Skepticism mot logik och matematik

Oj, oj, ibland skakas man om av något man läser. Jag har alltid fascinerats av skepticism, men en så radikal argumentation som i A Priori Skepticism”, accepterad för publicering i Philosophical and Phenomenological Research, har jag inte tidigare stött på. Däri argumenteras, som titeln antyder, för att skepticism också omfattar kunskap om vissa a priori-sanningar, t.ex. dessa:

(1.1) The sum of two and three is five.
(1.2) Whatever is square is rectangular.
(1.3) Whatever is red is colored.
(1.4) No surface can be uniformly red and uniformly blue at the same time.
(1.5) If ‘if p then q’ is true and ‘p’ is true, then ‘q’ is true.
(1.6) No statement can be both true and false at the same time and in the same respect.
(1.7) If A is taller than B, and B is taller than C, then A is taller than C.
(1.8) Everything is identical to itself.
(1.9) If the conclusion of an inductive argument is contingent, it is possible for the premises of that argument to be true and its conclusion to be false.

Hur kan man ens tänka sig att det inte går att ha kunskap om att dessa satser är sanna? Argumentationen kan uttryckas på följande sätt, där ”PAN” avser ”putatively a priori necessities” (av det slag som exemplifieras ovan) och där ”DW” är en person som, av skäl som Descartes och Wittgenstein har formulerat,* helt och ständigt har fel:

(7.1) For any PAN, if I know that the PAN is true, then I know that I am not a DW.
(7.2) I don’t know that I am not a DW.
(7.3) Therefore, for any PAN, I don’t know that the PAN is true.

If (7.3) is true, I cannot know (7.1) or (7.2) to be true, since they are PANs. Therefore, if the argument is sound, it cannot be known to be sound. The skeptical predicament is only worsened when we consider that the proposition that the argument from (7.1) to (7.3) is valid is itself a PAN. Since a priori skeptical hypotheses, as I conceive of them, can be used to challenge our ability to know that an argument is valid—including valid arguments that call into question our ability to know that an argument is valid—the soundness of the argument doubly implies the unknowability of its soundness.

Jag vet inte vad jag vet. Men som den fiktionalist jag är spelar det nog ingen roll.


*Om Descartes:

Although it can be difficult to see how a genuinely impossible skeptical hypothesis could ever pose a serious skeptical threat, Descartes nonetheless believed that it was possible. For example, in the first Meditation he considers the possibility that an all-powerful being might be deceiving him about basic a priori matters:

What is more, since I sometimes believe that others go astray in cases where they think they have the most perfect knowledge, may I not similarly go wrong every time I add two and three or count the sides of a square, or in some even simpler matter, if that is imaginable?

In the Third Meditation Descartes reflects upon the possibility that “some God could have given me a nature such that I was deceived even in matters which seemed most evident”:

I cannot but admit that it would be easy for him, if he so desired, to bring it about that I go wrong even in those matters which I think I see clearly with my mind’s eye.