More than one. Here is one. And as old Chisholm used to say, you are not philosophizing unless you have a puzzle. So try on this aporetic triad for size:
1. Purely fictional objects do not exist.
2. There are true sentences about purely fictional objects, e.g., 'Sherlock Holmes is a detective' and 'Sherlock Holmes is purely fictional.'
3. If a sentence of the form Fa is true, then there exists an x such that 'a' refers to x.
The triad is logically inconsistent: any two limbs entail the negation of the remaining one. So the limbs cannot all be true despite the considerable plausibility of each. So one of the propositions must be rejected. But the first is nonnegotiable since it is true by definition. The leaves two options: reject (2) or reject (3).
Suppose we reject (2). One way to do this is by supplying a paraphrase in which the apparent reference to the nonexistent is replaced by real reference to the existent. For example, the apparent reference to Sherlock, who does not exist, is replaced by real reference to a story in which he figures, a story that, of course, exists. The elliptical approach is one way of implementing this paraphrastic strategy. Accordingly,
4. Sherlock Holmes is a detective
5. Sherlock Holmes is fictional
are elliptical for, respectively,
6. In the Conan Doyle stories, Sherlock Holmes is a detective
7. In the Conan Doyle stories, Sherlock Holmes is fictional.
But note that while (5) is plainly true, (7) is plainly false. So (7) cannot be taken as elliptical for (5) This is a serious problem for the 'story operator' approach. Or consider the true
8. Sherlock Holmes does not exist.
(8) is surely not short for the false
9. In the Conan Doyle stories, Sherlock Holmes does not exist.
The point can be made with other 'extranuclear' predicates such as 'merely possible' and 'mythological.' If I say that Pegasus is mythological, I don't mean that, according to legend, Pegasus is mythological. But the story operator approach also has trouble with 'nuclear' predicates such as 'detective.' But I'll save that for a subsequent post.
I'll end with a different challenge to the story operator approach. Consider
10. Pinocchio was less of a liar than Barack Obama.
Whether you consider (1) true or false, it is certainly not elliptical for
11. In Carlo Collodi's The Adventures of Pinocchio (1883), Pinocchio was less of a liar than Barack Obama.
To put it vaguely, the the trouble with the story operator appoach is that it traps fictional characters within particular stories, songs, legends, tales, etc. so that (i) it becomes difficult to understand how they can show up in different different stories, songs, etc. as they obviously do in the cases of Faust and Pinocchio, and (ii) it becomes difficult to understand how they can show up in comparisons with nonfictional individuals.
As you use them, the terms 'fictional', 'intentional', 'possible', 'incomplete', and others like 'past' have a distinctive effect on the concept terms they qualify. Ordinary adjectives have the effect of narrowing the extension of the concept term they qualify: the red balls are a subset of the balls, the female prime ministers are a subset of the prime ministers, and so on. The terms in question have the opposite effect. They appear to widen, or indeed offset altogether, the extension of the qualified concept. They are thus potent alienating terms. So the question arises, What is the relation (if any) between the concepts 'fictional person' and 'person', between 'intentional object' and 'object', and 'possible X' and 'X'? Ordinary qualification can be uniformly understood in terms of set intersection. Is there a uniform explanation underlying these alienating qualifications?
1. First of all, contrary to what David says, there are plenty of ordinary adjectives that do not narrow the extension of the terms they qualify. There are redundant adjectives, alienans adjectives, and there is the construction known as the contradictio in adiecto. For example, 'decoy' in 'decoy duck' is an ordinary adjective despite its being an alienans adjective; it is just as ordinary as 'female' in 'female duck,' which I call a specifying adjective and which does narrow the extension of the noun 'duck.' I see no reason to say that specifying adjectives are the only ordinary ones.
2. We can agree on this: red balls are a proper subset of balls, and female prime ministers are a proper subset of prime ministers. We will also agree that round balls are a subset of balls, though not a proper subset, and that female girls are an improper subset of girls. We could say that the last two examples illustrate the null case of specification. We could make a distinction between properly specifying and improperly specifying adjectives corresponding to the distinction between proper and improper subsets.
3. We can also agree that specificatory qualification (but not all qualification) can be uniformly understood in terms of set intersection if the intersection is non-null. The set of cats and the set of dogs has an intersection, but it is the null set. Intersection is defined over all sets, disjoint or not, hence one cannot say that the set of dogs and the set of cats do not intersect. They intersect all right; it is just that their intersection is empty. 'Canine cat' is an example of a contradictio in adiecto which reflects the fact that the corresponding sets are disjoint. 'Canine' does not specify 'cat.' It does not divide the genus into two species, the canine cats and the non-canine cats.
4. I can't, pace David, think of an example in which an adjective widens the extension of the term it qualifies. Can you? For example, 'former' in 'former wife' does not widen the extension of 'wife.' It is not as if there are two kinds or species of wives, former and present. Tom's former wife is not his wife. 'Former' does not narrow the extension either. It is an alienans adjective. It is the same with 'artificial leather.' Alligator leather and cowshide are two kinds of leather, but artificial and real are not two kinds of leather.
5. We will agree that all or most the following constructions from ordinary, i.e., non-philosophical English feature alienans adjectives, adjectives that shift or 'alienate' or 'other' the sense of the term they qualify:
male chauvinist (on one disambiguation of its syntactic ambiguity; see article below)
generational chauvinist (I am a generational chauvinist when it comes to popular music: that of my generation is superior to that of the immediately preceding and succeding American generations.)
6. Note that the adjective in 'alienans adjective' is not alienans! Note also that 'putative' and 'artificial' function a little differently. Exercise for the reader: explain the difference and formulate a general test for alienans adjectives.
7. Observe that 'artificial' in 'artificial insemination' is not an alienans adjective in that artificial insemination is indeed insemination, albeit by artificial means. Whatever the means, you are just as pregnant. So whether an adjective is alienans or not depends on the context. A false friend is not a friend, but false teeth are teeth.
8. We now come to more or less controversial examples:
same-sex marriage (Conservative position: same-sex marriage is not marriage)
merely possible animal ('The chimera is a merely possible animal.')
Is a (purely) fictional man a man? You might be tempted to say yes: Hamlet is fictional and Hamlet is a man, so Hamlet is a fictional man. But the drift of what I have been arguing over the last few days is that a fictional man is not a man, and that therefore 'fictional' functions as an alienans adjective. But I am comfortable with the idea that a merely possible man is a man. What is the difference?
There might have been a man distinct from every man that exists. (Think of the actual world with all the human beings in it, n human beings. There could have been n + 1.) God is contemplating this extra man, and indeed the possible world or maximal consistent state of affairs in which he figures, but hasn't and will not ever actualize him or it. What God has before his mind is a completely determinate merely possible individual man. There is only one 'thing' this man lacks: actual existence. Property-wise, he is fully determinate in respect of essential properties, accidental properties, and relational properties. Property-wise the merely possible extra man and the actual extra man are exactly the same. Their quidditative content is identical. There is no difference in Sosein; the only difference is Sein, and Sosein is indifferent to Sein as Aquinas, Kant, and Meinong would all agree despite their differences. As Kant famously maintained, Sein is not a quidditative determination, or in his jargon 'reales Praedikat.'
For this reason a merely possible (complete) man is a man. They are identical in terms of essence or nature or quiddity or Sosein, these terms taken broadly. If God actualizes the extra man, his so doing does not alter the extra man in any quidditative respect. Otherwise, he ould not be the same man God had been contemplating.
9. Brightly hits upon a happy phrase, "alienating qualifications." In my first bullet list we have examples of alienating qualifications from ordinary English. I expect Brightly will agree with all or most of these examples. His questioin to me is:
Ordinary qualification can be uniformly understood in terms of set intersection. Is there a uniform explanation underlying these alienating qualifications?
If Brightly is looking for a test or criterion I suggest the following:
Let 'FG' be a phrase in which 'F' is an adjective and 'G' a noun. 'F' is alienans if and only if either an FG is not a G, or it does not follow from x's being an FG that x is a G. For example, your former wife is not your wife, a decoy duck is not a duck, artificial leather is not leather, and a relative truth is not a truth. Is an apparent heart attack a heart attack? It may or may not be. One cannot validly move from 'Jones had an apparent heart attack' to 'Jones had a heart attack.' So 'apparent' in 'apparent heart attack' is alienans.
Now it is obvious that a decoy duck is not a duck, and that a roasted turkey is not a turkey, but the cooked carcass of a turkey; but it is not so obvious that a fictional man is not a man, while a merely possible man is a man. To establish these controversial theses -- if 'establish' is not too strong a word -- requires philosophical inquiry which is of course very difficult and typically inconclusive. But once we have decided that a certain philosophical phrase is an alienating qualification, then my test above can be applied.
As an ornery aporetician, I want ultimately to say that an equally strong case can be made both for and against the thesis that ficta are impossibilia. But here I only make (part of) the case for thinking that ficta are impossibilia.
Every human being is either right-handed or not right-handed. (But if one is not right-handed, it doesn't follow that one is left-handed. One could be ambidexterous or ambisinistrous.) What about the fictional character Hamlet? Is he right-handed or not right-handed? I say he is neither: he is indeterminate with respect to the property of righthandedness. That makes him an incomplete object, one that violates the law of Excluded Middle (LEM), or rather one to which LEM does not apply.
Hamlet (the character, not the play) is incomplete because he has all and only the properties ascribed to him by the author of the play, and the author left Hamlet's handedness unspecified. It is worth noting that Hamlet the play is complete and this holds for each written token of the play, the type of which they are tokens, and each enactment of the play. This is because the play and its enactments are actualia.
But don't we say that Hamlet the play is fictional? We do, but what we mean is not that the play is an object of fiction, but that the people and events depicted therein are fictional. The play is not fictional but entirely real. Of course, there could be a play that is a mere object of fiction: a play within a play. The same holds for novels. My copies of Moby Dick are each of them complete and actual, hence full-fledged citizens of the real, with all the rights and privileges pertaining thereunto; but Ishmael, Queequeg, and Ahab are not. They are objects of fiction; those books are not. And presumably the type of which they are tokens, though an abstract object, is also actual and complete. A person's reading or 'enactment' of the novel is typically a long, interrupted process; but it too is complete and actual and resident in the real order.
Back to the character Hamlet: he is an incomplete object, having all and only the properties ascribed to him in the play (together with, perhaps, entailments of these properties). London Ed balks at this:
I don't follow this at all. I don't agree with the second sentence "He has all and only ….". Of course Shakespeare said that there was a person called ‘Hamlet’ who had certain properties (e.g. he said that Hamlet was a prince of Denmark. It doesn’t follow that there is someone who has or had such a property. For example, legend says that there was a horse called ‘Pegasus’ that flew. It doesn’t follow that there are or were flying horses.
This objection shows misunderstanding. I did not say or imply that there exists in actuality, outside the mind, a man named 'Hamlet.' The point is rather that when I read the play there appears before my mind a merely intentional object, one that I know is fictional, and therefore, one that I know is merely intentional. If Ed denies this, then he denies what is phenomenologically evident. And, as a matter of method, we must begin with the phenomenology of the situation.
Suppose I write a two-sentence novel:
It was a dark and rainy night. Shakey Jake, life-long insomniac, deciding he needed a nightcap, grabbed his flashlight and his raincoat and headed for the Glass Crutch bar and grill, a local watering hole a half a mile from his house.
Now I couldn't have written that, and you can't understand it, without thinking about various intentional objects that do not exist. Am I saying that there exist objects that do not exist? No, that would be a contradiction. Nor am I committed to saying that there are objects that have mind-independent being but not existence. Furthermore, I am not committed to Meinong's doctrine of Aussersein.
All I am doing is holding fast to a phenomenological datum: when I create a fictional character as I just did when I created Shakey Jake the insomniac, I bring before my mind an intentional object. (The act-object schema strikes me as having pretty good phenomenological credentials, unlike the adverbial schema.) What can we say about this merely intentional object? First, it is no part of the acts through which I think it. My acts of thinking exist in reality, but Shakey Jake does not exist in reality. (This point goes back to Twardowski.) When I think about Hamlet or Don Quixote or Shakey Jake, I am not thinking about my own mind or any state of my mind. I am not thinking about anything real. But it doesn' t follow that I am not thinking of anything.
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.
Ficta are Impossibilia
Let us confine ourselves to purely fictional objects and leave out of consideration real individuals who are partially fictionalized in fables, legends, apocryphal stories, so-called historical novels that blend fact and fiction, and the like. One of my theses is that purely fictional objects cannot exist and thus are broadly logically impossible. They are necessarily nonexistent, where the modality in question is broadly logical. It does not follow, however, that pure ficta have no ontological status whatsoever. They have a mode of being that could be called existential heteronomy. On this point I agree with Roman Ingarden, a philosopher who deserves more attention in the Anglosphere than he receives here.
Earlier I gave an argument from incompleteness: the incomplete cannot exist and so are impossible. But now I take a different tack.
Purely fictional objects are most plausibly viewed as made up, or constructed, by novelists, playwrights, et al. It may be that they are constructed from elements that are not themselves constructed, elements such as properties or Castaneda's ontological guises. Or perhaps fictional objects are constructed ex nihilo. Either way, they have no being at all prior to their creation or construction. There was no Captain Ahab before Melville 'cooked him up.' But if Ahab were a merely possible individual, then one could not temporally index his coming to be; he would not come to be, but be before, during, and after Melvlle's writing down his description.
The issue could be framed as follows. Are novels, plays, etc. which feature logically consistent pure ficta, something like telescopes that allow us to peer from the realm of the actual into the realm of the merely possible, both realms being realms of the real? Or are novels, etc. more like mixing bowls or ovens in which ficta are 'cooked up'? I say the latter. If you want, you can say that Melville is describing something when he writes about Ahab, but what he is describing is something he has made up: a merely intentional object that cannot exist apart from the acts of mind trained upon it. He is not describing something that has ontological status apart from his mind and the minds of his readers. He is also not descrbing some real feature or part of himself as subject. So we could say that in describing Ahab he is describing an item that is objectively but not subjectvely mind-dependent.
Here is an Argument from Origin:
1. Pure ficta are made up or constructed via the mental acts and actions of novelists, playwrights, et al.
2. Ahab is a pure fictum.
3. Ahab came into being via the mental activity of a novelist or playwright. (from 1,2)
4. No human being comes into being via the mental activity of novelists, et al., but via the uniting of human sperm and human egg.
5. Ahab is not a human being. (from 3, 4)
6. A merely possible human being is a human being, indeed a flesh-and-blood human being, though not an actual flesh-and-blood human being.
7. Ahab is not a merely possible human being, but a fictional human being where 'fictional' unlike 'merely possible' functions as an alienans adjective.
This argument does not settle the matter, however, since it is not compelling. A Meinongian or quasi-Meinongian could, with no breach of logical propriety, run the argument in reverse, denying (7) and denying (1). One man's modus ponens, etc.
1. There is first of all the 'is' of atemporality. Assuming that there are timeless entities such as God (concrete) and the number 13 (abstract), any sentences we use to talk about them must feature tenseless verbs and copulae. Consider the proposition expressed by the sentence, '13 is prime.' 13 is prime, but not now and not always. If the truth were always true, it would be in time. The truth is timeless and so is the object 13 and the property of being prime. The same goes for '13 exists.' It is not true now nor at every time. It is true timelessly. It is worth noting that the timeless is' and 'exists' do not abstract from the temporal determinations of pastness, presentness, and futurity for the simple reason that numbers and such are not in time in the first place. So the 'is' of atemporality is not the result of a de-tensing operation whereby we abtract from the temporal determinations to lay bare the pure copula, the copula that merely 'copulates.' The 'is' in question is tenseless from the 'git-go.'
Perhaps we should distinguish between grammatical tense and logical tense. Every verb has a grammatical tense. Thus the verb in 'God exists' is in the present tense. But God exists timelessly, and so 'exists' in this instance is logically without a tense.
Consider John 8:58: "Before Abraham was, I am." Is that ungrammatical? Yes, but logically it makes sense.
2. At the opposite end of the spectrum we find the 'is' of temporal presentness. Examples: 'Peter is smoking' and 'There are 13 donuts in the box.' There are now 13 donuts in the box.
3. The 'is' of omnitemporality. Savitt gives the example of 'Copper is a conductor of electricity.' The sentence is true at every time, not just at present. But it is not timelessly true since it is about something in time, copper. I think the example shows that the tenseless is not the same as the timeless. What is timelessly true is tenselessly true, but not conversely.
4. The Disjunctively Detensed 'Is.' We can de-tense 'is' as follows: x is detensedly F just in case x was F or is F or will be F. We can do the same with 'exists.' Thus, Socrates is detensedly wise iff Socrates was wise or is wise or will be wise. De-tensing involves abstracting from temporal determinations. A detensed copula is a pure copula: all it does is 'copulate' or link.
The 'am' in 'I am dead' is a pure copula, and the sentence is tenselessly true, but not presently true or timelessly true or omnitemporally true. Gott sei dank!
5. The Hypertenseless 'Is.' God exists atemporally and thus tenselessly while Socrates exists temporally but not presently or omnitemporally and thus he too exists tenselessly. If there is a hypertenseless sense of 'exist' it applies to both God and Socrates and abstracts from the way each exists, atemporally in the case of God, temporally in the case of Socrates.
In 'God and Socrates both exist,' the 'exist' is hypertenseless in that it is abstractly common to both the tenselessness of the 'exists' in 'God exists' and the tenselessness of the 'exists' in 'Socrates exists.'
Now what is this hypertenseless univocal sense of 'exists' that applies to both God and Socrates? Persumably it is the quantifier sense according to which x exists iff (Ey) x = y. Existence in this sense is identity-with-something-or-other. Absolutely everything, whatever its mode of existence, exists in this hypertenseless sense.
Now the presentist wants to say that, necessarily, it is always the case that only present items exist. But in what sense of 'exist'? It cannot be the first four, for reasons given in previous posts. So let's try the fifth sense. Accordingly, only present items are identical-with-something-or-other.
Clearly, a thing can exist without existing here. The Washington Monument exists but not in my backyard. Accordingly, 'x exists here' can be split up as follows:
1. x exists here iff (i) x exists & (ii) x is in the vicinity of the speaker.
It seems pretty obvious that existence and the indexical property of hereness are different properties if you want to call them properties.
A much more difficult question is whether a thing can exist without existing now. Is it true that:
2. x exists now iff (i) x exists & (ii) x is temporally present?
Clearly, we can prise apart the existence of a (spatially located) thing and its hereness. Anyone who maintained that to exist = to be here we would deem either crazy or not conversant with the English language, a sort of 'local yokel' in excelsis. But can we prise apart the existence of a thing and its temporal presentness? Is there a real distinction between the existence of a thing and its temporal presentness?
A. A negative answer will be returned by the presentist who maintains that only the temporally present exists. He will maintain that what no longer exists and what does not yet exist does not now exist, and therefore does not exist at all.
Note that it ought to be is perfectly obvious to anyone who understands English that what no longer exists and what does not yet exist does not now exist. What is not at all obvious is the part after 'therefore' in the sentence before last. It is not at all obvious that an individual or event or time that is wholly past or wholly future does not exist at all.
B. An affirmative answer will be returned by all those who reject presentism. Some will reject presentism on the ground that abstracta exist, but are not in time at all, and so cannot be said to exist now. A presentist can accommodate this point by restricting his thesis:
Restricted Presentism: Necessarily, only temporally present concreta exist.
Nevertheless, the anti-presentist will insist that there are past and perhaps also future concreta that exist but do not exist now. Scollay Square, for example, no longer exists. But that it not to say that it is now nothing. After all, we still refer to it and say true things about it. It is true, for example, that my father visited Scollay Square while on shore leave during WW II on a break from service on destroyer escorts in the North Atlantic. So it is true that a a sailor who no longer exists visited a place that no longer exists and was involved in events that no longer exist. It also true that Scollay Square had been demolished by the time I arrived in Boston in 1973. I can now argue as follows:
1. Various predicates (e.g., is remembered by some Bostonians) are true of Scollay Square. 2. Scollay Square does not exist now. 3. If x does not exist, then no predicate is true of x. Therefore 4. Scollay Square exists. (From 1 and 3) Therefore 5. Scollay Square exists but is not temporally present. (From 2 and 4) Therefore 6. Restricted Presentism is false.
I think there are three ways to attack this argument: (a) reject one or more of the premises; (b) find fault with the reasoning; (c) complain that it is not clear what Restricted Presentism amounts to.
Here is London Ed's most recent version of his argument in his own words except for one word I added in brackets:
1. There is no such thing as Caesar any more.
2. The predicate 'there is no such thing as -- any more' is satisfied by Caesar.
3. If a relation obtains [between] x and y, then there is such a thing as y.
4. (From 2) the relation 'is satisfied by' obtains between the predicate '-- is not a thing any more' and Caesar.
5. (3, 4) There is such a thing as Caesar.
6. (1, 5) contradiction.
Premiss (1) is Moorean. There is no longer any such thing or person as Caesar. (Or if you dispute that for reason of immortality of Caesar, choose some mortal or perishable object). (2) is a theoretical. (3) is a logical truth, and the rest is also logic. You must choose between (1) and (2), i.e. choose between a Moorean truth, and a dubious theoretical assumption.
(1) is indeed 'Moorean,' i.e., beyond the reach of reasonable controversy. (2) is indeed theoretical inasmuch as it involves an optional albeit plausible parsing in the Fregean manner of the Moorean sentence.
Ed tells us that (3) is a logical truth. I deny that it is. A logical truth is a proposition true in virtue of its logical form alone. 'Every cat is a cat' is an example of a logical truth as are 'No cat is a non-cat' and 'Either Max is a cat or Max is not a cat.' One can test for logical truth by negating the proposition to be tested. If the result is a logical contradiction, then the proposition is a logical truth. For example, if we negate 'Every cat is a cat' we get 'Some cat is not a cat.' The latter sentence is a logical contradiction, so the former sentence is a logical truth. The latter is a logical contradiction because its logical form -- Some F is not an F -- has only false substitution-instances.
Negating (3) yields 'A relation obtains between x and y, but there is no such thing as y.' But this is not a logical contradiction in the strict and narrow sense defined above. Suppose I am thinking about the Boston Common which, unbeknownst to me, ceases to exist while I am thinking about it. I stand in the 'thinking about' relation to the Common during the whole period of my thinking despite the fact that at the end of the period there is no such thing as the Boston Common. There are philosophers who hold that the intentional relation is a genuine relation and not merely relation-like as Brentano thought, and that in some cases it relates an existing thinker to a nonexisting object.
Now there are good reasons to reject this view as false, but surely it is not false as a matter of formal logic. If it is false, it is false as a matter of metaphysics. A philosopher such as Reinhardt Grossmann who holds that the intentional relation is a genuine relation that sometimes relates an existent thinker to a nonexistent object is not contradicting himself.
Since (3) is not a logical truth, one way to solve Ed's problem is by rejecting (3) and holding that there are genuine relations that relate the existent to the nonexistent. One could hold that the relation of satisfaction is such a genuine relation: it relates the existing predicate to the nonexistent emperor: Caesar satisfies the predicate despite his nonexistence.
Note that I am not advocating this solution to the puzzle; I am dismissing Ed's dismissal of this putative solution. I am rejecting Ed's claim that one is forced to choose between (1) and (2). One can avoid the contradiction by denying (3), and one is not barred from doing so by logic alone.
Ed claims that (1) and (5) are logical contradictories. But they are not. Just look carefully at both propositions and you will see. Ed thinks they are contradictories because he assumes that 'There is no such thing as y any more' is logically equivalent to 'There is no such thing as y.' But to make that assumption is to to assume the substantive metaphysical thesis known in the trade as
Presentism: Necessarily, only temporally present concrete objects exist.
Given Presentism, (1) and (5) are indeed contradictory. This is why I said earlier that Ed's argument cannot get off the ground without Presentism. For suppose we reject Presentism in favor of the plausible view that both past and present concreta exist, i.e., are within the range of our unrestricted quantifiers. Then Ed's puzzle dissolves. For then there is such a thing as Caesar, it is just that he is past. The relation of satisfaction connects a present item with a past item both of which exist. Or, since Ed is allergic to 'exist': both of which are such that there such things as them.
So a second way to solves Ed's puzzle is by rejecting the Presentism that he presupposes.
So I count at least three ways of solving Ed's puzzle: reject (2), reject (3), reject the tacit assumption of Presentism which is needed for (1) and (5) to be contradictory.
My inclination is to say that the puzzle is genuine, but insoluble. And this because the putative solutions sire puzzles as bad as the one we started with. Of course, I haven't proven this. But this is what my metaphilosophy tells me must be the case.
London Ed sends me a puzzle that I will formulate in my own way.
1. Boston's Scollay Square no longer exists. Hence 'Scollay Square no longer exists' is true.
2. Removing 'Scollay Square' from the closed sentence yields the open sentence, or predicate, or sentential function, '____ no longer exists.'
3. If a subject-predicate sentence is true, then its predicate is true of, or is satisfied by, the referent of the sentence's subject term.
4. If x is satisfied by y, then both x and y exist. (Special case of the principle that if x stands in a relation to y, then both relata exist.)
5. What no longer exists, does not exist. (An entailment of presentism.)
6. The referent of 'Scollay Square' does not exist. (from 1 and 5)
7. The referent of 'Scollay Square' exists. (from 1, 3, and 4)
How do we avoid the contradiction? As far as I can see we have exactly three options. The first is to posit an haecceity property that individuates Scollay Square across all possible worlds, and then construe the original sentence as saying, of that haecceity property, that it is no longer instantiated. Thus the original sentence is not about Scollay Square, which does not exist, but about an ersatz item, an abstract deputy that does exist., and indeed necessarily exists. About this ersatz item we say that it now fails of instantiation. The second option is to reject the principle that if a relation obtains between x and y, then both x and y exist. One might say that past objects are Meinongian nonexistent objects. The third option is to reject presentism and say that what no longer exists exists alright, it just doesn't exist now. (Analogy: the cat that is no longer in my lap exists alright, it just doesn't exist here.)
None of these options is palatable. I should like London Ed to tell me which he favors. Or does he see another way out?
Addendum (26 February): Steven comments, "I have my doubts about "crap" meaning "anything." I think it means "nothing", but appears in acceptable double-negative propositions which, because of widespread colloquial usage. The evidence I bring forth is the following. "You've done shit to help us" means "You've done nothing to help us," not "You've done anything to help us."
BV: I see the point and it is plausible. But this is also heard: 'You haven't done shit to help us.' I take that as evidence that 'shit' can be used to mean 'anything.' Steven would read the example as a double-negative construction in which 'shit' means 'nothing.' I see no way to decide between my reading and his.
Either way, it is curious that there are quantificational uses of 'shit,' 'crap,' etc!
In the opening pages of More Kinds of Being: A Further Study of Individuation, Identity, and the Logic of Sortal Terms (Blackwell, 2009), E. J. Lowe distinguishes five uses of ‘is’ as a copula: 1. The ‘is’ of attribution, as in ‘Socrates is wise’ and ‘Grass is green’.2. The ‘is’ of identity, as in ‘Napoleon is Bonaparte’ and ‘Water is H2O’.3. The ‘is’ of instantiation, as in ‘Mars is a planet’ and ‘A horse is a mammal’.4. The ‘is’ of constitution, as in ‘This ring is gold’ and ‘A human body is a collection of cells’.5. The ‘is’ of existence, as in ‘The Dodo is no more’.He says some may be reducible to others, and that one or two must be primitive. I thought this was a helpful spread.
That is indeed helpful, but here are some comments and questions.
1. First of all, I would be surprised if Lowe referred to the five uses as five uses of 'is' as a copula. The 'is' of existence is not a copula because it doesn't couple. There is no copulation, grammatical or logical, in 'God is.' The 'is' of existence does not pick out any sort of two-termed relation such as identity, instantiation, or constitution. Calling the 'is' of identity a copula is a bit of a stretch, and I don't think most philosophers would.
2. Is there a veritative use of 'is'? 'It is so.' 'It is the case that Frege died in 1925.' One could say, though it is not idiomatic: 'Obama's being president is.' One would be expressing that the state of affairs obtains or that the corresponding proposition is true. So it looks as if there is a veritative use of 'is.'
3. Reducibility of one use to another does not show that they are not distinct uses. Perhaps the veritative use can be reduced to what Lowe calls the attributive use. Attributions of truth, however, imply that truth is a property. Frege famously argued that truth cannot be a property. That is a messy separate can of worms.
4. There are also tensed and tenseless uses of 'is.' 'Obama is president' versus '7 + 5 is 12.' With respect to the latter, it would be a bad joke, one reminiscent of Yogi Berra, were I to ask,"You mean now?" Yogi Berra was once asked the time. He said,"You mean now?"
'Hume is an empiricist' can be used both in a tensed way and an untensed way. If I say that Hume is an empiricist what I say is true despite the present nonexistence of Hume. 'Grass is green,' however, is never used in a tensed way, though one can imagine circumstances in which it could.
5. One and the same tokening of 'is' can do more than one job. Is the 'is' in 'Max is black' as used by me in the presence of my cat Max the 'is' of predication merely? I don't think so. It also expresses existence. But this requires argument:
1. 'Max is black' and 'Black Max exists' are intertranslatable. 2. Intertranslatable sentences have the same sense. Therefore 3. 'Max is black' and 'Black Max exists' express the very same (Fregean) sense. Therefore 4. Both sentences express both predication and existence: a property is predicated of something that cannot have properties unless it exists. Therefore 5. The 'is' in 'Max is black' has a double function: it expresses both predication and existence.
Note that both sentences include a sign for the predicative tie. The sign is 'is' in the first sentence and in the second sentence the sign is the immediate concatenation of 'black' and 'Max' in that order. This shows that to refer to logical (as opposed to grammatical) copulation does not require a separate stand-alone sign. 'Black Max exists' expresses both existence via the sign 'exsts' and predication via the immeditae concatenation of 'black' and 'Max' in that order in the context of the sentence in question.
I put the question to Manny K. Black, brother of Max Black, but all I got was a yawn for my trouble. The title question surfaced in the context of a discussion of mereological models of the Trinity. Each of the three Persons is God. But we saw that the 'is' cannot be read as the 'is' of identity on pain of contradiction. So it was construed as the 'is' of predication. Accordingly, 'The Father (Son, etc.) is God' was taken to express that the Father (Son, etc.) is divine. But that has the unwelcome consequence that there are three Gods unless it can be shown that something can be F without being an F. At this point the cat strolls into the picture. Could something be feline without being a feline? The skeleton of a cat, though not a cat, is a proper part of a cat. And similarly for other cat parts. As a proper part of a cat the skeleton of a cat is feline. And it is supposed to be feline in the same sense of 'feline' as the cat itself is feline.
Now if the proper parts of a cat can be feline in the very same sense in which the cat is feline, without themselves being cats, then we have an analogy that renders intelligible the claim that the Persons of the Trinity are divine without being Gods. The picture is this: God or the Godhead or the Trinity is a whole the proper parts of which are exactly the Father, the Son, and the Holy Spirit. The Persons are distinct among themselves, but each is divine in virtue of being a proper part of God. There is one God in three divine Persons. The mereological model allows us to avoid tritheism and to affirm that God is one and three without contradiction.
I have already expressed my doubt whether the mereological model can accommodate the divine unity. But now I raise a different question. Is 'feline' being used univocally -- in the very same sense -- when applied to a cat and when applied to a proper part of a cat such as a cat's skeleton?
This is not obvious. It appears to be being used analogically. We can exclude equivocity of the sort illustrated by the equivocity of 'bank' as between 'money bank' and 'river bank.' Clearly, we are not simply equivocating when we apply 'feline' to both cat and skeleton. But can we exclude analogicity?
To cop an example from Aristotle, consider 'healthy.' The cat is healthy. Is its food healthy? In one sense 'no' since it is not even alive. In another sense 'yes' insofar as 'healthy' food conduces to health in the cat. Similarly with the cat's urine, blood, exercise, and coat. Urine cannot be healthy in exactly the same sense in which the cat is healthy, but it is healthy in an analogical sense inasmuch as its indicates health in the animal.
Since a skeleton is called feline only by reference to an animal whose skeleton it is, I suggest 'feline' in application to a cat skeleton is being used analogically. If this is right,then the Persons are divine in only an analogical sense, a result that does not comport well with orthodoxy.
As magnificent a subject as philosophy is, grappling as it does with the ultimate concerns of human existence, and thus surpassing in nobility any other human pursuit, it is also miserable in that nothing goes uncontested, and nothing ever gets established to the satisfaction of all competent practitioners. (This is true of other disciplines as well, but in philosophy it is true in excelsis.) Suppose I say, as I have in various places:
That things have properties and stand in relations I take to be a plain Moorean fact beyond the reach of reasonable controversy. After all, my cat is black and he is sleeping next to my blue coffee cup. ‘Black’ picks out a property, an extralinguistic feature of my cat.
Is that obvious? Not to some. Not to the ornery and recalcitrant critter known as the ostrich nominalist. My cat, Max Black, is black. That, surely, is a Moorean fact. Now consider the following biconditional and consider whether it too is a Moorean fact:
1. Max is black iff Max has the property of being black.
As I see it, there are three main ways of construing a biconditional such as (1):
A. Ostrich Nominalism. The right-hand side (RHS) says exactly what the left-hand side (LHS) says, but in a verbose and high-falutin' and dispensable way. Thus the use of 'property' on the RHS does not commit one ontologically to properties beyond predicates. (By definition, predicates are linguistic items while properties are extralinguistic and extramental.) Predication is primitive and in need of no philosophical explanation. On this approach, (1) is trivially true. One needn't posit properties, and in consequence one needn't worry about the nature of property-possession. (Is Max related to his blackness, or does Max have his blackness quasi-mereologically by having it as an ontological constituent of him?)
B. Ostrich Realism. The RHS commits one ontologically to properties, but in no sense does the RHS serve to ground or explain the LHS. On this approach, (1) is false if there are no properties. For the ostrich realist, (1) is true, indeed necessarily true, but it is not the case that the LHS is true because the RHS is true. Such notions as metahysical grounding and philosophical explanation are foreign to the ostrich realist, but not in virtue of his being a realist, but in virtue of his being an ostrich.
C. Non-Ostrich Realism. On this approach, the RHS both commits one to properties, but also proffers a metaphysical ground of the truth of the LHS: the LHS is true because (ontologically or metaphysically speaking) the concrete particular Max has the property of being black, and not vice versa.
Note 1: Explanation is asymmetrical; biconditionality is symmetrical.
Note 2: Properties needn't be universals. They might be (abstract) particulars (unrepeatables) such as the tropes of D. C. Williams and Keith Campbell. Properties must, however, be extralinguistic and extramental, by definition.
Note 3: Property-possession needn't be understood in terms of instantiation or exemplification or Fregean 'falling-under'; it might be construed quasi-mereologically as constituency: a thing has a property by having it as a proper ontological part.
Against Ostrich Nominalism
On (A) there are neither properties, nor do properties enter into any explanation of predication. Predication is primitive and in need of no explanation. In virtue of what does 'black' correctly apply to Max? In virtue of nothing. It just applies to him and does so correctly. Max is black, but there is no feature of reality that explains why 'black' is true of Max, or why 'Max is black' is true. It is just true! There is nothing in reality that serves as the ontological ground of this contingent truth. Nothing 'makes' it true. There are no truth-makers and no need for any.
I find ostrich nominalism preposterous. 'Black' is true of Max, 'white' is not, but there is no feature of reality, nothing in or at or about Max that explains why the one predicate is true of him and the other is not!? This is not really an argument but more an expression of incomprehension or incredulity, an autobiographical comment, if you will. I may just be petering out, pace Professor van Inwagen.
Can I do better than peter? 'Black' is a predicate of English. Schwarz is a predicate of German. If there are no properties, then Max is black relative to English, schwarz relative to German, noir relative to French, and no one color. But this is absurd. Max is not three different colors, but one color, the color we use 'black' to pick out, and the Krauts use schwarz to pick out. When Karl, Pierre, and I look at Max we see the same color. So there is one color we both see -- which would not be the case if there were no properties beyond predicates. It is not as if I see the color black while Karl sees the color schwarz. We see the same color. And we see it at the cat. This is not a visio intellectualis whereby we peer into some Platonic topos ouranos. Therefore, there is something in, at, or about the cat, something extralinguistic, that grounds the correctness of the application of the predicate to the cat.
A related argument. I say, 'Max is black.' Karl says, Max ist schwarz. 'Is' and ist are token-distinct and type-distinct words of different languages. If there is nothing in reality (no relation whether of instantiation or of constituency, non-relational tie, Bergmannian nexus, etc.) that the copula picks out, then it is only relative to German that Max ist schwarz, and only relative to English that Max is black. But this is absurd. There are not two different facts here but one. Max is the same color for Karl and me, and his being black is the same fact for Karl and me.
Finally, 'Max is black' is true. Is it true ex vi terminorum? Of course not. It is contingently true. Is it just contingently true? Of course not. It is true because of the way extralinguistic reality is arranged. It is modally contingent, but also contingent upon the way the world is. There's this cat that exists whether or not any language exists, and it is black whether or not any language exists.
Therefore, I say that for a predicate to be contingently true of an individual, (i) there must be individuals independently of language; (ii) there must be properties independently of language; and there must be facts or truth-making states of affairs independently of language. Otherwise, you end up with (i) total linguistic idealism, which is absurd; or (ii) linguistic idealism about properties which is absurd; or (iii) a chaos, a world of disconnected particulars and properties.
The above is a shoot-from-the hip, bloggity-blog exposition of ideas that can be put more rigorously, but it seems to to me to show that ostrich nominalism and ostrich realism for that matter are untenable -- and this despite the fact that a positive theory invoking facts has its own very serious problems.
Metaphilosophical Coda: If a theory has insurmountable problems, these problems are not removed by the fact that every other theory has problems. For it might be that no theory is tenable,while the poroblem itself is genuine.
Chapter III of Etienne Gilson's Being and Some Philosophers is highly relevant to my ongoing discussion of common natures. Gilson appears to endorse the classic argument for the doctrine of common natures in the following passage (for the larger context see here):
Out of itself, animal is neither universal nor singular. Indeed, if, out of itself, it were universal, so that animality were universal qua animality, there could be no singular animal, but each and every animal would be a universal. If, on the contrary, animal were singular qua animal, there could be no more than a single animal, namely, the very singular to which animality belongs, and no other singular could be an animal. (77)
This passage contains two subarguments. We will have more than enough on our plates if we consider just the first. The first subargument, telescoped in the second sentence above, can be put as follows:
1. If animal has the property of being universal, then every animal would be a universal. But:
2. It is not the case that every animal is a universal. Therefore:
3. It is not the case that animal has the property of being universal.
This argument is valid in point of logical form, but are its premises true? Well, (2) is obviously true, but why should anyone think that (1) is true? It is surely not obvious that the properties of a nature must also be properties of the individuals of that nature.
There are two ways a nature N could have a property P. N could have P by including P within its quidditative content, or N could have P by instantiating P. There is having by inclusion and having by instantiation.
For example, 'Man is rational' on a charitable reading states that rationality is included within the content of the nature humanity. This implies that everything that falls under man falls under rational. Charitably interpreted, the sentence does not state that the nature humanity or the species man is rational. For no nature, as such, is capable of reasoning. It is the specimens of the species who are rational, not the species.
This shows that we must distinguish between inclusion and instantiation. Man includes rational; man does not instantiate rational.
Compare 'Man is rational' with 'Socrates is rational.' They are both true, but only if 'is' is taken to express different relatons in the two sentences. In the first it expresses inclusion; in the second, instantiation. The nature man does not instantiate rationality; it includes it. Socrates does not include rationality; he instantiates it.
The reason I balk at premise (1) is because it seems quite obviously to trade on a confusion of the two senses of 'is' lately distinguished. It confuses inclusion with instantiation. (1) encapuslates a non sequitur. It does not follow from a nature's being universal that everything having that nature is a universal. That every animal would be a universal would follow from humanity's being universal only if universality were included in humanity. But it is not: humanity instantiates universality. In Frege's jargon, universality is an Eigenschaft of humanity, not a Merkmal of it.
Since the first subargument fails, there is no need to examine the second. For if the first subargment fails, then the whole Avicennian-Thomist argument fails.
It is obviously true that something exists. This is not only true, but known with certainty to be true: I think, therefore I exist, therefore something exists. That is my Grand Datum, my datanic starting point. Things exist!
Now it seems perfectly clear to me that 'Something exists' cannot be translated adequately as 'Something is self-identical' employing just the resources of modern predicate logic (MPL), i.e., first-order predicate logic with identity. But it seems perfectly clear to van Inwagen that it can. See my preceding post on this topic. So one of us is wrong, and if it is me, I'd like to know exactly why. Let me add that 'Something is self-identical' is the prime candidate for such a thin translation. If there is a thin translation, this is it. Van Inwagen comes into the discussion only as a representative of the thin theory, albeit as the 'dean' of the thin theorists.
Consider the following formula in first-order predicate logic with identity that van Inwagen thinks adequately translates 'There are objects' and 'Something exists':
1. (∃x) (x = x).
It seems to me that there is nothing in this formula but syntax: there are no nonlogical expressions, no content expressions, no expressions like 'Socrates' or 'cat' or placeholders for such expressions such as 'a' and 'C.' The parentheses can be dropped, and van Inwagen writes the formula without them. This leaves us with '∃,' three bound occurrences of the variable 'x,' and the identity sign '=.'
Now here is my main question: How can the extralogical and extrasyntactical fact that something exists be a matter of pure logical syntax? How can this fact be expressed by a string of merely syntactical symbols: '∃,' 'x,' '='?
It is not a logical truth that something exists; it is a matter of extralogical fact. There's this bloody world out there and it certainly wasn't sired by the laws of logic. Logically, there might not have been anything at all. It is true, but logically contingent, that something exists. Compare (1) with the universal quantification
2. (x)(x =x).
If (1) translates 'Something exists,' then (2) translates 'Everything exists.' But (2) is a logical truth, and its negation a contradiction. Since (1) follows from (2), (1) is a logical truth as well. But (1) is not a logical truth as we have just seen. We face an aporetic triad:
a. '(x)(x =x)' is logically true. b. '(∃x) (x = x)' follows from '(x)(x = x).' c. '(∃x) (x = x)' adequately translates 'Something exists.'
Each limb is plausible, but they cannot all be true. The truth of any two linbs entails the falsehood of the remaining one. For example, the first two entail that '(∃x) (x = x)' is logically true. But then (c) is false: One sentence cannot be an adequate translation of a second if the first fails to preserve the modal status of the second. To repeat myself: 'Something exists' is logically contingent whereas the canonical translation is logically necessary.
Now which of the limbs shall we reject? It is obvious to me that the third limb must be rejected, pace van Inwagen.
Now consider 'Everything exists.' Can it be translated adequately as '(x)(x = x)'? Obviously not. The latter is a formal-logical truth. and its negation is a formal-logical contradiction. But the negation of 'Everything exists' -- 'Something does not exist' -- is not a formal logical contradiction. Therefore, 'Everything exists' is not a formal-logical truth. And because it is not, it cannot be given the canonical translation.
Finally, consider 'Nothing exists.' This is false, but logically contingent: there is no formal-logical necessity that something exist. One cannot infer the existence of anything (or at least anything concrete) from the principles of formal logic alone. The canonical translation of 'Nothing exists,' however -- (x)~(x = x)' - is not contingently false, but logically false. Therefore, 'Nothing exists' cannot be translated adequately as 'Everything is not self-identical.'
Van Inwagen and his master Quine are simply mistaken when they maintain that existence is what 'existential' quantification expresses.
Suppose we acquiesce for the space of this post in QuineSpeak.
Then 'Horses exist' says no more and no less than that 'Something is a horse.' And 'Harry exists' says no more and no less than that 'Something is Harry.' But the 'is' does not have the same sense in both translations. The first is the 'is' of predication while the second is the 'is' of identity. The difference is reflected in the standard notation. The propositional function in the first case is Hx. The propositional function in the second case is x = h. Immediate juxtaposition of predicate constant and free variable [with the predicate constant coming first] is the sign for predication. '=' is the sign for identity. Different signs for different concepts. Identity is irreducible to predication which is presumably why first-order predicate logic with identity is so-called.
Those heir to the 'Fressellian' position, such as Quine and his epigoni, dare not fudge the distinction between the two senses of 'is' lately noted. That, surely, is a cardinal tenet of their brand of analysis.
So even along Quinean lines, the strict univocity of 'exist(s)' across all its uses cannot [pace van Inwagen] be upheld. It cannot be upheld across the divide that separates general from singular existentials.
But the next morning I had a doubt about what I had written. Is there an 'is' of predication in MPL (modern predicate logic)? I argued (above) that 'exist(s)' is not univocal: it does not in MPL have the same sense in 'Fs exist' and 'a exists.' The former translates as 'Something is (predicatively) an F' while the latter translates as 'Something is (identically) a.' Kicked out the front door, the equivocity returns through the back door disguised as an equivocation on 'is' as between predication and identity.
But if the 'is' in 'Grass is green' or 'Something is green' is bundled into the predicate in the Fregean manner, then it could be argued that there is no 'is' of predication in MPL distinct from the 'is' of identity and the 'is' of existence. If so, my equivocity argument above collapses, resting as it does on the unexpungeable distinction between the 'is' or identity and the 'is' of predication.
Yesterday a note from Spencer Case shows that he is on to the same (putative) difficulty with my argument:
Hey Bill, I have a professor whose pet peeve is the claim that there is an 'is' of identity and an 'is' of predication. I don't know his arguments for thinking so, but his view is that 'is' is univocal and what differs is the content of the copula. If he's right, that would be a problem for you here. Do you know more about this position than I do?
To sort this out we need to distinguish several different questions:
Q1. Is there a predicative use of 'is' in English? Yes, e.g., 'Al is fat.' This use is distinct from the existential use and the identitative use (and others that I needn't mention). So I hope Spencer's professor is not denying the plain linguistic fact that in English there is an 'is' of predication and an 'is' of identity and that they are distinct.
Q2. Must there be a separate sign for the predicative tie in a logically perspicuous artificial language such as MPL (modern predicate logic, i.e., first-order predicate logic with identity)? No. When we symbolize 'Al is fat' by Fa, there is no separate sign for the predicative tie. But there is a sign for it, namely, the immediate juxtaposition of the predicate constant and the individual constant with the predicate constant to the left of the individual constant. So we shouldn't confuse a separate or stand-alone sign with a sign. Other non-separate signs are conceivable exploiting different fonts and different colors, etc.
Q3. Must there be some sign or other for predication in a logically adequate language such as MPL? How could there fail to be? If our logical language is adequate, then it has to be able to symbolize predications such as 'Al is fat.' And note that existentials such as 'Fat cats exist' cannot be put into MPL without a sign for predication. '(∃x)(Fx & Cx)' employs non-separate signs for predication.
Q4. Is the predicative tie reducible or eliminable? No. For Frege, there is no need for a logical copula or connector to tie object a to concept F when a falls under F. The concept is "unsaturated" (ungesaettigt). Predicates and their referents (Bedeutungen) are inherently gappy or incomplete. So the predicate 'wise' would be depicted as follows: '___ wise.' What is thereby depicted is a sentential function or open sentence. A (closed) sentence results when a name is placed in the gap. The concept to which this predicate or sentential function refers is gappy in an analogous sense. Hence there is no need for for an 'is' of predication in the logical language or for an instantiation relation. Object falls under concept without the need of a tertium quid to connect them.
I would imagine that Spencer Case's professor has some such scheme in mind. One problem is that it is none too clear what could be meant by a gappy or incomplete or unsaturated entity. That a predicate should be gappy is tolerably clear, but how could the referent of a predicate be gappy given that the referent of a predicate is a single item and not the manifold of things to which the predicate applies? The idea is not that concepts exist only when instantiated, but that their instantiation does not require the services of a nexus of predication: the concept has as it were a slot in it that accepts the object without the need of a connector to hold them together. (Think of a plug and a socket: there is no need for a third thing to connect the plug to the socket: the 'female' receptacle just accepts the 'male' plug.)
There are other problems as well.
But here is the main point. Frege cannot avoid speaking of objects falling under concepts, of a's falling under F but not under G. If the notion of the unsaturatedness of concepts is defensible, then Frege can avoid speaking of a separate predicative tie that connects objects and concepts. But he cannot get on without predication and without a sign for predication.
I conclude that my original argument is sound. There is is and must be a sign for predication in any adequate logic, but it needn't be a stand-alone sign. (Nor need its referent be a stand-alone entity.) Compare '(∃x)Hx' to '(∃x)(x = h)' as translations of 'Horses exist' and 'Harry exists,' respectively. The identity sign occurs in only one of the translations, the second. And the sign for predication occurs only in the first. There is no univocity of 'exist(s)' because there is no univocity of 'is' in the translations.
I grant that logical equivalents not containing 'exist(s)' or cognates can be supplied for all singular and general existentials. Thus, 'Socrates exists' can be translated, salva veritate, as 'Something is identical to Socrates,' or, in canonical notation, '(∃x)(x = Socrates).' Accordingly,
Socrates exists =df (∃x)(x = Socrates).
But if the definiens preserves the truth of the definiendum, then the definiendum must be true, hence must be meaningful, in which case first-level uses of 'exist(s)' must be meaningful. Pace Russell, 'Socrates exists' is nothing like 'Socrates is numerous.'
What's more, the definiendum is prior in the order of understanding to the definiens. If I didn't already understand 'Socrates exists,' then I would not be able to understand '(∃x)(x = Socrates).' You couldn't teach me the Quinean translation if I didn't already understand the sentence to be translated.
One conclusion we can draw from this is that if 'exist(s)' is univocal across general and singular existentials, then existence cannot be instantiation. For the left-hand side of the definition does not make an instantiation claim. It is simply nonsense to say of an individual that it is instantiated. And if the right-hand side makes an instantiation claim, then we need those creatures of darkness, haecceity-properties.
But we don't have to give the RHS a Fressellian reading; we can give it a Quinean-Inwagenian reading. (We could call this the 'Van' reading.) Accordingly: There exists an x such that x = Socrates. On the Van reading, in stark contrast to the Fressellian reading, 'exist(s)' can be construed as a first-level predicate, as synonymous to the predicate 'is identical to something.' Accordingly:
y exists =df(∃x)(x = y).
On the reasonable assumptions that (i) 'exist(s)' is an admissible first-level predicate and that (ii) there are no nonexistent objects, this last definition is unobjectionable. If Tom exists, then there exists an object to which he is identical. And if there exists an object to which Tom is identical, then Tom exists. No doubt!
The interesting question, however, is whether any of this affords aid and comfort to the thin theory. Well, what exactly is the thin theory? It is the theory that existence is exhaustively understandable in purely logical, indeed purely syntactical, terms. The thin theory is a deflationary theory that aims to eliminate existence as a metaphysical topic. It aims to supplant the metaphysics of existence (of whatever stripe: Thomist, Heideggerian, etc.) with the sober logic of 'exist(s).' The aim of the thin theory is to show that there is no sense in which existence is a non-logical property of individuals. The aim is to be able to consign all those tomes of metaphysical rubbish to the flames with a good conscience.
Now glance back at the definition. Every mark on the RHS is a bit of logical syntax. Ignoring the parentheses which in this instance can be dropped, we have the backwards-E, two bound occurrences of the variable 'x,' a free occurrence of the variable 'y,' and the sign for identity. There are no non-logical expressions such as 'Socrates' or 'philosopher.' On the LHS, however, we find 'exists' which is not obviously a logical expression. Indeed, I claim that it is not a logical expression like 'some' or 'all' or 'not.' It is a 'content' expression. What could be more important and contentful than a thing's existing? If it didn't exist it would be nothing and couldn't have properties or stand in relations.
Surely my sheer be-ing is my most impressive 'feature.' "To be or not to be, that is the question."
Since there is content on the LHS there has to be content on the RHS. But how did it get there, given that every expression on the RHS is just a bit of syntax? In only one way: the domain of the bound variables is a domain of existents. But now it should be clear that the definition gives us no deflationary account of existence. What it does is presuppose existence by presupposing that the domain of quantification is a domain of existents. Existence is that which existents have in common and in virtue of which they exist.
In short, I have no objection to the definition read in the 'Van' as opposed to the 'Fressellian' way. It is perfectly trivial! My point, however, is that it gives no aid and comfort to the thin theory. A decent thin theory would have to show how we can dispence with existence entirely by eliminating it in favor of purely logical concepts. But that is precisely what we cannot do given that the domain of quantification is a domain of existents. (Of course, if the domain were populated by Meinongian nonexistent objects, then the definition would be false).
Suppose we acquiesce for the space of this post in QuineSpeak.
Then 'Horses exist' says no more and no less than that 'Something is a horse.' And 'Harry exists' says no more and no less than that 'Something is Harry.' But the 'is' does not have the same sense in both translations. The first is the 'is' of predication while the second is the 'is' of identity. The difference is reflected in the standard notation. The propositional function in the first case is Hx. The propositional function in the second case is x = h. Immediate juxtaposition of predicate constant and free variable is the sign for predication. '=' is the sign for identity. Different signs for different concepts. Identity is irreducible to predication which is presumably why first-order predicate logic with identity is so-called.
Those heir to the Fressellian position, such as Quine and his epigoni, dare not fudge the distinction between the two senses of 'is' lately noted. That, surely, is a cardinal tenet of their brand of analysis.
So even along Quinean lines, the strict univocity of 'exist(s)' across all its uses cannot be upheld. It cannot be upheld across the divide that separates general from singular existentials.
This post continues my examination of Peter van Inwagen's "Being, Existence, and Ontological Commitment." The first post in this series is here. There you will find the bibliographical details.
We saw that van Inwagen gives something like the following argument for the univocity of 'exists':
1. Number-words are univocal
2*. 'Exist(s)' is a number-word
3*. 'Exist(s)' is univocal.
The second premise is pure Frege. The question arises: is van Inwagen committed to the Fregean doctrine that 'exists(s)' is a second-level predicate? He says he isn't. (484)
How should we understand a general existential such as 'Horses exist'? Frege famously maintained that 'exist(s)' is a second-level predicate: it is never a predicate of objects, but always only a predicate of concepts. What the sample sentence says is that the concept horse has instances. Despite appearances, the sentence is not about horses, but about a non-horse, the concept horse. The concept horse is not a horse! (Frege also famously and perplexingly maintains that the concept horse is not a concept, but let's leave that for another occasion.) And what our general existential says about the concept horse is not that it exists (as we ordinarily understand 'exists') but that it is instantiated. Van Inwagen, though endorsing Frege's key notion that (as PvI puts it) "existence is closely allied to number" (482) does not follow Frege is in holding that 'exists' is a second-level predicate.
Van Inwagen thus appears to be staking out a middle position between the following extremes:
A. 'Horses exist' predicates existence of individual horses.
B. 'Horses exist' predicates instantiation of the concept horse.
Van Inwagen's view is that 'Horses exist' says that horses, taken plurally, number more than zero. So 'Horses exist,' contra Frege, is about horses, but not about individually specified horses such as Secretariat and Mr Ed. 'Horses exist' is not about the concept horse or any other abstract object such as a property or a set: it is about concrete horses, but taken plurally.
I am trying to understand this, but I find it obscure. One thing I do understand is that there are predicates that hold plurally (collectively) but not distributively, but are not, for all that, second-level. Van Inwagen gives the example:
1. Horses have an interesting evolutionary history.
Obviously, the predicate in (1) is not true of each individual horse. No individual horse evolves in the sense pertinent to evolutionary theory. But the predicate is also not true of the concept horse or the set of horses or the property of being a horse or any other abstract object. No concept, set, or property evolves in any sense. So what is the logical subject of (1)? Horses in the plural, or horses taken collectively. Or suppose the cops have a building surrounded. No individual cop has the building surrounded, and of course no abstract object has the building surrounded. Cops have the building surrounded. Suppose Manny is one of the cops. Then the following argument would commit the fallacy of division: (a) The cops have the building surrounded; (b) Manny is one of the cops; ergo (c) Manny has the building surrounded. What is true of cops in the plural is not true of any cop in the singular.
If I have understood PvI, he is saying that 'exists' functions like the predicate in (1), and like the predicate in 'The cops have the building surrounded.' But this strikes me as problematic. Consider these two arguments:
Horses have evolved Secretariat is a horse ergo Secretariat has evolved.
Horses exist Secretariat is a horse ergo Secretariat exists.
The first argument is invalid, committing as it does the fallacy of division. The second argument is perfectly in order.
So it seems, contra Van Iwagen, that 'Horses exist' is importantly disanalogous to 'Horses have evolved' and 'The cops have the building surrounded.' 'Exists' is predicable of specified individuals, individuals in the singular. 'Evolved' is not predicable of specified individuals, individuals in the singular, but only of individuals in the plural.
I take van Inwagen to be saying that the logical subject of 'Horses exist' is not the concept horse, but horses, horses in the plural, and what it says of them is that they number more than zero. What I am having trouble understanding is how 'more than zero' can attach to a plurality as a plurality, as opposed to a one-over-many such as a concept (which has an extension) or a set (which has a membership).
A plurality as a plurality is not one item, but a mere manifold of items: there is simply nothing there to serve as logical subject of the predicate 'more than zero.'
"But look, Bill, it is the horses that are more than zero; so there is a logical subject of the predicate."
Response: You can't say what you want to say grammatically. If there IS a logical subject of the predicate, then it is not a mere manyness. But if there ARE many subjects of predication, then 'more than zero' applies to each horse which is not what you want to say. There must be something that makes the particulars you are calling horses horses, and that would have to be something like the concept horse; otherwise you have an unintelligible plurality of bare particulars. But then when you say that the horses are more than zero you are saying that the concept horse has more than one instance, and number-words become second-level predicates.
My suspicion is that van Inwagen's middle path is unviable and that his position collapses into the full-throated Fregean position according to which (a) "existence is allied to number" and (b) number-words are second-level predicates.
In "Being, Existence, and Ontological Commitment" (in Metametaphysics: New Essays on the Foundations of Ontology, eds. Chalmers et al., Oxford 2009, pp. 472-506), Peter van Inwagen argues that 'exists' is univocal: it does not have "different meanings when applied to objects in different categories." (482) This post will examine one of his arguments, an argument found on p. 482. All quotations are from this page.
Van Inwagen begins by noting that number words such as 'six' or 'forty-three' do not "mean different things when they are used to count objects of different sorts." Surely he is correct: "If you have written thirteen epics and I own thirteen cats, the number of your epics is the number of my cats." So the first premise of the argument is the indisputable:
1. Number-words are univocal in sense: they mean the same regardless of the sorts of object they are used to count.
Van Inwagen takes his second premise straight from Frege:
2. "But existence is closely allied to number."
How so? Well, to say that unicorns do not exist is equivalent to saying that the number of unicorns is zero, and to say that horses exist is equivalent to saying that the number of horses is one or more. Surely that is true for both affirmative and negative general existentials. Whether it is true for singular existentials is a further question.
Van Inwagen proceeds: "The univocacy [univocity] of number and the the intimate connection between number and existence should convince us that existence is univocal." The conclusion of the argument, then, is:
3. Existence is univocal.
The first thing to notice about this argument is that it is not even valid. Trouble is caused by the fudge-phrase 'closely allied to' and van Inwagen's shift from 'exists' to existence. But repairs are easily made, and charity demands that we make them. Here is a valid argument that van Inwagen could have given:
1. Number-words are univocal
2*. 'Exist(s)' is a number-word
3*. 'Exist(s)' is univocal.
The latter argument is plainly valid in point of logical form: the conclusion follows from the premises. It is the argument van Inwagen should have given. Unfortunately the argument is unsound. Although (1) is indisputably true, (2*) is false.
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.
This question makes sense: 'How many cats are there in BV's house?' But this question makes no sense: 'How many Max are there in BV's house?' Why not? Well, 'Max' is a proper name (Eigenname in Frege's terminology) not a concept-word (Begriffswort in Frege's terminology). Of course, I could sensibly ask how many Maxes there are hereabouts, but then 'Max' is not a proper name, but a stand-in for 'person/cat named "Max" .' The latter phrase is obviously not a proper name.
Van Inwagen's argument strikes me as very bad, and I am puzzled why he is seduced by it. (Actually, I am not puzzled: van Inwagen is in lock-step with Quine; perhaps the great prestige of the latter has the former mesmerized.) Here is my counterargument:
4. 'Exists' sometimes functions as a first-level predicate, a predicate of specific (named) individuals.
5. Number-words never function as predicates of specific (named) individuals
6. 'Exists' is not a number-word.
7. The (obvious) univocity of number-words is not a good reason to think that 'exists' is univocal.
Of course, there is much more to say -- in subsequent posts. For example if you deny (4), why is that denial more reasonable than the denial of (2*)?
It is a commonplace that the grammatical form of a sentence is no sure guide to its logical form or to the ontological structure of the chunk of reality the sentence is about, if anything. For example, 'Kato Kaelin is home' and 'Nobody is home' are grammatically similar. They both seem to have the structure: singular subject/copula/predicate. But logically they are distinct: the first is singular, being about Kato Kaelin, America's most famous houseguest, while the second is existentially general. The second (standardly interpreted) is not about some dude named 'Nobody.' What is says is that it is not the case that there exists a person x such that x is at home. It is not about any particular person.
So grammatical form and logical form need not coincide.
It interests me (and may even interest you) that one can make both affirmative and negative assertions using sentences in the interrogative mood. What is grammatically interrogative need not be logically interrogative.
Suppose someone asks whether God exists. A convinced theist can answer in the affirmative by uttering a grammatically interrogative sentence, for example, 'Is the Pope Catholic?' An adamant atheist can answer in the negative by a similar means: 'Is there an angry unicorn on the dark side of the moon?' (Example from Edward 'Cactus Ed' Abbey.)
Thus in this situation the theist expresses the indicative proposition that God exists by uttering the interrogative form of words, 'Is the Pope Catholic?' while the atheist expresses the indicative proposition that God does not exist by uttering the interrogative form of words, 'Is there an angry unicorn on the dark side of the moon?'
How labile the lapping of language upon the littoral of logic!
Three hours before showtime, Brian Wilson says: “There is no Rhonda.” Sitting backstage at Merriweather Post Pavilion, gathering strength for the evening’s 48-song, 150-minute concert, Wilson was not asked about her, he just volunteered this fact. The other members of the Beach Boys seem mildly surprised to learn that the 1965 song “Help Me, Rhonda” was about no one in particular.
The philosopher of language in London Ed should find the above intriguing. The song was about no one in particular in that Brian Wilson had no actual person in mind as Rhonda. But surely the song was about three people, one named 'Rhonda,' another girl referred to only by an antecedent-less 'she,' and the singer. "Since she put me down, I was out doin' in my head." There is a sense in which these are three particular, numerically distinct, persons.
If you deny that, aren't you saying that the song is not about anybody? And wouldn't that be wrong?
Of course, the persons in question are incomplete objects. They violate the property version of the Law of Excluded Middle. We know some of Rhonda's properties but not all of them. We know that she looked "so fine" to the singer. And we know that she caught the singer's eye. But we don't know her height, the color of her eyes or her blood pressure. With respect to those properties she is indeterminate. Same with the other girl. We know she was going to be the singer's wife, and he was going to be her man, but not much else.
Now nothing incomplete can exist. So the three persons are three particular nonexistent objects, and the song is about three persons in particular.
I wrote this just to get London Ed's goat. The record will show that I myself eschew Meinongianism.
What follows is a guest post by Peter Lupu with some additions and corrections by BV. 'CCB' abbreviates 'concrete contingent being.' The last post in this series is here. Thanks again to Vlastimil Vohamka for pointing us to Maitzen's article, which has proven to be stimulating indeed.
1. As a general rule, dummy sortals such as ‘thing’, ‘object’, ‘CCB’, etc., are not referential terms, unless there is an explicit or implicit background presupposition as to which sortal term is intended as a replacement. This presupposition, if satisfied, fixes the referent of the dummy sortal. In the absence of the satisfaction of such a presupposition, sentences in which they are used (not mentioned) have no truth-conditions and questions in which they are used (not mentioned) have no answer-conditions.
2. Examples such as ‘Cats are CCBs’ are no exception. Either this sentence has no truth-conditions because the term ‘CCB’ is merely a place holder for an unspecified sortal or it should be understood along the lines of: ‘Cats are animals’, etc., where ‘animal’ is (one possible) substitution term for the dummy sortal ‘CCB.'
BV adds: Right here I think a very simple objection can be brought against the semantic thesis. We know that cats exist, we know that they are concrete, and we know that they are contingent. So we know that 'Cats are concrete contingent beings' is true. Now whatever is true is meaningful (though not vice versa). Therefore, 'Cats are concrete contingent beings' is meaningful. Now if a sentence is meaningful, then its constituent terms are meaningful. Hence 'CCB' is meaningful despite its being a dummy sortal. I would also underscore a point I have made several times before. The immediate inference from the admittedly true (a) to (b) below is invalid:
a. The question 'How many CCBs are there?' is unanswerable, hence senseless
b. The question 'Why are there any CCBs?' is unanswerable, hence senseless.
3. The semantic thesis is the driving force behind Steve M’s view. It is the fallback position in all of his responses to challenges by Bill, Steven, and others. So far as I can tell, Steve M. did not defend the general form of the semantic thesis in his original paper. It is, therefore, surprising that it has been ignored by almost everyone in these discussions and that neither Bill nor Steven challenged the semantic thesis. I have written an extensive comment on this thesis and challenged it on several grounds.
B. Explanatory Thesis
1. As a general rule, Why-Questions are answered by giving an explanation. ‘Why are there any CCBs?’ is a [explanation-seeking] Why-Question. [It is worth noting that the grammatically interrogative form of words 'Why is there anything at all?' could be used simply to express wonder that anything at all should exist, and not as a demand for an explanation.] Therefore, it invites an explanation. What sort of explanation? Steve M. holds two theses about this last question:
(MI) The Adequacy Thesis: empirical explanations typical in science offer (at least in principle) adequate explanations for the Why-CCBs question, provided the Why-CCB questions are meaningful at all (and their meaningfulness is a function of satisfying the semantic thesis);
(MII) The Completeness Thesis: Once an empirical explanation is given to Why CCBs?, there is nothing left to explain. And in any case there are no suitable forms of explanation beyond empirical explanations that could be even relevant to explain Why-CCBs?
2. Bill and Steven certainly deny (MII). They may also have some reservations about MI. What is the basis on which Bill and Steven challenge MII? They maintain that even if we assume that an adequate empirical explanation is offered (i.e., MI is satisfied) to each and every CCB, there is something else left over to explain. What is that “something else” that is left over that needs explaining (Steve M. asks)?
3. It is at this juncture that the discussion either reverts back to the semantic thesis or it needs to be advanced into a new metaphysical realm.
C. Metaphysical Thesis
Dummy sortals do not pick out any properties or universals (monadic or relational) except via the mediation of genuine sortals. i.e., there are no properties over and beyond those picked out by genuine sortals.
1. Steven attempted to answer the challenge posed by the question at the end of B2 in one of his posts. His answer is this: what is left over after all empirical explanations favored by Steve M. are assumed to have been given is a very general property, feature, or aspect that all CCBs, and only CCBs, have in common. So why shouldn't ‘Why-CCBs’ questions be understood as inquiring into an explanation of this general feature that all and only CCBs share? Call this alleged general feature ‘X’.
2. The dispute has turned to whether X has any content, i.e., Steve M. challenged the contention that there is any phenomenon described by X that was not already accounted for by his favorite empirical explanations. Bill and Steven tried to articulate the content of X without (apparently) noticing that every such effort was rebutted by Steve M. either by appealing to the semantic thesis or to the explanatory thesis or both.
3. So what could X be? I suggest the following: X is the (second-order) property such that the property of *is a contingent being* is instantiated (or something along these lines). [I would put it this way: X is the being-instantiated of the property of being a contingent being.]
4. Since the universal/property *is a contingent being* need not be instantiated, the fact that it is in fact instantiated in the actual world (i.e., that X holds) needs explaining (So claim Bill and Steven). And whatever is the explanation (including a “brute-fact” explanation) for this fact, it cannot take the form of an empirical explanation.
5. The Metaphysical Thesis I am attributing to Steve M. of course rules out that there is a property such as X. Why? Two reasons: first, the property *is a contingent being* is not a sortal property; second, the predicate ‘is a contingent being’ (or any of its variants) contains a dummy sortal and therefore it does not pick out a property (nor does it have an extension) in the absence of a specific background presupposition of a specific sortal substituend.
Unless these three theses are clearly separated, the discussion will be going in circles. As one can see, the driving force behind the explanatory and metaphysical theses is ultimately the semantic thesis. No one challenged this thesis directly (except me in a comment that was ignored by everyone with the exception of Bill).
0. Am I identical to my (living) body, or to the objectively specifiable person who rejoices under the name 'BV'? Earlier I resoundingly denied this identity, in (rare) agreement with London Ed, but admitted that argument is needed. This post begins the argument. We start with the problem of first-person identity sentences.
1. 'I am I' and 'BV is BV' are logical truths. They have the logical form a = a. They are not particularly puzzling. But 'I am BV' presents a puzzle, one reminiscent of Frege's puzzle concerning informative identity statements. 'I am BV' is not true as a matter of logic, any more than it is true as a matter of logic that the morning star is the evening star. And yet it is presumably true that I am BV where 'am' expresses strict numerical identity. It is not as if 'I' and 'BV' refer to two different entities. Or at least this is not a view we ought to begin by assuming. The proper procedure is to see if we can make sense of 'I am BV' construed as an identity statement. Dualism comes later if it comes at all.
2. Here is a theory. When I say 'I am BV' I am referring to one and the same thing in two different ways, just as, when I say 'The morning star is the evening star' I am referring to one and the same thing (the planet Venus) in two different ways. Expressions have sense and they have reference. Difference of sense is compatible with sameness of reference. The difference in sense of 'morning star' and 'evening star' explains why the identity statement composed of them is informative; the sameness of reference explains the identity statement's truth.
In Frege's famous example, the common referent is the planet Venus. What is the common referent of 'I' and 'BV'? Presumably the common referent is the publicly identifiable person BV. But when BV designates himself by means of the thought or utterance of 'I, he designates BV under the aspect, or via the sense, expressed by 'I,' a semantically irreducible sense that cannot be captured by any expression not containing 'I.'
Here then we seem to have a solution to our problem. In general, one can refer to the same thing in different ways, via different modes of presentation (Darstellungsweisen, in Frege's German). So apply that to the special case of the self. What I refer to when I say 'I' is the same entity that I refer to when I say 'BV' and the same entity that Peter refers to when he says 'BV.' It is just that I refer to the same thing in different ways, a first-person way and third-person way. There is no need to suppose that 'I and 'BV' have numerically distinct referents. There is no need to deny the numerical identity of me and BV. Unfortunately, this Fregean solution is a pseudo-solution. I have two arguments. I'll give one today.
3. Consider the sentence 'I am this body here' uttered by the speaker while pointing to his body. If, in this sentence, 'I' refers to this body here (the body of the speaker), albeit via a Fregean sense distinct from that of 'this body here,' then the sense of 'I,' whatever it might be, must be the sense of a physical thing inasmuch as it must be the mode of presentation of a physical thing. Note that the 'of' in the italicized phrases is a genitivus objectivus. Somehow this 'I'-sense must determine a reference to a physical thing, this body here. But that it is the sense of a physical thing is no part of the sense of 'I.' We understand fully the sense of this term without understanding it to be the sense of a physical thing, a sense that presents or mediates reference to a physical thing. Indeed, considerations adduced by Anscombe and Castaneda show that the 'I'-sense cannot be the sense of a physical thing. For if the sense of 'I' cannot be captured by 'this body here,' then a fortiori it cannot be captured by any other expression designating a physical thing.
The analogy with the morning star/evening star case breaks down. One cannot use 'morning star' and 'evening star' with understanding unless one understands that they refer to physical things, if they refer at all. It is understood a priori that these terms designate physical things if they designate at all; the only question is whether they designate the same physical thing. But one can use the first-person singular pronoun with understanding without knowing whether or not it refers to a physical thing.
In other words, there is nothing in the sense of 'I' to exclude the possibility that it refer to a nonphysical thing, a res cogitans, for example. Descartes' use of 'ego' to refer to a thinking substance did not violate the semantic rules for the use of this term. What's more, if 'I' is a referring term and refers via a Fregean sense, then that sense cannot be the sense of a physical thing.
So that's my first argument against the Fregean approach to the problem of first-person identity sentences. The argument rests on the assumption that 'I' is a referring term. That assumption has been denied by Wittgenstein, and more rigorously, by Anscombe. That denial deserves a separate post. And in that post we ought to rehearse the reasons why 'I' cannot be replaced salva significatione by any such word or phase as 'the person who is now speaking.'
I said something yesterday that isn't right, as I realized this morning. I said, ". . . a necessary condition of a term's being a sortal is that it be such that, if it applies to a thing, then it does not apply to the proper parts of the thing."
What I said works for some examples. 'Red thing,' 'physical object,' and 'entity' are not sortals. A red thing can easily have proper parts that are red things. The proper parts of a physical object are physical objects. The proper parts of entities are themselves entities. And so on.
But isn't 'rope' a sortal? If I have a ten foot rope and cut into two equal pieces, then I have two ropes. The same goes for 'rubber hose,' 'cloud,' 'amoeba.' (These latter examples from Nicholas Griffin, Relative Identity, Oxford, 1977, p. 38.) So it cannot be true that, if 'T' is a sortal, then you cannot divide T into two parts and get two Ts.
This is a response to a post of the same name by London Ed. I am much in his debt for his copious and relentless commentary. My responses are in blue.
After reading some of Maverick’s other posts on the subject, and reading some material he sent me, it is clear I have misrepresented his argument. Although I am still some way from understanding it, I think it is this.
Suppose there is only one American philosopher, and suppose that it is Vallicella. Then the sentence ‘an American philosopher exists’ is true because Vallicella (qua American philosopher) exists. Now we can translate ‘an American philosopher exists’ into ‘some philosopher is American’, which reduces the verb ‘exists’ to the copula ‘is’. But we can’t translate ‘Vallicella exists’ in the same way. Thus general existential statements presuppose the truth of singular existential statements (or a disjunction or conjunction of singular existential statements). But we cannot analyse away ‘exists’ from singular existential statements. Therefore there is circularity: the same word appears on the right and left hand side of the definition. An American philosopher exists if and only if Vallicella exists.
That is not quite what I say, but it is a fair approximation.
But there is an obvious route out of this problem. What actually makes ‘some philosopher is American’ true is ‘Vallicella is an American philosopher’, which does not use the word ‘exist’. Vallicella may object that ‘Vallicella exists’ has to be true for that to work. Certainly, but we can reply in two ways. We could suppose that empty proper names are meaningless, and that ‘Vallicella’ is only meaningful because it names something. I.e. if it names something, it must name an existing something. ‘Vallicella exists’ is therefore true in virtue of the meaning of the proper name ‘Vallicella’. Or we could allow that empty proper names are meaningful, and that they have a sense but not a reference. Then we can appeal to the idea of instantiation, as with general concepts. ‘Vallicella exists’ means that the sense of ‘Vallicella’ has a referent or instance. ‘An American philosopher exists’ means that the sense of ‘American philosopher’ has an instance.
That is, either common names and proper names fall into different logical categories, in which case we don’t need to use the word ‘exists’ in singular sentences at all. Or they fall into the same category, in which case we can analyse singular existential statements exactly as we analyse general existential statements. In neither case is the definition of ‘exists’ circular.
The second alternative is available only if there are haecceity properties to serve as the Fregean senses of proper names. Now I have argued many times in these pages and in print against such properties. It follows that we cannot analyze 'Vallicella exists' in the same as as 'American philosophers exist.' This leaves the first alternative, according to which the meaning of 'Vallicella' is its referent, an existing individual. Ed claims that on this alternative "‘Vallicella exists’ is therefore true in virtue of the meaning of the proper name ‘Vallicella’."
I would say that Ed has it precisely backwards. What he should say is that 'Vallicella' has meaning in virtue of the truth of 'Vallicella exists.' What Ed says illustrates the linguistic idealism that I have more than once criticized him for. V.'s existence does not depend on his name or on its meaning. The point is clearer in terms of a non-human example. So consider Stromboli, the island volcano. Presumably Stromboli existed long before the emergence of language. So what we should say is that 'Strromboli' has meaning in virtue of the fact that Stromboli extralinguistically and extramentally exists, and not vice versa.
Ed and I agree that 'Island volcanos exist' is logically equivalent to 'Some volcano is an island.' This equivalence, however, rests on the assumption that the domain of quantification is a domain of existing individuals. (If the domain were populated by Meinongian nonexistent objects, then the equivalence would fail.) The attempted reduction of existence to someness is therefore circular. For when we think it through we come to realize that the general existence expressed by sentences like 'Some volcano is an island' presupposes the singular existence of the individuals in the domain of quantification. This singular existence, obviously enough, precisely because it is singular, cannot be understood in terms of the logical quantity, someness. So we move in a circle: from existence to someness and then back to existence.
The same argument can be couched in terms of instantiation. 'Island volcanos exist' is logically equivalent to the second-level predication 'The concept island volcano is instantiated.' But if a first-level concept is instantiated, it is instaniated by at least one individual. Obviously, this individual must exist. (If it were a nonexistent individual, the link between existence and instantiation would be broken.) So again we move in an explanatory circle,from existence to instantiation and back to existence again. It follows that existence cannot be reduced to instantiation.
Pace Quine, existence is NOT what 'existential' (i.e., particular) quantification expresses. What the particular quantifier expresses is instantiation, and instantiation is not existence.
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.
Again, show what? 'There are objects' is nonsense. One cannot say that there are objects. This is shown by the use of variables. But what is shown if not that there are objects? There, I've said it!
Ray Monk reports on a discussion between Wittgenstein and Russell. L. W. balked at Russell's 'There are at least three things in the world.' So Russell took a sheet of white paper and made three ink spots on it. 'There are three ink spots on this sheet.' L. W. refused to budge. He granted 'There are three ink spots on the sheet' but balked at the inference to 'There are at least three things in the world.'
W's perspective is broadly Kantian. The transcendental conditions of possible experience are not themselves objects of possible experience. They cannot be on pain of infinite regress. But he goes Kant one better: it is not just that the transcendental conditions cannot be experienced or known; they cannot be sensibly talked about. Among them is the world as the ultimate context of all experiencing and naming and predicating and counting. As transcendental, the world cannot be sensibly talked about as if it were just another thing in the world like the piece of paper with its three spots. And so, given that what cannot be said clearly cannot be said at all but must be passed over in silence, one cannot say that the world is such that it has at least three things it it. So W. balked and went silent when R. tried to get him to negotiate the above inference.
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.
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)
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."
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?
London Ed of Beyond Necessitydoes a good job patiently explaining the 'morning star' - 'evening star' example to one of his uncomprehending readers. But I don't think Ed gets it exactly right. I quibble with the following:
Summarising: (1) The sentence “the morning star is the evening star” has informational content. (2) The sentence “the morning star is the morning star” does not have informational content. (3) Therefore, the term “the morning star” does not have the same informational content as “the evening star”.
One quibble is this. Granted, the two sentences differ in cognitive value, Erkenntniswert. (See "On Sense and Reference" first paragraph.) The one sentence expresses a truth of logic, and thus a truth knowable a priori. The other sentence expresses a factual truth of astronomy, one knowable only a posteriori. But note that Frege says that they differ in cognitive value, not that the one has it while the other doesn't. Ed says that the one has it while the other doesn't -- assuming Ed is using 'informational content' to translate Erkenntniswert. There is some annoying slippage here.
More importantly, I don't see how cognitive value/informational content can be had by such subsentential items as 'morning star' and 'evening star.' Thus I question the validity of the inference from (1) & (2) to (3). Neither term gives us any information. So it cannot be that they differ in the information they give. Nor can they be contrasted in point of giving or not giving information. Information is conveyable only by sentences or propositions.
I say this: neither of the names Morgenstern (Phosphorus) or Abendstern (Hesperus) have cognitive value or informational content. (The same holds, I think, if they are not proper names but definite descriptions.) Only indicative sentences (Saetze) and the propositions (Gedanken) they express have such value or content. As I see it, for Frege, names have sense (Sinn) and reference (Bedeutung), and they may conjure up subjective ideas (Vorstellungen) in the minds of their users. But no name has cognitive value. Sentences and propositions, however, have sense, reference, and cognitive value. Interestingly, concept-words (Begriffswoerter) or predicates also have sense and reference, but no cognitive value.
I also think Ed misrepresents the Compositionality Principle. Frege is committed to compositionality of sense (Sinn), not compositionality of informational content/cognitive value. So adding the C. P. to his premise set will not validate the above inference.
Bill Clinton may have brought the matter to national attention, but philosophers have long appreciated that much can ride on what the meaning of 'is' is.
Edward of London has a very good post in which he raises the question whether the standard analytic distinction between the 'is' of identity and the 'is' of predication is but fallout from an antecedent decision to adhere to an absolute distinction between names and predicates. If the distinction is absolute, as Frege and his epigoni maintain, then names cannot occur in predicate position, and a distinction between the two uses of 'is' is the consequence. But what if no such absolute distinction is made? Could one then dispense with the standard analytic distinction? Or are there reasons independent of Frege's function-argument analysis of propositions for upholding the distinction between the two uses of 'is'?
To illustrate the putative distinction, consider
1. George Orwell is Eric Blair
2. George Orwell is famous.
Both sentences feature a token of 'is.' Now ask yourself: is 'is' functioning in the same way in both sentences? The standard analytic line is that 'is' functions differently in the two sentences. In (1) it expresses identity; in (2) it expresses predication. Identity, among other features, is symmetrical; predication is not. That suffices to distinguish the two uses of 'is.' 'Famous' is predicable of Orwell, but Orwell is not predicable of 'famous.' But if Blair is Orwell, then Orwell is Blair.
Now it is clear, I think, that if one begins with the absolute name-predicate distinction, then the other distinction is also required. For if 'Eric Blair' in (1) cannot be construed as a predicate, then surely the 'is' in (1) does not express predication. The question I am raising, however, is whether the distinction between the two uses of 'is' arises ONLY IF one distinguishes absolutely and categorially between names and predicates.
Fred Sommers seems to think so. Referencing the example 'The morning star is Venus,' Sommers writes, "Clearly it is only after one has adopted the syntax that prohibits the predication of proper names that one is forced to read 'a is b' dyadically and to see in it a sign of identity." (The Logic of Natural Language, Oxford 1982, p. 121, emphasis added) The contemporary reader will of course wonder how else 'a is b' could be read if it is not read as expressing a dyadic relation between a and b. How the devil could the 'is' in 'a is b' be read as a copula?
This is what throws me about the scholastic stuff peddled by Ed and others. In 'Orwell is famous' they seem to be wanting to say that 'Orwell' and 'famous' refer to the same thing. But what could that mean?
First of all, 'Orwell' and 'famous' do not have the same extension: there are many famous people, but only one Orwell. But even if Orwell were the only famous person, Orwell would not be identical to the only famous person. Necessarily, Orwell is Orwell; but it is not the case that, necessarily, Orwell is the only famous person, even if it is true that Orwell is the only famous person, which he isn't.
If you tell me that only 'Orwell' has a referent, but not 'famous,' then I will reply that that is nominalism for the crazy house. Do you really want to say or imply that Orwell is famous because in English we apply the predicate 'famous' to him? That's ass-backwards or bass-ackwards, one. We correctly apply 'famous' to him because he is, in reality, famous. (That his fame is a social fact doesn't make it language-dependent.) Do you really want to say or imply that, were we speaking German, Orwell would not be famous but beruehmt? 'Famous' is a word of English while beruehmt is its German equivalent. The property, however, belongs to neither language. If you say there are no properties, only predicates, then that smacks of the loony bin.
Suppose 'Orwell' refers to the concrete individual Orwell, and 'famous' refers to the property, being-famous. Then you get for your trouble a different set of difficulties. I don't deny them! But these difficulties do not show that the scholastic view is in the clear.
This pattern repeats itself throughout philosophy. I believe I have shown that materialism about the mind faces insuperable objections, and that only those in the grip of naturalist ideology could fail to feel their force. But it won't do any good to say that substance dualism also faces insuperable objections. For it could be that both are false/incoherent. In fact, it could be that every theory proposed (and proposable by us) in solution of every philosophical problem is false/incoherent.
Earlier, I presented the following, which looks to be an antilogism. An antilogism, by definition, is an inconsistent triad. This post considers whether the triad really is logically inconsistent, and so really is an antilogism.
1. Temporally Unrestricted Excluded Middle: The principle that every declarative sentence is either true, or if not true, then false applies unrestrictedly to all declarative sentences, whatever their tense. 2. Presentism: Only what exists at present exists. 3. Temporally Unrestricted Truth-Maker Principle: Every contingent truth has a truth-maker.
Edward objects: "First, I don't see why the three statements are logically inconsistent. Why can't the truthmaker for a future tense statement exist now, in the present?"
Objection sustained. The triad as it stands is not logically inconsistent.
'Miss Creant will die by lethal injection in five minutes.' Let this be our example. It is a future-tensed contingent declarative. By (1) it is either true or, if not true, then false. By (3), our sample sentence has a truth-maker, an existing truth-maker obviously, if it is true. By (2), the truth-maker exists only at present. Edward is right: there is no inconsistency unless we add something like:
4. If a sentence predicts a contingent event which lies wholly in the future, and the sentence is true, then the truth-maker of the sentence, if it has one, cannot exist at any time prior to the time of the event.
(4) is extremely plausible. Suppose it is true now that Miss Creant will die in five minutes. The only item that could make this true is the event of her dying. But this event does not now exist and cannot exist at any time prior to her dying.
So our antilogism, under Edwardian pummeling, transmogrifies into an aporetic tetrad which, he will agree, is logically inconsistent.
The solution, for Edward, is obvious: Deny the Temporally Unrestricted Truth-Maker Principle as stated in (3). Of course, that is a solution. But can Edward show that it must be preferred to the other three solutions? After all, one could deny Presentism, and many distinguished philosophers do. I would hazard the observation that the majority of the heavy-hitters in the 20th century Anglosphere were B-theorists, and thus deniers of Presentism. Or one could deny Unrestricted LEM, or even (4).
Although I said that (4) is extremely plausible, one could conceivably deny it by maintaining that the truth-makers of future-tensed sentences are tendencies in the present. For example, I say to wifey, "Watch it! The pot is going to boil over!" Assuming that that's a true prediction, one might claim that it is the present tendencies of the agitated pasta-rich water that is the truth-maker.
Please note also that I too could solve the tetrad by denying Unrestricted T-maker. Not by rejecting T-makers tout court in the Edwardian manner, but by restricting T-makers to contingent past- and present-tensed declaratives. I hope Edward appreciates that the above problem does not give aid and comfort to his wholesale rejection of T-makers.
One can always solve an aporetic polyad by denying one of its limbs. Sure. But then you face other daunting tasks. One is to show in a compelling way that your preferred solution should be preferred by all competent practitioners. You have to show that your solution is THE solution and not merely a solution relative to your background assumptions and cognitive values. A school-immanent solution is no final and absolute solution. Another task is to show that your solution can be embedded in a theory that does not itself give rise to insoluble problems.
I made the point that the vocabularies of phenomenology and neuroscience are radically disparate, such that nonsense arises when one says things like, 'This burnt garlic smell is identical to a brain state of mine.' To which a Viet Nam veteran, altering the example, replied by e-mail:
. . . when a neuro-scientist says your smelling this odor as napalm is nothing but a complex neural event activating several regions of the brain..., he isn't claiming you can replace your talk about smells with talk about neural signals from the olfactory bulb. Different ways of talking have evolved for different purposes. But he is saying that beneath these different ways of talking & thinking there is just one underlying reality, namely, neural events in our brain.
The idea, then, that is that are are different ways of referring to the same underlying reality. And so if we deploy a simple distinction between sense and reference we can uphold the materialist/physicalist reduction of qualia to brain states. Well, I have my doubts . . . .
I agree with Thomas Nagel, John Searle, and others that conscious experiences are irreducible to physical states. I have endorsed the idea that felt pain, phenomenal pain, pain as experienced or lived through (er-lebt), the pain that hurts, has a subjective mode of existence, a "first-person ontology" in Searle's phrase. If this is right, then phenomenally conscious states cannot be reduced to physical states with their objective mode of existence and third-person ontology. As a consequence, an exclusively third-person approach to mind is bound to leave something out. But there is an objection to irreducibility that needs to be considered, an objection that exploits Frege's distinction between sense and reference.
The basic idea is that linguistic and epistemic access to one and the same item can be had in different ways, and that duality of linguistic and/or epistemic access need not be taken to argue ontological duality in that to which one gains access. Reference to one and the same item can be routed through different senses or modes of presentation (Frege's Darstellungsweisen). Different terms, with different senses, can be used to target one and the same referent. 'Morning Star' and 'Evening Star,' though differing in sense, can be used to refer to the same celestial body, the planet Venus.
Why not say something similar about the physical state I am in when I feel pain? Why not say that there are two ways of accessing the same physical state? The one mode of access is via neuroscience, the other is 'from the inside' via the pain's qualitative feel to the one who endures it. If so, there are not two states or events one physical and the other mental differing in mode of existence; there is exactly one state or event, and it is physical. Dualism is avoided. The upshot is that, contra Nagel, the third-person physicalistic approach to the mind does not leave anything out. One may go on to tax Nagel, Searle, and Co. with illicitly inferring a difference in mode of existence from a difference in mode of linguistic/epistemic access. Something like this objection is made by Christopher Peacocke in his review of Nagel's The View from Nowhere (Philosophical Review, January 1989.)
It's a nice try, a very nice try. And it is exactly what one would expect from someone who takes an objectifying third-person view. What's more, it would be in keeping with Occam's Razor if mind could be seamlessly integrated into nature. Unfortunately, the pain I am in is not a mode of presentation, or means of epistemic access, to the underlying brain state. Thus the Fregean analogy collapses. The sense of 'morning star' mediates my reference to Venus; but my pain quale, even if it is caused by the brain state, does not mediate my reference to it.
Let me see if I can make this clear. The suggestion is that the same physical reality appears, or can appear, in two different ways, a third-person way and a first-person way, and that this first-person way of access is no evidence of a first-person way of being. One problem is the one I just alluded to: there is no clear sense in which a pain quale is an appearance of a brain state. The former may be caused by the latter. But that is not to say that the pain quale is of the brain state. The felt pain does not present the brain state to me. It does not present anything (distinct from itself) to me. After all, the felt pain is a non-intentional state. No doubt it has a certain content, but not an intentional or representational content. One can describe it without describing what it is of, for the simple reason that there is nothing it is of. An intentional state, however, cannot be described without describing what it is of.
The Fregean sense/reference analogy therefore breaks down. The basic idea was that one and same reality can appear in different ways, and that the numerical difference of these ways is consistent with a unitary mode of existence of the reality. A felt pain, however, is not an appearance of a reality, but an appearance that is a reality. The appearing of a felt pain is its being, and its being is its appearing. And because this is so, the felt pain is a distinct reality from the brain state. Not only is it a distinct reality, it is a distinct reality with a distinct, irreducibly subjective, mode of existence.
Nagelus vindicatus est. There is something essentially incomplete about a third-person approach to reality. It leaves something out, and what it leaves out is precisely that which makes life worth living. For as Wilfrid Sellars once said to Daniel Dennett over a fine bottle of Chambertin, "But Dan, qualia are what make life worth living!" (Consciousness Explained, p. 383)
There are good reasons to introduce facts as truth-makers for contingently true atomic sentences. (Some supporting reasoning here.) But if there are facts, and they make-true contingent atomic sentences, then what is the semantic relation between these declarative sentences and their truth-makers? It seems we should say that such sentences name facts. But some remarks of Leo Mollica suggest that this will lead to trouble. Consider this aporetic triad:
1. 'Al is fat' is the name of the fact of Al's being fat. 2. 'Al is fat' has a referent only if it is true. 3. Names are essentially names: a name names whether or not it has a referent.
Each limb of the triad is very plausible, but they can't all be true. The conjunction of (1) and (3) entails the negation of (2). Which limb should we abandon? It cannot be (1) given the cogency of the Truth Maker Argument and the plausible assumption that the only semantic relation between a sentence and the corresponding fact is one of naming.
(2) also seems 'ungiveupable.' There are false sentences, and there may be false (Fregean) propositions: but a fact is not a truth-bearer but a truth-maker. It is very hard to swallow the notion that there are 'false' or nonobtaining facts. If 'Al is fat' is false it is because Al and fatness do not form a fact. The existence of a fact is the unity of its constituents. Where there is the unity of the right sort of constituents you have a fact; where there is not, you don't.
As for (3), suppose that names are only accidentally names, than a name names only on condition that it have a referent. We would then have to conclude that if the bearer of a name ceases to exist, that the name ceases to be a name. And that seems wrong. When Le Verrier put forth the hypothesis of an intra-Mercurial planent that came to be called 'Vulcan,' he did not know whether there was indeed such a planet, but he thought he had good evidence of its existence. When it was later decided that there was no good evidence of the planet in question, 'Vulcan' did not cease to be a name. If we now say, truly, that Vlucan does not exist we employ a name whose naming is not exhausted by its having a referent.
So it seems that names name essentially. This is the linguistic analog of intentionality: one cannot just think; if one thinks, then necessarily one thinks of something, something that may or may not exist. If I am thinking of something, and it ceases to exist, my thinking does not cease to be object-directed. Thinking is essentially object-directed. Analogously, names are essentially names.
So far, then, today's triad looks to be another addition the list of insolubilia. The limbs of the triad are more reasonably accepted than rejected, but they cannot all be true. A pretty pickle.
Now I claim that in systems where there is no distinction between predicate and sentence negation, we have ‘direct reference’. This is easily shown. Direct reference in a singular sentence is when the sentence is meaningless when the singular subject fails to refer. Assume that ‘a is F’ is not meaningless. If it is true, then there is a referent for ‘a’. If it is not true, the sentential negation ‘It is not the case that a is F’ is true. If sentential negation is equivalent to predicate negation, it follows that ‘a is non-F’ is true, and so a exists, and so, there is a referent for ‘a’. But (by excluded middle) either ‘a is F’ is true, or its contradictory (the sentential negation) is true. In either case, ‘a’ has a referent. Thus if ‘a is F’ is not meaningless, ‘a’ has a referent. Conversely if ‘a’ does not have a referent, ‘a is F’ is meaningless. But that is Direct Reference, as I have defined it.
This reasoning strikes me as correct. The notion of an atomic sentence is foundational for modern predicate logic (MPL). For such sentences there is no distinction between predicate and sentence negation. And given Edward's definition of 'direct reference,' I am persuaded that MPL entails direct refence for the subject terms of atomic sentences.
Note that I am substituting 'atomic sentence' for Edward's 'singular sentence.' Every atomic sentence (whether monadic or relational) is singular, but not every grammatically singular sentence is atomic. Or at least that is not obviously the case. Thus it is far from obvious that 'Peter smokes,' which is grammatically singular, is logically atomic. If one holds, with Russell, that grammatically proper names are definite descriptions in disguise, then the grammatically singular 'Peter smokes' will have an analysis that is existentially general.
Correct me if I'm wrong, but the subject term of an atomic sentence is what Russell called a logically proper name and distinguished from a grammatically proper name. So what Edward has shown is that Direct Reference holds for logically proper names. But this does not show that Direct Reference holds for ordinary names, grammatically proper names, such as 'Edward' in 'Edward is English' or 'Peter' in 'Peter smokes.'
Direct Reference for grammatically proper names, whether nonvacuous or vacuous (e.g. 'Vulcan') is false. But as far as I can see MPL is not committed to Direct Reference for such names. So while I am persuaded by Edward's reasoning above, I am not sure what its relevance is.
Causal theories of reference strike me as hopeless. Let's see how they fare with the problem of negative existentials.
There are clear cases in which 'exist(s)' functions as a second-level predicate, a predicate of properties or concepts or propositional functions or cognate items, and not as a predicate of individuals. The affirmative general existential 'Horses exist,' for example, can be understood as making an instantiation claim: 'The concept horse is instantiated.' Accordingly, the sentence does not predicate existence of individual horses; it predicates instantiation of the concept horse.
This sort of analysis is well-nigh mandatory in the case of negative general existentials such as 'Flying horses do not exist.' Here we have a true sentence that cannot possibly be about flying horses for the simple reason that there aren't any. (One can make a move into Meinong's jungle here, but there are good reasons for not going there.) On a reasonable parsing it is about the concept flying horse, and says of this concept that it has no instances.
The same analysis works for negative singular existentials like 'Pegasus does not exist.' Pace Meinong, everything exists. So, given the truth of 'Pegasus does not exist,' 'Pegasus' cannot be taken as naming Pegasus. Since 'Pegasus' has meaning, contributing as it does to the meaning of the true sentence, 'Pegasus does not exist,' and since 'Pegasus' lacks a referent, a natural conclusion to draw is that the meaning of 'Pegasus' is not exhausted by its reference: it has a sense whether or not it has a referent. So, along Russellian lines, we may analyze 'Pegasus does not exist' as, 'It is not the case that there exists an x such that x is the winged horse of Greek mythology.' Or we can take a page from Quine and say that nothing pegasizes. What we have done in effect is to treat the singular term 'Pegasus' as a predicate and read the sentence as a denial that this predicate applies to anything.
In this way the paradox attaching to singular negative existentials is removed. But the Russell-Quine analysis is based on the assumption that names are definite descriptions in disguise (Russell) or else transformable into predicates (Quine). But how does one deal with the problem of negative existentials if one denies the Russell-Quine approach to proper names, holding instead that they refer directly to their nominata, and not via the sense of a definite description or Searlean disjunction of definite descriptions?
Keith Donnellan tackles this problem in "Speaking of Nothing" (reprinted in S. P. Schwarz, ed., Naming, Necessity, and Natural Kinds, Cornell UP, 1977, pp. 216-244).
Consider 'Santa Claus does not exist.' What does a child come to learn when he learns this truth? He does not learn, as a Russellian would have it, that nothing in reality answers to (satisfies) a certain description; what he learns is that the historical chain leading back from his use of 'Santa Claus' ends in a 'block':
When the historical explanation of the use of a name (with the intention to refer) ends in this way with events that preclude any referent being identified, I will call it a "block" in the history. In this [Santa Claus] example, the block is the introduction of the name into the child's speech via a fiction told to him as reality by his parents. (237)
Having defined 'block,' Donnellan supplies a rule for negative existence statements, a rule which he says does not purport to supply the meaning of negative existentials but their truth-conditions:
If N is a proper name that has been used in predicative statements with the intention to refer to some individual, then 'N does not exist' is true if and only if the history of those uses ends in a block. (239)
'God' would appear to satisfy the antecedent of this conditional, so Donnellan's theory implies that 'God does not exist' is true if and only if the history of the uses of 'God' ends in a block.
There is something wrong with this theory. If 'God does not exist' is true, then we may ask: what makes it true? What is the truthmaker of this truth? The most natural answer is that extralinguistic reality makes it true, more precisely, the fact that reality contains nothing that could be referred to as God. There is nothing linguistic about this truthmaker. Of course, if 'God does not exist' is true, then 'God' does not refer to anything, and if 'God' does not refer to anything then the sentence 'God does not exist' is true. But the wholly nonlinguistic fact of God's nonexistence is not identical to the partially linguistic fact of 'God''s not referring to anything. Why not? Consider the following modal argument:
1. God's nonexistence, if it obtains, obtains in every possible world. 2. The fact of 'God''s not referring to anything obtains in only some possible worlds. (Because the English language exists in only some worlds.) Therefore 3. The two facts are distinct.
The argument just given assumes in its initial premise Anselm's Insight: if God exists, then he necessarily exists, and if he does not, then he is impossible. But I don't need this assumption. I can argue as follows:
5. God's nonexistence, if it obtains, obtains in some possible worlds. 6. Among these possible worlds, some are worlds in which English does not exist. Therefore 7. There is at least one world in which neither God nor the English language exists, which implies that God's nonexistence in that world cannot have as truthmaker any fact involving the name 'God.'
Let me put it another way. If 'God does not exist' is true, then the same fact can be expressed in German: 'Gott existiert nicht.' This is one fact expressible in two different languages. But the fact of 'God''s not referring to anything is a different fact from the fact of 'Gott''s not referring to anything. The facts are different because they involve different word-types. Therefore, neither fact can be identical to the fact of God's nonexistence.
Since the two facts are different, the wholly nonlinguistic fact of God's nonexistence cannot have as a truth-condition the partially linguistic fact of the history of uses of 'God' ending in a block, contrary to what Donnellan says. If one assertively utters 'God does not exist,' and if what one says is true, then extralingustic reality must be a certain way: it must be godless. This godlessness of reality, if it indeed obtains, cannot be tied to the existence of any contingent language like English.
Note that the descriptivist need not fall into Donnellan's trap. When he assertively utters 'God does not exist' he says in effect that all or most of the properties associated with the use of 'God' -- such properties as omniscience, etc. -- are not instantiated: nothing in extralinguistic reality has them. Since these properties can be viewed as having an objective, extralinguistic existence, the descriptivist needn't tie the existence/nonexistence of God to the existence of any contingent language.
Edward Ockham of Beyond Necessity is back from his Turkish holiday and reports that, besides lazing on the beach at Bodrum, he
. . . spent some time thinking about singular concepts. Do you accept singular meaning? Either you hold that a proper name has a meaning, or not (Aquinas held that it does not, by the way). If it does, then what is it that we understand when we understand the meaning of a proper name? The scholastics held that there was a sort of equivalence between meaning and signifying ("unumquodque, sicut contingit intelligere, contingit et significare"). What I signify, when I use a term in the context of a proposition, is precisely what another person understands, when he grasps that proposition that I have expressed.
Do I accept singular meaning? That depends on what we mean by 'meaning' and by 'singular.' Let's see if we can iron out our terminology.
1. Without taking 'sense' and 'reference' in exactly the way Frege intended them to be taken, I would say that 'meaning' is ambiguous as between sense and reference. Unfortunately, Edward seems to be using 'meaning' to mean 'sense.' Of course, he is free to do that.
2. Edward also uses the word 'signify.' I should like him to explain exactly how he is using this word. Is the signification of a proper name the same as what I am calling its sense? Or is the signification of a proper name its referent? Or neither? Or both?
3. Suppose I assertively utter a token of 'Peter is tired' in the presence of both Peter and Edward. My assertion is intended to convey a fact about Peter to Edward. The latter grasps (understands) the proposition I express by my assertive tokening of the sentence in question. And of course I understand the same proposition. What I signify -- 'express' as I would put it -- by my use of 'Peter' is what Edward understands when he grasps the proposition I express.
4. Now the issue seems to be this. Is the meaning or signification or sense I express, and that I understand, when I say 'Peter' a singular meaning? More precisely: is it an irreducibly singular meaning, one that cannot be understood as logically constructed from general concepts such as man, philosopher, smoker?
5. I say No! I don't deny that 'Peter' has a sense. It has a sense and a referent, unlike 'Vulcan' which has a sense but no referent. But the sense of 'Peter' is not singular but general. So, to answer Edward's question, I do not accept singular meaning.
Corollary: the haecceity of Peter - Peterity to give it a name -- cannot be grasped. All thinking is general: no thinking can penetrate to the very haecceity and ipseity of the thing thought about. One cannot think about a particular except as an instance of multiply exemplifiable concepts/properties. This is 'on all fours' with my earlier claim that there are no singular or individual concepts. The individual qua individual is conceptually ineffable. So if we know singulars (individuals) at all, we do not know them by conceptualization.
If Edward disagrees with this he must tell us exactly why. He should also tell us exactly how he is using 'proposition' since that is another potential bone of contention. Is he a Fregean, a Russellian, or a Geachian when it comes to propositions? Or none of those?
Your most recent post (for which many thanks) inspired the below-expressed argument, and I was curious as to your opinion of it . . . . I think it has something behind it, but right now I feel uncertain about my examples in (2).
0. There is something curious about the relation between a proposition or declarative sentence and the terms or words that compose it: the list L ("Christ," "Judas," "betrays") clearly differs, at the very least in not having a truth value, from the sentence "Judas betrays Christ," yet nothing immediately presents itself as the ground G of this difference. One plausible candidate for G is some kind of union or togetherness amongst the members of L present in "Judas betrays Christ" and not in L itself, but this proposal is open to a serious challenge.
1. Suppose we accept Barry Miller's thesis, from "Logically Simple Propositions," that some declarative sentences have only one semantic element. His favorite such sentence is the Romanian "Fulgura," whose only constituent word translates (if I remember aright) the English "brightens," and which is interesting in requiring no actual or implied subject to form a complete sentence (like "It's raining" in English, but without the dummy subject).
2. Now, the lone word in "Fulgura" seemingly can occur outside any proposition. If, for example, someone were to ask me to recite my favorite Romanian word, or to translate "brightens" into Romanian, it would be strange to take me as telling them something false, or to have them respond "No, it isn't," upon my replying with "fulgura." There would, however, be nothing strange about the sentence "Fulgura" being false and someone telling me as much. [. . .]
3. Even in such simple sentences, therefore, there is a distinction between the sentence and the words contained therein, for one can be had without the other. But the ground of this distinction cannot be any union or togetherness among the words that enter into the sentence for the simple reason that no union or togetherness amongst items can be had without distinct items to unify or bind together. It can, therefore, be at least plausibly argued that the general ground of the difference between a sentence and its constituent words is no kind of union or togetherness.
I take Mr Mollica's basic argument to be this:
a. If there are logically simple sentences/propositions, then the problem of the unity of the sentence/proposition is not one that arises for every sentence/proposition. b. There are logically simple sentences/propositions. Therefore
c. The problem of the unity of the proposition is not one that arises for every sentence/proposition.
My response is to reject (b) while granting (a). I discussed the question of logically simple sentences/propositions with Barry Miller back in the '90s in the pages of Faith and Philosophy. My "Divine Simplicity: A New Defense (Faith and Philosophy, vol. 9, no. 4, October 1992, pp. 508-525) has an appendix entitled "Divine Simplicity and Logically Simple Propositions." Miller responded and I counter-responded in the July 1994 issue, pp. 474-481. It is with pleasure that I take another look at this issue. I will borrow freely from what I have published. (Whether this counts as plagairism, depends, I suppose, on one's views on diachronic personal identity.)
A. A logically simple proposition (LSP) is one that lacks not only propositional components, but also sub-propositional components.Thus atomic propositions are not logically simple in Miller's sense, since they contain sub-propositional parts. A proposition of the form a is F, though atomic, exhibits subject-predicate complexity.
B. Miller's examples of LSPs are inconclusive. Consider the German Es regnet ('It is raining'). As Miller correctly notes, the es is grammatical filler, and so the sentence can be pared down to Regnet, which is no doubt grammatically simple. He then argues:
Now there is no question of Regnet being a predicate; for as a proposition it has a complete sense, whereas as a predicate it could have only incomplete sense. Hence, Regnet and propositions like it seem logically simple. (Barry Miller, "Logically Simple Propositions," Analysis, vol. 34, no. 4, March 1974, p. 125.)
I find it hard to avoid the conclusion that Miller is confusing propositions with the sentences used to express them. Regnet and fulgura are grammatically simple. But it scarcely follows that the propositions they express are logically simple. What makes them one-word sentences is the fact that they express propositions; otherwise, they would be mere words. So we need a sentence-proposition distinction. But once that distinction is in place then it becomes clear that grammatical simplicity of sentence does not entail logical simplicity of the corresponding proposition.
C. It is also unclear how any intellect like ours could grasp a proposition devoid of logical parts, let alone believe or know such a proposition. To believe that it is snowing, for example, is to believe something logically complex, albeit unified, something formulatable by some such sentence as 'Snow is falling.' So even if there were logically simple propositions, they could not be accusatives of minds like ours. And if propositions are defined as the possible accusatives of propositional attitudes such as belief and knowledge, then the point is stronger still: there cannot be any logically sinple propositions.
D. So it seems to me that 'the problem of the list' or the problem of the unity of the sentence/proposition is one that pertains to every sentence/proposition. It is a problem as ancient as it is tough, and, I suspect, absolutely intractable. For a glimpse into the state of the art, I shamelessly recommend my June 2010 Dialectica article, "Gaskin on the Unity of the Proposition."
According to Fred Sommers (The Logic of Natural Language, p. 166), ". . . one way of saying what an atomic sentence is is to say that it is the kind of sentence that contains only categorematic expressions." Earlier in the same book, Sommers says this:
In Frege, the distinction between subjects and predicates is not due to any difference of syncategorematic elements since the basic subject-predicate propositions are devoid of such elements. In Frege, the difference between subject and predicate is a primitive difference between two kinds of categorematic expressions. (p. 17)
Examples of categorematic (non-logical) expressions are 'Socrates' and 'mammal.' Examples of syncategorematic (logical) expressions are 'not,' 'every,' and 'and.' As 'syn' suggests, the latter expressions are not semantic stand-alones, but have their meaning only together with categorematic expressions. Sommers puts it this way: "Categorematic expressions apply to things and states of affairs; syncategorematic expressions do not." (164)
At first I found it perfectly obvious that atomic sentences have only categorematic elements, but now I have doubts. Consider the atomic sentence 'Al is fat.' It is symbolized thusly: Fa. 'F' is a predicate expression the reference (Bedeutung) of which is a Fregean concept (Begriff) while 'a' is a subject-expression or name the reference of which is a Fregean object (Gegenstand). Both expressions are categorematic or 'non-logical.' Neither is syncategorematic. And there are supposed to be no syncategorematic elements in the sentence: there is just 'F' and 'a.'
But wait a minute! What about the immediate juxtaposition of 'F' and 'a' in that order? That juxtaposition is not nothing. It conveys something. It conveys that the referent of 'a' falls under the referent of 'F'. It conveys that the object a instantiates the concept F. I suggest that the juxtaposition of the two signs is a syncategorematic element. If this is right, then it is false that atomic sentence lack all syncategorematic elements.
Of course, there is no special sign for the immediate juxtaposition of 'F' and 'a' in 'Fa.' So I grant that there is no syncategorematic element if such an element must have its own separate and isolable sign. But there is no need for a separate sign; the immediate juxtaposition does the trick. The syncategorematic element is precisely the juxtaposition.
Please note that if there were no syncategorematic element in 'Fa' there would not be any sentence at all. A sentence is not a list. The sentence 'Fa' is not the list 'F, a.' A (declarative) sentence expresses a thought (Gedanke) which is its sense (Sinn). And its has a reference (Bedeutung), namely a truth value (Wahrheitswert). No list of words (or of anything else) expresses a thought or has a truth value. So a sentence is not a list of its constituent words. A sentence depends on its constituent words, but it is more than them. It is their unity.
So I say there must be a syncategorematic element in 'Fa' if it is to be a sentence. There is need of a copulative element to tie together subject and predicate. It follows that, pace Sommers, it is false that atomic sentences are devoid of syntagorematic elements.
Note what I am NOT saying. I am not saying that the copulative element in a sentence must be a separate sign such as 'is.' There is no need for the copulative 'is.' In standard English we say 'The sea is blue' not 'The sea blue.' But in Turkish one can say Deniz mavi and it is correct and intelligible. My point is not that we need the copulative 'is' as a separate sign but that we need a copulative element which, though it does not refer to anything, yet ties together subject and predicate. There must be some feature of the atomic sentence that functions as the copulative element, if not immediate juxtaposition then something else such as a font difference or color difference.
At his point I will be reminded that Frege's concepts (Begriffe) are unsaturated (ungesaettigt). They are 'gappy' or incomplete unlike objects. The incompleteness of concepts is reflected in the incompleteness of predicate expressions. Thus '. . . is fat' has a gap in it, a gap fit to accept a name such as 'Al' which has no gap. We can thus say that for Frege the copula is imported into the predicate. It might be thought that the gappiness of concepts and predicate expressions obviates the need for a copulative element in the sentence and in the corresponding Thought (Gedanke) or proposition.
But this would be a mistake. For even if predicate expressions and concepts are unsaturated, there is still a difference between a list and a sentence. The unsaturatedness of a concept merely means that it combines with an object without the need of a tertium quid. (If there were a third thing, then Bradley's regress would be up and running.) But to express that a concept is in fact instantiated by an object requires more than a listing of a concept-word (Begriffswort) and a name. There is need of a syncategorical element in the sentence.
So I conclude that if there are any atomic sentences, then they cannot contain only categorematic expressions.
I should issue a partial retraction. I wrote earlier,"The TFL representation of singular sentences as quantified sentences does not capture their logical form, and this is an inadequacy of TFL, and a point in favor of MPL." ('TFL' is short for 'traditional formal logic'; 'MPL' for 'modern predicate logic with identity.' )
The animadversions of Edward the Nominalist have made me see that my assertion is by no means obvious, and may in the end be just a dogma of analytic philosophy which has prevailed because endlessly repeated and rarely questioned. Consider again this obviously valid argument:
1. Pittacus is a good man 2. Pittacus is a wise man ----- 3. Some wise man is a good man.
The traditional syllogistic renders the argument as follows:
Every Pittacus is a wise man Some Pittacus is a good man ----- Some wise man is a good man.
This has the form:
Every P is a W Some P is a G ----- Some W is a G.
This form is easily shown to be valid by the application of the syllogistic rules.
In my earlier post I then repeated a stock objection which I got from Peter Geach:
But is it logically acceptable to attach a quantifier to a singular term? How could a proper name have a sign of logical quantity prefixed to it? 'Pittacus' denotes or names exactly one individual. 'Every Pittacus' denotes the very same individual. So we should expect 'Every Pittacus is wise' and 'Pittacus is wise' to exhibit the same logical behavior. But they behave differently under negation.
The negation of 'Pittacus is wise' is 'Pittacus is not wise.' So, given that 'Pittacus' and 'every Pittacus' denote the same individual, we should expect that the negation of 'Every Pittacus is wise' will be 'Every Pittacus is not wise.' But that is not the negation (contradictory) of 'Every Pittacus is wise'; it is its contrary. So 'Pittacus is wise' and 'Every Pittacus is wise' behave differently under negation, which shows that their logical form is different.
My objection, in nuce, was that 'Pittacus is wise' and 'Pittacus is not wise' are contradictories, not contraries, while 'Every Pittacus is wise' and 'Every Pittacus is not wise' ('No Pittacus is wise') are contraries. Therefore, TFL does not capture or render perspicuous the logical form of 'Pittacus is wise.'
To this, Edward plausibly objected:
As I have argued here before, ‘Pittacus is wise’ and ‘Pittacus is not wise’ are in fact contraries. For the first implies that someone (Pittacus) is wise. The second implies that someone (Pittacus again) is not wise. Both imply the existence of Pittacus (or at least – to silence impudent quibblers - that someone is Pittacus). Thus they are contraries. Both are false when no one is Pittacus.
I now concede that this is a very good point. A little later Edward writes,
The thing is, you really have a problem otherwise. If 'Socrates is wise' and 'Socrates is not wise' are contradictories, and if 'Socrates is not wise' implies 'someone (Socrates) is not wise', as standard MPC holds, you are committed to the thesis that the sentence is not meaningful when Socrates ceases to exist (or if he never existed because Plato made him up). Which (on my definition) is Direct Reference.
So you have this horrible choice: Direct reference or Traditional Logic.
But must we choose? Consider 'Vulcan is uninhabited.' Why can't I, without jettisoning any of the characteristic tenets of MPL, just say that this sentence, though it appears singular is really general because 'Vulcan' is not a logically proper name but a definite description in disguise? Accordingly, what the sentence says is that a certain concept -- the concept planet between Mercury and the Sun -- has as a Fregean mark (Merkmal) the concept uninhabited.
Now consider the pair 'Socrates is dead' - 'Socrates is not dead.' Are these contraries or contradictories? If contraries, then they can both be false. Arguably, they are both false since Socrates does not exist, given that presentism is true. Since both are false, both are meaningful. But then 'Socrates ' has meaning despite its not referring to anything. So 'Socrates' has something like a Fregean sense. But what on earth could this be, given that 'Socrates' unlike 'Vulcan' names an individual that existed, and so has a nonqualitative thisnsess incommunicable to any other individual?
If, on the other hand, the meaning of 'Socrates' is its referent, then, given that presentism is true and Socrates does not exist, there is no referent in which case both sentences are meaningless.
So once again we are in deep aporetic trouble. The proper name of a past individual cannot have a reference-determining sense. This is because any such sense would have to be a Plantingian haecceity-property, and I have already shown that these cannot exist. But if we say that 'Socrates' does not have a reference-determining sense but refers directly in such a way as to require Socrates to exist if 'Socrates' is to have meaning, then, given presentism, 'Socrates' and the sentence of which it is a part is meaningless.
In Plural Reference, Franklin Mason writes that "Vallicella is often a delight, but upon occasion he annoys me to no end." Apparently I remind him of a "philosophical pugilist," a former colleague perhaps, who is obnoxious in the manner of all-too-many analytic philosophers. (One such told me once that if one is not willing to become a bit of an asshole in a philosophical discussion one is not taking it seriously.) Now I probably irritate Mason in a number of ways since I am an outspoken conservative while he is a liberal. But the proximate source of his umbrage is a comment I made in a quick and polemical entry entitled In Debt We Trust. There I wrote:
One of the people interviewed [in the movie In Debt We Trust] states that "Society preaches the gospel of shopping." That is the sort of nonsense one expects to hear from libs and lefties. First of all, there is no such thing as society. To think otherwise is to commit the fallacy of hypostatization.
When one begins a sentence with "society", one does not thereby assent to the existence of some bizarre, spatially disconnected entity whose parts are people. (Well, very few mean any such thing, and those who do are invariably deeply misguided philosophers. Plain folk never mean any such thing. Philosophers hardly ever mean such a thing. ) One uses "society" to refer plurally to, well, a plurality of people.
I sympathize with Mason's irritation. I once wrote a post in which I approvingly quoted from Ralph Waldo Emerson's great essay "Self-Reliance" the line, "Society everywhere is in conspiracy against the manhood of every one of its members." Tony Flood, the anarcho-capitalist, took me to task for presupposing that there is some entity 'society' above and beyond its members. But of course I presupposed no such thing and I was annoyed by Flood's objection. Clearly, what Emerson meant, and what I approved of, was the idea that the members of society engage in a sort of tacit conspiracy with one another to the end of enforcing conformity.
Our nominalist friend 'Ockham' pulled the same thing on me once. I used a sentence featuring the word 'property' and he took my use of that term as committing me to properties in some realist acceptation of the term. It annoyed me and struck me as a perverse refusal to take in the plain sense of what I wrote. Suppose I say, of a certain person, 'She has many fine attributes.' That is an ontologically noncommittal form of words and as such neutral in respect of the issue that divides nominalists and realists.
I submit, however, that Mason goes too far when he confidently asserts that "Plain folk never mean any such thing." I strongly suspect that the lady I was quoting never in her life thought about the issue now under discussion. She was most likely just repeating some liberal boilerplate she had picked up second-hand. She was probably confused and meant nothing definite when she said, "Society preaches the gospel of shopping." If she meant nothing definite, then Mason cannot confidently claim that "Plain folk never mean any such thing." And precisely because the lady meant nothing definite it is important to point out that one commits the fallacy of hypostatization if one assumes that for every substantive there is a corresponding substance. If I pinned the lady down, she would probably deny that there is some entity distinct from every member of society, an entity that preaches the gospel of shopping. But then I would ask her what she did mean. Did she mean that every member of society preaches said gospel? Or only that some do? I would get her to accept the latter. And then I would get her to admit that she was allowing those few people, advertisers, for example, to influence her. By showing her that there was no such thing as 'society,' I would be 'empowering' her -- to use a squishy liberal word -- I would make her see that she was not confronting some irresistible Power, but that she had the power to resist the siren song of the advertisers.
The reason this is important is that liberals have a tendency to remove responsibility from the agent and displace it onto something external to the agent such as 'society.' Thus 'society' made the punk kill the pharmacist, etc.
So, contra Mason, many people do confusedly think of society as some irresistible Power over against them to which blame can be assigned. It would be a mistake to think that no one commits the fallacy of hypostatization.
There are clear cases in which 'exist(s)' functions as a second-level predicate, a predicate of properties or concepts or propositional functions or cognate items, and not as a predicate of individuals. The affirmative general existential 'Horses exist,' for example, is best understood as making an instantiation claim: 'The concept horse is instantiated.' Accordingly, the sentence does not predicate existence of individual horses; it predicates instantiation of the concept horse.
This sort of analysis is well-nigh mandatory in the case of negative general existentials such as 'Flying horses do not exist.' Here we have a true sentence that cannot possibly be about flying horses for the simple reason that there aren't any. (One can make a Meinongian move here, but if possible we should try to get by without doing so.) On a reasonable parsing, 'Flying horses do not exist' is about the concept flying horse, and says of this concept that it has no instances.
But what about singular existentials? Negative singular existentials like 'Pegasus does not exist' pose no problem. We may analyze it as, 'It is not the case that there exists an x such that x is the winged horse of Greek mythology.' Or we can take a page from Quine and say that nothing pegasizes. What we have done in effect is to treat the singular term 'Pegasus' as a predicate and read the sentence as a denial that this predicate applies to anything.
Problems arise, however, with affirmative singular existentials such as 'I exist' and with sentences like 'I might not have existed' which are naturally read as presupposing the meaningfulness of 'I exist' and thus of uses of 'exists' as a first-level predicate. Thus, 'I might not have existed' is construable in terms of the operator 'It might not have been the case that ____' operating upon 'I exist.'
C.J.F. Williams, following in the footsteps of Frege, maintains the draconian thesis that all meaningful uses of 'exist(s)' are second-level. He must therefore supply an analysis of the true sentence 'I might not have existed' that does not require the meaningfulness of 'I exist.' His suggestion is that
. . . my assertion that I might not have existed is the assertion that there is some property . . . essential to me, which I alone possess, and which might never have been uniquely instantiated . . (What is Existence?, Oxford 1981, p. 104)
Williams is suggesting that for each individual x there is a property H such that (i) H is essential to x in the sense that x cannot exist except as instantiating H; and (ii) H, if instantiated, is instantiated by exactly one individual. Accordingly, to say that x might not have existed is to say that H might not have been instantiated. And to say that x exists is to say that H is instantiated.
This analysis will work only if the right properties are available. What is needed are essentially individuating properties. Suppose Ed is the fastest marathoner. Being the fastest marathoner distinguishes Ed from everything else, but it does not individuate him since it is not bound up with Ed's identity that he be the fastest marathoner. Ed can be Ed without being the fastest marathoner. So Ed's existence cannot be equivalent to, let alone idenctical with, the instantiation of the property of being the fastest marathoner since this is an accidental property of anything that possesses it, whereas the existence of an individual must be essential to it. After all, without existence a thing is nothing at all!
On the other hand, Ed's existence is not equivalent to his instantiation of any old essential property such as being human since numerous individuals possess the property whereas the existence of an individual is unique to it.
What is needed is a property that Ed alone has and that Ed alone has in every possible world in which he exists. Such a property will be essentially individuating: it will individuate Ed in every possible world in which Ed exists, one of these being the actual world.
Williams suggests the property of having sprung from sperm cell S and ovum O. Presumably Ed could not have existed without this origin, and anything possessing this origin is Ed. The idea, then, is that the existence of Ed is the instantiation of this property.
The property in question, however, is one that Michael Loux would call 'impure': it makes essential reference to an individual or individuals, in this case to S and O. Since S and O each exist, the question arises as to how their existence is to be analyzed.
For an analysis like that of Williams to work, what is needed is a property that does not refer to or presuppose any existing individual, a property that somehow captures the haecceity of Ed but without presupposing the existence of an individual. If there were such a haecceity property H, then one could say that Ed's existence just is H's being instantiated.
But as I argue in tedious detail in A Paradigm Theory of Existence and in this post such haecceity properties are creatures of darkness. That is one of the reasons I reject Frege-style theories of existence.
Existence, real pound-the-table existence, belongs to individuals. The attempt to 'kick it upstairs' and make it a property of properties or concepts or propositional functions is completely wrongheaded, pace such luminaries as Frege, Russell, and their epigoni.
Edward Ockham uses ‘Direct Reference’ to refer to "the theory that part or all of the meaning of a proper name requires the existence of a named object." This implies that a proper name cannot have a meaning unless there exists an object it names. He then gives the following argument:
A term signifies either a property or an object. But properties are repeatable. A property like being white, or running, or being bald can be instantiated by many individuals. Even a property that can only be had by one individual at a time (being the tallest living philosopher) can be instantiated by different individuals at successive times, or could be instantiated by a different individual than the one that possesses it now. If a proper name like 'Socrates' signified a property, even a unique property, it would make sense to say that this individual is Socrates on Tuesday, but that someone else is Socrates on Wednesday. Or that this individual is Socrates today, but might not have been Socrates. But that makes no sense. A proper name does [NOT] signify something that is repeatable, therefore does not signify a property. Therefore it signifies an object. Therefore an object is part or all of the meaning of a proper name, and the theory of Direct Reference, as defined above, is true.
As it stands, this argument is not compelling. To be compelling, it would have to close off the 'haecceity escape route.' Haecceitas is Latin for 'thisness.' Let us say that H is an haecceity property, an haecceity for short, if and only if H is a first-level property which, if instantiated, is instantiated by the same individual ('object' in Edward's terminology) at every time and in every possible world in which it is instantiated. Accordingly, 'the tallest living philosopher' does not express an haecceity property: it has different instances at different times and at different possible worlds, even though at a given time in a given world it has only one instance. If there are haecceity properties, then they are not repeatable, i.e., multiply instantiable, whether at different times or in different worlds.
Consider the property of being identical to Socrates. If there is such a property, it can serve as the sense of 'Socrates,' or, to use Edward's word, that which 'Socrates' "signifies." In the case of a vacuous proper name such as 'Vulcan,' the property of being identical to Vulcan could serve as its sense. If this is tenable, then 'Vulcan' is a genuine proper name despite it having no referent, and the Direct Reference theory as defined above is false.
Haecceities can either be nonqualitattive or qualitative. Identity-with-Socrates is an example of a nonqualitative haecceity. But one can imagine an haecceity property that is compounded out of qualitative properties where the latter are not tied to specific individuals in the way in which identity-with-Socrates is tied to the individual Socrates. The logical construction goes like this. We first form the huge conjunction K1 of all the qualitative properties that Socrates instantiates in the actual world. K has as conjuncts being snubnosed, being married, being a plebeian, being poor, etc. We do the same for every possible world in which Socrates exists. This yields a series of conjunctive properties, K1, K2, K3, etc. We then make a monstrous disjunctive property each disjunct of which is one of the Ks. This property is Socrates' qualitative haecceity. It is a property but it is clearly not repeatable (multiply instantiable). If there are such properties, they defeat Edward's argument above.
I myself do not believe in haecceity properties, nonqualitative or qualitative. See A Difficulty With Haecceity Properties. My point is that Edward's argument above is not compelling unless he can persuasively exclude them.
Now, given that I reject haecceity properties, I ought to find the above argument compelling. But this lands me in a quandry. For I hesitate to say that 'Vulcan' or 'Pegasus' are not proper names. They seem to be perfectly good proper names albeit vacuous. If so, then no part of their meaning involves the existence of a referent, and the DR theory is false.
Or consider 'Moses.' Was there some one man who received, or claimed to receive, the Torah from YHWH on Mount Sinai? Aren't we strongly tempted to say that the meaning of 'Moses' is what it is whether or not Moses existed? If we say that, then it can be no part of the name's meaning that it have an existing referent. Nor can it be any part of the name's meaning that there be a causal chain leading back to an initial baptism. If Moses never existed, then there was nothing to baptize.
Peter Geach, Mental Acts, Chapter 16 (RKP, 1957) is eminently relevant to present concerns and quite sensible. Herewith, an interpretive summary. Per usual, I take the ball and run with it.
Geach rejects the Russellian view that ordinary proper names are definite descriptions in disguise, but he also rejects the notion that proper names have no connotation at all. As for the disguised description view, it is "palpably false" since " . . . when I refer to a person by a proper name, I need not either think of him explicitly in a form expressible by a definite description, or even be prepared to supply such a description on demand. . ." (pp. 66-67)
This seems correct. Thomas Aquinas once came up in a conversation I had with my unlettered brother-in-law. The latter said something like, "Aquinas was a big name in Catholic theology." My brother-in-law was undoubtedly referring to the same person I was referring to even though he would not have been able to supply even one definite description. Recall that to be definite a description must be of the form, the unique x such that [insert description]. 'A big name in Catholic theology' is an indefinite description.
Geach also provides an interesting critique of Quine's "intransigent" extension of the Russellian line whereby names are transformed into predicates. Thus for Quine 'Pegasus is winged' goes over into something like 'There is exactly one x such x pegasizes, and x is winged.' Perhaps we will discuss Geach's Quine critique in a separate post.
Geach also rejects the view that ordinary proper names -- which, nota bene, are to be distinguished from logically proper names -- are devoid of connotation. On this view, "no attributes logically follow from a thing's being given a proper name." (67) Proper names are bestowed by fiat, whence it follows that there is no right or wrong about the application of a name: there is no property possession of which by a thing is a necessary condition of the name's being attached to it. It is different in the case of a general term. If 'fat' is true of Al, it follows that there is a property in virtue of whose possession by Al the term is correctly applied to him. By contrast, on the view under consideration, we cannot speak of a name being true of its nominatum, or not true of it.
As I said, Geach rejects this theory of names according to which the meaning of a name is exhausted by its reference. In the typical case, the same name applies to a person throughout his life from infancy to dotage. Geach takes this to imply that "the baby, the youth, the adult, are one and the same man." (69) They are not the same absolutely, or the same thing, but the same man. Here Geach sounds his theme of the sortal-relativity of identity. One cannot say sensibly of two things that they are the same absolutely; what one can say is that they are the same relative to some sortal under which both fall. If so,
. . . my application of the proper name is justified only if (e.g.) its meaning includes its being applicable to a man and I keep on applying it to one and the same man. On this account of proper names, there can be a right and wrong about the use of proper names. (69)
This jives with what I was saying earlier about 'God.' The notion that 'God' could denote anything at all, whether a sense of fear, a bolt of lightning, or what have you, strikes me as absurd. But that is the consequence one must swallow if one thinks of names as mere external tags devoid of sense. Geach now considers an objection:
It has often been argued that it cannot be part of the meaning of a proper name that its bearer should be a man, because we cannot tell this by hearing the name, and because there is nothing to stop us from giving the same name to a dog or a mountain. You might as well argue that it cannot be part of the meaning of 'beetle' that what it is applied to must be an insect, because we cannot learn this meaning just from the sound of the words, and because 'beetle' is also used for a sort of mallet. In a given context, the sense of 'beetle' does include: being an insect, and the sense of 'Churchill' does include: being a man. (70)
What Geach is saying here contradicts what our friend Edward maintains, namely, that ordinary proper names are tags whose meaning is exhausted by their reference. Suppose a one-eared rabbit wanders into my yard and I give it the name 'Gulky.' Just before the moment of baptism, the arbitrary sound 'Gulky' has no meaning at all. At the moment of baptism, it acquires a meaning which is its referent. Now suppose the rabbit wanders off and a coyote comes into the yard and I say, 'There's Gulky again.' You say,'That's not Gulky, Gulky's a rabbit!' The point here is that once 'Gulky' is introduced as a name for a particular rabbit, it acquires not only a referent but also the connotation rabbit-name, a connotation that prevents me from applying that name to anything other than a rabbit.
And then one day the coyote kills Gulky. Does 'Gulky' cease to be a rabbit-name and go back to being a meaningless sound?
As Geach says, there can be a right and wrong about the use of a proper name. Having introduced 'Gulky' as the name of a rabbit, I misuse that name if I apply it to a coyote. But if proper names are tags whose meaning is exhausted by their reference, then this would not be a misuse at all. Ergo, etc.
My point is that this is a non sequitur:
1. Reference of proper names is direct, i.e., not routed through sense. Therefore 2. The meaning of a proper name is exhausted by its reference.
Most direct reference theories of proper names would seem to be committed to the following four theses:
1. A proper name denotes, designates, refers to, its nominatum directly without the mediation of any properties. There is no description or disjunction of descriptions satisfaction of which is necessary for a name to target its nominatum. Accordingly, ordinary proper names are not definite descriptions in disguise as Russell famously maintained. The reference of a name is not routed through its sense or any component of its sense. A name may have a sense, but if it does it won't play a role in determining whether the name has a referent and which referent it is.
2. Proper names are first introduced at a 'baptismal ceremony' in which an individual is singled out as the name's nominatum. For example, a black cat wanders into my yard and I dub him 'Max Black.' Peter Lupu reminds me that names can get attached to objects also by the use of reference-fixing definite descriptions.
3. The connection established between name and nominatum at the baptism is rigid: once name N is attached to object O, N designates O in every possible world in which O exists. On the DR theory, then, 'Socrates' designates Socrates even in possible worlds in which Socrates is not the teacher of Plato, the husband of Xanthippe, etc. This is because the reference of 'Socrates' is not determined by any definite description or disjunction such descriptions.
Indeed, the DR theory has the strange implication that the following is possible: none of the definite descriptions we associate with the use of 'Socrates' is true of him, yet the name refers to him and no one else. Well, if the sense of the name does not determine reference, what does? What makes it the case that 'Socrates' designates Socrates?
4. A speaker S's use of N refers to O only if there is a causal chain extending from S's use of N back to the baptism, a chain with the following two features: (a) each user of N receives the name from an earlier user until the first user is reached; (b) each user to whom the name is transmitted uses it with the intention of referring to the same object as the previous user.
Problem: How is (1) consistent with (4)? Suppose I first encounter the name 'Uriel Da Costa' in a book by Leo Strauss. If I am to refer to the same man as Strauss referred to, I must use the name with the intention of doing so. Otherwise I might target some other Uriel Da Costa. It seems to follow that my use of 'Uriel Da Costa' must have associated with it the identifying attribute, same object as was referred to by Strauss with 'Uriel Da Costa.' But then the reference is not direct, but mediated by this attribute. (4) conflicts with (1).
First of all, how does an atheist deny the existence of God? Well, he might just assertively utter
1. God does not exist.
But suppose our atheist is also a direct reference theorist, one who holds that the reference of a name is not routed through sense or mediated by a Russellian definite description that gives the sense of the name. The direct reference theorist denies the following tenet of (some) descriptivists:
The referent of a name N is whatever entity, if any, that satisfies or fits the descriptive content associated with N in the mind of the speaker of N.
For example, on the descriptivist approach there is associated with the name 'God' a certain concept in the mind of the person who uses the name, a concept which includes various subconcepts (immaterial, unchanging, omnibenevolent, etc.). The name has a referent only if this concept is instantiated. Further, nothing having a property inconsistent with this concept can be the referent of the name. Now if our atheist were a descriptivist, his denial of the existence of God could be expressed by an assertive utterance of
2. The concept of an immaterial, omniqualified, etc. being is not instantiated.
Clearly, if one's denial of the existence of God is to be true, the existence of God cannot be a presupposition of one's denial, as (1) seems to suggest; so (2) seems to be a well-nigh mandatory rewrite of (1) that avoids this well-known difficulty pertaining to negative existentials. Whether or not God exists, the concept God exists, and is available to be the subject of judgments. We cannot say of God that he does not exist without presupposing what we aim to deny; but we can say of the concept God that it is not instantiated.
But our atheist is a direct reference theorist, and so cannot avail himself of (2). He cannot say that the nonexistence of God is the noninstantiation of a certain concept. This is because the direct reference theory implies that the referent of a name can exist whether or not it instantiates any of the concepts associated with the use of the name. The theory implies that 'Socrates' names Socrates even if it should turn out to be false that Socrates was the teacher of Plato, the wife of the shrewish Xanthhippe, snubnosed, a stone-cutter by trade, etc., etc.
On the direct reference theory, for 'God' to have a referent it suffices that (i) there be an initial baptism of some being as 'God,' (ii) there be an historical chain whereby this name gets passed down to the present user; (iii) each user in the chain have the intention of using the name with the same reference as the one from whom he received it. Thus it is not necessary that the referent of 'God' fit any concept of God that the end-user might have.
Now the direct reference theory has an advantage I have already noted. It allows a Jew, a Christian, and a Muslim to be referring to the same being when they utter sentences containing 'God' despite the fact that their conceptions of God are quite different.
How then does the direct reference theorist deny the existence of God? Since his denial cannot be about a concept of God, it must be about the transmission of word 'God' anits equivalents in other languages. He must deny that the name 'God' was ever introduced in an initial baptism; or he must deny that the historical chain is unbroken; or he must deny that all the various users had the intention of using the name with the reference of the one from whom they received it.
But how can the nonexistence/existence of God hinge on such linguistic and historical facts? The nonexistence of God, if a fact, is an objective fact: it has nothing to do with the nonexistence of some initial baptism ceremony, or some break in a link of name transmission, or some failure of intention on the part of the name-users.
More fundamentally, is it not just absurd to hold, as direct reference theorists seems to hold, that it is not necessary that the referent of 'God' fit ANY concept of God that the end-user might have? For that seems to imply that anything could be God. Could God be Abraham's fear during a lightning storm on a high mountain? Obviously not. Why not? Because 'God' used intelligently encapsulates a certain descriptive content or sense that constrains what can count as God.
Richard M. Gale, On the Nature and Existence of God (Cambridge UP, 1991), p. 11 :
First, because God is a supernatural being, he seem to defy being indexically pinned down or baptized. There are no lapels to be grabbed hold of by a use of 'this.' Some would contend that we can ostensively pin down the name 'God' by saying 'this' when having or after just having a mystical or religious experience, in which 'this' denotes the intentional accusative or content of the experience. This would seem to require that these experiences are cognitive and that their objective accusative is a common object of the experiences of different persons as well as of successive experiences of a single person.
Suppose Abraham or someone has an experience the intentional object of which he dubs 'God.' Suppose the experience is not 'cognitive,' i.e., not veridical: nothing in reality corresponds to the intentional object, the accusative, of the experience. Then there will not have been a successful reference to God. Successful reference is existence-entailing: If I succeed in referring to X, then X exists. Pace Meinong, one cannot refer to what does not exist. Reference is in every case to the existent. It therefore seems that Gale is right when he says that a successful baptizing of God requires the veridicality of mystical experience.
Andrew V. Jeffrey (Faith and Philosophy, January 1996, p. 94) responds to Gale as follows:
. . . the religious language-game could be played as if theistic experiences were both veridical and cognitive even if they were not; i.e., people could play the referential game even with a radically misidentified referent.
It seems to me that this response misses the point. Suppose the referent has been radically misidentified: Abraham dubs his Freudian superego, or an overwhelming sense of anxiety, or what have you, as 'God.' Then no successful reference will have been achieved. Is a long disquisition necessary to explain that God cannot be a feeling of anxiety?
And if you say that all baptisms are successful in that, after all, something gets baptized, then I say that this shows the utter hopelessness of the causal theory of reference. For the question to be answered is this: How in the utterance of a name does the speaker succeed in referring to an object? Under what conditions is successful reference achieved? A theory that implies that one always succeeds, that there are no conditions in which one fails to succeed, is worthless.
Yesterday I argued that whether 'God' and equivalents as used by Jews, Christians, and Muslims refer to the same being depends on one's philosophy of language. In particular, I suggested that only on a causal theory of names could one maintain that their respective references are to the same entity. The causal theory of names, however, strikes me as not very plausible. Here is one consideration.
The causal theory of names of Saul Kripke et al. requires that there be an initial baptism of the target of reference, a baptism at which the name is first introduced. This can come about by ostension: Pointing to a newly acquired kitten, I bestow upon it the moniker, 'Mungojerrie.' Or it can come about by the use of a reference-fixing definite description: Let 'Neptune' denote the celestial object responsible for the perturbation of the orbit of Uranus. In the second case, it may be that the object whose name is being introduced is not itself present at the baptismal ceremony. What is present, or observable, are certain effects of the object hypothesized. (See Saul Kripke Naming and Necessity, Harvard 1980 p. 79, n. 33 and p. 96, n. 42.)
As I understand it, a necessary condition for successful reference on the causal theory is that a speaker's use of a name be causally connected (perhaps indirectly) with the object referred to. We can refer to objects only if we stand in some causal relation to them (direct or indirect). So my use of 'God' refers to God not because there is something that satisfies the definite description or disjunction of definite descriptions that unpack the sense of 'God' as I use it, but because my use of 'God' can be traced back though a long causal chain to an initial baptism, as it were, of God by, say, Moses on Mt. Sinai.
If this is what the causal theory (or at least the Kripkean version thereof) requires, then the theory rules out all reference to abstracta: Fregean propositions, numbers, sets, etc. But it also rules out reference to future events.
Suppose meteorologists predict a hurricane that has the power to wipe out New Orleans a second time. Conservatives to a man and a woman, they introduce the name 'Hillary' for this horrendous event, and they introduce it via some appropriately complex definite description. (They can't point to it since it doesn't yet exist.) The meteorologists continue with their work using 'Hillary' for the event in question. Since the event lies in the future, there is no question of its causing directly or indirectly any use of the name 'Hillary.' Nor is there any question of the name's being introduced on the basis of effects of the event.
What we seem to have here is a legitimate use of a proper name that cannot be accounted for by the causal theory. For the causal theory rules out reference to a thing or event to which one does not stand in a causal relation. This suggests that there is something very wrong with the theory. (See John Searle, Intentionality, Cambridge 1983, p. 241.)
One morning an irate C-Span viewer called in to say that he prayed to the living God, not to the mythical being, Allah, to whom Muslims pray. The C-Span guest made a standard response, which is correct as far as it goes, namely, that Allah is Arabic for God, just as Gott is German for God. He suggested that adherents of the three Abrahamic religions (Judaism, Christianity, Islam) worship the same God under different names. No doubt this is a politically correct thing to say, but is it true?
Our question, then, is precisely this: Does the normative Christian and the normative Muslim worship numerically the same God, or numerically different Gods? (By 'normative Christian/Muslim' I mean an orthodox adherent of his faith who understands its content, without subtraction and without addition of private opinions.) Islam and Christianity are both monotheistic. So if Christian and Muslim worship different Gods, then one is worshipping a nonexistent God, or, if you prefer, is failing to worship the true God.
1. Let's start with the obvious: 'Allah' is Arabic for God. So if an Arabic-speaking Coptic Christian refers to God, he uses 'Allah.' And if an Arabic-speaking Muslim refers to God, he too uses 'Allah.' From the fact that both Copt and Muslim use 'Allah' it does not follow that they are referring to the same God, but it also does not follow that they are referring to numerically different Gods. So we will not make any progress with our question if we remain at the level of words. We must advance to concepts.
2. We need to distinguish between the word for God, the concept (conception) of God, and God. God is not a concept, but there are concepts of God and, apart from mystical intuition, we have no access to God except via our concepts of God. Now it is undeniable that the Christian and Muslim conceptions of God partially overlap. The following is a partial list of what is common to both conceptions:
a. There is exactly one God. b. God is the creator of everything distinct from himself. c. God is transcendent: he is radically different from everthing distinct from himself. d. God is good.
Now if the Christian and Muslim conceptions of God were identical, then we would have no reason to think that Christian and Muslim worship different Gods. But of course the conceptions, despite partial overlap, are not identical. Christians believe in a triune God who became man in Jesus of Nazareth. Or to put it precisely, they believe in a triune God the second person of which became man in Jesus of Nazareth. This is the central and indeed crucial (from the Latin, crux, crucis, meaning cross) difference between the two faiths. The crux of the matter is the cross.
3. Now comes the hard part, which is to choose between two competing views:
V1: Christian and Muslim worship the same God, but one of them has a false belief about God, whether it be the belief that God is unitarian or the belief that God is trinitarian.
V2: Christian and Muslim worship different Gods precisely because they have different conceptions of God. So it is not that one of them has a false belief about the one God they both worship; it is rather that one of them does not worship the true God at all.
There is no easy way to decide rationally between these two views. We have to delve into the philosophy of language and ask how reference is achieved. How do linguistic expressions attach or apply to extralinguistic entities? How do words grab onto the (extralinguistic) world? In particular, how do nominal expressions work? What makes my utterance of 'Socrates' denote Socrates rather than someone or something else? What makes my use of 'God' (i) have a referent at all and (ii) have the precise referent it has?
4. It is reasonable to hold, with Frege, Russell, and many others, that reference is routed through, and determined by, sense: an expression picks out its object in virtue of the latter's satisfaction of a description associated with the referring expression, a description that unpacks the expression's sense. If we think of reference in this way, then 'God' refers to whatever entity, if any, that satisfies the definite description encapsulated in 'God' as this term is used in a given linguistic community.
Given that God is not an actual or possible object of (sense) experience, this seems like a reasonable approach to take. The idea is that 'God' is a definite description in disguise so that 'God' refers to whichever entity satisfies the description associated wth 'God.' Now consider two candidate definite descriptions, the first corresponding to the Mulsim conception, the second corresponding to the Christian.
D1: 'the unique x such that x is omnipotent, omniscient, omnibenevolent, created the world ex nihilo and is unitarian'
D2: 'the unique x such that x is omnipotent, omniscient, omnibenevolent, created the world ex nihilo, and is triune.'
Suppose that reference is not direct, but routed through sense, or mediated by a description, in the manner explained above. It is easy to see that no one entity can satisfy both (D1) and (D2). So if reference is routed through sense, then Christian and Muslim cannot be referring to the same being. Indeed, one of them is not succeeding in referring at all. For if God is triune, nothing in reality answers tothe Muslim's conception of God. And if God is unitarian, then nothing in reality answers to the Christian conception.
And so, contrary to what Miroslav Volf maintains, the four points of commonality in the Christian and Muslim conceptions listed above do NOT "establish the claim that in their worship of God, Muslims and Christians refer to the same object." (Allah: A Christian Response, HarperCollins 2011, p. 110.) For if reference to God is mediated by a conception which includes the subconcept triune or unitarian, the reference cannot be to the same entity.
A mundane example (adapted from Kripke) will make this more clear. Sally sees a handsome man at a party standing in the corner drinking a clear bubbly liquid from a cocktail glass. She turns to her companion Nancy and says, "The man standing in the corner drinking champagne is handsome!" Suppose the man is not drinking champagne, but sparkling water instead. Has Sally succeeded in referring to the man or not? Argumentative Nancy, who knows that no alcohol is being served at the party, and who also finds the man handsome, says, "You are not referring to anything: there is no man in the corner drinking champagne. The man is drinking sparkling water. Nothing satisfies your definite description. There is no one man we both admire. Your handsome man does not exist, but mine does."
Now in this example what we would intuitively say is that Sally did succeed in referring to someone using a definite description even though the object she succeeded in referring to does not satisfy the description. Intuitively, we would say that Sally simply has a false belief about the object to which she is successfully referring, and that Sally and Nancy are referring to and admiring the very same man.
But note how this case differs from the God case. Both women see the man in the corner. But God is not an object of possible (sense) experience, of Kant's moegliche Erfarhung. Hence the reference of 'God' cannot be nailed down perceptually. And so it seems that what we succeed in referring to is whatever satisfies the definite description that unpacks our conception of God.
5. My tentative conclusion, then, is that (i) if we accept a description theory of names, the Christian and Muslim do not refer to the same being when they use 'God' or 'Allah' and (ii) that a description theory of names is what we must invoke given the nonperceivability of God.
If, on the other hand, 'God' is a logically proper name whose meaning is exhausted by its reference, a Kripkean rigid designator, rather than a Russellian definite description in disguise, then what would make 'God' or a particular use of 'God' refer to God?
A particular use is presumably caused by an earlier use. But eventually there must be an initial use. Imagine Moses on Mt. Sinai. He has a profound mystical experience of a being who conveys to his mind such locutions as "I am the Lord thy God; thou shalt not have false gods before me." Moses applies 'God' or 'Yahweh' to the being. But what makes the name the name of the being? One may say: the fact that the being or an effect of the being causes the use of the name.
But a certain indeterminacy seems to creep in if we think of the semantic relation of referring as explicable in terms of causation. For is it the (mystical) experience of God that causes the use of 'God'? Or is it God himself who causes the use of 'God'? If the former, then 'God' refers to an experience had by Moses and not to God. Surely God is not an experience. But how can God be the cause of Moses' use of 'God'? Causes are events, God is not an event, so God cannot be a cause.
If these difficulties could be ironed out and a causal theory of names is tenable, and if the causal chain extends from Moses down to Christians and (later)to Muslims, then a case could be made that Jews, Christians, and Muslims are all referring to the same God when they use 'God' and such equivalents as 'Yahweh' and 'Allah.'
So it looks like there is no easy answer to the opening question. It depends on the resolution of intricate questions in the philosophy of language.