HOW DO YOU KNOW A=A?

Prerequisite: Necessity Vs Truth

When one knows something, one believes that it is true. One also has some form of justification for believing something is true. When you are asked for a justification of the principles of logic, such as the principle of identity (A=A), you are being asked to provide a reason for assigning a truth value to your belief. As it is the case that A=A is necessary, a truth value for A=A would be nonsensical. What they are asking is for you to give a justification for a truth value where a truth value is not applicable.

We can not believe that A=A, as a belief is holding a proposition to be true, where there is a coherent false value. Further, the concept of justification is incoherent when applied to necessities, as it implies that there is a coherent contrary that one need reason to reject. If the contrary is incoherent, the concept of rejecting or accepting an incoherent condition would be itself incoherent. One can recognize that A=A is a necessity, however, that recognition can not change one's perception of reality, as believing something is true can.

One could say, "You used A=A in order to determine that A=A is necessary, and that is circular". For this, we can look at the the first premise of a syllogism, "if A=A, then it can be determined that A=A is necessary". At first glance, this looks like it would entail a circularity, however, the beginning of the first premise, "If A=A", is incoherent, as it entertains that "A might equal A" or "A might not equal A", and offers them both as coherent choices. To posit that one could have "used A does not equal A", is a contradiction. Circularity is a consequence of uninformative justification, and justification only applies when evaluating coherent cases against competing coherent cases.

You could think to answer, "How do you know A=A?" with "I don't know". However, by doing so, you are entertaining that this is a coherent belief question, entailing that it has a truth value. Answering "I don't know" is to claim that you understand on a conceptual level what it is for it not being the case that A=A, such that you can evaluate the existence or non-existence of justification for or against it. Interestingly, if it is not the case that A=A, then you did not understand the question, yet you answered the question. Since A=A is a necessity, the question and your answer are incoherent.

If you mistakenly try to justify "How do you know A=A?" with "Because A=A.", you would be accused of offering a circular argument. However, there is no circularity here, just an incoherent question and incoherent answer. Answering "Because A=A" assumes the question was intelligible. If the question is incoherent, there is nothing intelligible to be evaluated. The question and your answer are incoherent. Any answer to "How do you know A=A?", other than "That question is incoherent", is incoherent.

 

August 2019