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Wednesday, July 20, 2011

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>> 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.'

This is William of Ockham’s position, almost exactly. Note, however, his condition that the ontological constituents must have a real unity less than numerical unity (unitas realis minor unitate numerali). Only then, according to Ockham, does the problem arise, but he denies there is any such unity. It’s not that he is denying ‘ontological constituents’, rather, he is denying that such constituents, if there be any, have any kind of unity at all. (Although it’s hard to see how there could be a real constituent without it having some form of unity).

>> The ontological problem of individuation is actually two problems.

I agree with the two that you list, but you omit a third, which goes to the heart of the meaning of ‘individual’ (i.e. indivisible). Every species higher than the individual can be divided into ‘subjective parts’ http://www.logicmuseum.com/wiki/Subjective_part such that the ‘whole’ (i.e. the universal) can be truly predicated of the part. Thus the universal ‘animal’ can be divided into man, giraffe, insect etc, of each of which ‘animal’ can be truly be predicated. Similarly ‘man’ can be divided into Socrates, Plato, Rupert Murdoch, etc, of each of which ‘man’ can be truly be predicated. But you can’t divide Socrates into similar parts. The Porphyrian tree comes to a stopping point with ‘individuals’. The individual is individuum, incapable of further subdivision. It is the most specific species.

This ‘indivisibility’ criterion is closely related to your second problem “of what makes an individual an individual as opposed to a member of some other category of entity”. The answer to this could be, that an individual is not the same category of entity as genus or species precisely because of this indivisibility. Or: it is a special type of species, namely the most specific species.

>>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.

Who would that ‘certain nominalist’ be, I wonder :-)

Thanks for the response, Edward. I wasn't trying to give Ockham's actual position, but merely to formulate the strongest objection I could think of - along the lines of earlier remarks of yours -- to the position I favor. But I am glad I hit upon Ockham's actual view.

But the bit about real unity less than numerical unity is not very clear to me. Aren't two distinct universals numerically different from each other? And why should the problem arise only then? This is unclear.

You are the 'certain nominalist.' Did I fairly represent your position?

Indivisibility is not a problem but a criterion. So I don't think there are three subproblems here, but two.

Avoiding the obscure scholastic jargon, I would say that an individual is an entity that has properties and stands in relations but is not itself a property or a relation. Individuals, unlike properties, are impredicable entities. You can't predicate Socrates of anything, but you can predicate properties of him.

Now isn't that much more clear than what those scholastic dudes are saying? (Of course, I am being mildly provocative. There is the off-chance that I am missing something.)

You say that 'animal' is predicable of the species giraffe, etc. I don't get that. Surely no species is an animal!

It has long seemed to me that these scholastic dudes were not hip to Frege's Eigenschaft-Merkmal distinction. A property of a concept is not the same as a mark of a concept. A property predicable of a concpet is not included within its content. Thus *male* is a mark of *bachelor,* but *male* cannot be predicated of the concept *bachelor* No concept has a penis!

Maybe I'm missing something.

>>But the bit about real unity less than numerical unity is not very clear to me. Aren't two distinct universals numerically different from each other? And why should the problem arise only then? This is unclear.

I think Ockham means that the only things that are numerically different are the predicates corresponding to the universals – since there are no such things as universals. Once we allow an additional sort of unity to the universals themselves, as entities subsisting outside the soul, then we get the problem of individuation. But Ockham disagrees with that, and the problem dissolves.

>>Indivisibility is not a problem but a criterion. So I don't think there are three subproblems here, but two.

I should have phrased this better. There is a definition of ‘individual’ as ‘indivisible into subjective parts’, which you did not mention. This is not really a criterion but rather a definition. Being an ‘individual’ simply is being that. Corresponding to this there is the problem of explaining why certain things do have this feature of being indivisible into subjective parts. (Assuming this is intelligible in the first place).

>>Avoiding the obscure scholastic jargon, I would say that an individual is an entity that has properties and stands in relations but is not itself a property or a relation. Individuals, unlike properties, are impredicable entities. You can't predicate Socrates of anything, but you can predicate properties of him.

This is a bit Fregean, and presupposes a logical distinction that the scholastics didn’t really make.

>>Now isn't that much more clear than what those scholastic dudes are saying? (Of course, I am being mildly provocative. There is the off-chance that I am missing something.)

See below.

>>You say that 'animal' is predicable of the species giraffe, etc. I don't get that. Surely no species is an animal!
It has long seemed to me that these scholastic dudes were not hip to Frege's Eigenschaft-Merkmal distinction. A property of a concept is not the same as a mark of a concept. A property predicable of a concpet is not included within its content. Thus *male* is a mark of *bachelor,* but *male* cannot be predicated of the concept *bachelor* No concept has a penis!

Absolutely right, and I think Russell was making exactly the same point when he says “The insistence on the distinction between e[psilon – is a member of] and the relation of whole and part between classes is due to Peano, and is of very great importance to the whole technical development and the whole of the applications to mathematics. In the scholastic doctrine of the syllogism, and in all previous symbolic logic, the two relations are confounded, except in the work of Frege”. http://www.logicmuseum.com/cantor/pofmathematics.htm

I.e. the logical relation between ‘Socrates’ and ‘man’, in the predicate calculus and modern logic, is entirely different from that between ‘man’ and ‘animal’. As Russell notes, ‘the two relations are confounded’ in syllogistic logic. Does this mean the syllogistic logic is wrong, however? Why can’t we say that ‘man’ is predicated of ‘Socrates’ means that the concept ‘Socrates’ is subsumed under the concept ‘man’. And if so, how do we explain the indivisibility, i.e. the fact that there is no concept subsumed under ‘Socrates’ in the way that ‘man’ is subsumed under ‘animal’?

Indeed, if entities do have ‘ontological components’, so that Socrates = animal + rational + individuating-principle, why should there be any distinction between the relation of Socrates to ‘man’ and ‘man’ to ‘animal’? Thus animal + rational is subsumed under animal, and animal + rational + individuating-principle is subsumed under animal + rational.

Also, is there any problem of individuation at all once we express propositions in the predicate calculus, where there is an absolute and fundamental distinction between the significate of the lower-case letter in argument place, and that of the upper-case letter in predicate place? It seems to me that in order for there to be a problem in the first place, you have to ‘confound’ the two relations that Russell is talking about.

I said: Avoiding the obscure scholastic jargon, I would say that an individual is an entity that has properties and stands in relations but is not itself a property or a relation. Individuals, unlike properties, are impredicable entities. You can't predicate Socrates of anything, but you can predicate properties of him.

Ed said: This is a bit Fregean, and presupposes a logical distinction that the scholastics didn’t really make.

I say: What is specifically Fregean is the notion that properties (concepts, Begriffe) cannot be named. But I didn't go that far. If the scholastics do not distinguish between an individual and a property in such a way that an individual cannot be predicated, then their thinking is hopelessly muddled.

But I know there is more to it than this. Theirs is a weird doctrine that guys like you need to explain to the rest of us in extremely clear terms congenial to contemporary analytic types without using their mumbo-jumbo.

>>Why can’t we say that ‘man’ is predicated of ‘Socrates’ means that the concept ‘Socrates’ is subsumed under the concept ‘man’? And if so, how do we explain the indivisibility, i.e. the fact that there is no concept subsumed under ‘Socrates’ in the way that ‘man’ is subsumed under ‘animal’?<<

First of all, there is no concept expressed by 'Socrates.' That would have to be an individual concept and they don't exist any more than haecceity properties exist. And so the problem you raise is a pseudo-problem that rests on a false assumption.

The Frege- Russell view has a clear sense: the relation between S. and 'man' is different than the relation between 'man' and 'animal.' But the scholastic view seems to be a muddle. There cannot be a concept that grasps the very haecceity of Socrates. Every concept is general, even concepts that have only one instance. But S. is a singular.

THis will have to be taken up in a separate post.

I think we are talking in the same place, and that place is the chapter of Sommer's The Logic of Natural Language in the chapter called 'the two term theory'.

On the one side is Geach expounding Frege, thundering "To Frege we owe it that modern logicians almost universally accept an absolute category difference between names and predicable; this comes out graphically in the choice of letters from different founts of type for the schematic letters or variables answering to these two categories". I take it we are absolutely clear about what is meant by the 'Frege-Russell' view, yes?

On the other side, the scholastic-Aristotelian view - which seems less clear because they are generally very sloppy about use-mention distinctions. When they talk about predication, sometimes they mean the relation between predicate-word and subject-word, other times between predicate-concept and subject-concept. Other times, between two things in reality. I can't deny an element of confusion.

But what they mean is clear: a singular proposition like 'Socrates is a man' has the logical form of a universal proposition. It means something like 'everything that falls under the signification of 'Socrates' also falls under the signification of 'man'.

Or perhaps: every composite containing the ontological constituents 'man+individuating principle of Socrates' also contains the ontological constituent 'man'. Just as everything containing the constituents 'animal+rational' also contains the ontological constituent 'animal'.

It seems to me that if you buy the ontological constituent malarkey, you also have to buy the indivuating principle malarkey. And if you buy that, you have to walk out of the shop with the 'two term' theory, according to which the term 'Socrates' is equally fitted to predicate as well as subject.

>>There cannot be a concept that grasps the very haecceity of Socrates.

Well maybe not, but if you buy ontological constituents, surely you buy the concepts of such constituents. If 'man' contains the constituents 'animal' and 'rational', then surely our concept of a man contains corresponding constituent concepts. And if we are committed us to an individuating principle that distinguishes one rational animal from another, then aren't we committed to the concept of such an individuating principle? I really don't see how you can escape this.

In summary, my view is that

1. under the Frege-Russell scheme of representing propositions, there simply is no problem of individuation.

2. To get the problem, we have to buy the "ontological constituent" idea.

3. That in turn requires accepting the scholastic view that there is no fundamental logical difference between singular terms and general terms (except that singular terms have a built-in 'every').

>>It seems to me that if you buy the ontological constituent malarkey, you also have to buy the indivuating principle malarkey. And if you buy that, you have to walk out of the shop with the 'two term' theory, according to which the term 'Socrates' is equally fitted to predicate as well as subject.<<

I agree with the first sentence, without agreeing with the malarkey part. But how does constituent ontology commit one to the two-term theory?

I said: There cannot be a concept that grasps the very haecceity of Socrates.

Edward says: Well maybe not, but if you buy ontological constituents, surely you buy the concepts of such constituents. If 'man' contains the constituents 'animal' and 'rational', then surely our concept of a man contains corresponding constituent concepts. And if we are committed us to an individuating principle that distinguishes one rational animal from another, then aren't we committed to the concept of such an individuating principle? I really don't see how you can escape this.

I now say: Suppose the differentiator/individuator is a bare particular. (A thin particular in Armstrong's jargon.) Then we do indeed have a concept of that which individuates/differentiates. But this concept is general. What I deny is that we have a concept of Socrates' bare particular.

To put it another way, one can have a general concept of a nonqualitative thisness. But one cannot have a concept of this particular nonqualitative thisness.

So you are confusing two distinct questions.

What I don't get is the transition from (2) to (3). G. Bergmann didn't feel compelled to make that move.

>>Suppose the differentiator/individuator is a bare particular. (A thin particular in Armstrong's jargon.)

Can you elaborate on thin/bare particular. I'm not familiar with this technical concept.

>>What I don't get is the transition from (2) to (3).

Step (2) is the acceptance of universals as having real existence, and as being 'ontological constituents' of the subject. This in turn requires an 'individuating principle' as the ultimate differentiating constituent.

However I think your objection is that we can explain the individuating principle in terms of the 'thin particular' idea, thus blocking the move. But I need to understand this idea better. (Sorry - I no longer read much analytic philosophy, or at least not the Armstrong bits).

I wasn't asking about (2), but about the inference from (2) to (3).

>>I wasn't asking about (2), but about the inference from (2) to (3).

Correct, and I replied "I think your objection is that we can explain the individuating principle in terms of the 'thin particular' idea, thus blocking the move" meaning the move from (2) to (3).

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