What is a proof?

[Muslim Scholar]

No the proof or lack proof is needed before you can claim the premise to be true or false. The premises would be true because we can use evidence to give insight on truth whether true or false. Those statements become proof for a claim once back up with evidence. Deductive logic is not technically used for proof but for right reasoning. So proof must be established before hand of logic hence to why i made previous statement.

I don't understand what are you saying here!
Do you mean a proof to prove the premises? this is outside the context of the proof itself
Because it may be just an Axiom
For example: Premises 1: A circle has one radius
I don't have to prove that because we defined a circle like that

Rational criticism would be the same as deductive proof technically. Deduce would mean to reduce or breakdown and criticism would doubt the doubt able which would be used to break it down to it's truth (or lack of). Rationalizing would be just using logical thought which logical thought demands (in deductive) proof of premises.

I think here you mean Inductive reason

Like
Socrates was Greek. (premise)
Most Greeks eat fish. (premise)
Socrates ate fish. (conclusion)

in which the premises are supposed to support the conclusion in such a way that if the premises are true, it is improbable that the conclusion would be false. Thus, the conclusion follows probably from the premises and inferences.