COMMENSAL ISSUE 95


The Newsletter of the Philosophical Discussion Group
Of British Mensa

Previous Article in Current Issue

Number 95 : February 1999

Next Issue (Commensal 96)


ARTICLES
10th October 1998 : Valerie Ransford

COMMENTS ON C94

Dear Theo,

Seasons’ greetings and welcome to new members.

The best in Commensal 94, for me, was Albert Dean’s The Thinking Process (C94/27). It’s going to be incredibly useful. Ideas like these are what one joins Mensa for.

As for John Neary’s advice (C94/15), I’ll read Dancy’s Contemporary Epistemology as soon as I find it. At the moment, all I know about epistemology is in the Oxford Companion to the Mind. Here J.G. Cottingham reminds us of the question : "In what sense does a person who has knowledge differ from one who has a belief that happens to be true ?".

I am grateful, too, for Rick Streets’ messages on C94/33. I do, I do admit my own ignorance whenever I think of Descartes. What’s new to me is Rick’s idea that overuse of the word knowledge is holding back the development of mankind. Smashing. I’ll remember this for ever and quote it often.

As for John Stubbings (C94/13); it is always rewarding to enlighten someone. I believe he is mistaken about mathematics, however. Unless one believes with Marshall McLuhan that "The Medium is the Message", (and J.S. clearly does not) mathematics is not "just another medium" as he puts it. He’s probably a bit mixed up, confusing mathematics with statistics or accounts. Mathematics, like other Arts, is for itself. More enlightenment ?

Have fun. Happy new year.

Valerie Ransford


Valerie : having a mathematical background, I think I ought to say something about your parting shot to John Stubbings, though I’m not too clear what your point is ! I’ll leave John to defend himself against the charge of confusion and proceed to the ontological status of mathematics.

Most working mathematicians are, it is said, Platonists, who believe that Mathematics is discovered rather than invented. But, in this case, where is the undiscovered mathematics ? Hence the reference to Platonism. The form of the true circle is out there somewhere, and all real-life circles are but pale reflections of the "really" real thing. However, I believe it’s easy to get confused between mathematics as an end in itself and mathematics as a description of the world. Also, between the mathematics and its theorems. The mathematics is invented - in the sense of the mathematical game we want to play - with its axioms and transformation rules for generating theorems. Given the invented mathematics, the theorems are discovered; but these are not discoveries about the real world, but only discoveries within a mathematical world of our own devising.

The world, however, is out there, not invented. The remarkable thing is that it is, at least sometimes, describable by mathematics. If this is the case, then the theorems derived from mathematics also correspond to facts about the world, at least if we make the correct "simplifying assumptions" and ignore second order effects and other issues that make the mathematics intractable. Kepler’s approximate laws are explained precisely by the mathematical theorems associated with inverse square laws operating in Euclidean space.

The role of beauty differs between mathematics and the sciences. In mathematics, beauty is allied to elegance and economy, and applies either to the mathematics itself, or to the manner in which the theorems are proved. The mathematics - the axioms and transformation rules - may be more or less quirky. A true theorem may be proved more or less elegantly, and an inelegant proof, while maybe not invalid, is "wrong". On the other hand, a physical theory, however, elegant, is not thereby correct, being disproved by that famously ugly fact. Physicists are, though, led, and sometimes misled, by a search for beautiful (that is elegant) theories.

Anyone know why the world should be subject to mathematical description, and why at least some correct physical theories should be mathematically elegant - other than the old favourites of the faithfulness of God and Kant’s intuitions, which deny that we perceive the world as it is in itself, but only in conformity to our faculties ?

I look forward to a repost from Alan Edmonds on this one !

Theo



Previous Article in Current Issue (Commensal 95)
Index to Current Issue (Commensal 95)