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Topic: Is logic part of mathematics - or is mathematics part of logic?
Replies: 52   Last Post: Jul 5, 2013 1:27 AM

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 Wayne Bishop Posts: 5,465 Registered: 12/6/04
Re: Is logic part of mathematics - or is mathematics part of
logic?

Posted: Jun 28, 2013 1:03 PM

is the not very profound "YES". Nearly always
emphasis on one rather than the other - almost
exclusion of one in deference to the other - is
implicitly obvious from the context so the real
question is: Why waste anymore time on it?

Wayne

At 09:13 PM 6/27/2013, GS Chandy wrote:
>The questions in the subject-line have long
>interested me most keenly during my decades-long
>efforts to develop practical means that could
>help people at large design and improve existing
>'systems' of various kinds' - 'individual'; 'organisational; and 'societal'.
>
>Over the years, I've invested a fair amount of
>time and effort contemplating and considering
>the above questions. I must confess I do not
>yet have a definitive answer by any means except
>the not very profound insight that the answer
>has to be 'YES' to both questions, i.e.:
>
>i) Logic (in a sense) "IS INCLUDED IN" math; and
>
>ii) Math (in a sense) "IS INCLUDED IN" logic.
>
>(Of course, both statements demand that the
>transitive relationship "IS INCLUDED IN" would
>need to be clearly specified. Also, the 'sense'
>of the qualifier would need to be adequately clarified).
>
>Of course, the above statements imply that:
>
>a) Logic (in a sense) "INCLUDES" math; and
>b) Math (in a sense) "INCLUDES" logic.
>
>[None of the above statements is 'universally' true).
>
>ALL of the above would become somewhat clearer
>if we could in parallel use what I call
>'structural graphics' [i.e. use 'prose +
>structural graphics'' (p+sg)] to extend the 'pure prose' I am using here.
>
>(I note that 'p+sg' would include Venn diagram
>illustrations of various prose statements -
>these are most useful indeed. The greatest
>particular benefit of p+sg is that it enables
>people at all levels of knowledge and
>understanding to communicate with considerable
>clarity on the most complex and troubling
>issues. It's generally a lack of clarity in
>communications between different parties to any
>argumentation, anger, litigation - even war!!!
>
>Unfortunately such needed facilities to use p+sg
>effective do not currently exist - I hope to
>have a website developed in a few months, at
>which I shall be making such facilities available.
>
>All of the above would become considerably more
>clear if we were to construct (and discuss)
>structural representations of a few of our
>'mutual mental models' when we discuss these
>questions - representations of my mental models
>models. This requires a little learning (of
>Warfield's approach to systems science) along
>with a little 'unlearning' that our conventional
>education systems have stuffed into our minds since we were children.
>
>In particular, the (transitive) relationship I
>have found that most helps clarify (to the
>inquiring mind) the structure of a system is:
>
>"CONTRIBUTES TO" (in various strengths: 'may';
>'would'; 'does'). We do need to use 'prose _
>structural graphics' (p+sg) for effective discussion of these issues.
>[The question will, most likely, never be
>clarified to the mind that does not construct an
>Models (ISMs) using the "CONTRIBUTION" relationship].
>
>The transitive relationship "PRECEDES" - much
>beloved by managers, 'management experts' and
>'conventional thinkers' is not very useful to
>clarify 'system structure': in fact, using
>'PRECEDENCE' as the primary system relationship
>the nature of the systems under consideration.
>
>Probably the most profound insights on issues
>related to the subject title have developed from:
>
>i) Bertrand Russell (and Alfred North Whitehead) in "Principia Mathematica";
>ii) Ludwig Wittgenstein in Tractatus
>Logico-Philosophicus, and the works of his students and followers;
>iii) Benjamin Peirce (BP) particularly in "The
>Science of Necessary Conclusions";
>iv) Charles Sanders Peirce (BP's son).
>
>[I must confess I have not by any means studied
>the works of the above-noted
>mathematicians/philosophers as closely as I
>probably should have to gain needed clarity on
>the inter-relationships between math and logic.
>
>John N. Warfield (a fair bit of whose work I
>HAVE studied and applied in some depth and
>fairly extensively) had developed a great many
>of his logical, mathematical AND 'systems'
>insights from the works of Charles Sanders
>Peirce - and his works have led to what I claim
>is probably THE most effective way to real
>progress on the issues relating mathematics and
>logic, specifically in matters relating to societal problems and issues.
>
>I am not certain I have all that is relevant to
>the above-noted questions. I provide in the
>following a partial list of useful references
>follows: it is highly eclectic, and eclectically arranged.
>
>If you need something better organised, you will
>have to approach me when my OPMS book is
>published - or you can check the book itself,
>which will contained an organised list of references.
>
>(This is in NO PARTICULAR ORDER, items have just
>been put down as they came to mind). The
>simplest way now available of gaining insights
>into the above questions would be by using the
>'OPMS', described at No. 2 below - and to create usable models for yourself.
>
>(Note: "SEP" - 'Stanford Encyclopedia of
>Philosophy' - a most useful, largely free resource).
>
>1. John N. Warfield - website:
>http://www.jnwarfield.com and the "John N.
>Warfield Collection" -
>
>2. 'One Page Management System' (OPMS) - a
>simple, practical aid to problem solving and
>decision making developed on the seminal
>contributes to 'systems science' from John N.
>Warfield. OPMS is briefly described at the
>attachments to my post at the thread "Democracy:
>
>3. Charles Sanders Peirce -
>http://www.peirce.org/ . Contains quite
>extensive archive of his writings on a variety
>of issues, including math and logic. Arisbe -
>The Peirce Gateway - http://www.cspeirce.com/
>3a. Peirceâs Philosophy of Logic, Jay Zeman -
>http://web.clas.ufl.edu/users/jzeman/csphiloflogic.htm
>
>4. Benjamin Peirce and "The Science of Necessary
>Conclusions" -
>http://www.lib.noaa.gov/noaainfo/heritage/coastandgeodeticsurvey/Peircechapter.pdf
>"Linear Associative Algebra" -
>http://ia600306.us.archive.org/4/items/linearassociati00peirgoog/linearassociati00peirgoog_djvu.txt
>- -- Benjamin Peirce in SEP -
>http://plato.stanford.edu/entries/peirce-benjamin/
>
>5. Ludwig Wittgenstein - 'Tractatus...' -
>'Philosophy of Mathematics' - http://plato.stanford.edu/entries/wittgenstein/
>5a. The Cambridge Wittgenstein Archive - http://www.wittgen-cam.ac.uk/
>
>6. A Crash Course in Arrow Logic, Yde Venema -
>http://staff.science.uva.nl/~yde/papers/arrow.pdf
>
>7. Logic and Mathematics, Stephen G. Simpson -
>http://www.math.psu.edu/simpson/papers/philmath/
>
>8. "Creativity and Logic"
>http://www.wetcanvas.com/forums/archive/index.php/t-231129.html
>
>9. Jan Brouwer - -
>- -- "The Development of Intuitionistic Logic"
>(in SEP) - http://plato.stanford.edu/entries/intuitionistic-logic-development/
>
>Mathematica" - promotes 'logicism': the view
>that (some or all of) mathematics can be reduced
>to (formal) logic - a view somewhat contrary to
>the position from which OPMS is developed -
>http://plato.stanford.edu/entries/principia-mathematica/.
>
>10. Gaurav Tiwari - "A trip to mathematics" -
>http://gauravtiwari.org/2011/10/25/a-trip-to-mathematics-part-i-logic/
>(A simple overview for beginners)
>
>11. Zermello's The Axiom of Choice; The Axiom
>of Choice and Logic; Zorn's Lemma; Maximal
>principles - SEP
>http://plato.stanford.edu/entries/axiom-choice/
>(et seq) - the Axiom of Choice has several 'deep
>connections' with the approach of the OPMS, not
>all of which I've explored adequately.
>
>12. "Phenomenology" - Avi Sion - in The
>Logician -
>http://www.thelogician.net/2b_phenome_nology/2b_chapter_08.htm
>(Based on an approach 'somewhat' different from
>that of the OPMS - but not logically contrary to it).
>
>13. Lotfi A. Zadeh: "Fuzzy Sets and Fuzzy
>Mathematics"; 'Soft Computing' -
>an approach to math philosophically quite
>congruent to that of OPMS - very much against
>
>14. "Logical Foundations of Fuzzy Mathematics" -
>based on the 'fuzzy mathematics' approach
>initiated by Lotfi A. Zadeh -
>http://www.mathfuzzlog.org/images/4/4d/Behounek-PhD.pdf
>(the doctoral thesis of one of the students of
>one of the followers of Lotfi A. Zadeh).
>
>GSC
>P.S.: On re-reading the above, I find that, on
>each issue and question discussed, I have left
>out much more than I have discussed. This
>deficiency may be rectified (at least to an
>extent) when I bring out the OPMS book).
>
>------- End of Forwarded Message

------- End of Forwarded Message

Date Subject Author
6/28/13 GS Chandy
6/28/13 Wayne Bishop
6/28/13 Joe Niederberger
6/30/13 GS Chandy
6/29/13 GS Chandy
6/29/13 Joe Niederberger
6/29/13 Joe Niederberger
6/30/13 Robert Hansen
6/30/13 stefen
7/1/13 GS Chandy
6/30/13 Joe Niederberger
6/30/13 Joe Niederberger
6/30/13 GS Chandy
7/1/13 GS Chandy
7/1/13 GS Chandy
7/1/13 Joe Niederberger
7/2/13 Robert Hansen
7/2/13 Wayne Bishop
7/3/13 Robert Hansen
7/3/13 Louis Talman
7/3/13 Wayne Bishop
7/4/13 Robert Hansen
7/1/13 GS Chandy
7/1/13 GS Chandy
7/2/13 Joe Niederberger
7/2/13 Joe Niederberger
7/2/13 Robert Hansen
7/2/13 GS Chandy
7/2/13 GS Chandy
7/3/13 GS Chandy
7/3/13 Joe Niederberger
7/3/13 Robert Hansen
7/3/13 Joe Niederberger
7/3/13 Anna Roys
7/3/13 Joe Niederberger
7/3/13 Robert Hansen
7/3/13 Wayne Bishop
7/3/13 Robert Hansen
7/3/13 Joe Niederberger
7/3/13 Joe Niederberger
7/3/13 Joe Niederberger
7/3/13 Robert Hansen
7/3/13 Joe Niederberger
7/3/13 Robert Hansen
7/3/13 GS Chandy
7/3/13 GS Chandy
7/3/13 Joe Niederberger
7/3/13 Robert Hansen
7/4/13 Wayne Bishop
7/4/13 Joe Niederberger
7/4/13 Joe Niederberger
7/4/13 Joe Niederberger
7/5/13 Robert Hansen