Identity and Individuation – Page 4

Singular Concepts and Singular Negative Existentials

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

1. Vulcan does not exist.

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

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

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

Reduction, Elimination, and Material Composition

Yesterday I wrote, "And yet if particular a reduces to particular b, then a is nothing other than b, and is therefore identical to b." This was part of an argument that reduction collapses into elimination. A reader objects: "I am not sure that this is an accurate definition of reduction."

He gives an argument having to do with material composition. I'll put the argument in my own way, so as to strengthen it and make it even more of a challenge for me.

1. Whether or not minds are physically reducible, physical reductionism is surely true of some things, statues for example. A statue is reducible to the matter that composes it, a hunk of bronze, say. No one is a statue-hunk dualist. It is not as if there are two things in the same place, the statue and the hunk of bronze. Nor is anyone an eliminativist when it comes to statues.There are such things, but what they are is just hunks of matter. We avoid both dualism and eliminativism by adopting reductionism.

2. But surely the matter of the statue might have been configured or worked in some other way to make a different statue or a non-statue. Before the sculptor went to work on it, the hunk of bronze was just a hunk, and after it became a statue it could have reverted back to being a mere hunk if it were melted down.

Therefore

3. The statue and the hunk differ property-wise: the hunk, but not the statue, has the property of existing at times at which the statue does not exist. And at every time at which both hunk and statue exist, the hunk, but not the statue, has the modal property of being possibly such as to be a non-statue.

Therefore

4. By the indiscernibility of Identicals, statue and hunk are not identical.

Therefore

5. The statue is reducible to its constituent matter but not identical to it. (By 1, 4)

Therefore

6. It is not the case that if particular a reduces to particular b, then a is identical to b.

This is an impressive argument, but I don't see that it shows that one can have reduction without identity of the reduced to the reducer. I take the argument as further evidence of the incoherence of the notion of the reduction of one particular to another. The first premise, though plausible, is not obviously true. What's more, it seems inconsistent with the second premise. I have argued many times before that in cases like these, statue and lump, fist and hand, brick house and bricks, the thing and its matter differ property-wise and so cannot be identical. They are both temporally and modally discernible. If fist and hand cannot be numerically identical, then they must be numerically distinct. When I take my hand and make a fist of it, the hand does not cease to exist, but something new comes into existence, a fist. Hand and fist, as long as both exist, are two numerically different things occupying exactly the same spatiotemporal position. Admittedly, that sounds strange. Nevertheless, I claim here is just as much reason to be a hand-fist dualist as there is to be a fist-to-hand reductionist.

One could also be an eliminativist. Amazingly, Peter van Inwagen — no slouch of a philosopher; you don't get a chair if you slouch — is an eliminativist about artifacts such as the house built by the Wise Pig. See here.

Perhaps I can drive the reductionist onto the horns of a dilemma. Either fist and hand are identical or they are not. They cannot be identical because they differ property-wise. If two things are not numerically identical, however, then they are numerically different. But if fist and hand are numerically different, then the fist does not reduce to the hand.

So I persist in my view that reduction is an incoherent notion. There is no viable via media between dualism and eliminativism.

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

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

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

To illustrate the putative distinction, consider

1. George Orwell is Eric Blair

and

2. George Orwell is famous.

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

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

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

This is what throws me about the scholastic stuff peddled by Ed and others. In 'Orwell is famous' they seem to be wanting to say that 'Orwell' and 'famous' refer to the same thing. But what could that mean?

First of all, 'Orwell' and 'famous' do not have the same extension: there are many famous people, but only one Orwell. But even if Orwell were the only famous person, Orwell would not be identical to the only famous person. Necessarily, Orwell is Orwell; but it is not the case that, necessarily, Orwell is the only famous person, even if it is true that Orwell is the only famous person, which he isn't.

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

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

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

Accidental Sameness and its Logical Properties

I should thank Richard Hennessey for motivating me to address a topic I haven't until these last few days discussed in these pages, namely, that of accidental sameness. Let us adopt for the time being a broadly Aristotelian ontology with its standard nomenclature of substance and accident, act and potency, form and matter, etc. Within such a framework, how can we account for an accidental predication such as 'Socrates is seated'?

In particular, what is expressed by 'is' in a sentence like this? Hennessey seems to maintain that it expresses an identity which holds, if the sentence is true, between the referent of the subject term 'Socrates' and the referent of the predicate term 'seated.' Here is what Hennessey says:

Let us take the proposition “Socrates is sitting” or the strictly equivalent “Socrates is a sitting being.” The referent of the subject term here is the sitting Socrates and that of the predicate term is one and the same sitting Socrates. Similarly, the referent of the subject term of “Plato is sitting” is the sitting Plato and that of its predicate term is one and the same sitting Plato. Here, once again, only if the referent of the “Socrates” and that of the “sitting” of “Socrates is sitting” are identical can it be true that Socrates is actually the one sitting. And, only if the referent of the “Plato” and that of the “sitting” of “Plato is sitting” are identical can it be true that Plato is actually the one sitting.

Hennessey is making two moves in this passage. The first is the replacement of 'Socrates is seated' with 'Socrates is a seated being.' (I am using 'seated' instead of 'sitting' for idiosyncratic stylistic reasons; the logic and ontology of the situation should not be affected.) I grant that the original sentence and its replacement are logically equivalent. Hence I have no objection to the first move.

The second move is to construe the 'is' of the replacement sentence as expressing identity. Together with this move goes Hennessey's claim that ONLY in this way can the truth of the sentence be insured. This claim is false for reasons given earlier, but this is not my present concern. My concern at present is the second move by itself. Can the 'is' of the replacement sentence be construed as expressing identity?

The answer to this is in the negative if by 'identity' is meant strict identity. Strict identity, symbolized by '=,' is an equivalence relation: it is reflexive, symmetrical, and transitive. It is furthermore governed by the Indiscernibility of Identicals (If a = b, then everything true of a is true of b and vice versa) and the Necessity of Identity (If a = b, then necessarily a = b). Now if the referent of 'Socrates' and the referent of 'seated' are strictly identical, then this is necessarily so, true in every possible world in which Socrates exists, in which case our sentence cannot be contingently true as it obviously is. Socrates is seated only at some of the times at which he exists, not at all such times. And at any time at which he is seated he is possibly such as not to be seated at that time. (The modality in question is broadly logical.)

So if Hennessey wants to construe the 'is' as expressing a type of sameness, it cannot be that sameness which is strict identity. An option which is clearly open to him as an Aristotelian is to construe the 'is' as expressing accidental sameness. But what is that?

It is a dyadic relation that connects one substance and one accidental compound. (Thus by definition it never connects two substances or two compounds.) An accidental compound is a particular, not a universal. It is a hylomorphic compound the matter of which is a substance and the form of which an accident inhering in that substance. It is admittedly a somewhat 'kooky' object, to borrow an epithet from Gareth Mathews. An example is seated-Socrates. Socrates is a substance. His seatedness is an accident inhering in him. The two together form an accidental compound which can be denoted by 'seated-Socrates' or by 'Socrates + seatedness.' Seated-Socrates is neither a substance nor an accident, but a transcategorial hybrid composed of one substance and one accident, but only if the accident inheres in the substance. (An accidental compund is therefore not a mereological sum of a substance and any old accident.)

The compound is not a substance because it cannot exist on its own, but it is parasitic upon its parent substance, in our example, Socrates. It is also not a substance because it is not subject to alterational change. Change for an accidental compound is existential change, either coming into being or passing out of being. When Socrates sits down, seated-Socrates comes into being, and when he stands up it passes out of being. An accidental compound is not an accident because it is not related to its parent substance by inherence, but by accidental sameness. A key difference is that inherence is an asymmetrical relation, while accidental sameness is symmetrical.

Hennessey can say the following: 'Socrates is seated' expresses the accidental sameness of Socrates with the accidental compound, seated-Socrates. He needs to posit two objects, not one: a substance and an accidental compound. If he holds that the referent of 'Socrates' and the referent of 'seated' are strictly identical, then the accidentality of the predication cannot be accommodated, and all predications become essential. That was my initial objection to Hennessey's view before I figured out a way to salvage it.

What are the logical properties of the accidental sameness relation? Like strict identity, it is symmetrical. This should be obvious. If Socrates is accidentally the same as seated-Socrates, then the latter is accidentally the same as the former. The inherence relation, by contrast, is asymmetrical: if A inheres in S, then S does not inhere in A. This is one of the differences between the accidental sameness relation and the inherence relation.

Accidental sameness is irreflexive. This can be proven as follows:

1. No substance is an accidental compound.
2. If a is accidentally the same as b, then either a is a subtance and b a compound, or vice versa.
Therefore
3. No object, whether substance or compound, is accidentally the same as itself.

It can also be proven that accidental sameness is intransitive. Thus, if a is accidentally the same as b, and b accidentally the same as c, it follows that a is not accidentally the same as c. Suppose a is a substance. Then b is a compound. But if b is a compound, then c is a substance, with the result that a substance is accidentally the same as a substance, which violates the definition of accidental sameness. On the other hand, if a is a compound, then b is a substance, which makes c a compound, with the result that a compound is accidentally the same as a compound, which also violates the definition. So accidental sameness is intransitive.

Clearly, there is accidental sameness only if there are accidental compounds. But are there any of the latter? Consider a fist. A fist is not strictly identical to the hand whose fist it is. (They have different persistence conditions.) But a fist is not strictly different from the hand whose fist it is. But surely there are fists, and surely what we have in a situation like this is not two individuals in the same place. So it is reasonable to maintain that a fist is an accidental compound which is accidentally the same as the hand whose fist it is.

Still, there is something 'kooky' about accidental compounds. So I'll end with a challenge to Hennessey, enemy of universals. Why are accidental compounds less 'kooky' than universals, whether immanent or transcendent?

Accidental Sameness: Defending Hennessey Against My Objection

Yesterday I made an objection to Richard Hennessey's neo-Aristotelian theory of accidental predication. But this morning I realized that he has one or more plausible responses. By the way, this post has, besides its philosophical purpose, a metaphilosophical one. I will be adding support to my claim lately bruited that philosophy — the genuine article — is not a matter of debate, as I define both 'philosophy' and 'debate.' For have you ever been to a debate in which debater A, having made an objection to something debater B has said, says, "Wait a minute! I just realized that you have one or more plausible ways of turning aside my objection. The first is . . . ."?

1. 'Socrates is seated' is an example of an accidental predication. For surely it is no part of Socrates' essence or nature that he be seated. There is no broadly logical necessity that he be seated at any time at which he is seated, and there are plenty of times at which he is not seated. 'Socrates is seated' contrasts with the essential predication 'Socrates is human.' Socrates is human at every time at which he exists and at every world at which he exists.

2. Hennessey's theory is that ". . . only if the referent of the 'Socrates' and that of the 'sitting' of 'Socrates is sitting' are identical can it be true that Socrates is actually the one sitting." The idea seems to be that accidental predications can be understood as identity statements. Thus 'Socrates is seated' goes over into (what is claimed to be) the logically equivalent 'Socrates is (identical to) seated-Socrates.' Accordingly, our sample sentence is construed, not as predicating a property of Socrates, a property he instantiates, but as affiming the identity of Socrates with the referent of 'seated-Socrates.'

3. But what is the referent of 'seated-Socrates'? If the referent is identical to the referent of 'Socrates,' namely Socrates, then my objection kicks in: how can the predication be contingently true, as it obviously is, given that it affirms the identity of Socrates with himself? Socrates is essentially Socrates but only accidentally seated.

4. Perhaps Hennessey could respond to this objection by saying that 'Socrates' and 'Socrates-seated' do not refer to the same item: they refer to different items which are, nonetheless, contingently identical. This would involve distinguishing between necessary identity and contingent identity where both are equivalence relations (reflexive, symmetrical, transitive) but only the former satisfies in addition the Indiscernibility of Identicals (InId) and the Necessity of Identity (NI). It is obvious that if a and b are contingently identical, but distinct, then these items must be discernible in which case InId fails. It is also obvious that NI must fail for contingent identity.

5. Closer to Aristotle is a view described by Michael C. Rea in "Sameness Without Identity: An Aristotelian Solution to the Problem of Material Constitution" in Form and Matter, ed. Oderberg, Blackwell 1999, pp. 103-115. I will now paraphrase and interpret from Rea's text, pp. 105-107. And I won't worry about how the view I am about to sketch differs — if it does differ — from the view sketched in #4.

When Socrates sits down, seated-Socrates comes into existence. When he stands up or adopts some other nonseated posture, seated-Socrates passes out of existence. This 'kooky' or 'queer' object is presumably a particular, not a universal, though it is not a substance. It is an accidental unity whose existence is parasitic upon the existence of its parent substance, Socrates. It cannot exist without the parent substance, but the latter can exist without it. The relation is like that of a fist to a hand made into a fist. The fist cannot exist without the hand, but the hand can exist without being made into a fist.Though seated-Socrates is not a substance it is like a substance in that it is a hylomorphic compound: it has Socrates as its matter and seatedness as its form. As long as Socrates and seated-Socrates exist, the relation between them is accidental sameness, a relation weaker than strict identity.

Accidental sameness is not strict identity presumably because the former is not governed by the Indiscernibility of Identicals. Clearly, Socrates and seated-Socrates do not share all properties despite their sameness. They differ temporally and modally. Socrates exists at times at which seated-Socrates does not exist (though not conversely). And it is possible that Socrates exist without seated-Socrates existing (though not conversely).

Are Socrates and seated-Socrates numerically the same? They count as one and so they are one in number though not one in being. So says Aristotle according to Rea. After all, if Socrates and Alcibiades are seated at table we count two philosophers not four. We don't count: Socrates, seated-Socrates, Alcibiades, seated-Alcibiades.

But I will leave it to Hennessey to develop this further. It looks as if this is the direction in which he must move if his theory is to meet my objection.

What about essential predication? Is there a distinction between Socrates and human-Socrates? These two cannot be accidentally the same. They must be strictly identical. If 'Socrates is human' is parsed as 'Socrates is identical to human-Socrates' then how does the latter differ from 'Socrates is Socrates'? The sense of 'Socrates is human' differs from the sense of 'Socrates is Socrates.' How account for that? 'Socrates is Socrates' is a formal-logical truth, trivial and uninformative. 'Socrates is human' is not a formal-logical truth; it is informative.

‘Leibniz’s Law’: A Useless Expression

Pedant and quibbler that I am, it annoys me when I hear professional philosophers use the phrase 'Leibniz's Law.' My reason is that it is used by said philosophers in three mutually incompatible ways. That makes it a junk phrase, a wastebasket expression, one to be avoided. Some use it as Dale Tuggy does, here, to refer to the Indiscernibility of Identicals, a principle than which no more luminous can be conceived. (Roughly, if a = b, then whatever is true of a is true of b, and vice versa.) Fred Sommers, referencing Benson Mates, also uses it in this way. (See The Logic of Natural Language, p. 127)

Others, such as the distinguished Australian philosopher Peter Forrest, use it to refer to the Identity of Indiscernibles, a principle rather less luminous to the intellect and, in my humble opinion, false. (Roughly, if whatever is true of a is true of b and vice versa, then a = b.) And there are those who use it as to refer to the conjunction of the Indiscernibility of Identicals and the Identity of Indiscernibles.

So 'Leibniz's Law' has no standardly accepted usage and is insofar forth useless. And unnecessary. You mean 'Indiscernibility of Identicals'? Then say that. If you mean its converse, say that. Ditto for their conjunction.

There is also the problem of using a great philosopher's name to label a principle that the philosopher may not even have held. Analytic philosophers are notorious for being lousy historians. Not all of them, of course, but the run-of-the-mill. If Sommers is right, Leibniz was a traditional logician who did not think of identity as a relation as Frege and Russell do. (p. 127) Accordingly, 'a = b' as this formula is understood in modern predicate logic does not occur in Leibniz.

The Problem of Individuation: Genuine or Pseudo?

1. The ontological problem of individuation is actually two problems. One is the problem of what makes two or more numerically different individuals numerically different. What grounds numerical difference? The other is the problem of what makes an individual an individual as opposed to a member of some other category of entity. What grounds individuality? If the first question is about the differentiator (the ground of numerical difference), the second is about the individuator (the ground of individuality).

The two questions are often conflated, but as you can see, they are different. The conflation is aided and abetted by the fact that on some theories the entity posited to do the differentiating job also does the individuating job. For example, in Gustav Bergmann's ontology, bare particulars are both differentiators and individuators. But if I both load the truck and drive the truck it doesn't follow that loading and driving are the same job. So we cannot just assume that what does the differentiating job will also do the individuating job. I won't say anything at the moment about the details of Hector-Neri Castaneda's ontology, but in it, the individuator is not a differentiator.

Therefore, 'problem of individuation' is a bit of a misnomer. A better phrase would be 'problem(s) of individuation/differentiation.' Having said that, I revert to the stock phrase.

Note also that we are talking ontology here, not epistemology. 'Individuate' can be used in an epistemological way to mean: 'single out,' 'pick out,' 'make an identifying reference to,' etc. Suppose I single out x as the only item that has properties P, Q, R . . . . It doesn't follow that having exactly those properties is what makes x an individual or makes x numerically different from y. It could be like this: concrete particulars a and b are told apart by their difference is properties, but that makes them numerically different is that each has a numerically different bare particular, or a different nonqualitative thisness, where this is not understood to be a bare particular.

2. Before going any deeper into this we ought to ask whether our two problems are genuine.

Taking the first one first, why is there any need for a differentiator? If S and P are numerically distinct concrete particulars, why not just take that as a brute fact? Brute facts need no explaining. That's what their bruteness consists in.

A constituent ontologist might answer as follows. Concrete particulars have ontological consituents, among them, their properties. Properties are universals. It is possible that two particulars share all their properties. Since they are not different due to a difference in properties, there must a further ontological factor that accounts for their difference.

This sketch of an answer won't cut any ice with a certain nominalist of our acquaintance. He will presumably deny both that concrete particulars have ontological constituents, and that there are any universals. He may even go so far as to claim that the very idea of an ontological constituent is senseless. He will take our first question as a pseudo-question that rests on false assumptions.

Our nominalist will say something similar about the first question. 'Only if one starts with the assumption that individuals have ontological constituents, that among these are properties, and that these are universals, will one have the problem of explaining why the individual is an individual and not a collection or conjunction of universals. The assumptions are false, so the problem is pseudo.'

Future Individuals and Haecceities

According to a wisecrack of Schopenhauer, the medievals employed only three examples: Socrates, Plato, and an ass. In keeping with this hoary if not 'asinine' tradition, I too in my capacity as humble footnoter to Plato shall employ Socrates as my example. To point out the obvious: he stands in for any concrete individual whatsoever, animate or inanimate.

I have been arguing (drawing on the work of the late Barry Miller with whom I was privileged to have enjoyed a lengthy correspondence) that before Socrates came to be there was no such property as identity-with-Socrates. The astute Franklin Mason objects:

If there is no such thing as Socrates' identity before he came to be, it would seem that there's no such thing as his identity after he ceases to be. If we need the man Socrates if we are to speak about him, then we can't do so either before or after he exists. But clearly we can now speak of Socrates though he is long since dead. Thus we don't need the man to speak of the man, and so whatever reason we had to deny the existence of haecceities that predate the things to which they attach collapses.

Socrates came to exist in 470 B.C. So we can say:

1. It is now the case that Socrates did exist.

From this it follows that

2. It was the case (e.g. in 470 B.C.) that Socrates does exist.

Mason seems to think that from (2) one can also validly infer

3. It was the case (e.g.. in 472 B.C.) that Socrates will exist.

But if I am right, the second inference fails. For if I am right, before Socrates came to exist, not only was there no Socrates, there was no singular or de re possibility of Socrates' existing. At most there was the general possibility that someone come to have the properties that Socrates subsequently had.

To appreciate that the inference from (2) is invalid, consider a parallel argument. Suppose I promise Tom that I will buy him a book for his birthday. On the morning of his birthday I spy a first-edition copy of On the Road in a book store and I buy it. Once the purchase has been made we can say:

1*. It is now the case that a copy of OTR was selected for Tom.

From this it follows that

2*. It was the case that a copy of OTR is selected for Tom.

But until I bought the book on the morning of Tom's birthday I had no idea what I would buy. So before I bought the book no one was entitled to say

3*. It was the case that a copy of OTR will be selected for Tom.

The most one would be entitled to say is

4. It was the case that a book will be selected for Tom.

Just as (3*) does not follow from (2*), (3) does not follow from (2).

Only present and past actual individuals are genuine individuals. Future 'individuals,' not having yet come into existence, are not genuine individuals.

REFERENCE: Barry Miller, "Future Individuals and Haecceitism," Review of Metaphysics 45 (September 1991), 3-28, esp. 10-11.

Does Classical Theism Require Haecceitism?

Haecceitism is the doctrine that there are haecceities. But what is an haecceity?

Suppose we take on board for the space of this post the assumptions that (i) properties are abstract objects, that (ii) they can exist unexemplified, and that (iii) they are necessary beings. We may then define the subclass of haecceity properties as follows.

A haecceity is a property H of x such that: (i) H is essential to x; (ii) nothing distinct from x exemplifies H in the actual world; (iii) nothing distinct from x exemplifies H in any metaphysically possible world.

So if there is a property of Socrates that is his haecceity, then there is a property that individuates him, and indeed individuates him across all times and worlds at which he exists: it is a property that he must have, that nothing distinct from him has, and that nothing distinct from him could have. Call this property Socrateity. Being abstract and necessary, Socrateity is obviously distinct from Socrates, who is concrete and contingent. Socrateity exists in every world, but is exemplified (instantiated) in only some worlds. What's more, Socrateity exists at every time in every world that is temporally qualified, whereas Socrates exist in only some worlds and only at some times in the worlds in which he exists.

Now suppose you are a classical theist. Must you accept haecceitism (as defined above) in virtue of being a classical thesist? I answer in the negative. Franklin Mason answers in the affirmative. In a comment on an earlier post, Mason gives this intriguing argument into which I have interpolated numerals for ease of reference.

[1] When God created the world, he knew precisely which individuals he would get. Thus [2] he didn't need to have those very individuals in front of him to know which ones they were. Thus [3] there must be a way to individuate all possible individuals that in no way depends upon their actual existence. [4] Such a thing is by definition a haecceity. Thus [5] there are haecceities.

I don't anticipate any disagreement with Mason as to what an haecceity is. We are both operating with the Plantingian notion. We disagree, however, on (i) whether there are any haecceities and (ii) whether classical theism is committed to them. In this post I focus on (ii). In particular, I will explain why I do not find Mason's argument compelling.

My reservations concern premise [1]. There is a sense in which it is true that when God created Socrates, he knew which individual he would get. But there is also a sense in which it is not true. So we need to make a distinction. We may suppose, given the divine omniscience, that before God created Socrates he had before his mind a completely determinate description, down to the very last detail, of the individual he was about to bring into existence. In this sense, God knew precisely which individual he would get before bringing said individual into existence. Now either this description is pure or it is impure.

A pure description is one that includes no proper names, demonstratives or other indexicals, or references to singular properties. Otherwise the description is impure. Thus 'snubnosed, rationalist philosopher married to Xanthippe' is an impure description because it includes the proper name 'Xanthippe.' 'Snubnosed, rationalist, married philosopher,' by contrast, is pure. (And this despite the fact that 'married' is a relational predicate.) Pure descriptions are qualitative in that they include no references to specific individuals. Impure descriptions are nonqualitative in that they do include references to specific individuals.

Now if God has before his mind a complete pure description of the individual he wills to create then it could apply to precisely one individual after creation without being restricted to any precise one. (Cf. Barry Miller, "Future Individuals and Haecceitism," Review of Metaphysics 45, September 1991, p. 14) This is a subtle distinction but an important one. It is possible that Socrates have an indiscernible twin. So the complete description 'snubnosed, rationalist philosopher, etc.' could apply to precisely one individual without applying to Socrates. This is because his indiscernible twin would satisfy it just as well as he does. The description would then apply to precisely one individual without being restricted to any precise one. So there is a clear sense, pace Mason, in which God, prior to creation, would not know which individual he would get. Prior to creation, God knows that there will be an individual satisfying a complete description. But until the individual comes into existence, he won't know which individual this will be.

Creation is not the bestowal of existence upon a a pre-existent, fully-formed, wholly determinate essence. It is not the actualization of a wholly determinate mere possible. There is no individual essence or haecceity prior to creation. Creation is the creation ex nihilo of a a new individual. God creates out of nothing, not out of pre-existent individual essences or pre-existent mere possibles. Thus the very individuality of the individual first comes into being in the creative act. Socrates' individuality and haecceity do not antedate (whether temporally or logically) his actual existence.

Mason would have to be able rationally to exclude this view of creation, and this view of the relation of existence and individuality, for his argument to be compelling. As it is, he seems merely to assume that they are false.

Could God, before creation, have before his mind a complete impure description, one that made reference to the specific individual that was to result from the creative act? No, and this for the simple reason that before the creative act that individual would not exist. And therein lies the absurdity of Plantingian haecceities. The property of identity-with-Socrates is a nonqualitative haecceity that make essential reference to Socrates. Surely it is absurd to suppose that that this 'property' exists at times and in possible worlds at which Socrates does not exist. To put it another way, it is absurd to suppose that this 'property' could antedate (whether temporally or logically) the existence of Socrates.

We are now in a position to see why Mason's argument is not compelling. If [1] is true, then [2] doesn't follow from it. And if [2] follows from [1], then [1] is false. Thus [1] conflates two distinct propositions:

1a. When God created the world, he knew precisely which pure complete descriptions would be satisfied.

1b. When God created the world, he knew precisely which individuals would exist.

(1a) is true, but it does not entail

2. God didn't need to have those very individuals in front of him to know which ones they were.

(1b) entails (2), but (1b) is false.

I conclude that classical theism does not entail haecceitism. One can be such a theist without accepting haecceities.

C. J. F. Williams’ Analysis of ‘I Might Not Have Existed’

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.

The Rabbit of Real Existence and the Empty Hat of Mere Logic

Consider again this curious piece of reasoning:

1. For any x, x = x. Ergo:
2. a = a. Ergo:
3. (Ex)(x = a). Ergo:
4. a exists.

This reasoning is curious because it seems to show that one can deduce the real existence of an individual a from a purely formal principle of logic, the Law of Identity. And yet we know that this cannot be done. We know that the rabbit of real existence cannot be pulled from the empty hat of mere logic. Since the argument cannot be sound, it must be possible to say where it goes wrong. (It is a strange fact of philosophical experience that arguments that almost all philosophers reject nevertheless inspire the wildest controversy when it comes to the proper diagnosis of the error. Think of the arguments of Zeno, Anselm, and McTaggart.)

The move from (1) to (2) appears to be by Universal Instantiation. One will be forgiven for thinking that if everything is self-identical, then a is self-identical. But I say that right here is a (or the) mistake. To move from (1) to (2), the variable 'x' must be replaced by the substituend 'a' which is a constant. Now there are exactly three possibilities:

Either 'a' refers to something that exists, or 'a' refers to something that does not exist or 'a' does not refer at all. On the third possibility it would be impossible validly to move from (2) to (3) by Existential Generalization. The same goes for the second possibility: if 'a' refers to a Meinongian nonexistent object, then one could apply existentially-neutral Particular Generalization to (2), but not Existential Generalization. This leaves the first alternative. But if 'a' refers to something that exists, then right at this point real existence has been smuggled into the argument.

I hope the point is painfully obvious. One cannot move from (1) to (2) by logic alone: one needs an extralogical assumption, namely, that 'a' designates something that exists. To put it another way, one must assume that the domain of quantification is not only nonempty but inhabited by existing individuals. After all, (1) is true for every domain, empty or not. (1) lacks Existential Import. The truth of (1) is consistent with there being no individuals at all.

Let's now consider Peter's supposed counterexample to the principle that if p entails q and p is necessary, then q is also necessary. He thinks that the above argument shows that there are cases in which necessary propositions entail contingent ones. Thus he thinks that the conjunction of (1) and (2) entails (3), but that (3) is contingent.

Well, I agree that if we are quantifying over a domain the members of which are contingent individuals, then (3) is contingent. But surely the conjunction of (1) and (2) is also contingent. For the conjunction of a necessary and a contingent proposition is a contingent proposition. Now of course (1) is necessary. But (2), despite appearances, is contingent. For if 'a' designates a contingent individual, then it designates an individual that exists in some but not all worlds, and in those worlds in which a does not not exist it is not true that a = a.

In the worlds in which a exists, a is essentially a. But a is not necessarily a because there are worlds in which a does not exist.

What accounts for the illusion that if (1) is necessary, then (2) must also be necessary? Could it be the tendency to forget that while 'x' is a variable, 'a' is an arbitrary constant?

Deducing John McCain from the Principle of Identity

What, if anything, is wrong with the following argument:

   1. (x)(x = x) (Principle of Identity)
   Therefore
   2. John McCain = John McCain (From 1 by Universal Instantiation)
   Therefore
   3. (Ex)(x = John McCain) (From 2 by Existential Generalization)
   Therefore
   4. John McCain exists. (From 3 by translation into ordinary idiom)

The initial premise states that everything is identical to itself, that nothing is self-diverse. Surely this is a necessary truth, one true no matter what, or in the jargon of possible worlds: true in every (broadly logically) possible world.

(2) follows from (1) by the intuitively clear inference rule of Universal Istantiation. Surely, if everything is self-identical, then John McCain is self-identical. The inferential move from (2) to (3) is also quite obvious: if McCain is self-identical, then something is identical to McCain. But (3) is just a complicated way of saying that John McCain exists. So we get the surprising result that the existence of John McCain is validly deducible from an a priori knowable necessary truth of logic!

You understand, of course, that the argument is not about John McCain: it is about any nameable entity. Supposedly, Wilhelm Traugott Krug (1770-1842) once demanded of Hegel that he deduce Herr Krug's pen. If we name that pen 'Skip,' we can then put that name in the place of 'John McCain' and run the argument as before.

There is one premise and three inferences. Does anyone have the chutzpah to deny the premise? Will anyone make bold to question inference rules U.I. and E.G.? And yet surely something has gone wrong. Intuitively, the existence of a contingent being such as McCain cannot be deduced from an a priori knowable necessary truth of logic. For that matter, the existence of a necessary being such as God cannot be deduced from an a priori knowable necessary truth of logic. Surely nothing concrete, not even God, is such that its existence can be derived from the Law of Identity.

So what we have above is an ontological argument gone wild whereby the rabbit of real existence is pulled from the empty hat of mere logic!

St. Bonaventura said that if God is God, then God exists. If such reasoning does not work in the case of God, then a fortiori it does not work in the case of McCain or Herr Krug's pen.

Note that (1) is necessarily true. (It doesn't just happen to be the case that each thing is self-identical.) If (2) follows immediately from (1), (2) is also necessarily true. And if (2) is necessarily true, then (3) is necessarily true. And the same holds for (4). But surely it is not the case that, necessarily, John McCain exists. He cannot be shown to exist by the above reasoning, and he certainly cannot be shown to necessarily exist by it.

So what went wrong? By my count there are three essentially equivalent ways of diagnosing the misstep.

A. One idea is that the argument leaves the rails in the transition from (3) to (4). All that (3) says is that something is identical to John McCain. But from (3) it does not follow that John McCain exists. For the something in question might be a nonexistent something. After all, if something is identical to Vulcan, you won't conclude that Vulcan exists. To move validly from (3) to (4), one needs the auxiliary premise:

3.5 The domain of quantification is a domain of existents only.

Without (3.5), John McCain might be a Meinongian nonexistent object. If he were, then everything would be logically in order up to (3). But to get from (3) to (4) one must assume that one is quantifying over existents only.

But then a point I have been hammering away at all my philosophical life is once again thrown into relief: The misnamed 'existential' quantifier, pace Quine, does not express existence, it presupposes existence!

B. Or one might argue that the move from (1) to (2) is invalid. Although (1) is necessarily true, (2) is not necessarily true, but contingently true: it is not true in possible worlds in which McCain does not exist. There are such worlds since he is a contingent being. To move validly from (1) to (2) a supplementary premise is needed:

1.5 'John McCain' refers to something that exists.

(1.5) is true in some but not all worlds. With this supplementary premise on board, the argument is sound. It also loses the 'rabbit-out-of-the-hat' quality. The original argument appeared to be deducing McCain from a logical axiom. But now we see that the argument made explicit does no such thing. It deduces the existence of McCain from a logical axiom plus a contingent premise which is indeed equivalent to the conclusion.

C. Finally, one might locate the error in the move from (2) to (3). No doubt McCain = McCain, and no doubt one can infer therefrom that something is identical to McCain. But this inferential move is not existential generalization, if we are to speak accurately and nontendentiously, but particular generalization. On this diagnosis, the mistake is to think that the particular quantifier has anything to do with existence. It does not. It does not express existence, pace Quine, it expresses the logical quantity someness.

In sum, one cannot deduce the actual existence of a contingent being from a truth of logic alone. One needs existential 'input.' It follows that there has to be more to existence than someness, more than what the 'existential' quantifier expresses. The thin conception of existence, therefore, cannot be right.

Now let me apply these results to what Peter Lupu has lately been arguing. Here he argues:

(i) (x)(x=x);

(ii) a=a, for any arbitrarily chosen object a; (from (i))

(iii) (Ex)(x=a); (from (ii) by existential generalization);

Now, (i) is necessary, but (iii) is contingent. Yet (i) entails (iii) via (ii), which is also necessary. So I simply do not see how the principle (1*) which you and Jan seem to accept applies in modal logics that include quantification plus identity.

Peter thinks he has a counterexample to the principle that if p entails q, and p is necessary, then q is also necessary. For he thinks that *(x)( x = x)*, which is necessary, entails *(Ex)(x = a)*, which is contingent.

But surely if *a = a* is necessary, i.e. true in all worlds, then *(Ex)(x = a)* is necessary as well.

The mistake in Peter's reasoning comes in with the move from *Necessarily, (x) (x = x)* to *Necessarily, a = a*. For surely it is false that in every possible world, a = a. After all, there are worlds in which a does not exist, and an individual cannot have a property in a world in which it doesn't exist. One must distinguish between essential and necessary self-identity. Every individual is essentially (as opposed to accidentally) self-identical: no individual can exist without being self-identical. But only some individuals are necessarily self-identical, i.e, self-identical in every world. Socrates, for example, is essentially but not necessarily self-identical: he is self-identical in every world in which he exists (but, being contingent, he doesn't exist in every world). By contrast, God is both essentially and necessarily self-identical: he is self-identical in every world, period (because he is a necessary being).

An Argument for Direct Reference

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.

Can the Chariot Take Us to the Land of No Self?

An abbreviated version of the following paper was published under the same title in The Proceedings of the Twenty-First World Congress of Philosophy, vol. 9, ed. Stephen Voss (Ankara, Turkey), 2006, pp. 29-33.

……………….

According to Buddhist ontology, every (samsaric) being is impermanent, unsatisfactory, and devoid of self-nature. Anicca, dukkha, anatta: these are the famous three marks (tilakkhana) upon which the whole of Buddhism rests. I would like to consider a well-known Buddhist argument for the third of these marks, that of anatta, an argument one could call ‘The Chariot.’ The argument aims to show that no (samsaric) being is a self, or has self-nature, or is a substance. My thesis will be that, successful as this argument may be when applied to things other than ourselves, it fails when applied to ourselves.

Continue reading “Can the Chariot Take Us to the Land of No Self?”

Self-Reference and Individual Concepts

The following can happen. You see yourself but without self-recognition. You see yourself, but not as yourself. Suppose you walk into a room which unbeknownst to you has a mirror covering the far wall. You are slightly alarmed to see a wild-haired man with his fly open approaching you. You are looking at yourself but you don't know it. (The lighting is bad, you've had a few drinks . . . .) You think to yourself

1. That man has his fly open!
but not
2. I have my fly open!

Now these propositions — assuming they are propositions — are obviously different. For one thing, they have different behavioral consequences. I can believe the first without taking action with respect to my fly, or any fly. (I'm certainly not going to go near the other guy's fly.) But if I believe the second I will most assuredly button my fly, or pull up my zipper.

So it seems clear that (1) and (2) are different propositions. I can believe one without believing the other. But how can this be given the plain fact that 'that man' and 'I' refer to the same man? Both propositions predicate the same property of the same subject. So what makes them distinct propositions?

I know what your knee-jerk response will be. You will say that, while 'I' and 'that man' have the same referent, they differ in sense just like 'Hesperus' and 'Phosphorus.' Just as one can believe that Hesperus is F without believing that Phosphorus is F despite the identity of the two, one can believe that (1) without believing that (2) despite the fact that the subject terms are coreferential.

The trouble with this response is that it requires special 'I'-senses, and indeed a different one for each user of the first-person singular pronoun. These go together with special 'I'-propositions which are a species of indexical proposition. When I believe that I am F, I refer to myself via a special Fregean sense which has the following property: it is necessarily a mode of presentation of me alone. We can also think of this 'I'-sense as an individual concept or haecceity-concept. It is a concept such that, if it is instantiated, it is instantiated (i) by me, (ii) by nothing distinct from me, (iii) and by the same person in every possible world in which it is instantiated.

But what on earth (or on Twin Earth) could this concept be, and how could I grasp it? The concept has to 'pin me down' in every possible world in which I exist. It has to capture my very thisness, or, in Latin, my haecceitas. But a better Latin word is ipseitas, ipseity, selfhood, my being a self, this one and no other. In plain old Anglo-Saxon it is the concept of me-ness, the concept of being me.

The theory, then, is that my awareness that

3. I am that man!

consists in my awareness that the concept expressed by 'I' and the concept expressed by 'that man' are instantiated by one and the same individual. But this theory is no good because, even if my use of 'I' expresses an haecceity-concept, that is not a concept I can grasp or understand. Maybe God can grasp my haecceity, but I surely can't. Individuum ineffabile est said the Scholastics, echoing Aristotle. No finite mind can 'eff' the ineffable. The individual in his individuality, in his very haecceity and ipseity, is ineffable.

Self-reference is not routed though sense, however things may stand with respect to other-reference. When I refer to myself using the first-person singular pronoun, I do not refer to myself via a Fregean sense.

So here is the problem expressed as an aporetic pentad:

a. (1) and (2) express different Fregean propositions.
b. If two Fregean propositions are different, then they must differ in a constituent.
c. The difference can only reside in a difference in subject constituents.
d. The subject constituent of (2) is ineffable.
e. No sense (mode of presentation) or humanly-graspable concept can be ineffable.

This pentad is inconsistent: (a)-(d), taken together, entail the negation of (e). The only limb that has a chance of being false is (a). One could say that (1) and (2), though clearly different, are not different by expressing different Fregean propositions. But then what would our positive theory have to be?