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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: 7,978 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 9:09 PM

Robert Hansen posted Jul 5, 2013 6:09 PM (GSC's remarks interspersed):
>
> On Jul 5, 2013, at 6:32 AM, GS Chandy
> <gs_chandy@yahoo.com> wrote:
>

> > Well, most people DO have a 'sense of smell'. In
> fact, the whole 'education system' has been built on
> the premise that the great majority of children who
> come into and pass through the system do indeed have
> senses of smell, sight, sound, touch - AND a few
> other useful/necessary senses (including some basic
> ideas of modus ponens and modus tollens in their
> practical lives even thouugh they are unaware of
> these technical names.

> >
> > One of the 'senses' that the education system

> presumes that most incoming students DO have is a
> basic sense of 'modus ponens' (and 'modus tollens') -
> and the whole educational system' is (supposed to be
> designed to) then help them develop, extend,, refine
> and reinforce these 'senses' in various ways, too
> many for me to recount. The entire 'Montessori
> system' (in which you are a firm disbeliever) is
> founded on this basic concept.
>
> The education system presumes a sense of modus
> ponens.
> For the majority of students, this presumption is
> wrong.
>
> Thus the results achieved.
>

I: The above (whatever it might happen to mean) is what you claim. It might be useful if you would clarify the above.

II: As I understand modus ponens, it consists of the logical train:
'A' implies 'B';
'A' is true;
Thus 'B' is true.

III: To my mind, the above logical train appears to be almost essentially a part of living in the real world. I would claim that it appears entirely unlikely that a child could grow to school age (and then beyond) without developing through his/her life experiences a 'sense of modus ponens'. It's not quite as fundamental as, say, breathing - but we all do develop it to some extent or other. To be sure, most students are not adequately trained in logical thinking so that they properly develop such senses and abilities for their own and society's benefit.

(In a recent posting, Clyde Greeno had suggested what I believe would be the right approach of helping to inculcate and develop this sense)

I observe, from your arguments above (and below), that some students are not adequately trained in clearly expressing whatever it might be that they want to state.
>
> > In fact, this is just what is done in ALL of
> 'teaching', of whatever subject. Which is why I had
> suggested (in various other posts) that what teachers
> should actually seek to do is to arouse the child's
> curiosity, excite his/her interest - and then
> everything flows naturally. From a sizable
> background of experience and learning, the teacher
> shows the learner some 'rules' and and 'examples' -
> the child then 'teaches' him-/herself and THEREBY
> learns. What the educational system should not
> forget is that there is no such thing as 'teaching'
> in isolation. 'Teaching' is, in fact, one part of
> the dyad 'teaching + learning'.
>
> Curiosity is not the causal agent for modus ponens.
>

i) I had nowhere stated that "curiosity IS the causal agent for modus ponens". So I fail to understand the context of your above statement.

ii) Even if I did understand the context, I must confess that I don't at all understand what you mean by the above.

(I guess you should put me down as one of the 'not-gets' [see below]).
>
> >> People engage in routine conversation all the
> time,
> >> more than anything else they do, yet, without
> modus
> >> ponens.
> >>

> > WRONG! Modus ponens (and modus tollens) are
> integrated into a great many of the experiences that
> people go through, into a great many of the thoughts
> that people think.
>
> Then they would get algebra easily, and many other
> things. They do not get these things, and when I say
> "do not get" I do not mean it in a small way. You can
> interview a 100 people, people who took algebra, and
> verify this. Whatever it was that they did get in
> those classes, was quickly forgotten, and you never
> forget the key elements of algebra, thus they never
> got it in the first place. I realize that your
> premise is that this is because they teach it wrong.
> My premise is simpler, supported by actual evidence,
> and unfortunately, correct. They do not get it
> because the senses required to get it are too weak to
> support getting it. There is no ignition.
>

I would agree entirely with the part of your argument in the above claiming that humans are very differently gifted, I must confess that I have not been able "to get" most of whatever else it is that you may be wishing to convey in the above. This may be attributable to a deficiency in the way I think (as a "not-get") or a deficiency in the way you express yourself.

Based on whatever I HAVE been able "to get" (possibly incorrectly), I'd suggest that - if you are correct - it may well now be time to rescind a good number of the 'societal advances' we humans believe we have made over the past several centuries and reform our societal systems into "the gets" and the "don't gets".

That becomes far too complicated for me to follow as, by and large, I have gotten myself accustomed broadly to the idea of 'democracy', i.e., "government OF the people, BY the people and FOR the people" - the aim being to enable 'equitable treatment' of all. Of course, we have little accomplished that aim in any society in our world, but that is quite another matter.

I recall that you had in another post expressed the possibility that some of us - in comparison to 'ordinary human beings', I presume - may be 'mutants' of sorts (in regard to our abilities of 'getting' and 'not-getting' certain subtleties of thinking). To which I had responded, "X-MEN FOREVER!" (words to that effect). If you are correct in your premise and arguments, this may well be an idea worth exploring for yourself and others who think like you. I must confess that I'm not much 'in tune' with this line of thinking: frankly, it truly repels me.
>
> Also, as I have noted before, I work in a demanding
> field that relies heavily on those elements I
> expressed earlier. Intuition, instinct and habits of
> mind. And through necessity and experience you become
> keenly aware of those elements in others or the lack
> thereof. While educationalists may have banned the
> word "smart", out here it is still a very big deal.
>

I am not an 'educationalist' or an 'educationist', and I have not banned the word "smart". I really would like to see people be as smart as they are capable of being - and I believe that many of our societal systems contain very major barriers to this.
>
> As I explained to Clyde, human thought, the kind
> shared by all humans, is based on analogy, not
> reasoning. And you can be functional without modus
> ponens. Just not in subjects that require the
> intuition, instinct and habits of mind that come with
> modus ponens. The real problem with a lack of modus
> ponens in the general population has nothing to do
> with algebra, it has to do with all those important
> decisions one must make as they navigate life. But
> society has (had) a way around this issue. It is
> called "culture".
>

I believe the jury is still out on just what kind of mix of 'reasoning' and/or 'analogy' (and/or anything else) "human thought" may be based on. If you have managed successfully to resolve the matter, a paper or book explaining that resolution might be in order.
>
> >> I guess you meant to say routine LOGICAL
> >> conversation.
> >>

> > Nope. I believe that was NOT what Clyde Greeno had
> 'meant to say' (at all).
> >>
> >> 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.
> >>

> > DEFINITELY, the way most conventional schools
> 'teach' is profoundly wrong and in fact the whole
> system contradicts the way people actually learn.
>

> >From what I see, schools are trying to teach the
> wrong subjects to the wrong students. That is why the
> subjects are reduced (dumbed down) to a useless
> facsimile of their former selves. It is no wonder
> that these students don't have a clue as to what they
> want to do or study in college. The other countries
> have it right. Students begin to form the bonds with
> their future selves by the 9th grade. That is almost
> impossible to do here (in the U.S.), unless you have
> parents driving you.
>

Well, I have earlier stated my arguments for parents (and other authority figures) ENCOURAGING children and not PUSHING them to learn. Nothing you have argued here or elsewhere has brought about any change to the 'mental models' on which is based the above approach of ENCOURAGING rather than PUSHING.
>
> > What they (schools) have generally forgotten
> (except in the cases of a few 'exceptional teachers')
> is that there is no such thing as 'teaching' in
> isolation. There IS 'teaching + learning' - and the
> child mostly teaches him-/herself and thereby learns.
>
> Well, I haven't seen anyone arresting students for
> teaching themselves, so I assume that they are
> teaching themselves as much as they care to.
>

No? Neither have I, and such was never claimed or suggested.

However, I HAVE seen schools (and other parts of the societal systems in which we function) setting up huge barriers and discouragements that tend to hinder or even prevent children learning effectively.
>
> > I am not able to view videos easily, so haven't
> looked at Clyde Greeno's videos. As to how a child
> learns how to "put X and X together" from the
> (perhaps innate) sense of what '2' and '2' amounts
> to, I do not know - and I don't believe the most
> advanced 'learning theories' know either (though they
> might make a guess at it).
>
> We know when a child learns, GS. Trust us, we know.
>

I could agree that we do know (to some extent, a least) "when" a child learns.

If you will kindly look a bit more carefully at what had been claimed in the above, you may (or may not) observe that the argument presented was that we do not know "HOW" a child learns.

Trust me, RH, you do NOT know "how" a child learns. (If you believe you do, perhaps a major paper or book would be in order).

And perhaps you might like to apply some 'intuition, instinct and habits of mind' to the minor issue of at least arguing specifically on issues raised and not on those not raised.
>
> analogy that you might understand...
>
> You have heard the line "If a tree falls in the
> forest and no one is there to hear it, does it make a
> sound?" This is a play on the semantics of sound and
> the sense of sound.
>
> Logic is the sense of sound.
> Mathematics is the sound.
>
> But mathematics isn't the only sound.
>

I have indeed heard the line about a tree falling in a forest and whether it makes a sound when no one is there to hear it fall. I have long enjoyed the saying - and still do find it very well worth contemplating (and exploring).

Thank you for enlightening me that it is "a play on the semantics of sound and the sense of sound". (I had always believed it was an expression of something rather deeper, but thank you anyway).

But I'm afraid I don't 'get' your analogy at all, alas. I ask the question:

"When an analogy is drawn, and no one 'gets it', does the analogy actually exist?"

I'm not here claiming that NO ONE 'gets' your analogy - just that I don't.

Sorry about that: I guess you should just put me into the category of "not-gets" in your brave new world.

GSC
("Still Shoveling!")

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 Crabtree
7/5/13 GS Chandy
7/5/13 Robert Hansen
7/7/13 GS Chandy
7/5/13 GS Chandy