In Logical Properties, a book I thought would have had a greater impact than it has had in philosophy, Colin McGinn endorses that identity is (i) unitary, (ii) indefinable, (iii), fundamental, and (iv) a genuine relation. There are at least two arguments I want to consider as a response to McGinn's four theses. If identity is indefinable, then there shouldn't be arguments offered for or against it. McGinn uses his chapter to argue that identity has these four fundamental components, one of which is its indefinability. First, McGinn endorses the idea that identity is unitary. Suppose that the identity relation, R, is between the relata, x and y. Identity is unitary when it is:
the relation that x has to y when x is nothing other than y, when there is no distinction between x and y, and when x is y.
Identity admits of no qualification or variation from the way that we have defined it. Is it possible to dislodge the belief that identity is unitary, that it requires no qualification? I think that there is reason to qualify identity in at least one way (if not more). If identity is unitary, then there should be no difference between different forms of identity statements. Consider the following: '4 = 4'. This is clearly an identity statement where the number 4 is equal to the number 4, but it is a different kind of identity statement than the following: 'the red house at the corner of Sunnyside and Arapeen = the red house at the corner of Sunnyside and Arapeen'. Let's begin with an obvious difference between identity statements. The first statement is a mathematical identity statement, and the second is an empirical proposition. Mathematical and empirical propositions may have unique conditions that make them identity statements. For example, it is a priori true that 4 is 4, and it is a posteriori true that the red house at the corner of Sunnyside and Arapeen is the red house at the corner of Sunnyside and Arapeen. If the two identity statements are identical under different conditions, then there is a difference between different forms of identity. That seems to go against McGinn's criterion of unity.
Is there anything else that distinguishes the two propositions? It seems that the identity of the former is stronger than the latter. If there is a difference in different forms of identity, then that shows there is a distinction between the different identity relations. For example, the truths of mathematics are not bound by time and spatial constraints in the same way that the red house is bound by them. No matter where we find ourselves in the universe 4 will always equal 4, but the red house at the corner of Sunnyside and Arapeen will not always stand as identical to itself. For instance, we could burn the house down. No longer will the red house be the red house, but it will be a pile of rubble that was the red house. Someone may claim that the pile of rubble is different (significantly so) than the red house. The pile of rubble used to be the red house. The red house has changed into a pile of burning embers, and the red house cannot be identical with the pile. Is this possible for the number 4? The number 4 will always be the number 4, and nothing else. We could uphold some sort of fantastic social convention where the number 4 is actually the number 5, but McGinn correctly eliminates this option because this would be more like a language game (family resemblance concept). At no point can we set the number 4 ablaze. Even if we could set fire to the number 4, who would believe that the number 4 had become a pile of rubble? There is clearly a distinction between identity statements. If this is the case, then we have no reason to uphold that identity is a unitary concept. In fact, we may have different conceptions of identity based upon our psychological make-up. (This is where we pick up Mill's System of Logic and read it -- seriously.) A second objection challenges McGinn's claim that identity is a genuine relation. Toward the end of the chapter (pp. 12-13), McGinn tries to show that he can undermine Wittgenstein's belief that identity is a pseudo-relation. I think this is gravely mistaken. Wittgenstein's point is not that identity is a pseudo-relation, in any rich sense. Wittgenstein merely wants to say that identity is nonsense. By nonsense, Wittgenstein seems to mean that there is nothing informative that such a proposition can tell us. Identity relations, tautologies, and contradictions are all nonsense for the early Wittgenstein. What can "the red house is red" really tell us? According to Wittgenstein, this is a ridiculous claim. Likewise, saying that "the red house is identical to that red house" is even more ridiculous. The sentence says nothing at all. Mightn't we extend the notion of nonsense to similar concepts than identity relations, tautologies, and contradictions? Possibly, but that I am working on in a larger paper. For now, it is enough to say that McGinn has mischaracterised Wittgenstein's claim. After I read McGinn's chapter on "Identity" the first time about twenty years ago, I had no quarrels with his 'endorsements'. After further review, I have reason to doubt that identity is what McGinn has argued for. I have other arguments objecting to the two remaining concepts, but I will leave that for another time. The point of this entry is to question what to McGinn might seem like a harmless chapter.