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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 5, 2013 8:39 AM

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.

> 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.

>> 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.

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.

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 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.

> 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.

> 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.

Now, the answer to your riddle, by means of an 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.

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