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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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Robert Hansen

Posts: 9,351
From: Florida
Registered: 6/22/09
Re: Is logic part of mathematics - or is mathematics part of logic?
Posted: Jul 7, 2013 11:36 PM
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On Jul 7, 2013, at 8:33 PM, Joe Niederberger <niederberger@comcast.net> wrote:

> Exactly, because logic is the reflective, refined, and systematized use of these primitives that we get first get "for free" so to speak, from language.

It is a sense. It has nothing to do with language or reflecting on language. Having the sense of RAIN = MOVIE is not the same as having the sense of RAIN IMPLIES MOVIE. If there was just an ounce of truth to your proposed relationship between language and logic then wouldn't logical people be the norm? Language is attained by just about everyone. Propositional logic, by very few. Do we have any census data?:)

I am not saying that if you keep challenging the kids to make logical statements and arguments (as you wrote) that it won't help some of them "see the light". I am just saying "seeing the light" has nothing to do with language. In other words "IF A then B" only means logic to you because you have the sense of it. It doesn't mean that to a student and analogizing it to the physical world isn't going to help. To them it means something more like A = B, or whatever sense they can tag that syntax to. They will have to develop or find the sense of A IMPLIES B and differentiate it from A=B (or any other senses), through many examples like you said. Until they have/find that sense, I don't see how they even have primitives.

I think this is one of the key things that will come from AI research. A better understanding of natural language and what it is and what it isn't.

On Jul 7, 2013, at 8:02 PM, Joe Niederberger <niederberger@comcast.net> wrote:

> 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.

Seriously? I came up with "implication" all on my own and I am pretty sure you did as well. That is like saying there is no such thing as an inbred sense of harmony. Of course being born with the sense and developing that sense to its full potential are two different things. Maybe you are talking more to the later. To the development of that sense, and not its source. Even though we are born with the sense, we profit from the reflections of prior individuals with the sense.

I would like to think that many people have the sense but in some it is just much more active and ready. I would like to think that we can help more students find the sense in themselves. I do think we could. But I also have to be realistic. Musicians have a great sense of tonality and harmony. Some of the greatest also had perfect pitch. I think we are talking the same thing here. The sense of reasoning stretches from very high, something even akin to "perfect pitch", to very low. The bar for useful ignition is probably moderately high.

I base this on observation.

Bob Hansen

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