Citat:
Ursprungligen postat av
rootswaller
Uttömmande svar har redan givits, men jag vill vara med på ett hörn ändå...
För att ett argument ska betraktas som sunt måste premisser och slutsats vara sanna, utöver logisk giltighet. Ett stort problem med cirkelresonemang är att de inte säger någonting om sanningshalten i varken premisser eller slutsats.
Vore logisk giltighet ända kravet skulle TS behöva godta följande som ett "bra" argument eftersom det är logiskt giltigt:
Premiss: Antingen så regnar det eller så regnar det inte.
Slutsats: Gud finns.
d.v.s.
P v -P
Q
Du har fått det hela lite upp och ned, men här är Martin-Löfs förklaring för den som är intresserad:
⊥-elimination.
⊥ true
-------
C true
Here, in analogy with the rule of disjunction elimination, C is presupposed
to be a proposition, not outright, but merely under the assumption
that ⊥ is true. This is the only divergence from Gentzen’s
formulation of ex falso quodlibet.
Explanation. When you infer by this rule, you undertake to verify
the proposition C when you are provided with a proof that ⊥ is true,
that is, by the definition of truth, with a method of verifying ⊥. But
this is something that you can safely undertake, because, by the defi-
nition of falsehood, there is nothing that counts as a verification of ⊥.
Hence ⊥ is false, that is, cannot be verified, and hence it is impossible
that you ever be provided with a proof that ⊥ is true. Observe the
step here from the falsity of the proposition ⊥ to the unprovability of
the judgement that ⊥ is true. The undertaking that you make when
you infer by the rule of falsehood elimination is therefore like saying,
I shall eat up my hat if you do such and such,
where such and such is something of which you know, that is, are
certain, that it cannot be done.
