[FOM] Deflationism and the Godel phenomena

Torkel Franzen torkel at sm.luth.se
Thu Feb 17 01:26:25 EST 2005

Tim Chow says, referring to

(1)     Prov_S(psi&~psi)->psi&~psi

>First of all, in a certain sense, (1) doesn't "directly state" that S
>is consistent.  A more "direct" reading of (1) is, "if S proves that
>psi both holds and does not hold, then psi both holds and does not hold."

  It must be a delicately semantical argument indeed that distinguishes
between ~A and A->B&~B. So what do you take that argument to be? You

>Neil Tennant appears to be arguing that if I *really* am willing to assert 
>*any* sentence phi for which I have an S-proof, then that means that I 
>would even be willing to assert psi & ~psi if I had an S-proof of it.  And
>I don't see anything incomprehensibly baffling about such a claim; it 
>could for example be interpreted as saying that my loyalty to S is so 
>strong that it exceeds my commitment to avoid asserting contradictions.

  But then I must object that "if I am willing to assert ..." etc is
not at all what is stated in (1). So just what do you take to be the
actual argument? How do you get from "if i am willing to assert ..."
to (1)?

  As a more general comment, a "semantical argument" that includes the
statement that we must be prepared to accept contradictions - as your
reading seems to suggest - raises other issues.

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