@JLNobody,
JLN and Neo
Mathematical proofs are not "empirical" in an experimental sense as in physics. They usually rely on the application of
traditional logical rules such as "the law of the excluded middle". (There are of course other "logics" with their own consistent rule structures). Traditional logic is based on static set theory whose pictorial (Venn Diagram) proofs are "self evident". The "findings" which are involved with such proofs (e.g. the angle subtended by a diameter is a right angle) are tautological rather than empirical, despite the fact that dynamic human activity is involved in the proving process in which we also use the verb "to find". The fact that physicists may indeed exploit those "mathematical findings" to direct their empirical observation is another matter, and is involved in epistemological analysis of terms like "explanation".
With respect to philosophical statements, my own rejection of traditional logical analysis is that
static set theory already assumes the first level of measurement...the nominal...the naming of "a thing" which
by definition retains its "identity" (set membership) throughout subsequent discussion. B
ut as modern philosophers/psychologists have pointed out, that "identity" shifts
dynamically with the shifting of context. The observer/thinger undergoes continous state changes such that "self" and "world" at the start of a discussion have shifted by the end of it*. (Examine yourself prior to reading this, relative to where you are now!
)
Thus traditional logic ultimately fails on the deeper general questions about "certainty", for example, because it is based on the assumption of an objective unchanging world. The rejection of this assumption implies an ontological infinite regress. Yet logic still has its uses in limited non-philosophical contexts such as "I am absolutely certain I put my wallet on this table" because the phrase is being used for socially dynamic purposes, rather than as an epistemological exercise.
(*Refs: Wittgenstein; Meaning is Use ....Piaget; Assimilation-Accommodation)