about maths: strictly speaking, off topic, but justified.
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From: tonyb on 16 Mar 2010 16:57 On 16 Mar, 20:29, rabid_fan <r...(a)righthere.net> wrote: > On Tue, 16 Mar 2010 12:14:03 -0700, tonyb wrote: > > this language game extremely carefully. From a series of analysed games > > he then attempts to form a foundation for logic. > > Which then completely blows up when Goedel and his incompleteness > enters the picture. Wittgenstein was forever opposed to this > indeterminacy introduced by Goedel. In reality, there can be > no overarching foundation, only ad hoc and disjointed fragments > generated to meet some utility or purpose. > > > > > The relationship is that > > mathematics and music both carry signification - they evoke meaning. > > Well, music is much closer to basal motility. It has no meaning > in the usual sense of the term. Music is a direct substitute > for motility, or, less awkwardly stated, music *is* motility. > > In fact, thought itself, and hence meaning, is able to dissolve > completely into movement. This is the phenomenon of the dance -- > dance in a very primordial sense involving an actual suspension > of consciousness. > > In other words, there is no distinction between thought, meaning, > and motility. > > The nervous system has evolved to control motility. There is no > other purpose. The question is therefore: how does thought and > meaning arise from this motility control structure? Thought and > meaning seem to be beyond physicality, and this apparent uniqueness > has beguiled philosophers throughout human history. > > > > > have a feeling I'm not understanding the your point/question here > > Well, it is difficult to be clear using only very few words. I am more > or less rambling do the unexpected turns of the topic. > > There is much background material to introduce before a serious undertaking > of this subject can be begun. well, thanks for the interesting ramble/ its been fun.
From: Sam Wormley on 16 Mar 2010 18:04 On 3/16/10 3:39 PM, Urion wrote: > Mathematics is a language but it is also an art, just like chess or a > painting is also an art. Perhaps for you!
From: jmfbahciv on 17 Mar 2010 08:10 rabid_fan wrote: > On Tue, 16 Mar 2010 08:14:01 -0500, jmfbahciv wrote: > >> I'll ask the damn question again...if you claim that math is a language, >> what are the verbs? >> > > I will answer the damn question again: not verbs, but predicates. > > Another, more general, name for mathematics, is, guess what, logic: > > http://www.cs.rochester.edu/~nelson/courses/csc_173/predlogic/ > No, it is not. /BAH
From: jmfbahciv on 17 Mar 2010 08:12 tonyb wrote: >>> I'll ask the damn question again...if you claim that math is a language, >>> what are the verbs? >> I will answer the damn question again: not verbs, but predicates. >> Another, more general, name for mathematics, is, guess what, logic: > > I don't think a language has to have any verbs in order to be > considered a language in the first place. > > My understanding of Wittgenstein (??) is that we use language to point > to pre-existing learnt concepts; these are learnt through 'language > games' played as a child (see below); that concepts are essentially > abstracted experiences e.g. "give dad the blue block" is a compound of > many integrated language-games involving pointing at 'dad', 'block' > and holding one various lumps of wood in your hand etc... Language > then, is just like pointing at abstracted memories using symbols > (words and other things) and our shared experience allows us to convey > meaning. > > If you hold with this definition of a language and then think about > how we learnt to count as children, you have the basis of mathematics. > I'm no an expert here (any ideas rabid_fan?) but I think Russell then > takes this 'definition' of counting as the starting point of formal > logic. > > Then think about your early experiences of velocity, perhaps sitting > on a river-bank watching the water. You may have even spotted a guy in > a white-wig sitting near you, muttering something about fluxions. Good > language for rivers, that one. > > (From Wikipedia: Wittgensten:) > The classic example of a language-game is the so-called "builder's > language" introduced in �2 of the Philosophical Investigations: > The language is meant to serve for communication between a builder A > and an assistant B. A is building with building-stones: there are > blocks, pillars, slabs and beams. B has to pass the stones, in the > order in which A needs them. For this purpose they use a language > consisting of the words "block", "pillar" "slab", "beam". A calls them > out; � B brings the stone which he has learnt to bring at such-and- > such a call. > Later "this" and "there" are added (with functions analogous to the > function these words have in natural language), and "a, b, c, d" as > numerals. An example of its use: builder A says "d � slab � there" and > points, and builder B counts four slabs, "a, b, c, d..." and moves > them to the place pointed to by A. The builder's language is an > activity into which is woven something we would recognize as language, > but in a simpler form. This language-game resembles the simple forms > of language taught to children, and Wittgenstein asks that we conceive > of it as "a complete primitive language" for a tribe of builders. It's a shorthand form of the builder's language which contained verbs. Each keyword implies an action which had to be taught to the assistant using verbs. Now, where are the verbs in math? /BAH
From: rabid_fan on 17 Mar 2010 11:40
On Wed, 17 Mar 2010 07:10:00 -0500, jmfbahciv wrote: >> >> Another, more general, name for mathematics, is, guess what, logic: >> >> > No, it is not. > Yes, it is. Mathematics is a formal system, which contains symbols, a grammar, a set of axioms, and inference rules. Logic is the process by which the whole thing proceeds from axioms and inferences to statements, based on the grammar, and theorems. "Verbs" are to be construed as the assertions made regrading any of the objects, as they are in ordinary language. But actually, the statement that "mathematics is a language" is being used a bit more loosely, I would think, in this discussion. Mathematics, like language, is used to convey meaning about the world, and mathematical objects, like the objects of language, are used as a basis for thought and conjecture. |