Wittgenstein:

Logic depends on there being something in existence and there being facts; it is independent of what the facts are, of things being thus and so. That there are facts is not something which can be expressed in a proposition. If one wants to call there being facts a matter of experience, then one can say logic is empirical. But when we say something is empirical we mean that it can be imagined otherwise; in this sense every proposition with sense is a contingent proposition. And in this sense the existence of the world is not an empirical fact, because we cannot think it otherwise.

This passage cries out for commentary.

1. Does logic depend on there being something in existence? Yes, if we are talking about the Frege-Russell logic that young Ludwig cut his teeth on. In 'Fressellian' logic, existence is instantiation. To say that cats exist is to say that something is a cat. (The concept cat is instantiated.) To say that dragons do not exist is to say that nothing is a dragon. (The concept dragon is not instantiated.) This works nicely – but only on the assumption that individuals exist. So Kenny is surely right that (Frege-Russell) logic requires that something exists, in particular that individuals exist.

3. I surmise that this is one of the motivations for Wittgenstein's infamous and paradoxical saying/showing distinction. What can be said can be said clearly. But not everything can be said. It cannot be said that there are beings or that there are objects or that there are individuals. For again, how does one express (say) that there are beings (existents) in Frege-Russell logic? This system of logic rests on presuppositions that cannot be expressed within the system. The presuppositions cannot be said but thay can be shown by the use of variables such as the individual variable 'x.' That is the Tractarian line.

4. Kenny also says that logic depends on there being facts. That's not clear. Near the beginning of the Tractatus, LW affirms the existence of facts. He tells us that the world is the totality of facts (Tatsachen) not of things (Dinge). But does the Frege-Russell logic require that there be facts? Not as far as I can see. The mature Frege certainly did not posit facts. Be that as it may.

5. Is Wittgenstein a rejectionist? Does he reject the question 'Why is there anything at all?' as senseless or ill-formed? The case can be made that he does or at least could within his framework.

When I raise the question why anything at all exists, I begin with the seemingly empirical fact that things exist: me, my cat, mountains, clouds . . . . I then entertain the thought that there might have been nothing at all. I then demand an explanation as to why there is something given (a) that there is something and (b) that there might not have been anything.

A Wittgensteinian rejection of the question might take the following form. "First of all, your starting point is inexpressible: it cannot be said that things exist. That is a nonsensical pseudo-proposition. You can say, sensibly, that cats exist, but not that things exist. That things exist is an unsayable presupposition of all thinking. As such, we cannot think it away. And so one cannot ask why anything exists."

6. This form of rejectionism is as dubious as what it rests upon, namely, the Frege-Russell theory of existence and the saying/showing distinction.

Siger of Brabant on Why Something Rather Than Nothing

London Ed offers this quick, over-breakfast but accurate as far as I can tell translation from the Latin (available at Ed's site):

For not every being has a cause of its being, nor does every question about being have a cause. For if it is asked why there is something in the natural world rather than nothing, speaking about the world of created things, it can be replied that there is a First immoveable Mover, and a first unchangeable cause. But if it is asked about the whole universe of beings why there is something there rather than nothing, it is not possible to give a cause, for it's the same to ask this as to ask why there is a God or not, and this does not have a cause. Hence not every question has a cause, nor even every being.

Ed comments, "I'm not sure how Siger's reply falls into the categories given by Bill." Note first that the question that interests me is in the second of Siger's questions, the 'wide-open' question: not the question why there are created things, but the question why there is anything at all. To that wide-open question Siger's response falls under Rejectionism in my typology of possible responses. Siger rejects the question as unanswerable when he says, idiosyncratically to our ears, "it is not possible to give a cause," and "not every question has a cause." That could be read as saying that not every interrogative form of words expresses a genuine question.

Ed also mentions Wittgenstein and suggests that he "had a go" at the Leibniz question. I don't think so. We must distinguish between 'Why is there anything at all?' as an explanation-seeking why-question and the same grammatically interrogative formulation as a mere expression of wonderment equivalent to 'Wittgenstein's "How extraordinary that anything should exist!" Wittgenstein was not raising or trying to answer the former. He was merely expressing wonder at the sheer existence of things.

I would be very surprised if someone can find in the history or philosophy, or out of his own head, a response to the wide-open explanation-seeking Leibniz question that cannot be booked under one of my rubrics. (Credit where credit is due: my catalog post is highly derivative from the work of N. Rescher.)

A Catalog of Possible Types of Response to ‘Why Is There Anything At All?’

By my count there are seven possible types of response to the above question, which I will call the Leibniz question. I will give them the following names: Rejectionism, Mysterianism, Brutalism, Theologism, Necessitarianism, Nomologism/Axiologism, and Cosmologism. As far as I can see, my typology, or rather my emendation of Rescher's typology, is exhaustive. All possible solutions must fall under one of these heads. You may send me an e-mail if you think that there is an eighth type of solution.

Either the Leibniz question is illegitimate, a pseudo-question, or it is a genuine question. If the former, then it cannot be answered and ought to be rejected. Following Rescher, we can call this first response

Rejectionism. The rejectionist rejects the question as ill-formed, as senseless. Compare the question, 'How fast does time flow?' The latter is pretty obviously a pseudo-question resting as it does on a false presupposition, namely, that time is a measurable process within time. Whatever time is, it is not a process in time. If it flows, it doesn't flow like a river at some measurable rate. One does not answer a pseudo-question; one rejects it. Same with such complex questions as 'When did you stop smoking dope?' The Leibniz question in its contrastive formulation — Why is there something rather than nothing? — may well be a pseudo-question. I gave an argument for this earlier.

If the the Leibniz question is legitimate, however, then it is either unanswerable or answerable. If unanswerable, then the question points to a mystery. We can call this response

Mysterianism. On this approach the question is held to be genuine, not pseudo as on the rejectionist approach, but unanswerable. The question has a clear sense and does not rest on any false presupposition. But no satisfying answer is available.

If the question is answerable, then there are five more possible responses.

Brutalism or Brute Fact Approach. On this approach there is no explanation as to why anything at all exists. It is a factum brutum. As Russell said in his famous BBC debate with the Jesuit Copleston, "The universe is just there, and that is all." (Caveat lector: Quoted from memory!) A brute fact may be defined as an obtaining state of affairs that obtains without cause and without reason. If the Principle of Sufficient Reason holds, then of course there are no brute facts. The principle in question, however, is contested.

Theologism or Theological Approach. There is a metaphysically necessary and thus self-explanatory being, God, whose existence and activity explains the existence of everything other than God. Why is there anything at all? Because everything is either self-explanatory (causa sui) or caused to exist by that which is self-explanatory.

Necessitarianism. On this approach, the metaphysical necessity that traditional theology ascribes to God is ascribed to the totality of existents: it exists as a matter of metaphysical necessity. It is necessary that there be some totality of existents or other, and (what's worse) that there be precisely this totality and no other. There is no real contingency. Contingency is merely epistemic. Why is there anything at all? Because it couldn't have been otherwise!

Nomologism/Axiologism. Theories of this type have been proposed by A. C. Ewing (Value and Reality, 1973), John Leslie (Universes, 1989), and Nicholas Rescher, The Riddle of Existence, 1984). I will provide a rough sketch of Rescher's approach.

For Rescher, there is a self-subsistent realm of real possibilities or "proto-laws" whose mode of being is independent of the existence of substances. This realm of real possibilities is not nothing, but it is not a realm of existents. Rescher's claim is that the proto-laws account for the existence of things "without being themselves embodied in some existing thing or things." (27) Some facts, e.g., that there are things (substances) at all, is "Grounded in the nature of possibility." (27) What is the nature of this grounding? R. speaks of "nomological causality" as opposed to "efficient causality." (21) Somehow — and I confess to finding this all rather murky — the proto-laws nomologically cause the existence of physical substances. How does this explain why there is something rather than nothing?

R. argues, p. 31: (a) If every R-possible world is F, then the actual world is F. (b) Every R-possible world is nonempty. Therefore, (c) The actual world is nonempty: there is something rather than nothing (31). That is, only nonempty worlds are really possible. As R. remarks, the reasoning here is like the ontological argument: only an actual God is really possible. Rescher's view seems to be that, while there is a plurality of possible worlds, there is no possible world empty of physical existents. But how does Rescher support premise (b): Every R-possible world is nonempty? He gives a ridiculous question-begging argument (p. 32) that I won't bother to reproduce.

Cosmologism. The above six approaches are listed by N. Rescher (The Riddle of Existence, 1984, Ch. 1). But I believe there is a seventh approach which I learned from my old friend Quentin Smith. (A later post will deal with this in detail.) On this approach the Leibniz question is genuine (contra Rejectionism) and has an answer (contra Mysterianism). Moreover, the answer has the form of an explanation (contra Brutalism). But the answer do not involve any necessary substance such as God, nor does it take the line that the universe itself exists of necessity. Nor does the answer ascribe any causal efficacy to abstract laws or values. The idea is that the universe has the resources to explain its own existence: it caused itself to exist. Roughly, everything (space-time, matter, laws) came into existence 13.7 billion years ago; it was caused to come into existence; but it was not caused to come into existence by anything distinct from the universe. How? Well, assume that the universe is just the sum total of its states. Assume further that if each state has an explanation, then this suffices as an explanation of the sum total of states. Now each state has a causal explanation in terms of an earlier state. There is no first state despite the fact that the universe is metrically finite in age: 13.7 billion years old. There is no first state because of the continuity of time and causation: for every state there are earlier states in its causal ancestry. Because every state has a cause, and the universe is just the sum-total of its states, the universe has a cause. But this cause is immanent to the universe. So the universe caused itself to exist!

The Ultimate Explanation-Seeking Why-Question and Contrastive Explanations

I argued yesterday that the following questions are distinct:

   Q1. Why does anything at all exist, rather than nothing?

   Q2. Why does anything at all exist?

Today I explore a little further the difference between non-contrastive and contrastive explanations. Consider the difference between:

1. Why is Mary walking rather than swimming?

2. Why is Mary walking?

An answer to (2) might be: She exercises daily and her preferred form of exercise is walking. But this answer is no answer to (1). For here it is not the phenomenon of her walking that needs explaining, but the contrastive phenomenon of her walking instead of swimming. An answer to (1) might run: Mary is walking rather than swimming because she had an operation on her arm and she doesn't want to get the bandage wet.

So answering (2) does not answer (1). But it is also true that answering (1) does not answer (2). For if she is walking rather than swimming so as not to get her bandage wet, this does not explain why she is walking in the first place. It leaves open whether she walks to exercise, or to meet her neighbors, or for some other reason.

I conclude that (1) and (2) are distinct. They are distinct because their answers need not be the same.

Now let us consider the presuppositions of (1). It is obvious — isn't it? — that only what is the case can be explained. That there are leprechauns cavorting in my yard cannot be explained since it is not the case. I will allow you to say that there is a possible world in which leprechauns cavort in my yard; but since that world is merely possible, nothing in it needs to be explained. So (1) presupposes that Mary is walking. (1) also presupposes that Mary is not swimming. No one can both walk and swim at the same time; so a person who is walking is not swimming.

A third presupposition of (1) is that it is possible that Mary be swimming. If I aim to explain why she is walking rather than swimming, then I presuppose that she is not swimming. But her not swimming is consistent with the possibility of her swimming. Her not swimming is also consistent with the impossibility of her swimming. Nevertheless, if I ask why walking rather than swimming, I presuppose that she might have been swimming. 'Rather than' means 'instead of' (in place of). So if she is walking instead of swimming, and walking is possible because actual, then swimming must also be possible if it is to be something that can be done instead of walking. It might help to consider

3. Why is Mary walking rather than levitating?

4. Why is Mary walking rather than levitating and not levitating at
the same time?

These two questions have presuppositions that are false. (3) presupposes that it is possible that Mary be doing something nomologically impossible, while (4) presupposes that it is possible that Mary being doing something that is narrowly-logically impossible. Questions (3) and (4) are therefore not to be answered but to be rejected — by rejecting the false presuppositions upon which they rest.

The same holds for the rather more interesting (Q1) and (Q2). (Q1) presupposes that it is possible that nothing exist. For again it is a contrastive phenomenon that wants explaining: something rather than nothing. Either (Q1)'s presupposition is false, or it is such that, if it were true, then every being would be contingent, in which case there could be no ultimate regress-stopping explanation of why something rather than nothing exists. That is the point I made yesterday.

So the correct response to (Q1) is either to reject it by rejecting the false presupposition upon which it is based, or to reject it by pointing out that, if said presupposition were true, no ultimate regress-stopping explantion would be possible. (Q2), however, does not presuppose that it is possible that nothing exist. It does not suffer from the internal defect that bedevils (Q1).

Two Forms of the Ultimate Explanation-Seeking Why-Question

Why does anything at all exist? Someone could utter this interrogative form of words merely to express astonishment that anything should exist at all. But it is more natural to take the question as a request for an explanation: Why, for what reason or cause, does anything at all exist? What explains the sheer existence of things? Suppose we call this the ultimate explanation-seeking why-question.

Before attempting to answer this question, one ought to examine it carefully. One ought to question the question. If we do so, we soon realize that the question why anything at all exists can be formulated in two ways. One formulation is contrastive, the other non-contrastive:

Q1. Why does anything at all exist, rather than nothing?

Q2. Why does anything at all exist?

What this post argues is that Q1 suffers from a defect that makes it unanswerable, but that Q2 does not suffer from this defect. Failure to distinguish Q1 and Q2 may lead one to reject both questions as unanswerable. It appears that Paul Edwards makes this mistake in his entry "Why?" in the Encyclopedia of Philosophy. Anthony Flood may be repeating it here.

That these are distinct questions becomes apparent when we note that the questions rest on different presuppositions. Both questions presuppose that something exists. If that were not the case, there would be nothing to explain. But Q1 also presupposes that it is possible that nothing at all exist. Call this further presupposition P. P is no part of Q2, as I will explain in a moment.

Let us first think about P and what it entails. P may be expressed in several logically equivalent ways:

There might have been nothing at all
It is possible that nothing exist
Possibly, nothing exists
There is a possible world in which nothing exists

where ‘possible’ and cognates pick out broadly logical possibility.

No matter how P is formulated, it entails that everything that exists is contingent, equivalently, that nothing that exists is a necessary being. For if there might have been nothing at all, then any thing X that exists is such that it might not have existed. That is just to say that X is a contingent being. So given that Q1 presupposes P, and that P entails that there are no necessary beings, it follows that Q1 presupposes that there are no necessary beings. But this seems to imply that the question Q1 cannot be answered.

For if Q1 – or the asking of Q1 – presupposes that no being is a necessary being, then the asking of Q1 presupposes that there is nothing in terms of which an ultimate explanation could be couched. This is because an ultimate explanation of why anything at all exists cannot be in terms of a contingent entity. A contingent explainer would need explanation just as much as any other entity. An ultimate explanation, if one is to be had, must invoke a noncontingent, but possible, entity: one that either explains itself or at least is not in need of an explanation by another. (I am assuming that there cannot be an actually infinite regress of contingent explainers. This assumption is quite easy to defend, but I won’t address that task here.)

The upshot is that Q1 entails its own unanswerability. This is not because we are unable to know the answer, but because the question itself by its very structure rules out an answer. In other words, Q1 is self-defeating in that it rests on a presupposition that rules out an answer. The proper procedure with respect to Q1, then, is to reject it, not try to answer it.

But the situation is different with Q2. Q2 does not presuppose that every being is contingent. It does not presuppose the opposite (some being is noncontingent) either. Q2 is neutral on the question whether every being is contingent. This is why Q2 is not just a truncated form of Q1. It is not as if ‘rather than nothing’ is implied but not stated in Q2. Q2, resting as it does on different presuppositions than Q1, is a different question. Q2 does not presuppose the possibility of there being nothing at all, hence, does not presuppose that only what is contingent can exist.

Thus Q2 allows the possibility of a necessary being. Nothing about Q2 entails its own unanswerability. Q2 allows the following answer: things exist because one of the things that exist is a necessary being whose existence is self-explanatory, while everything else is explained in terms of this necessary being.

Whether this answer is correct is a further question. The present point is merely that Q2, unlike Q1, is answerable.

Can Things Be Counted?

From the mail:

I saw your blog post the other day titled Saying and Showing where you talked about Wittgenstein's exchange with Russell on 'things', along with his Kantian perspective. Toward the end you say this: "What goes for 'world' also goes for 'thing.' You can't count things. How many things on my desk? The question has no clear sense. It is not like asking how many pens are on my desk. So Wittgenstein is on to something. His nonsense is deep and important."

In fact, E. J. Lowe says something similar toward the beginning of his book The Possibility of Metaphysics. However, I have never entirely understood the motivation behind this claim. It seems to me that, as a matter of fact, a man *can* count the number of things on his desk. There will certainly be very *many* things (the composite objects, their parts down to the atoms, and so forth), but what stops them from being *in principle* counted? [. . .]

Let's begin by clearing up an ambiguity. I can count the cats in my house; cats are things (in the very broad sense in which the term means the same as: object, entity, existent, being, item); and so one might think that one can count things. I'll grant that. But what we cannot do — and this was my claim –is count things as things. I can sensibly ask how many cats, cat whiskers, unicorns, pachyderms, and bottles of tequila are presently in my house, and I can sensibly give the following answers: 2, <40, 0, 0, 1. What I cannot do is sensibly ask how many things or existents are in my house.

Why is this? Well, when I count Fs, what I am doing is counting instances of the concept F. To count I need a concept, a classificatory device. To count the spatulas in a drawer I have to have the concept spatula. I have to know what 'counts' as a spatula. I have to know WHAT a spatula is to know whether there are any and how many there are. I have to be able to identify a particular item as a spatula (as opposed to, say, a ladle) and I have to be able to re-identify it — so that I don't count it twice. To count three spatulas and two ladles I need the concepts spatula and ladle. That makes five utensils. How many electrical appliances? Zero. In each of these cases, what we are counting are the instances of a concept.

How many utensils in the drawer? Five. How many entities? This question has no clear sense. The question presupposes that some definite answer is possible in terms of a finite or even a transfinite cardinal. But any answer given, whether 5 or 50 or aleph-nought will be arbitrary. Do we count the handle of the ladle as distinct from the rest of it? Is one ladle two entities? But of course, parts themselves have parts, and they have parts, etc. Suppose the ladle is ultimately composed of simple (indivisible) bits of matter. Suppose there are n such bits. In the region of space occupied by the ladle are there n entities or n + 1 entities? Is the whole ladle countably distinct from its parts? Or is the whole ladle just those parts? (Compare van Inwagen's denial of artifacts.) And what about the space occupied by the ladle? It is not nothing! So do we count it too when we count the entities in the drawer? And the time during which it exists?

And then there are properties and relations and relational properties and perhaps also property-instances. Do I count the properties of the spatula and the relations in which it stands to the other things in the drawer when I (try to) count the entities in the drawer?

Suppose in the drawer there is a triangular piece of mental. Now everything triangular is trilateral, and vice versa. And this is true as a matter of broadly-logical necessity. So, when I count (or try to count) the entities in the drawer, do I count triangularity and trilaterality as two properties or as one property?

From considerations like these one can see that the question How many entities? has no clear sense. We can give a sense to it, but that would involve the arbitrary imputation of conceptual content into 'entity.' Suppose I define:

X is an entity _df= x is either a feral cat or a piece of cooked seaweed.

That 'definition' would allow me to count the entities in my house. And the answer is . . . (wait for it): zero.

To count is to count the instances of a concept. Existence is not a concept that has instances. Therefore, one cannot count existents as existents.

Geach on the Real Distinction II: The Argument from Intentionality

See Geach on the Real Distinction I for some background on the distinctio realis. This post lays out the argument from intentionality to the real distinction.

A theory of intentionality ought to explain how the objective reference or object-directedness of our thoughts and perceptions is possible. Suppose I am thinking about a cat, a particular cat of my acquaintance whom I have named 'Max Black.' How are we to understand the relation between the mental act of my thinking, which is a transient datable event in my mental life, and its object, namely the cat I am thinking of? What makes my thinking of Max a thinking of Max? Or perhaps Max is in front of me and I am seeing him. What makes my seeing a seeing of him?

Here is what Peter Geach has to say, glossing Aquinas:

What makes a sensation or thought of an X to be of an X is that it is an individual occurrence of that very form or nature which occurs in X — it is thus that our mind 'reaches right up to the reality'; what makes it to be a sensation or thought of an X rather than an actual X or an actual X-ness is that X-ness here occurs in the special way called esse intentionale and not in the 'ordinary' way called esse naturale. This solution resolves the difficulty. It shows how being of an X is not a relation in which the thought or sensation stands, but is simply what the thought or sensation is . . . .(Three Philosophers, Cornell UP, 1961, p. 95)

But what the devil does that mean? Allow me to explain. The main point here is that ofness or aboutness is not a relation between a mental act and its object. Thus intentionality is not a relation that relates my thinking of Max and Max. My thinking of Max just is the mental occurrence of the very same form or nature — felinity — which occurs physically in Max. Max is a hylomorphic compound, a compound of form and (signate) matter. Old Max himself, fleas and all, is of course not in my mind. It is his form that is in my mind. But if felinity informs my mind, why isn't my mind a cat? Here is where the distinction between esse intentionale and esse naturale comes in. One and the same form — felinity — exists in two different modes. Its mode of being in my mind is esse intentionale while its mode of being in Max is esse naturale.

Because my thought of Max just is the intentional occurrence of the same form or nature that occurs naturally in Max, there is no problem about how my thought reaches Max. One could call this an identity theory of intentionality.

What if Max were, unbeknownst to me, to cease to exist while I was thinking about him? My thinking would be unaffected: it would still be about Max in exactly the way it was about him before. The Thomist theory would account for this by saying that while the form occurs with esse intentionale in my mind, it does not occur outside my mind with esse reale.

That in a nutshell is the Thomist theory of intentionality. If you can see your way clear to accepting it as the only adequate account of intentionality, then it supplies a reason for the real distinction. For the account requires that there be two distinct modes of esse, an immaterial mode, esse intentionale, and a material mode, esse naturale. Now if F-ness can exist in two different modes, then it cannot be identical to either and must be really distinct from both. (Cf. "Form and Existence" in God and the Soul, pp. 62-64.)

This argument for the real dstinction is only as good as the Thomist theory of intentionality which in turn rests on the notion of a common nature, felinity, say, which is indifferent to existence inasmuch as it can exist with esse naturale in Max and with esse intentionale in a Max-thinker, but taken in itself and absolutely is neither material nor mental, neither many nor one.

The aporetics of common natures will be taken up in subsequent posts.

Geach on the Real Distinction I

Oceans of ink have been spilled over the centuries on the celebrated distinctio realis between essence and existence (esse). You have no idea how much ink, and vitriol too, has flooded the scholastic backwaters and sometimes spilled over into mainstream precincts. Anyway, the distinction has long fascinated me and I hold to some version of it. I will first give a rough explanation of the distinction and then examine one of Peter Geach's arguments for it.

1. First of all, we can say that the real distinction is so-called because it is not a merely conceptual or notional distinction. It is not like the distinction between the Morning Star and the Evening Star. It is not a distinction parasitic upon how we view things or refer to them. It is more like the distinction between Venus and Mars. The MS and the ES are two "modes of presentation" (Fregean Darstellungsweisen) of one and the same chunk of extramental physical reality, the planet Venus. But Venus and Mars are not modes of presentation but entities in their own right. Venus and Mars are distinct in reality not merely in conception.

2. But although the Venus-Mars distinction is a real distinction, the distinction between essence and existence cannot be like this. For while each of the planets can exist without the other, essence and existence cannot each exist without the other. A thing's existence is nothing wthout the thing whose existence it is, and thus nothing without the thing's essence. I hope it is obvious that the existence of this particular coffee cup would be nothing without the cup and the cup's individual essence.

3. It is less obvious that the individual essence would be nothing without existence. But to make the problem more difficult I will assume that there are no nonexistent individuals, that nothing is an individual unless it exists. This implies that before Socrates came into existence there was no individual essence Socrateity. His coming into being was not the actualization of a pre-existent wholly determinate individual essence. (This has implications for the theory of creation: it imples that creation is out of nothing, not out of mere possibles.) It also implies that there is no individual essence corresponding to the name 'Vulcan' when this is used to denote an intra-Mercurial planet. My assumption is anti-Meinongian and (I believe) also anti-Avicennian. (There was a time, long ago, when the Muslims weren't total slouches when it came to philosophy. 'Avicenna' is the Latinization of 'Ibn Sina.')

4. The essence and the existence of a particular individual are thus each dependent on the other but nonetheless really, not merely notionally, distinct. Really distinct (like Venus and Mars, but unlike the Morning Star and the Evening Star) but inseparable (unlike Venus and Mars). They are really distinct like my eye glasses and my head but not separable in the manner of glasses and head. So an analogy mght be the convexity and concavity of one of the lenses. The convex surface cannot be without the concave surafce and vice versa, but they are really distinct. 'Convex' and 'concave' are not merely two different ways of referring to the same piece of glass. There is a real mind-independent difference. But it is only an analogy.

5. Now what reason could we have for accepting something like the the real distinction? Here is one of Geach's arguments, based on Aquinas, from "Form and Existence," reprinted in Peter Geach, God and the Soul (Thoemmes Press, 1994), pp. 42-64. Geach's argument is on p. 61. I'll put the argument in my own way. I find the argument convincing.

Suppose you have two numerically distinct instances of F-ness. They don't differ in point of F-ness, since each is an instance of F-ness. But they are numerically distinct. So some other factor must be brought in to account for the difference. That factor is existence. They differ in their very existence. Since they differ in existence and yet agree in essence, essence and existence are really distinct.

Max Black was famous for his iron spheres. (Geach does not mention Black.) He hypothesizes a world consisting of just two of them and nothing else, the spheres being alike in every relational and monadic respect. In Black's boring world, then, there are two numerically distinct instances of iron sphere. Since both exist, and since they differ solo numero, I conclude that they differ in their very existence. Since they differ in their existence, but agree in their iron sphericity, there is a real distinction between existence and nature or essence.

Suppose you deny that. Suppose you say that the spheres do not differ in their very existence and that they share existence. The consequence, should one cease to exist, would be that the other would cease to exist as well, which is absurd.

Existence and Property-Possession

Necessarily, whatever exists has properties, and necessarily, whatever has properties exists. So, necessarily, x exists iff x has properties. But it does not follow that existence is the property of having properties. Why not?

Peter and Paul differ in their existence. But they don't differ in point of having properties. They have different properties, of course, but they don't differ in respect of the property of having properties. So singular existence (the existence in virtue of which each is and is not nothing) is not identical to the property of having properties.

And yet very competent philosophers make this mistake. To name names: Dallas Willard, J. P. Moreland, J. K. Swindler.

One source of the mistake (though it might not be the source of the mistake in any of the above-mentioned) is the confusion of (broadly logical) equivalence with identity. Necessarily, x is triangular iff x is trilateral: there is no broadly logically possible world in which the extensions of the terms differs. But it doesn't follow that triangulariy = trilaterality. They are distinct properties despite their being necessarily coextensive.

So from the fact that nothing can exist without having properties, and nothing can have properties without existing, pace Meinong, it does not follow that to exist = to have properties.

Besides, is it not obviously circular to say that the existence of a is its having properties when a cannot have properties without existing? Think about it.

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

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."

Can Every General Existential be Expressed as an Instantiation Claim?

Here are some general existentials:

An island volcano exists.
There are uninhabited planets.
Faithful husbands exist.
Unicorns do not exist.
There aren't many chess players in Bagdad, Arizona.

Each of these is expressible salva significatione et veritate (without loss of meaning or truth) by a corresponding instantiation claim:

The concept island volcano is instantiated.
The concept uninhabited planet is instantiated.
The property of being a faithful husband is exemplified.
The property of being a unicorn is not exemplified.
The concept Bagdad, Arizona chess player has only a few instances.

Should we conclude that every general existential is expressible as an instantiation claim? No. 'Everything exists' is a true general existential. It affirms existence and is not singular. But it does not make an instantiation claim. If you think it does, tell me which property it says is instantiated.

Please note that it cannot be the property of existence. For there is no first-level property of existence, and the whole point of translations such as the above is to disabuse people of the very notion that existence is a first-level property.

Addendum, 4:40 PM. The problem arises also for 'Something exists,' 'Something does not exist,' and 'Nothing exists.' Consider the latter. It is not true but it is (narrowly-logically) possibly true. In any case it is meaningful. Can it be expressed as an instantiation claim? If I want to deny the existence of unicorns I say that the concept unicorn has no instances. What if I want to deny the existence of everything? Which concept is it whose non-instantiation is the nonexistence of everything?