DO YOU PRESUPPOSE A=A?

Prerequisite: Necessity Vs Truth

Presupposition can be defined as "to believe that an unsupported antecedent condition to a proposition is true". With this definition, we can not refer to "A=A" as a presupposition, as "A=A" is not something one believes is true, it is a necessity. When one presupposes something, it is to say, "I am accepting that X is justified to be true, but I don't have or I'm not giving a justification for X". If there could be a justification for X, it entails that there could be reason to reject the contrary to X. In order to have reason to reject the contrary to X, the contrary to X must be coherent, or "can be the case". It is incoherent to believe a contrary of a necessity is something that can be rejected or accepted, as it is a contradiction.

One might say, "it is the case that the duck is in the water or it is not the case that the duck is in the water". In this example, one is presupposing that there is a "duck" and that there is "water". Each of these presuppositions have truth values, as it is coherent to find that there is no "duck" and/or there is no "water". If one asserts that "A=A" is also presupposed, it entails that there is a coherent contrary that could have been presupposed instead. Being that we have an incoherent contrary to "A=A", Presupposing "A=A" is incoherent.

When one states that they "know x is true", what they are most likely suggesting is that it is impossible that they are wrong. However, belief in a truth, however confident one is, is to say that it must be possible that one is wrong.  We can presuppose truths and build a foundation for subsequent truths, however, the foundation could be wrong. We can say that we live our life assuming x is true, but we can not say that we live our life such that it is impossible for x to be false. The only foundation that can not be wrong is a necessity, but it does not make sense to say that we presuppose it. It is analogous, in a colloquial sense, to predicting that the number 1 will come up on a roll of the die where all sides of the die are 1. It is nonsense to call that a prediction, as it is nonsense to refer to "A=A" as a presupposition.

August 2019