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Topic: Is logic part of mathematics - or is mathematics part of logic?
Replies: 32   Last Post: Jul 7, 2013 9:03 PM

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 Robert Hansen Posts: 11,345 From: Florida Registered: 6/22/09
Re: Is logic part of mathematics - or is mathematics part of logic?
Posted: Jul 4, 2013 10:22 PM
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On Jul 4, 2013, at 12:44 PM, "Clyde Greeno" <clydegreeno@cox.net> wrote:

> # You take them to a rose bush, and let them smell it, and say, "This is how roses smell". If you are unwilling to call that "teaching", you have have confused "teaching" with "telling" ... as have all too many American educators.

Absolutely, that is all you can do, and hope that they have a sense of smell.

>
> # Likewise, you take them to where they can experience modus ponens, and say "This is called 'modus ponens'."

Absolutely, that is all you can do, and hope that they have a sense of modus ponens.

> And the easiest and most meaningful place for learners to encounter modus ponens is within their own routine conversation.

People engage in routine conversation all the time, more than anything else they do, yet, without modus ponens. I guess you meant to say routine LOGICAL conversation. I would agree with that. That is why I am distressed when a school lumps everyone together and the first thing to go is the routine reliance on reasoning (and intelligence). Instead, the class is taught as if no one gets it, and no one ever will, even if they could, because it isn't there to be gotten. Whether you have the sense or not, it will not thrive in an environment where it is explicitly (or implicitly) prohibited.

> All functional humans naturally use it ... its built into the evolution of their thinking processes.

Well, I guess you don't believe that many humans are "functional" because you have been trying for decades to launch a clinic aimed at fixing this problem. I don't see anyone trying to launch a clinic to teach humans to talk or to use simple tools. The primary and natural mode of human thought (for all humans) is not reasoning and logic. It is analogy. That is our universal edge over the rest of the animal kingdom. We can put 2 and 2 together, they cannot. But we (universally) cannot put X and X together. And I know, you have a video of someone putting X and X together like putting 2 and 2 together, but that isn't the same thing.

> Any "teaching" of it is merely calling attention to it, and giving it a name ... which does, indeed, pave the way for further learning more about it.

Partly, yes, but that description doesn't give enough credence to the act of coaching and developing the sense, which is imo the point of teaching. However, I am open to two points of teaching. Teaching for appreciation and teaching for doing. I focus more on the second form because that should (reasonably) be the majority of the effort. I mean, a class aimed at just appreciating calculus would be easy and short (and shouldn't even require a grade) while a class aimed at mastering calculus would be much harder and much longer.

Bob Hansen

Date Subject Author
7/4/13 Clyde Greeno
7/4/13 Robert Hansen
7/4/13 Joe Niederberger
7/4/13 GS Chandy
7/4/13 Robert Hansen
7/5/13 Louis Talman
7/5/13 GS Chandy
7/5/13 GS Chandy
7/5/13 GS Chandy
7/5/13 Robert Hansen
7/5/13 Joe Niederberger
7/5/13 Robert Hansen
7/6/13 Wayne Bishop
7/6/13 Robert Hansen
7/6/13 Robert Hansen
7/7/13 Wayne Bishop
7/7/13 Robert Hansen
7/6/13 Wayne Bishop
7/5/13 Joe Niederberger
7/5/13 Joe Niederberger
7/5/13 Robert Hansen
7/5/13 Joe Niederberger
7/5/13 Robert Hansen
7/5/13 Louis Talman
7/6/13 Robert Hansen
7/6/13 Robert Hansen
7/6/13 Louis Talman
7/5/13 Jonathan J. Crabtree
7/5/13 GS Chandy
7/5/13 Robert Hansen
7/7/13 GS Chandy
7/5/13 GS Chandy

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