OrangeWizard posted...Nine_Breaker posted...

If the premise is an axiom

It can't be, because

A) There would be no way to distinguish axioms as premises from non-axiomatic premises.

B) There would be no way to distinguish a sound argument from an unsound argument.

Axioms are established, implicitly or explicitly, before the argument, not during.

I'm not sure I follow necessarily. It's been a while so I was looking some stuff up:

http://www.cogsci.rpi.edu/~heuveb/teaching/Logic/CompLogic/Web/Handouts/Axioms.pdf

This link outlines the Rosser System and its axioms:

R.S.1: A & (A & A) (so really ¬(A & ¬(A & A)) )

R.S.2: (A & B) > A

R.S.3: (A > B) > (¬(B & C) > ¬(C & A))

It takes two premises:

1. P > Q

2. ¬(Q & ¬R)

and uses R.S.3 to arrive show that this means:

5. ¬(¬R & P)

Which makes sense. I'm not sure if using R.S.3 in step 3 of the proof constitutes making it a premise as well. I could have constructed my argument earlier to be a lot better, for sure.

Does the above argument constitute arriving at a truth without use of evidence?