Topics Identity

Question (ill)Logical question: One formulation of the law of Identity states that a thing is equal to itself (e.g., "A=A"). The "thing" must always be represented (with a letter, a word, a number, a picture, etc.) in order to be communicated. These representations will have physical, measurable properties, and no two of them -- for instance, two spoken or written "A"s -- will have exactly identical physical properties. If you attempt to circumvent this mirror image comparison with, for example, an "A" with an arrow doing a U-turn back upon itself, you still must make a mental comparison, and that comparison takes time, and as Heraclitus famously puts it, you can't step in exactly the same river twice (in other words, the first thought "A" is gone by the time you think of its twin). So, without sprawling this out further with more examples, why doesn't it make more sense to assume that "a thing is NOT equal to itself"? I am probably just talking around some hackneyed epistemological issue. Can anyone sort out my fuzzy thinking a little (with a minimum of truth tables)?

Accepted:
June 30, 2006

Comments

You need here the distinction between a thing and its name(s) or representation(s).

When someone says or writes "Mozart = Mozart," the two sound tokens or ink tokens are indeed subtly different. And even if somehow they were not, they would still be different in that one spoken "Mozart" precedes the other in time and one written "Mozart" is to the Southwest of the other.

But the law of identity is not supposed to be about these name tokens, but about what they refer to. That referent, the entity being named by each of these tokens, is exactly the same: the man Wolfgang Amadeus Mozart.

That it's the referents, rather than the names one has in mind here is more easily appreciated by considering an "equation" with different signs on each side. Thus consider:

Wolfgang Amadeus = Mozart

Someone asserting this equation is not making the grotesque error of equating the two sound or ink tokens. Rather, she's claiming that these tokens refer to the very same thing.