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Topic: Is logic part of mathematics - or is mathematics part of logic?
Replies: 10   Last Post: Jul 9, 2013 4:09 AM

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GS Chandy

Posts: 6,719
From: Hyderabad, Mumbai/Bangalore, India
Registered: 9/29/05
Re: Is logic part of mathematics - or is mathematics part of logic?
Posted: Jul 8, 2013 4:23 AM
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Robert Hansen (RH) posted Jul 8, 2013 7:39 AM (GSC's remarks follow):
>
> On Jul 7, 2013, at 4:22 PM, "Clyde Greeno @ MALEI"
> <greeno@malei.org> wrote:
>

> > Hansen's reasoning (by his use of the humanly
> natural creative and rational processes that
> constitute the psychological meaning of "common
> sense") contradicts his own argument against common
> sense being "the seat of human reasoning."
>
> "Common sense is defined by Merriam-Webster as,
> "sound and prudent judgment based on a simple
> perception of the situation or facts."[1] Thus,
> "common sense" (in this view) equates to the
> knowledge and experience which most people already
> have, or which the person using the term believes
> that they do or should have. The Cambridge Dictionary
> defines it as, "the basic level of practical
> knowledge and judgment that we all need to help us
> live in a reasonable and safe way".[2]"
>
> https://en.wikipedia.org/wiki/Common_sense
>
> That sounds good enough for me.
>
> If you are saying that psychology identifies "common
> sense" with higher level reasoning, then what do they
> call the common sense as described in those
> dictionary entries? You are the first person that I
> know that doesn't make a distinction.
>

Clyde Greeno is NOT - to the best of my understanding - saying anything like what you've claimed above, namely: "psychology identifies 'common sense' with 'higher level reasoning'".

What he IS saying (to the best of my understanding - as we discuss these complex issues in 'pure prose') - is that 'common sense' "CONTRIBUTES TO" (or "COULD CONTRIBUTE TO") 'higher level reasoning'.

I buy that.

Various other propositions could develop from this (via application of 'modus ponens',' modus tollens' and such logical 'rules'), for e.g.:

I claim that (most of) 'higher level reasoning' develops on the basis of simple 'common sense' - developed appropriately; and:

"WITHOUT 'common sense', 'higher level reasoning' cannot develop effectively".

We often DO find floating around in our social discourse a sizable number of seriously flawed propositions (claimed by some to be 'higher level reasoning') . Most of these in fact would contradict 'common sense' if put to the test. However, they sometimes gain wide currency in society and are often promoted as social truths.

I put down below a few such 'articles of faith' that I recall having seen:

ARTICLES OF FAITH:
=====
+++++++
a) "To him that hath, more shall be given (and should be given); To him that hath not, more shall be taken away (and should be taken away)"

b) "The rich are different from you and me" - and even more they are fundamentally different from the poor"
b1) "We mutants are different from 'ordinary people'
b2) "The rich are rich because they deserve to be rich; the poor are poor because they deserve to be poor"

c) "Labour Unions are bad; industry associations are good"
c1)"Industry associations are bad; labour Unions are good"

d) "Democracy has reached the acme of its development in the Western nations of the USA, the UK and Europe"

e) "Society 'as it is' is society 'as it should be' and 'forever shall be'"
e1) "The inequities in society are forever immutable - this is the word of Our Lord"
e2) "Blacks are inferior people; whites are superior people. Other colors may be in-between"

f) "When you strive to change things in society, you are fighting against the will of God!"
f1) "When you strive to change things in society, you are fighting against the will of St. Josef Stalin!"

g) "Small government is good; big government is bad. Effective government is impossible"

h) "Capitalism is the root of all evil"
h1) "Socialism is the root of all evil"

i) "The USA is the 'home of the Brave!, Land of the Free, that Shining City on the Hill!"
i1) "India is the land of gurus, spiritualism and Mahatma Gandhi!"

j) "PUT THE EDUCATION MAFIA IN JAIL!"
k) "BLOW UP THE SCHOOLS OF EDUCATION!"
+++++++

And so on and so forth. There are almost an infinite number of such propositions. We can manufacture them at will, to help us bolster up whatever argument we may want to put forward.

It is not difficult to refute most such propositions (and the arguments that may develop with or from them). But somehow, they float around society, sometimes causing immense damage to individuals and groups.

Properly to refute such dangerous societal propositions requires that we discuss and communicate about the inter-relationships between the factors of the systems under discussion - and do that MUCH more effectively than we do in the conventional way.

This is extremely difficult - perhaps even impossible - to do using 'pure prose' as the 'language of discussion'. What happens is that the inter-relationships between the factors of the systems in question are very rarely clarified, and the discussion generally degenerates into empty argumentation.

By using what I call 'structural graphics' to our 'language', it becomes possible to articulate, with some clarity the inter-relationships between the factors of the systems in question. Most of such questionable propositions above are easily disposed of.

More information about 'prose + structural graphics' and tools to use them in our daily practice are described in the attachments to my post heading the thread "Democracy: how to achieve it?" - http://mathforum.org/kb/thread.jspa?threadID=2419536 .

GSC



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