warpspeedpetey: I’ve given much thought to your objection. As simple as it seems, it gives rise to a host of issues. I’ve spent a lot of time constructing the following response to it. I consider it to be a definitive and conclusive refutation of your objection. Thankfully, we’re dealing with logic here, so the issues are black or white, very much like mathematics. I believe each of the following points suffice, individually, to refute your objection.
The reason we’re currently debating about logic and circularity, etc. is because you proposed an objection to my arguments. This objection, you said, must be addressed before we consider the premises of the arguments.
The objection claims that my arguments are self-refuting, since they attempt to attack circularity but rely on circularity in doing so.
I’ve proven that this objection fails, at least because neither of my arguments are interested in refuting circularity, or showing that it is irrational, undesirable or…bad, etc. That’s not their purpose. This is an undeniable fact. So, regardless of whether A=A is circular, or if my arguments depend on circularity, your objection has already been defeated.
Having said that, you’re still proposing that my arguments depend upon circularity. It is this claim that I will now defeat.
Response:
1. The logic I’m employing here does not rely on the law of identity, formulated as A=A. That is demonstrably false. My logic includes the law of identity defined as ‘If p is true, then p is true’ or, in other words, p → p. [1] This is a tautology. But, do my arguments depend on this tautology? No more than they depend on the veracity of any other tautology [and there are many others]. There’s nothing special about the law of identity apropos my arguments. Also, not all logics accept this law. So, at least on this account, your objection is defeated.
2. Is it possible for the law of identity to be circular? Much less, epistemically circular?
No. Circularity is applicable only to arguments. The law of identity is not an argument.
What is an argument? “An argument, in the sense used in logic, is a set of statements consisting of premises and a conclusion. The premises are statements that give supporting evidence; the conclusion is what is allegedly supported by these statements.” [2]
So, circularity cannot possibly apply to this law. But, much less than epistemic circularity [a term coined by Alston]. Epistemic circularity occurs in an argument when the truth of the conclusion must be presupposed in order to have justified belief in a premise. Of course, the law of identity cannot be described in such terms.
So, at least on this account, your objection is defeated.
3. I charge your objection with equivocation.
(Your Objection): These arguments are self-refuting because they attempt to attack circularity, but they rely on circularity in order to do so.
The same word, circularity, is used above to communicate two different concepts and therefore, your objection equivocates. In the second part of the objection, “but they rely on circularity in order to do so” the word “circularity” is used to denote an idea applicable to the law of identity. In the first part, the same word is used to denote an idea applicable only to arguments.
At least on this account your objection has been defeated.
Taken together, I believe we should be in a position to discuss the premises now.
[1] The law of identity is defined as “If p is true, then p is true” [p → p] by, practically, all logic text books, here is an example:
“The principle of identity. This principle asserts that if any statement is true, then it is true. Using our notation we may rephrase it by saying that the principle of identity asserts that every statement of the form p → p must be true, that every such statement is a tautology.” (emphasis theirs)
Copi, Irving M., and Carl Cohen. Introduction To Logic. 12th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2005. p. 356.
speaking of which:
“Nevertheless, in regarding the entire system of deductive logic, these three principles [principle of identity, principle of non-contradiction and the principle of excluded middle] are no more important or fruitful than many others. Indeed, there are tautologies that are more fruitful than they are for the purposes of deduction, and in that sense more important than these three.” - ibid.
[2] Gensler, Harry. Introduction to Logic. New York: Taylor & Francis, 2010. p. 2
Without foundational beliefs which we’re justified in holding but which we don’t need to justify in holding them, we must provide inferential justification for all beliefs, and the attempted justifications never cease. They rest on no foundation.