Logical argument in the context of "Five Ways (Aquinas)"

In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.

In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as theorems only the most important results, and use the terms lemma, proposition and corollary for less important theorems.

Analogy is a comparison or correspondence between two things (or two groups of things) because of a third element that they are considered to share.

Logically, it is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction. It is also used where at least one of the premises, or the conclusion, is general rather than particular in nature. It has the general form A is to B as C is to D.

In epistemology (theory of knowledge), a self-evident proposition is a proposition that is known to be true by understanding its meaning without proof, and/or by ordinary human reason.

Some epistemologists deny that any proposition can be self-evident. For most others, one's belief that oneself is conscious and possesses free will are offered as examples of self-evidence. However, one's belief that someone else is conscious or has free will are not epistemically self-evident.

Self-deception or self-delusion is a process of denying or rationalizing away the relevance, significance, or importance of opposing evidence and logical argument. Self-deception involves convincing oneself of a truth (or lack of truth) so that one does not reveal any self-knowledge of the deception.