Date: Jul 5, 2013 2:23 AM
Author: GS Chandy
Subject: Re: Fwd: Is logic part of mathematics - or is mathematics part of logic?
Anna Roys posted Jul 5, 2013 6:38 AM:
> Responding to:
> Anna Wrote: > "Perhaps logic is plural and new logics
> may be developed ?"
> GSC response:"There is much to explore in that idea.
> Unfortunately, the
> 'language of pure prose' is, by and large, an
> inadequate vehicle to enable
> any such exploration."
> These questions come to mind:
> Why do you think that idea of creating new logic s
> limited to the "language
> of pure prose?"
> Why do you think it is an "inadequate vehicle to
> enable any such
> Where did the forms of logic used by many scholars
> come from in the first
> place ?
> Why cannot new logic forms be developed that
> intersect well with Maths?
I am very much 'in tune' with the spirit of your questions - though I may not myself use your phrase 'new forms of logic'. I believe it is all 'logic', which we do need to explore to considerably greater depth than we have done thus far.
I claim that we do need, nowadays, to go somewhat deeper into such issues than George Boole was able to go in his deservedly famous treatise "An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities". I claim that we've not done that adequately in the 'conventional ways' we have of discussing our issues of concern, i.e., via 'pure prose' - or at least, those explorations are not readily available and accessible to the lay observer (who is the person most affected by our inadequate explorations of logic and other fields).
Our societal failures in a whole range of areas of human concern - from our ineffective educational systems to our ineffective understanding at policy levels of world-changing matters such as 'climate change due to human exploitation of planetary resources' -- ALL of them bear testament to our 'failure of understanding' (despite the claims of several of us claiming considerable satisfaction with the world of 'academic scholarship and convivial discussion' and the like).
I believe much of logic - as well as most other fields of interest - could be quite fruitfully explored in some more depth (with some degree of effectiveness) using what I've described as 'prose + structural graphics' (p+sg). In my view, our current explorations (mainly via the 'pure prose' to which we're restricted in our forums) are neither 'effective' nor 'efficient'. [At this point, I must observe that several here disagree with this view of mine].
I notice that Robert Hansen has asked the moot question "Can you explain your phrase 'new forms of logic'"? [Words to that effect - I'm unable to locate that specific post of his].
I believe I could explain (to a fair extent if not to 100% satisfaction) what I mean by 'deeper exploration of logic' - but I'm unable to do such explanation in 'pure prose'. I'd need to shift to 'p+sg'. Which means we'd need adequate facilities to illustrate the representations of our mental models that we may discuss AND the reader would need to learn to read arguments using p+sg, and how to develop on them.
In due course, I hope to be able put up a website that enables such explorations as I've claimed are necessary and would be useful.
Meanwhile, at my post heading the thread "Democracy: how to achieve it?" (http://mathforum.org/kb/thread.jspa?threadID=2419536), I have attached some brief information about the modeling tools and ideas that could help, in particular about the 'One Page Management System' (OPMS).
The OPMS software is freely available on request to those who'd like to explore these systems tools of exploring issues in greater depth than is possible in 'pure prose'. This can be done right now, before my website is done.
In particular, it is not difficult for anyone to create action planning to accomplish any Mission of current interest, e.g.,
- --"To understand thoroughly all topics of my math syllabus and THEREBY to improve, very significantly, my results in my math exams, tests and quizzes". Done successfully by a college freshman, LONG BEFORE the OPMS software become available. I should emphasise that I gave this particular student NO MATH TUITION at all: I only explained the OPMS approach to him; then spent another hour or so each day helping him:
i) to 'generate elements' relating to his situation;
ii) to construct models from elements generated;
iii) to learn how to interpret his own models;
iv) find out 'what to do next' at every stage of development of his OPMS.
- -- "To develop the OPMS software" - done successfully by my software team at Interactive LogicWare (ILW), a company I had started to develop and market the OPMS software. Unfortunately, the company soon folded as I was unable to convince my co-directors to use the OPMS themselves. However, all members of our ILW software team did successfully work on the following Mission (BEFORE they were able to succeed in the above-noted one):
- -- "To become a highly competent/top-level software designer" (After ILW folded, ALL of them were able to get themselves EXCELLENT jobs at the very bottom of the 'dot-com bust' when practically no one was employing software engineers at all - precisely because they had, in fact, become highly competent software designers by then!!)
- -- "To get myself a good and satisfying job" - successfully done by several young people.
- -- "To convince ---- to use the OPMS system for his/her own Mission" - one of my Missions using the OPMS; done successfully in some instances (as noted above); unsuccessfully in more instances than I was successful in.
- -- "To propagate and apply the OPMS approach in India and worldwide" - ongoing. Success in a fair number of instances - for individual and organisational Missions. I've not yet succeeded in interesting government or voluntary organisation to take up any of the many major societal issues that I believe are of considerable importance.
- -- Several others (some before the OPMS s/w became available; some after).
Message was edited by: GS Chandy