Do we need identity?

January 31, 2017

A propos of a discussion going on at the Maverick Philosopher’s place, I revisited ‘Do we need Identity’, chapter 6 of The Logic of Natural Language, a work by the late Fred Sommers that should be on everyone’s bookshelf. As the title suggests, Sommers questions the doctrine of ‘relationism’, i.e. the view that identity is a relation, and that the verb ‘is’ functions both to connect subject and predicate, as in ‘Venus is a planet’, and to relate objects, as in ‘Hesperus is Venus’.

I summarise his argument as follows. First, the distinction between the ‘is’ of predication and the ‘is’ of identity is not obvious, otherwise philosophers would have spotted it earlier. It is sometimes attributed to Leibniz, but Sommers questions whether it is to be found in that philosopher’s writings. Second, it only seems obvious after we have accepted the category distinction made by modern logic between object words and concept words. If we agree that ‘Venus’ and ‘Hesperus’ must be represented in the syntax of modern logic by lower-case letters, we must represent them as ‘a’ and ‘b’. But then ‘a is b’ is ill-formed if we read the ‘is’ as the ‘is’ of predication. In the aptly named ‘predicate logic’, the verb ‘to be’ is swallowed up into the predicate: we must represent ‘Venus is a planet’ as ‘Fa’, where ‘F’ stands for ‘is a planet’. As Sommers ironically comments

It is therefore obvious that ‘a is b’ has the form F(a,b,) where F is the grammatical predicate which represents ‘is identical with’ or ‘is no other than’. 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.

It may still be objected that identity really is a relation, and that the modern syntax makes explicit what was there all along, but more of that later.

Ed Buckner
Ed Buckner studied and taught philosophy at the University of Bristol in England. He has a number of publications in the area of both analytic philosophy and medieval logic and philosophy. He is the author, with Jack Zupko, of Duns Scotus on Time & Existence, a translation of an early work by the philosopher-theologian Duns Scotus, with a comprehensive and detailed commentary. Now mostly retired, he curates the Logic Museum, a collection of primary sources in the history of logic.

2 thoughts on “Do we need identity?”

  1. Let me explain to everyone who does not understand what just happened. I was asking a Unitarian Ebionite someone who doesn’t believe that Jesus existed prior to his birth through Mary. I asked him if there is only one way to become a child of God. Any good Christian would say that Jesus is the only way to become a child of God. Once they answer that there’s only one way to become a child of God and that’s through Jesus. Then I asked him to clarify one more time that there is no other way to become a child of God except through Jesus. And then afterwords I was going to post John chapter 1 verse 12 which states

    12 But as many as received Him, to them He gave the right to become children of God, even to those who believe in His name,

    New American Standard Bible: 1995 update. (1995). (Jn 1:12). LaHabra, CA: The Lockman Foundation.

    What this means is that because where only in verse 12 and it says that whoever receives the logos becomes a child of God and there’s only one way to become a child of God and that’s through Jesus. Therefore any so Unitarian would have to agree would have to agree that the Logos is Jesus because there’s only one way to become a child of God in us through Jesus and in this chapter it’s saying that this logos is a way to become children of God. So it’s undeniable the logos in Chapter 1 is Jesus because if you say it’s not Jesus you’re saying there’s another way to become a child of God apart from Jesus. Unitarianism murdered right there.

  2. Interesting post, Ed. I’ve long thought that I understand treating numerical identity as a relation made enough sense – it gets the inferences right – but being hostile to all abstracta, I’m not sure I want to commit to it’s literally being a relation. You might think what makes identity statements true are just the facts about the relevant individual reality or realities.

    Whether you treat identity as a relation or not, you still have to make sense of inferences like these:

    Only John likes corn.
    That man likes corn.
    Therefore, that man is John.

    John likes chicken.
    That man doesn’t like chicken.
    Therefore, that man isn’t John.

    Both, I think, presuppose the idea of an individual (“self-identical”) being.

    Alston and Bennett point out how closely this is related to reference. You refer to a. Then you refer to b. We all understand the question: have you just referred to one thing twice (so a = b) or have you just referred to two things (so not-(a=b))? Then, we all have the concept of numerical sameness, or at least, of co-reference.

    How does Sommers deal with the obviously valid arguments above, or with Alston and Bennett’s point?

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