Aggregation

Is number a property of an aggregate of things? But what is an aggregate? Can the very same things have the same number once disaggregated? Frege (The Foundations of Arithmetic § 23, translation J.L. Austin) writes:

To the question: What is it that the number belongs to as a property? Mill replies as follows: the name of a number connotes, ‘of course, some property belonging to the agglomeration of things which we call by the name; and that property is the characteristic manner in which the agglomeration is made up of, and may be separated into, parts.’

Here the definite article in the phrase "the characteristic manner" is a mistake right away; for there are very various manners in which an agglomeration can be separated into parts, and we cannot say that one alone would be characteristic. For example, a bundle of straw can be separated into parts by cutting all the straws in half, or by splitting it up into single straws, or by dividing it into two bundles. Further, is a heap of a hundred grains of sand made up of parts in exactly the same way as a bundle of 100 straws? And yet we have the same number. The number word ‘one’, again, in the expression ‘one straw’ signally fails to do justice to the way in which the straw is made up of cells or molecules. Still more difficulty is presented by the number 0. Besides, need the straws form any sort of bundle at all in order to be numbered? Must we literally hold a rally of all the blind in Germany before we can attach any sense to the expression ‘the number of blind in Germany’? Are a thousand grains of wheat, when once they have been scattered by the sower, a thousand grains of wheat no longer? Do such things really exist as agglomerations of proofs of a theorem, or agglomerations of events? And yet these too can be numbered. Nor does it make any difference whether the events occur together or thousands of years apart.

Number, concepts and existence

The Maverick Philosopher is agonising about number and existence in this post. It would be simpler if we returned to the original text of Frege which started all this (Die Grundlagen der Arithmetik 1884. Page numbers are to the original edition).

Frege claims with a concept the question is always whether anything, and if so what, falls under it. With a proper name such questions make no sense. (§51, p. 64). He also claims that when you add the definite article to a concept word, it ceases to function as a concept word, although it still so functions with the indefinite article, or in the plural (ibid).

This is part of a section of the Grundlagen where he develops the thesis that number is a property of concepts, not of things. Thus if I say (§46, p. 59) that ‘the King’s carriage is drawn by four horses’, I am ascribing the number 4 to the concept horse that draws the King’s carriage. The number is not a property of the horses, either individually or collectively, but of a concept.

From these two claims, namely that number is a property of concept words, and that proper names are not concept words, it seems to follow that ‘Socrates exists’ makes no sense. If ‘Socrates’ is not a concept word, then it seems no concept corresponds to it, but existence means that some concept is instantiated, so ‘Socrates exists’cannot express existence. This is the difficulty that Bill is grappling with.

But why, from the fact that ‘Socrates’ is not a concept word, does it follow that there is no corresponding concept? Frege has already told us that a concept word ceases to be such when we attach the definite article to it. So while ‘teacher of Plato’ signifies a concept, ‘the teacher of Plato does not. Why can’t the definite noun phrase ‘Socrates’ be the same, except that the definiteness is built into the proper name, rather than a syntactical compound of definite article and concept word. Why can’t ‘Socrates’ be semantically compound? So that it embeds a concept like person identical with Socrates, which with the definite article appended gives us ‘Socrates’?

As I argued in one of the comments, the following three concepts all have a number

C1: {any man at all}
C2: {any man besides Socrates}
C3: {satisfies C1 but not C2}

If the number corresponding to C1 is n, then the number of C2 is n-1. And the number of C3 is of course 1, and if C3 is satisfied, then Socrates exists. Simple.

Metaphysical monstrosities

I have been looking at ‘Van Inwagen on Fiction, Existence, Properties, Particulars, and Method’, by Bill Vallicella (Studia Neoaristotelica Review Article 12 (2015) / 2). Bill is the famous Maverick Philosopher.

Section 3 deals with haecceity. A haecceity property is one which, unlike man or white cannot be multiply instantiated, or as Scotus said, not-predicable of several things (indicibilis de pluribus). For example, being Socrates (Socrateity) is a property which, if instantiated, is instantiated by Socrates alone in the actual world and by nothing distinct from Socrates in any possible world.

It is necessary to posit such properties, Bill argues, to support the semantic thesis of the univocity of ‘exists’ and ‘is’, and its ontological counterpart, that there are no modes of being/existence. It is essential to the thesis that number-words are univocal, and that ‘exists’ is a number-word. But it is not a number-word, for we can say of certain individual things that they exist, using referring terms.

Consider my cat Max Black. I joyously exclaim, ‘Max exists!’. My exclamation expresses a truth. Compare ‘Cats exist’. Now I agree with van Inwagen that the general ‘Cats exist’ is equivalent to ‘The number of cats is one or more’. But it is perfectly plain that the singular ‘Max exists’ is not equivalent to ‘The number of Max is one or more’. For the right-hand-side of the equivalence is nonsense, hence necessarily neither true nor false.

Right, but can’t a proper name N signify a property N* which can be instantiated, but by only one individual, and always and necessarily by the same individual? Then it makes sense to state there is only one object possessing N*, a statement which is false only if there are no (i.e. zero) objects possessing N*. Bill considers this, but thinks it a heavy price to pay for univocity across general and singular existentials.

‘Haecceity properties are metaphysical monstrosities’.

Why? His argument is that being properties, haecceities are necessary beings, and so exist at all possible times in all possible worlds. But how, before Socrates came into existence, could there have been any such property as the property of being identical to him. There would have been simply nothing to give content to the proposition that it is Socrates.

Now I agree that a haecceity predicate is essential to save the univocity of ‘exists’. And I agree, for the reasons given by Bill, that a haecceity property is absurd. But can there not be predicates, i.e. grammatical items, which have no properties corresponding to them?

More later.

Arizona Bill commits the existential fallacy

In a post today, Maverick Bill talks about fictional and incomplete objects again, which reminds me of an idea that originally occurred to me in February 2011, and which I developed in a series of posts on logical intransivity.

The idea was that there are certain verbs – I call them logically intransitive – which take a grammatical but not a logical accusative. Let me explain. In the sentence ‘Tom is looking for a wife’ the verb ‘wants’ is logically intransitive. It clearly has a grammatical accusative (‘a wife’), but there is no object corresponding to that term, i.e. the sentence can be true (Tom really is looking for a wife) without there being any person or wife to whom the term corresponds. Clearly so, for Tom would not be looking for one, if he had already found her. By contrast ‘Tom has found a wife’ is logically transitive. It cannot be true unless there is someone to whom ‘a wife’ corresponds.

I developed the idea as follows. There is a certain species of bad philosophy which proceeds by taking sentences which are not existential with respect to their accusative, because of logically intransitive verbs, and converting them into sentences which are existential with respect to the same accusative. This typically happens in two ways.

(1) By converting a logically intransitive verb phrase into a logically transitive one. For example by translating ‘Tom is thinking of a mermaid’ into ‘Tom stands in the relation ‘thinking of’ to some mermaid’. Clearly the first sentence does not imply the existence of mermaids because of the logically intranstive ‘is thinking of’. But the second does, because of the transitivity of ‘stands in the relation ‘thinking of’ to’. Bill commits this fallacy here when he argues “When Tom thinks about a nonexistent item such as a mermaid, he does indeed stand in a relation to something”.

(2) By converting a sentence from a passive to an active form, so that the object of the logically intransitive verb becomes its subject. Since subject terms (generally, not always) are existential, the sentence when converted implies existence, whereas before converted is does not. Both of these are specific versions of the existential fallacy, i.e. arguing from premisses which are not existential to a conclusion which is existential.

Arizona Bill’s blog is a wonderful and rich mine for instances of the fallacy. In today’s post there are at least three. In the first set of sentences below, the verbs ‘want’ and ‘imagine’ are clearly intransitive, and to not imply the existence of any table.

(A1) I want a table, but there is no existing table that I want
(A2) I want a table with special features that no existing table possesses.
(A3) In the first case I imagine the table as real; in the second as fictional.

In the next three sentences, he converts grammatical object to grammatical subject, in order to imply the existence of the wanted or imagined objects.

(B1) The two tables I am concerned with, however are both nonexistent.
(B2) There is a merely intentional object before my mind.
(B3) The table imagined as real is possible due to its ontic character of being intended .

Of course, this leads to the inconsistency of implying the existence of a non-existent object. In (B1) above, he asserts the existence of the tables by the apparently referring subject term ‘the tables’, then denies it using the predicate ‘non existent’. Bill usually evades this, when he can be bothered to, by claiming there are two sorts of existence.

Appeals to phenomenology

IN his latest post on ‘pure ficta’, Arizona Bill wheels out what looks like an argument from revelation.

If Ed denies that there are merely intentional objects, then he is denying what is phenomenologically evident. I take my stand on the terra firma of phenomenological givenness. So for now, and to get on with it, I simply dismiss Ed's objection. To pursue it further would involve us a in a metaphilosophical discussion of the role of phenomenological appeals in philosophical inquiry.

Well, it probably would involve us in such a discussion, and I wouldn’t want to go there, correct. I don’t recognise the validity of any kind of appeal to revelation in strictly philosophical enquiry.

None of these men [the pre-Socratics], it is to be noted, tried to answer these questions by an appeal to any revelation, to myth, or religious knowledge of any kind; but attempted to extract the answer by using their reason; and they used it almost without reference to sensible observation and experiments. Why was this ? Clearly because they were convinced that the thing they sought lay deeper in the heart of the world than the superficial aspect of things, of which alone the senses could tell them. (Modern Thomistic Philosophy, R.P. Phillips, London 1934)

But is Bill really making such an appeal? I don’t think so. He is actually appealing to premisses which are uncontroversial, such as our ability to create fictional characters, imagine centaurs etc, and then arguing from such uncontroversial premisses to a more controversial conclusion. So it’s a matter of logic, not ‘phenomenological appeal’. The argument looks like this:

(1) You cannot write or understand a story without thinking about various fictional characters. (2) When you create a fictional character, you bring before your mind an intentional object. (3) The existence of such intentional objects is therefore phenomenologically evident.

I can buy the first premiss. The second I can understand only figuratively. What is an intentional object? The third I reject. It is bizarre to make an existence claim about things which purportedly do not exist, and such existence is far from evident. It’s a neat example of the fallacy of logical intransitivity. You start with a premiss containing a logically intransitive verb, such as ‘imagine’, ‘desire’ and so on. A logically transitive verb is one which takes a grammatical accusative but not a logical one. The accusative of the sentence ‘Jake wants to marry a mermaid’ is ‘a mermaid’, but the sentence is consistent with ‘nothing is a mermaid’. A logically transitive verb, by contrast, requires a real object. The truth of ‘Jake married a mermaid’ requires that some person is such that she was married by Jake. The fallacy consists in drawing a conclusion that contains a logically transitive verb, and which for that reason is existential. The fallacy is a specific instance of the more general existential fallacy, in which we erroneously draw an existential conclusion from non-existential premisses.

Over to you Bill.

On the mode of being of poets

Arizona Bill has some more ideas about modes of being here, so we can pick up where we left off last year (see modes of being of hobbits). Bill picks up on a passage from Scotus’s Ordinatio cited by Lukas Novak (Ord. I, dist. 36, q. un., n. 46 (ed. Vat. VI, 289). The Latin is from the Logic Museum, the English from Bill’s post.

Latin

English

[46] Et si velis quaerere aliquod esse verum huius obiecti ut sic, nullum est quaerere nisi 'secundum quid', nisi quod istud 'esse secundum quid' reducitur ad aliquod esse simpliciter, quod est esse ipsius intellectionis; sed istud 'esse simpliciter' non est formaliter esse eius quod dicitur 'esse secundum quid', sed est eius terminative vel principiative, ita quod ad istud 'verum esse secundum quid' reducitur sic quod sine isto vero esse istius non esset illud 'esse secundum quid' illius.

And if you are looking for some “true being” of this object as such [viz. of the object qua conceived], there is none to be found over and above that “being in a qualified sense”, except that this “being in a qualified sense” can be reduced to some “being in an unqualified sense”, which is the being of the respective intellection. But this being in an unqualified sense does not belong to that which is said to “be in a qualified sense” formally, but only terminatively or principiatively — which means that to this “true being” that “being in a qualified sense” is reduced, so that without the true being of this [intellection] there would be no “being in a qualified sense” of that [object qua conceived].

The puzzle about the ‘being’ of objects of thought was a common topic in medieval literature and there were many attempts at solving it. Peter of Cornwall has a go at it here. (The English translation is my hurried attempt).

Latin

English

Sed nomen accidentis aliquando repraesentat aliquid in opinione secundum Aristotelem; ut ‘Homerus est aliquid, ut poeta’, hic ‘poeta’ repraesentat aliquid in opinione, quia secundum Aristotelem Homerus est poeta non sequitur ‘ergo Homerus est’. Ergo nomen substantiae potest aliquid repraesentare in opinione. Ergo sic dicendo ‘Caesar est homo’ potest ly ‘homo’ stare pro homine in opinione. Et sic erit vera.

But the name of an accident sometimes represents something in opinion according to Aristotle [De. Int. 11 21a25sqq]. For example ‘Homer is something, namely a poet’ – here ‘poet’ represents something in opinion, for according to Aristotle, Homer is a poet, but ‘Homer exists [est]’ does not follow. Therefore the name of a substance can represent something-in-opinion. Therefore when we say ‘Caesar is a man’, the word ‘man’ can stand for a man-in-opinion, so it will be true” Note that according to the medievals, past objects such as Caesar or Homer no longer exist.

Bill objects that this kind of thing is a form of ‘psychologism’.

For if the being of the purely intentional object reduces to the being of the act, then the purely intentional object has mental or psychic being -- which is not the case. The object is not a psychic content. It is not the act or a part of the act; not is it any other sort of psychic reality.

According to this objection, Homer is a poet and a man, and not an opinion or an intellection. I reply, Homer as conceived or as represented or as the object of opinion is a man. And ‘Homer’ stands for a man as the object of opinion, or as Peter Cornwall says ‘man in opinion’. So this trivial objection to the view does not stand. Whether it withstands deeper scrutiny is a more difficult question. Ockham has a more sophisticated view, see here, p. 366, by distinguishing the mode of reference or ‘supposition’ of words like ‘chimera’. Is the sentence ‘a chimera is understood’ or ‘thought about’ true or false? Ockham says that if the term ‘chimera’ is read as having ‘personal supposition’, so that the sentence is true if ‘chimera’ is satisfied by something in reality which is thought about, then if it false. But if it is read as having ‘simple’ or ‘material’ supposition, i.e. as referring to language or concepts, then it is true. For Ockham’s understanding of supposition theory, see here.

Modes of being (of hobbits)

Someone asked me what I thought of this post by the Maverick, about the ‘mode of being’ of holes. No thoughts, really, as I don’t know much about holes.

But there may be a parallel with the points I raised here, about numbers and hobbits. It’s an obvious mistake to say that hobbits have existence in a different way from cats, or that they have a different 'mode of being' from cats. To say that hobbits are fictional is not the same kind of thing as saying that cats are furry, nor do hobbits have a different 'mode of being' from cats. Cats exist, hobbits don't, and to say that hobbits are fictional is just to say that they don't exist, with the added connotation that writers say they do in works of fiction. (Fiction being, as I said elsewhere, a particular mode of falsity in which the writer does not intend to deceive, but rather to amuse, his reader).

As for holes, well they do exist, but as accidents of the cheese. But this needs further thought, as it begs many challenges by the Realist.

The Open Question question

The Maverick has argued (in effect) that the meaning of the word 'exist' is an open question. However, if the meaning of 'exist' is what the thin theorist stipulates it is, it would not be an open question. Therefore the meaning of 'exist' is not what the thin theorist stipulates it is.

Against. It is not an open question whether 'Pegasus does not exist' means the same thing as 'There is no such thing as Pegasus'. But the meaning of 'There is no such thing as Pegasus' is not an open question. Therefore the meaning of 'Pegasus does not exist' is not an open question. Our understanding of sentences such as 'there is such a thing as x' and 'there are such things as Fs' is entirely settled, and indeed is entirely the understanding advocated by the thin theorist.

The thin theorist can also explain why some philosophers think there is an open question. For the 'thick' theorist of existence is tempted to think that the following is a valid inference,

(A) Pegasus does not exist therefore there is something that does not exist

or at least that it is an open question as to whether it is a valid inference. However it is not an open question as to whether it is a valid inference. For the inference is equivalent to

(B) There is no such thing as Pegasus therefore there is something such that there is no such thing as it

which is obviously invalid (for the antecedent is true but the consequent is false). The 'thick' theorist is tempted by the grammar of 'Pegasus does not exist' into thinking that '- does not exist' is a predicate. However, the grammar of 'There is no such thing as Pegasus' does not tempt us into thinking that 'There is no such thing as –' is a predicate. Thus there is absolutely no question about the semantics of 'exist', although its grammar tempts some people into thinking that there is.

No true philosopher

In an earlier post, the Maverick extensively quotes the novelist Jean-Paul Sartre, intending to illustrate the "Continental" view of existence.

It left me breathless. Never, until these last days, had I understood the meaning of 'existence.' I was like all the others, like the ones walking along the seashore, all dressed in their spring finery. I said, like them, 'The ocean is green; that white speck up there is a seagull,' but I didn't feel that it existed or that the seagull was an 'existing seagull'; usually existence hides itself. It is there, around us, in us, it is us, you can't say two words without mentioning it, but you can never touch it. When I believed I was thinking about it, I must [have] believe[d] that I was thinking nothing, my head was empty, or there was just one word in my head, the word 'to be.' Or else I was thinking . . . how can I explain it? I was thinking of belonging, I was telling myself that the sea belonged to the class of green objects, or that that green was a part of the quality of the sea. Even when I looked at things I was miles from dreaming that they existed; they looked like scenery to me. I picked them up in my hands, they served me as tools, I foresaw their resistance. But that all happened on the surface.

If anyone had asked me what existence was, I would have answered, in good faith, that it was nothing, simply an empty form that was added to external things without changing anything in their nature. And then all of a sudden, there it was, clear as day: existence had suddenly unveiled itself. It had lost the harmless look of an abstract category: it was the very paste of things, this root was kneaded into existence. Or rather the root, the park gates, the bench, the sparse grass, all that had vanished: the diversity of things, their individuality, were only an appearance, a veneer. This veneer had melted, leaving soft, monstrous masses, all in disorder — naked, in a frightful, obscene nakedness. (p. 127 tr. Lloyd Alexander, ellipsis in original.)

Omitting the novelistic turn of phrase ('breathless', 'obscene nakedness'), what is left?

1. Roquentin says that never before had he understood the meaning of 'existence.' It seems clear he is talking about some non-standard meaning of the word, which cannot be grasped by the normal process of learning a language, such as in childhood or in school. For Roquentin is an educated adult.  By implication, the standard meaning of the word 'existence', as in 'black swans exist', which can be easily learned, cannot be what he is talking about here.

2. He says he once felt that "'The ocean is green; that white speck up there is a seagull,' but I didn't feel that it existed or that the seagull was an 'existing seagull'; usually existence hides itself." This is baffling. He says that the ocean is green, but doesn't 'feel' that it existed? Again, he cannot be talking about the standard meaning, where 'the ocean is green' implies 'the ocean exists'. He then says that usually existence 'hides itself'. More evidence that he is using the word 'exist' in some specific, novelistic sense, rather than the ordinary, standard one. Maverick comments here that analytic types will guffaw at this, and that they are 'existence-blind' - "to the blind, that which is luminous must appear dark." Of course, but this confirms the point I made in yesterday's post, about philosophy eschewing revelation and all knowledge whose acquisition requires a special state of awareness of some kind. Such knowledge may be important and interesting, but it is not the subject matter of philosophy, properly understood.

3. He says that existence is all around us, but that we cannot touch it. Is he making some scientific claim, then? Is existence like the air or like electricity or gravity, that we cannot touch, but whose existence we infer? Do we infer the existence of existence? If so, do we also infer the existence of the existence of existence? It seems entirely circular.

4. I'm not sure is meant by the next part – Roquentin seems to be contrasting his old way of thinking about existence, such as being asserted by the verb 'to be', or being an assertion of class-membership ("I was telling myself that the sea belonged to the class of green objects") with this new revelation. He would have once said that existence "was nothing, simply an empty form that was added to external things without changing anything in their nature". Now he sees that "existence had suddenly unveiled itself. " OK, existence is now something that reveals itself to his senses or experience. "It had lost the harmless look of an abstract category: it was the very paste of things, this root was kneaded into existence. " Which may be all be true, but it is so mystical as to be meaningless. As for "the diversity of things, their individuality, were only an appearance, a veneer. This veneer had melted, leaving soft, monstrous masses, all in disorder — naked, in a frightful, obscene nakedness", it is sheer poetry. But is it philosophy? Can everyone share the revelation given to Roquentin? Or is it mere euphony, sound and language that is impressive in a novel, but has no real place in a work of true philosophy?

Number and Existence

I go away for a week or two and look what happens. Discussing the Maverick's post on number and existence, and Brandon's comment, Michael Sullivan argues against conflating statements about number with existential statements. Consider:

(a) The number of cats in the room right now is two.

(b) Of the four hobbits that set out for Mount Doom, the number that arrived is two.

The two statements are true: his cats are two and Frodo and Sam are two, and in the same sense of 'two'.

But obviously the two hobbits don't have existence in the way that the cats do: my cats have actual existence and the hobbits don't and never did.

Thus we cannot conflate existence with number.

Contra: we clearly can reduce statements about number to existential statements, even when they are in a book. For example

(1) Tolkien said that two hobbits arrived at Mount Doom
(2) Tolkien said that a hobbit arrived with another hobbit at Mount Doom
(3) Tolkien said for some x, y: x was a hobbit, y was a hobbit, not x = y, and x arrived at Mount Doom and y arrived at Mount Doom

But we can't infer from any of these that there are such things as hobbits, or that hobbits exist. What about the claim that 'Hobbits don't have existence in the way that cats do'? Wrong: it's not that hobbits have a different kind of existence. They don't have any existence at all. The book says that, or pretends that hobbits exist. Indeed, it pretends or states that two hobbits – two existing hobbits – arrived at Mount Doom. But what it says is literally false. Nothing of the sort really happened. No hobbits arrived at any mountain. There is an implicit 'says that' or 'pretends that' operator around 'true' fictional statements such as 'two hobbits arrived at Mount Doom', which blocks any inference to existing things.

The problem is that we easily confuse such operators with spatial operators like 'In Europe', 'In London' and so on. We tend to move easily from statements like (4) below to (6), via (5).

(4) According to The Lord of the Rings, two hobbits arrived at Mount Doom
(5) In The Lord of the Rings, two hobbits arrived at Mount Doom
(6) In the universe of The Lord of the Rings, two hobbits arrived at Mount Doom

Now 'In Europe, there are hobbits' implies 'there are hobbits'. But 'In the universe of The Lord of the Rings there are hobbits' doesn't, because there are no hobbits anywhere. Objection: Can we not say that there are hobbits somewhere, namely in the universe of LOTR? Reply: yes, if 'somewhere' means 'it is said somewhere that …'. But then we are equivocating on 'somewhere'. There should be a special name for this fallacy, but I don't think there is one.

On the meaning of 'exists'

There is progress, so much so that I mostly need to report it, rather than make it happen. Maverick concedes the points I made here. He agrees that if 'Some man is white' and 'A white man exists' have exactly the same meaning, then 'Some man is white because a white man exists' is unintelligible. “That's entirely clear”. So he must show that the two sentences -- call them the some-sentence and the existence-sentence* -- do not have the same meaning.

He gives a negative reason. If we stipulate that the two sentences have the same meaning, the thin theory “is wholly without interest. Substantive philosophical questions cannot be answered by framing stipulative definitions.” Correct, but this begs the question as to whether there is any substantive philosophical question. A thin theorist is likely to be a positive or a nominalist, who wants to show how apparently ‘metaphysical’ questions really arise from a misunderstanding of language, or from being misled by it.

He goes on to give a positive reason.

‘A white man exists’ says all that ‘Some man is white’ says, but it says more: it makes explicit that there are one or more existing items that are such that they are both human and white. The existence-sentence is richer in meaning than the some-sentence. It makes explicit that the item that is both human and white exists, is not nothing, is mind-independently real -- however you want to put it.

Will this work? I’m not sure. For the thin theorist, ‘there are one or more existing items’ and ‘there are one or more items’ or equivalent in meaning, by stipulation. The realist has failed to communicate anything.

On the point that “It makes explicit that the item that is both human and white exists, is not nothing, is mind-independently real”. Well, so does the ‘some’ sentence’. ‘Some man is white’ makes it explicit that the item that is both human and white exists, and that it is not nothing, and is mind-independently real. How could it say any less. If ‘some buttercups are blue’ is true, then blue buttercups exist (in virtue of the meaning alone), and so blue buttercups are not nothing, otherwise ‘no buttercups are blue’ would be true. And blue buttercups are mind-independently real, for ‘some buttercups are blue’ does not merely say that people think there are blue buttercups, or that they are figments of some kind. Over to Phoenix.

*We neo-scholastics call these ‘categorial’ and ‘existential’ sentences respectively. The medievals made a similar distinction between the use of the verb ‘is’ as a second elements, as in ‘Socrates is’, and as a third element or copula, as in ‘Socrates is white’.

Circularity and the Euthyphro Dilemma

The Maverick has said a bit more about his conception of metaphysical circularity in a post about Plato's Euthyphro Dilemma. Do the gods love piety because it is pious, or is it pious because they love it? He argues that the question is intelligible, and therefore, by implication, his questions about existence is intelligible. That is, we can intelligibly ask whether a man is white because a white man exists, or not.

Now I'm still puzzled. The Euthyphro question is intelligible because the terms "That which is loved by the gods"and 'that which is pious' have clearly different meanings. The gods may disagree on the nature of pious. Even if they agree, this offers us no insight into the nature of the pious. In later Western theology, this turned into the question of whether something is good simply because God wills it or whether God wills it because it is good and just. And the question is intelligible because 'good' does not have the same meaning as 'willed by God', even if the two referents turn out to be the same. (Perhaps it is similar to the question of whether Shakespeare was Edward de Vere, or not).

Now I agree that if 'a white man exists' has a different meaning from 'some man is white', then the question of whether some F is a G because some FG exists, is an intelligible one. But it is not intelligible if they have the same meaning, as London 'thin' theorists claim. After all, the statement

(1) Some man is white because some man is white

is not intelligible. Nor is

(2) Some man is white because the sentence 'quidam homo est albus' is true

For the Latin sentence 'quidam homo est albus' means the same as 'some man is white'. The one sentence translates into the other. So there is no meaningful 'because' here. So why does Maverick think that

(3) Some man is white because some white man exists.

is intelligible? He says as much in his comment #6. So does he think that 'some man is white' has the same meaning as 'a white man exists'? Surely not, for the reasons stated here. But if the meaning is different, what is that difference?

Metaphysical circularity

Following my post on my return from sunny Greece, the Maverick now has finally conceded that the 'thin' definition of 'exists'

(1) A-B exists =df A is B

cannot be circular, at least in the strict and ordinary sense of circular. However, he insists that the following equivalence (note the omitted 'df') is still circular.

(1a) A-B exists = existing A is B

He adds: "One response I anticipate Ed making is to say that there is no difference between 'x' and 'existing x': whatever is a value of the one is a value of the other, and vice versa. If so, then perhaps (1a) collapses into (1) and there is no circularity in the sense in which the examples above are circular." That's roughly right, but let's see why I am saying that. It follows from definition (1) that "A man who is white" is equivalent to "an existing white man", and it clearly follows from this that "existing white man" is equivalent to "white man". Thus (1a) above is a mere logical consequence of the original definition.

But Maverick goes on to claim that I am confusing semantic with metaphysical circularity. He says (I modify his wording to accommodate my example):

A presupposition of (1)'s truth is that the domain of quantification -- the domain over which the variable 'A' ranges -- is a domain of existents. Therefore, if I want to know what it is for A to exist, you have not given me any insight by telling me that for A to exist is for A to be identical to something that exists. For of course the A is identical to something that exists, namely the A! Suppose we distinguish between semantic and metaphysical circularity. I am willing to concede that (1) is not semantically circular. But I do maintain that (1) is metaphysically circular: its truth presupposes that the domain of quantification is a domain of existing items.

I reply: the fact that the "domain of quantification", i.e. all the items which satisfy 'A is B' is not a presupposition of the definition, but rather a consequence of it, for essentially the same reason I gave above. Let's first define 'satisfy':

(2) 'A is B' is satisfied by any A that is B

And then make the following assumption:

(3) 'A man is white' is satisfied by that man over there.

Then the following statements logically follow:

(4) That man is white (2, 3)

(5) That white man exists (1, 4)

(6) 'A man is white' is satisfied by an existing white man (3, 5)

So of course the items in the domain of quantification have to be existing items, but the sense in which they 'have to be' existing is a matter of logical consequence alone. They 'have' to exist in the same sense that a bachelor 'has' to be unmarried.

He adds that his claim that the thin conception is 'ontologically' or 'metaphysically' circular is something I fail to understand. This I agree with, of course, for the reason that 'metaphysical circularity' is incoherent.

Circularity of the thin conception after a spell in the sun

Back in the rain-drenched UK.  Returning seems like entering a room with a low, darkened ceiling (I was in sun-drenched Greece, not far from Aristotle's birthplace in Stagira, though did not have time to visit).

Meanwhile, I had time to think long and carefully about Maverick's 'circularity objection' to the thin conception of existence, and I now think I missed a trick.  The thin conception rests on a definition.  But how can a definition be circular at all, so long as it truly is a definition?  Suppose we forget the word 'exists'.  Suppose I want to define the verb 'xxxxts'.  Thus

(1) A-B xxxxts =def A is B

I mean that anything of the form 'A-B xxxxts' -- for example 'A white man xxxxts' -- means exactly what 'A man is white' means.  That's all. Nothing more, nothing less.  I am explaining a term whose meaning is not initially known (the verb 'xxxxts') by the use of terms whose meaning is known.  How can that be 'circular'?  So long as the term I am trying to define does not appear in the definiens side, the right-hand side, so that I have to return to the left-hand side and so on in an infinite regress, there is not even a hint of circularity.

Why then does the Maverick even think the definition is circular?  I think I have an answer to that as well, but more tomorrow.

Getting the Londoners' goat

A post yesterday by the Maverick which is 'guaranteed to get London Ed's goat'. The argument he alludes to can be summarised as follows:

Brian Wilson's song says that there is a girl called Rhonda
The song does not say how tall she was
Therefore there is someone (Rhonda) who is indeterminate with respect to the property of being tall

He ends "The record will show that I myself eschew Meinongianism". It's a mystery to us Londoners.

Is time travel possible?

Maverick quotes John Locke (great English philosopher and father of the American constitution) on the impossibility of two beginnings of existence, as follows.

When therefore we demand whether anything be the same or no, it refers always to something that existed such a time in such a place, which it was certain, at that instant, was the same with itself, and no other. From whence it follows, that one thing cannot have two beginnings of existence, nor two things one beginning; it being impossible for two things of the same kind to be or exist in the same instant, in the very same place; or one and the same thing in different places.

He infers from this the impossibility of a soul not existing from the death of its body in 1890 (say) to its rebirth in a different body in 1990 (say). Does this also refute the possibility of time travel? Dr Who gets into his trusty police box in 1999 and travels to the year 2101. He lives out the rest of his life in the 22nd century and never travels to the 21st century. Therefore, Dr Who never existed in the 21st century. But he exists at the end of the 20th, and exists again at the beginning of the 22nd. Is this inconsistent with Locke's maxim about the impossibility of two beginnings? It's odd. The maxim seems correct, and it seems impossible that the same thing cannot have two beginnings. It seems almost a logical truth. Yet the impossibility of time travel does not seem a logical truth at all.

Maverick on circularity again

Maverick repeats his circularity argument, which boils down to this:

(*) If concept F is instantiated, then it is instantiated by an individual that exists.

He has still not replied to my detailed critique of his argument, however. My critique, in brief, was that not every sentence of the form of (*) contains a circularity. For example "If a man is a bachelor then he is a bachelor who is unmarried".

I gave another objection here, which he has also clearly ignored. The objection is that if the word 'exists' on the right hand side of this definition

Some philosopher is American = An American philosopher exists

is merely a copula, then we cannot 'descend to singulars' via 'American philosopher' but only via the subject of the left hand side, namely 'philosopher'. Maverick may object that 'exist' is not a copula, in which case I accept his argument – but that does not appear to be his argument.

Direct reference and existence

Maverick asked me the other day what connection could possibly be between the theory of direct reference and existence. Well, there is certainly a connection between direct reference and the verb 'exists'. If the direct reference theory is correct, then this verb cannot take a singular term as a subject. So we can say 'An American philosopher exists', meaning that 'philosopher' is truly predicated of at least one singular term referring to an American, (e.g. 'William Lane Craig'). But we can't say 'William Lane Craig exists', because it is ill-formed. We can predicate 'exists' of general terms only. See the argument I gave here.

The direct reference theory is not to be confused with 'linguistic idealism' – whatever that is. The theory does not deny there is any 'extra linguistic reality'. It simply denies that 'William Lane Craig exists' is meaningful, in the strictest sense of 'meaningful'. If it means anything, the sentence means that the proper name 'William Lane Craig' refers to something. But if it referred to nothing, it would not be a proper name – for the direct reference theory says that whatever counts as a proper name must be meaningful (as opposed to a string of letters or an utterance), and that its meaning is what it refers to. Therefore if the utterance refers to nothing, it means nothing, and so cannot be a proper name. And the fact it refers to something guarantees that it refers to something in 'extra linguistic reality'.

As far 'existence', which is an abstract noun formed from the verb 'exists' – well, 'The existence of William Lane Craig' presumably alludes to the fact that 'William Lane Craig' refers to something. Simple.

Consciousness and existence

Sometimes I ponder on the possibility of being born again into a different existence, without any memory (if materialism is correct) of my previous existence in this life here and now.

Then it occurred to me, on waking up this morning, that perhaps this had already happened, and that today was the first day of my conscious existence.  To be sure, I have the recollection of a previous existence in this body, and there is a whole list of posts on this blog that I have been maintaining since 2006.  But that could just be an implanted set of memories.

Perhaps the whole world was created today?  Does anyone here have any evidence otherwise?

Quidam philosophus Americanus est

Yesterday we looked at the argument from descent to singulars.  There are two ways of descent, depending on whether we take the right hand or the left hand side of the definition below:

Some American philosopher exists = Some philosopher is American

If we take the right hand, we range over every philosopher and test whether they are American.  E.g., we ask whether Quine is American.  This test does not explicitly test for 'existence'.  But if we take the left hand, we range over every American philosopher, and test for existence.  This test explicitly invokes the  concept of existence.  E.g. we have to ask whether Quine exists.  Therefore the definition above is circular.  Even though 'exist' isn't explicitly invoked on the right hand side, it is implicitly and irreducibly part of the sentence.

Against, consider the Latin translation of the definition above.

Quidam philosophus Americanus est = Quidam philosophus est Americanus

The only difference is word order. Latin is flexible about word order, as its semantics are given by inflection, unlike in English.  So we can either put the copula 'est' at the end of the sentence, as on the left, or we can interpose it between 'philosophus' and 'Americanus', as on the right.  The semantics, indeed the syntax of the two sentences is identical. What becomes of our argument?  Well, it is invalid because it involves a mistake about logical form. We can only descend via the subject of a subject-predicate sentence, if all such sentences really have the logical form subject-copula-predicate. We obviously can't pretend that the subject and predicate are really a single subject, and that the copula 'is' is really a predicate.  That was the whole point of Aristotle's remark about 'is' being used as a 'second element', which I discussed here.  Therefore we cannot descend to singulars by ranging over individuals which satisfy subject and predicate together, and the 'descent' argument is invalid.

Against that.  In reply, the Phoenician may object that a sentence like 'Quine exists' (or 'Quine is', if you like) is certainly meaningful. Then either (a) the proper name 'Quine' embeds a hidden subject and predicate Qa-Qb, just like 'American philosopher', and so 'Quine exists' really means 'Qa is Qb'.  But that seems implausible.  Or (b) the verb 'is' is genuinely a predicate, in which case the descent to singulars argument is valid.

PS today I drive to Rushmoor in Surrey, hoping to locate the place where Russell began work on Principia Mathematica, and where he wrote the letter to Frege that I discuss here.   If this is successful, I may return with photographs.