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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: 6,939
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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

(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
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Clyde Greeno
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Jonathan Crabtree
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy

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