Oct 7, 2019, 8:02 PM
Lets discuss the term ‘proof’.
A mathematician creates a PROOF, not a truth.
When we promise a proof is ‘true’ we mean we promise we have DEMONSTRATED a deduction is possible or necessary. The person makes the truth claim since only people can make truth claims: promises. A promise we don’t err. That’s what ‘true’ means because it’s all it can existentially mean.
We use the term ideal truth meaning ‘ that most parsimonious testimony we would give if we were omnipotent and omniscient and produced a vocabulary consisting entirely of operational names.” Because only then would we be possibly free of error.
But testimonial truth is only that most parsimonious description we can make in present language with present knowledge, having performed due diligence against ignorance, error, bias, wishful thinking, suggestion, fictionalism, and deceit.
In logic when we say a proposition ‘is true’ we mean that the constant relations stated or implied in the premise or premises are not inconstant. That we don’t err.
Now in law, we say proof but it means beyond reasonable doubt. In other words, it must falsify all other possibilities. We cannot promise we don’t err. We can only promise we have performed due diligence.
There are no non-trivial logical proofs. Or as others have said all logic is just tautology. Or stated differently, there is no possibility of closure without appeal to information external to the set. Or stated more clearly, non-tautological logical statements are meaningless without appeal to context.
So there are no non-tautological, no-trivial proofs of anything other than the internal consistency of deductions from invariant constant relations (meaning mathematics of the single dimension of positional name).
Instead, all epistemology regardless of context consists of the sequence: perception, free association, hypotheses, theory, (and possibly law), with each step in that series consisting of falsification by a process of elimination, by the mind (hypothesis), by actions (theory), by market (‘law’ or ‘settled science’) until sufficient new knowledge evolves to improve it’s precision. And where that falsification is performed by tests of the consistency of identity, internal consistency (logic), external correspondence, operational possibility, and if involving choice, rational choice, and if involving human interaction reciprocity, warrantied or not by due diligence in scope and parsimony.
So grow the f–k up and leave your secular version of scriptural interpretation (pilpul) in the dark ages of semitic ignorance where they belong.
If you can understand this you know more about truth than the upper tenth of one percent.