A Question About Predication and Identity

Chad M. sent me a paper of his in which he illustrates the distinction between the 'is' of predication and the 'is' of identity using the following examples:

1. Joseph Ratzinger is [the] Pope

and

2. Water is H₂O

where the first sentence is proposed as an example of a predication and the second as an identity sentence.  If I were to explain the distinction, I would use these examples:

3. Joseph Ratzinger is German

and  (for consistency of subject matter)

4. Joseph Ratzinger is Pope Benedict XVI.

(2) and (4) are clearly sentences expressing strict, numerical, identity.  Identity is an equivalence relation: reflexive, symmetrical, transitive.  It is also governed by the Indiscernibility of Identicals: if x = y, then whatever is true of  x is true of y, and vice versa.  By these four tests, the 'is' in (4) is the 'is' of identity.  The 'is' in (3) expresses a different relation.  Frege would say that it is the relation of falling under: the object JR falls under the concept German.  That relation fails each of the four tests. It is not reflexive, not symmetrical, etc.

Now my problem is that I don't find (1) to be a clear example of a predication in the way that (3) is a clear example. 

Although 'The Pope' is a definite description, not a name (Kripkean rigid designator), (1) could be construed as asserting an identity, albeit a contingent identity, between the object picked out by 'JR' and the object picked out by 'the Pope.'  After all, the sentence passes the four tests, at least if we confine ourselves to the present time and the actual world.  The relation is reflexive, symmetrical, and transitive.  For example, if JR is the Pope, and the Pope is the vicar of Christ, then JR is the vicar of Christ.  Furthermore, whatever is true of JR now is also true of the Pope now, and vice versa. So the indiscernibility test is satisfied as well.

Why not then say that (1) expresses contingent identity and that the 'is' is an 'is' of identity, not of predication?  The fact that one could maintain this, with some show of plausibility, indicates that Chad's example is not a clear one.  That is my only point, actually.

I grant that the notion of contingent identity can be questioned.  How could x and y just happen to be identical?  For Kripke, identity is governed by the Necessity of Identity: if x = y, then necessarily x = y.  This has the interesting implication that if it is so much as possible that x and y are distinct, then x and y are distinct.  (Shades of the ontological argument!)

But there are philosophers who propose to speak of contingent sameness relations.  Hector Castaneda is one.  So I am merely asking Chad why he uses the puzzling and provocative (1) as illustrative of the 'is' of predication.

There is a labyrinth of deep questions lurking  below the surface, questions relevant to Chad's real concern, namely the coherence of the Trinity doctrine and its (in)coherence with the doctrine of divine simplicity. 

Related articles

The 'Is' of Identity and the 'Is' of Predication

Comments

[Chad McIntosh]

Thank you for the comment, Dr. Vallicella. Surely you are correct. (1) isn't at all a clear case of the 'is' of predication (though neither is it a clear case of identity. Your suggestion of contingent identity is an intriguing one, as I am quite warm to contingent identity, despite its unpopularity). I should no doubt amend (1) to something like (3), where it is clearly a property being ascribed (say, "Nebakanezer is regal"), rather than a title or office ("Nebakanezer is king").

I repent in dust and ashes!

[Bill Vallicella]

There are interesting questions here that I am not clear about. I agree with you that (1) is not a clear case of identity.

I wonder whether Keith Donnellan's distinction between referential and attributive uses of defeinite descriptions is relevant here.

[Peter Lupu]

Bill is right that Chad's (1) is not a clear case of identity; at least not in a Kripkean sense. But (1) may not be an identity statement at all. For if we construe the phrase 'the Pope' as a definite description, then (1) can be recast a-la Russell's analysis of definite descriptions as "there exists a unique x who is a Pope and is identical to Joseph Ratzinger." The statement as a whole is contingent; hence, the sense that (1) seems contingent. Viewing (1) in this way preempts any need to entertain the notion of contingent identity in cases of Krikean rigid designators.

[Chad McIntosh]

Dr. Vallicella, would you regard the following statements as representative of our three uses of 'is' (respectively: identity, that which we know not, predication)?

(1) Gillibrand is daughter of Polly Noonan and Douglas Rutnik
(2) Gillibrand is senator
(3) Gillibrand is democratic

[Bill Vallicella]

Peter,

No matter how we parse 'JR is the Pope' it will be contingent for the same reason that 'JR = Pope Benedict XVI' is contingent. It is not true in every world because the names flanking '=' do not have referents in every world.

The issue is whether every world in which JR exists is a world in which he is pope. The answer to that is No.

The Russellian translation occurred to me. But then it seems we should say that (1) is to be classified as an existential sentence.

[Bill Vallicella]

Chad,

I don't know what you mean by "that which we know not." Standardly, three uses of 'is' are distinguished: existential, predicative, identitative.

As for (a), for it to be good English you need a definite or indefinite article between 'is' and 'daughter.' Which do you mean:

1a. Gillibrand is a daughter of Polly Noonan and Douglas Rutnik

or

1b. Gillibrand is the daughter of Polly Noonan and Douglas Rutnick?

Same goes for (2). 'Gillibrand is a senator' clearly features the 'is' of predication. And the same goes for (3).

[Elliott]

Bill,

You noted that there are deep questions lurking below the surface. With this in mind, perhaps there is another sense of ‘is’, in addition to the existential, predicative, and identitative. There might be, for lack of a better term, an ‘is of mental and volitional progeny’. This sense of ‘is’ would transfer the essence of one thing to another thing via an intimate act of mental and volitional begetting, not by physical creation, thereby uniting the two things. The ‘is of mental and volitional progeny’ is not numerical identity, but its unity is similarly indivisible. The ‘is of mental and volitional progeny’ is not predicative or existential or sortal, either.

[Elliott]

If I may, here is an example. War and Peace is the mental and volitional progeny of Tolstoy. In one sense, the novel is distinct from him; in another sense, the novel is him. The novel is directly generated by his mind and will. The life of his mind and will exists in the story and in each character. Tolstoy pours his mind (intellectual love) and will (volitional love) into the book. His novel and his characters have the same nature insofar as each is of his mind and will. His personality pervades the book. The book is, in a sense, indivisible from him though not numerically identical to him. A literary scholar who reads War and Peace might say “This book is true Tolstoy” or "All of Tolstoy is in this book". Or he might say “Prince Andrei is Tolstoy” or “Pierre is Tolstoy” or “Tolstoy’s mind and will are present throughout this book” or “No one but Tolstoy could have written this book”.

[Chad McIntosh]

In the opening pages of More Kinds of Being: A Further Study of Individuation, Identity, and the Logic of Sortal Terms (Blackwell, 2009), E. J. Lowe distinguishes five uses of ‘is’ as a copula:

1. The ‘is’ of attribution, as in ‘Socrates is wise’ and ‘Grass is green’.
2. The ‘is’ of identity, as in ‘Napoleon is Bonaparte’ and ‘Water is H2O’.
3. The ‘is’ of instantiation, as in ‘Mars is a planet’ and ‘A horse is a mammal’.
4. The ‘is’ of constitution, as in ‘This ring is gold’ and ‘A human body is a collection of cells’.
5. The ‘is’ of existence, as in ‘The Dodo is no more’.

He says some may be reducible to others, and that one or two must be primitive. I thought this was a helpful spread.

[Elliott]

This is a good list of standard uses of ‘is’. There are other uses, which may or may not be reducible to the five that Chad noted. For example:

- The ‘is’ of analogy: The tortoise is like a tank. (Is this an example of the ‘is’ of attribution?)

- The ‘is’ of personification: The sprinter is speed personified. (attribution? instantiation?)

- The ‘is’ of assumption: The assumption is that the beach will be crowded this weekend. (attribution? none of the above?)

- The ‘is’ of purpose: This automobile is designed for high speed. (attribution? none of the above?)

- The ‘is’ of inquiry: What is knowledge? Where is Athens? (none of the above?)

- The ‘is’ of mental and volitional progeny: The 5th symphony is pure Beethoven. (relational? none of the above?)

- The ‘is’ of location: Athens is in Greece. (none of the above?)