Re: What Logic Really Is

Chris Menzel wrote:
> On 23 Apr 2005 09:45:55 -0700, Charlie-Boo <chvol@xxxxxxx> said:
> >> Pardon me? I've made a simple historical claim here. What
> >> historical fact do you dispute?
> >
> > The belief that the systematic study of valid inferences concerns
only
> > Logic and not all of Mathematics.
>
> You appear to be confusing type and instance here. Of course all of
> mathematics studies all sorts of particular valid inferenceS -- e.g.,
> the proof that there are infinitely many primes. But Logic studies
> valid INFERENCE in general,

I learned in school that if I have X+3=10 then I can subtract 3=3 from
that to infer X=7 and I have solved the equation for X. Where does
Logic tell me about this inference?

Logic isn't about inferences per se. It's about a particular data type
(variable domain) and how to manipulate it, just as Arithmetic draws
conclusions about numbers and Geometry draws conclusions about figures.

> >> Well, I have no idea at all what a "base for computing" is, but
the
> >> claim sure seems false no matter how you mean it.

It means "1+1=2".

> You seem to think this is some sort of standard terminology. I don't
> believe it is. You probably should define it.

A system that defines a function from an r.e. set onto the set of r.e.
sets (or other types of mathematical objects.)

> >> But to
> >> say capital "L" Logic is a "base for computing", well, that just
sounds
> >> confused.
> >
> > Then you have a real mental block at thinking abstractly.
>
> I'm quite certain that I don't. But your curious response -- to lash
> out with an insult upon being pressed for clarification -- suggests
this
> might not be a constructive discussion.

Sorry, but you said that I was confused and I respectfully disagree and
point out that abstracting from various systems to bases of computing
in general is fundamental to Computer Science.

> > Do you agree that the sets representable by PA wffs (provable iff
its
> > free variable is replaced by a memeber of the set)

> Yeah, I think I agree. Not that I see the relevance.

It shows that Logic is a base of computing.

> >> > But can you prove 1-3?
> >>
> >> 1-3?
> >
> > See OP.
>
> Nah.

Maybe with a hint?

C-B

> Chris Menzel

.