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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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 GS Chandy Posts: 8,307 From: Hyderabad, Mumbai/Bangalore, India Registered: 9/29/05
Re: Is logic part of mathematics - or is mathematics part of logic?
Posted: Jul 5, 2013 12:58 AM

(Posted earlier, did not appear. Now reposted, after modification).
Robert Hansen (RH) posted Jul 4, 2013 5:09 AM:
>
> On Jul 3, 2013, at 2:21 PM, Joe Niederberger
> <niederberger@comcast.net> wrote:
>

> > I think you could teach modus ponens to a sixth
> grader though, and it *may* help
>
> Forget a sixth grader, how exactly do you teach modus
> ponens to anyone? Again, to my analogy, how do you
> teach someone what a rose smells like?
>

IMHO, *teaching* anyone anything is mainly a matter of getting him//her interested in what you (the 'teacher') are interested in 'teaching' - and then providing examples, discussing general rules, if any, etc, etc. In general, whatever is sought to be taught should be 'age-appropriate'. The *teacher* does need to remember that *teaching* does not 'stand alone', but is ALWAYS part of the dyad of 'teaching + learning'. (This seems to be self-evident - but it is remarkable how many 'teachers' forget it and treat *teaching* as the whole thing).
.
A: E.g.: 'Teaching' modus ponens (to a sixth-grader; or to anyone else):
The *teacher* has first of all to convince him-/herself that the dyad of 'teaching + learning' is fundamental, not *teaching* alone. He/she may then convince him-/herself that what is actually needed is mainly to convince the student that "Hey, this stuff IS interesting!". (It is believed that, in general, kids younger than sixth-graders may not be much interested in modus ponens, etc (though they may well find interest in sniffing the roses).

After *teacher* has *captured the student's interest*, the student will more or less teach him-/herself (and will thereby 'learn' what modus ponens might be). The teacher's job is then mainly to:

i) Suggest plenty of examples, instances, etc, from situations that may interest the student;

ii) Try and help the student resolve the doubts he/she may express (/not express).

That's it. The student will surely learn by 'teaching' him-/herself just what modus ponens is - as well as modus tollens. In fact, I'd suggest that plenty of modus tollens will automatically appear while examples/instances are generated of modus ponens.

B: Likewise for 'teaching' someone how to smell a rose.

Provide rose, near nose (or other smell-sense organ) of learner. Say, "This is a rose". Student will get the whiff of the rose's perfume - and will then 'teach' him-/herself just how to go about smelling it, what the smell 'feels' like, etc, etc, etc. I suggest that - for completeness of 'lesson' - other flowers may also be provided (in similar fashion). Perhaps a rotten egg also, for completeness of 'lesson'.

C: In general, as may be gauged from 'A' and 'B' above, I believe that 'common sense' will help a lot, in this and in most other situations.

GSC
("Shoveling Away!")

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