virus: PCR Three Axioms

Tadeusz Niwinski (
Fri, 19 Sep 1997 15:09:10 -0700

Eric Boyd wrote:
>A=A is only a model, and the map is never the terrain. One must be
>prepared to abandon A=A if it gets falsified. But more than that,
>actually, one of the first requirement of science and PCR is that the
>statement to be analyzed must in principle *be* falsifiable. If it
>ain't, it's either a "tautology" or an "axiom" -- and neither of those
>are useful at all, for the first is *useless*, and the second is
>assumption making. (are there any other possiblities besides these two,
>and their combinations?)

Thank you for a clear intro to PCR axioms (I couldn't get it from David R's

(1) Any statement is either falsifiable or it's either a "tautology" or an

(2) Falsifiable statements are useful, tautologies and axioms are not.

(3) A falsifiable statement (A) cannot be a tautology or an axiom (B) at the
same time. In other words A=A.

(I flexibly change my mind: I want to become the Ayn Rand of PCR).

Seriously. Can we prove *anything* without axioms? Isn't a proof by
definition something like: "If a then b". The first "a" (the "pra-a") must
be assumed. The other option is to follow an authority (like Popper) and
believe that "no-axiom" logic is possible.

Regards, Tadeusz (Tad) Niwinski from planet TeTa (604) 985-4159