The following is a paper on the views of Gottlob Frege, a 19th Century German philosopher who founded modern logic and analytic philosophy. In two of his most famous works (Begriffsschrift and On Sense and Nominatum) he tried to determine what kind of thing an identity statement (like A=A or A=B) is.
In Begriffsschrift, Frege suggested identity is a relation between names or signs of objects. This means that what is expressed by something like A=B is simply that the name “A” and the name “B” both refer to the same object. This seems like a reasonable view but it is wrong. Frege realized his error more than a decade later and returned to the topic in On Sense and Nominatum to explain why he previously thought identity was a relation between names, why this is wrong, and what to make of identity now.
The text is marginally dense but does not require prior knowledge to understand. Do pay attention to footnotes, they serve as guideposts to keep the wayward reader on course.
I In this section I will explain why Frege correctly rejected the view that identity (an identity is something like A=A or A=B where true) is a relation between objects, the problem of viewing identity as a relation between names, and how he tries to resolve these problems with his theory in On Sense and Nominatum.
The problem with viewing identity as a relation between objects is A=A and A=B, if true, would not be different in any important respect. Both would state a logical, a priori truth (namely that some object is identical to itself) because the names “A” and “B” would both stand for the same object and nothing more. However, there are many cases in which A=A and A=B express genuine, non-a priori knowledge.
Imagine A represents “the sun in the sky today” and B represents “the sun in the sky yesterday”. A=A (the sun in the sky today is the same as the sun in the sky today) is an obvious, somewhat trivial point, but A=B (the sun in the sky today is the same as the sun in the sky yesterday) represents real, scientific knowledge. Thus, identity cannot simply be a relation between objects because there are identity statements that express genuine knowledge, and identity relations between objects are not capable of expressing genuine knowledge.
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