Nominalism and an Identity Theory of Predication

The Worthy Opponent comments,

We nominalists hold that 'God is good' is true when what is signified by 'God' and what is signified by 'good' are numerically one and the same thing.

I stumble over this. 

Apparently, it is The Opponent's view that a sentence such 'Socrates is good' is true when what is signified by 'Socrates' and what is signified by 'good' are numerically one and the same thing. I don't understand. 'Good,' unlike 'Socrates,' is a common term: it applies to many individuals. So there cannot be numerically one thing that both 'Socrates' and 'good' signify. 'Socrates' signifies one thing; 'good' signifies many things.

If, contrary to fact, there were only one good thing, then it would make some sense to say that 'Socrates is good,' which is by its surface grammar a predication, could be read as asserting the numerical identity of Socrates with the one good thing.  But if Socrates is good, or seated, or conversing with Theaetetus, this is only contingently the case. So how analyze the possibly true 'Socrates is not good' on the assumption that there is only one good thing?  We would have to say that Socrates is distinct from himself -- which is absurd.  For if, in actuality, Socrates is good in virtue of being identical to the one good thing, then, in the possible counterfactual situation in which he -- the very same individual --  is not good, he would have to be numerically diverse from the one good thing, namely, himself!

The same argument goes through even if there are many good things. For the Opponent's claim is that Socrates is good in virtue of being identical to one of the many good things. Call this good thing G.  The claim is that 'Socrates is good' is an identity proposition in disguise, and that its deep logical form is: S = G.

The problem is that 'Socrates is good' is contingently true. But 'S = G' is not contingently true. So the predication is not an identity proposition in disguise.  

This looks to be a pretty powerful objection.

I am assuming something that is well-nigh self-evident, but which I fear the Illustrious Opponent will deny, namely, that if a = b, then this is non-contingently the case.  In other words, I am assuming that if a = b, then there is no possible situation in which a and b both exist but are numerically distinct.

Curiously, the Opponent's theory works in one case and one case only. But he has to admit the divine simplicity.  So assume that God exists, that God is essentially good, and that God is identical to his attributes, and that therefore God alone is good in this sense. If God is identical to his attributes, then God = the one and only good thing. (Socrates is good only in an analogical and derivative sense.) In this one case, 'God is good' is an identity proposition in disguise.  

Related articles

Peter van Inwagen, "A Theory of Properties," Exposition and Critique

Review of Barry Miller, A Most Unlikely God

<i>Luke</i> 2:21: Can the Not-Yet-Existent be Named?

Is God Beyond All Being?

Comments

[The Noble Opponent]

Obviously we were meant to read the 'good' in 'God is good' as referring to the goodness which only God can have.

[Robert Allen]

I don't understand WO's claim either. There's no way you can conflate the 'is' of predication and the 'is' of identity, except in the divinity case, for the reasons given as well as the following one. Socrates presumably has other attributes, such as baldness. So we have:

S = G

S = B

Any 2 things identical to a 3rd thing are identical to each other.

Thus, B = G (Baldness is one with Goodness)??

[The Noble Opponent]

>>Thus, B = G (Baldness is one with Goodness)??

No.

William of Ockham Summa Logicae II.2

For the truth of 'This is an angel' it is not required that the common term 'angel' be really the same thing as what is given on the side of the subject, or that it be really inhere that subject, or anything of this sort. Rather, it is sufficient and requisite that the subject and predicate denote the same thing.

So ‘Socrates is bald’ does not say that Socrates is identical with baldness. Rather, ‘bald’ denotes many things, ‘Socrates’ denotes one thing. The proposition ‘Socrates is bald’ is true if a one thing falls under both terms.

Bill: >> So there cannot be numerically one thing that both 'Socrates' and 'good' signify. 'Socrates' signifies one thing; 'good' signifies many things.

The proposition ‘Socrates is good’ does not say that one thing (Socrates) is identical with many things (good things). See above.

[BV]

Opponent,

I know what you are trying to say, but it makes no sense.

You mean to say that 'Socrates is bald' asserts the identity of Socrates with one of the many bald things.

But you ignored my counterargument. Now please read carefully what I said and respond.

[Opponent]

>>The claim is that 'Socrates is good' is an identity proposition in disguise, and that its deep logical form is: S = G.

I am not saying this, because what I say does not require the relation of identity. I merely require the relation of ‘denoting’, which is a relation between a term and any object which satisfies the term. A proposition of the form ‘A is B’ is true when there is at least one object which ‘A’ denotes and ‘B’ denotes. So ‘good’ is one way of denoting God. ‘God’ is another.

>>The problem is that 'Socrates is good' is contingently true. But 'S = G' is not contingently true. So the predication is not an identity proposition in disguise.

I agree that the predication is not an identity proposition in disguise, although not for the reason you suggest, given that all identity statements (as I hold, and recently proved) are contingently true.

>> I am assuming something that is well-nigh self-evident, but which I fear the Illustrious Opponent will deny, namely, that if a = b, then this is non-contingently the case.

Well (i) it is not self-evident, as I have demonstrated, and (ii) it is not required anyway.

>> If God is identical to his attributes, then God = the one and only good thing.

There is no language which the nominalist understands for ‘is identical with his attributes’.

..it is plain that many things that are customarily said about relations are improper, some false and fantastical, just as is very broadly clear to anyone scrutinising books about these things published by the moderns, although some of these have a true interpretation, such as ‘a father is a father by paternity’, and ‘a son is a son by filiation’, and ‘a similar thing similar by similitude’, and the like.

In these locutions we do not have to suppose some thing by which a father is a father or a son a son or a similar thing similar. Nor do we have to multiply things in such locutions as "a column is to the right by to-the-rightness", "God is creating by creation, is good by goodness, is just by justice, is powerful by power", "an accident inheres by inherence", "a subject is subjected by subjection", "a suitable thing is suitable by suitability", "a chimera is nothing by nothingness", "a blind thing is blind by blindness", " a body is mobile by mobility" and such other innumerable things.

I was recently explaining this to my son, who supposes there is some thing called ‘similarity’ which all similar objects possess.

[BV]

Now this is a proper reply. Thanks.

>>A proposition of the form ‘A is B’ is true when there is at least one object which ‘A’ denotes and ‘B’ denotes.<<

Counterexample: 'Trump is penniless' is of the form 'A is B' and is such that there is at least one object which 'A' denotes (Trump) and 'B' denotes (a penniless man). But 'Trump is penniless' is false.

You need to bring identity into the picture as you did when you wrote, "We nominalists hold that 'God is good' is true when what is signified by 'God' and what is signified by 'good' are numerically one and the same thing."

You say you need the relation of denoting only, not the relation of identity. But it seems to me that I have just shown that you need the relation of (numerical) identity.

[The Noble Opponent]

>>You say you need the relation of denoting only, not the relation of identity.

No. 'some S is P' is true iff Ex [ denotes('S',x) & denotes('P',x)

Show me the identity sign.

>>Counterexample: 'Trump is penniless' is of the form 'A is B' and is such that there is at least one object which 'A' denotes (Trump) and 'B' denotes (a penniless man). But 'Trump is penniless' is false.

See above.

[BV]

>>I agree that the predication is not an identity proposition in disguise, although not for the reason you suggest, given that all identity statements (as I hold, and recently proved) are contingently true.<<

If you think that there are identity statements, what do they express? Identity, I should think.

'George Orwell is Eric Blair' is an identity statement if anything is. It expresses that these 'two' are one and the same man.

So it sounds like you are contradicting yourself. You say there is no relation of identity, but then you presuppose that there is when you say that all [true] identity statements are contingently true.

There are counterfactual situations in which Eric Blair does not adopt the pen name 'George Orwell.' But in the actual situation we use these two names to refer to one and the man in every counterfactual situation in which Blair/Orwell exists.

I don't see that you have shown the contingency of identity.

[BV]

I shall have to rename you the Recalcitrant Opponent.

Seems now you are conflating identity with the sign for identity.

>>'some S is P' is true iff Ex [ denotes('S',x) & denotes('P',x)

Show me the identity sign.<<

Show me the sign for predication in 'Fa.' There is no separate sign for it. The 'is' of predication is represented by the immediate juxtaposition of 'F' and 'a' in that order.

Similarly, that the same x is denoted by 'S' and 'P' is indicated by the brackets. So, while '=' does not occur in the formula, there is nevertheless a sign for the identity of the values of the bound variable.

[The Noble Opponent]

Before we discuss this any more can I suggest you re-read chapter 6 of Sommers’ The Logic of Natural Language (‘Do we need Identity’). I am certain we have discussed this before, and you mentioned that chapter. If not, I am happy to explain it in more detail. Sommers argues for ‘anti-relationism’. There is little evidence that philosophers before Frege distinguished between the ‘is’ of identity and the ‘is’ of predication, and Sommers argues that it the distinction is merely an artefact of the category distinction between names and predicates.

If you haven’t read it, I will post something about it at Tuggy’s place.

>>If you think that there are identity statements, what do they express? Identity, I should think.
They do not express a relation. There is no relation of ‘identity’, except a grammatical one.

[The Noble Opponent]

>>But in the actual situation we use these two names to refer to one and the [same] man in every counterfactual situation in which Blair/Orwell exists.<<

If it is true that 'Orwell' designates Blair (and I agree it does) then everything follows as you say it does. I also agree that, by convention, 'Hesperus' designates Venus.

What you have not shown is that if 'a' designates a, and a=b, then it logically follows that 'a' designates b. There is a step in Kripke's argument that you keep jumping over without noticing. I have pointed this out many times, but you fail to grasp it.

[BV]

Opponent,

You failed to respond in any intelligible way to the counterexample @ 11:38 supra.

[The Noble Opponent]

>>You failed to respond in any intelligible way to the counterexample @ 11:38 supra.

Your 'counterexample' was this:

Counterexample: 'Trump is penniless' is of the form 'A is B' and is such that there is at least one object which 'A' denotes (Trump) and 'B' denotes (a penniless man). But 'Trump is penniless' is false.

I did respond above. It is not a counterexample. Perhaps my point would have been clearer if I had added the word ‘both’, i.e.
>>A proposition of the form ‘A is B’ is true when there is at least one object which BOTH ‘A’ denotes and ‘B’ denotes.<<

I am struggling to understand how you did realise that this was what was meant. There is a sailing exam where you are the skipper giving orders to a crew, where the crew are instructed to deliberately misunderstood the orders. Emphasis on ‘deliberate’. The crew clearly understand what was intended, but ignore this, thus violating the charity principle.

Did you honestly not realise that ‘both’ was intended? I then added :

>> 'some S is P' is true iff Ex [ denotes('S',x) & denotes('P',x)

where the ‘both’ is made explicit, and laid on with a trowel and extra lard. Writing with some frustration!

[The Noble Opponent]

Ah perhaps I am beginning to see your point. Are you saying that a predication of the form ‘A is B’ is really two separate predications, plus identity. Thus ‘some x is A and y is B and x=y’. Is that your point? Then the predication ‘‘some x is A’ is itself two predications plus identity, and so on to infinity?

[BV]

Well, you must say what you mean (and mean what you say). My counterexample was indeed a CE to what you actually said.

>>A proposition of the form ‘A is B’ is true when there is at least one object which BOTH ‘A’ denotes and ‘B’ denotes.<<

Fine, but that is equivalent to saying that 'A' and 'B' denote numerically the same object.

You have had to bring identity back into the discussion which seems to contradict what you say above @7:43, namely, that you don't need identity but only denotation.

What you are saying is that the denotatum of 'A' is identical to one of the denotata of 'B.' So 'Al is fat' is true because the denotatum of 'Al' is identical to one of the denotata of 'fat.' Call this object 'Fatso.' So you are committed to saying that Al = Fatso is the truth-maker of 'Al is fat.'

But Al might not have been fat. So you are committed to saying that Al might not have been identical to Fatso, i.e. Al -- which is absurd.

[Opponent]

>>Fine, but that is equivalent to saying that 'A' and 'B' denote numerically the same object.

You have your finger on a very interesting paradox.

[Richard]

May I suggest that the proposition, “Socrates is good” is but “Socrates is a good being,” lightly abbreviated?

The latter statement is true when that which is signified by “Socrates” and that which is signified by “a good being” are numerically one and the same thing, i.e., identical. That is, Socrates is identical with the good being which he is. Again, Socrates is identical with that one of the (at least potentially) many good things which the “a good being” at hand signifies.

If I am right, Bill, you are right that there is no possible situation in which Socrates and the good being which Socrates is both exist but are numerically distinct. But the good being which Socrates is can cease being good without ceasing to be Socrates, without Socrates ceasing to be that being. Accidental change is consistent with necessity of identity.

[BV]

Richard writes,

>>But the good being which Socrates is can cease being good without ceasing to be Socrates, without Socrates ceasing to be that being.<<

How? Can you explain it?

The pre-theoretical datum is that Socrates can cease being good. What needs to be explained is how that can happen give the theory that Socrates is good in virtue of being identical to the good thing that he is.

[Richard]

Two preliminaries, the first of which is: I think it that the translation of “Socrates is good” should have been “Socrates is a good human being” rather than “Socrates is a good being,” for the goodness in question in the original proposition is, I would take it, that of a human being.

The second preliminary: on the one hand, Socrates is the good human being that he is and, on the other, the good human being that Socrates is is Socrates. If that isn’t enough to establish that Socrates and the good human being that he is are identical, I don’t know what would be.

Preliminaries taken care of, I don’t think it is quite right to say that Socrates is good in virtue of being identical to the good human being that he is. I’d put it rather that Socrates is good in virtue of his possessing the attributes that make a human being good. And so too the good human being that Socrates is is good in virtue of possessing the attributes that make a human being good.

[BV]

So you bring in attributes. Very good. But then you veer from the nominalism the worthy opponent is espousing.