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Topic: Is logic part of mathematics - or is mathematics part of logic?
Replies: 8   Last Post: Jul 8, 2013 12:57 PM

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Louis Talman

Posts: 5,100
Registered: 12/27/05
Re: Is logic part of mathematics - or is mathematics part of logic?
Posted: Jul 8, 2013 12:57 PM
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On Sun, 07 Jul 2013 18:02:48 -0600, Joe Niederberger
<> wrote:

> R Hansen says:
>> I think getting the abstract notion of "implication" is critical for
>> any of this to pan out

> Of course, and the entire concept that we call "implication" in
> propositional logic is not something that somebody has a ingrained (or
> inbred) sense for. It is something that was discovered (, or if you
> like, invented,) worked out as a system with the other elements, and
> relies on cultural transmission to propagate to each new generation.

>> Kids actually get double negatives, inclusive, exclusive etc. almost as
>> soon as they get language.

> Not in an entirely clear and consistent way. But like if..then.., of
> course the seeds are there. Its a matter of training to take any
> informally tossed off utterance:
> "I ain't never going to school again", "I could care less", and distort
> its meaning into the logician's.
> Cheers,
> Joe N

This is especially so for kids who are born to an Indo-European
language---in which, according to a linguist I talked to, "double"
negatives occur naturally, grammatically, and as a matter of course. In
these languages, you negate a statement by negating everything in sight.

English is a major exception in its prohibition of these
constructions---and that prohibition was grafted onto the language by
scholars of the Middle Ages. (The graft took only partially; witness the
widespread use of double negatives among people who have been "properly
educated" about their use.)

- --Louis A. Talman
Department of Mathematical and Computer Sciences
Metropolitan State University of Denver


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