Re: Why are rules of inference not laws of sentential calculus?

Torkel Franzen wrote:
> andrewspencers@xxxxxxxxx writes:
>
> > But can't the rule of detachment be stated in a formal language, and if
> > it can, then wouldn't it have the same form as this theorem of the
> > sentential calculus?
>
> No, a theorem is a sentence, whereas a rule is a relation between
> sentences.
By "No", did you mean "the rule of detachment can't be stated in a
formal language" or "it wouldn't have the same form as this theorem of
the sentential calculus"?
If the latter, then what form _would_ it have?
If the former, then how is it possible to create an automated theorem
prover, which is mechanical and therefore requires formal rules of
proof?
Also I don't understand why you say that a relation between sentences
is not a sentence. Isn't "[(p->q) ^ p] -> q" both a sentence and a
relation between the sentences p and q (as well as a relation between
the sentences [(p->q) ^ p] and q)?

.

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