On 06 Mar 2012, at 20:44, Pzomby wrote:

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On Mar 6, 10:14 am, Bruno Marchal <marc...@ulb.ac.be> wrote:On 06 Mar 2012, at 17:32, meekerdb wrote:On 3/6/2012 4:26 AM, Bruno Marchal wrote:It's a language game.The word "game" is so fuzzy that this says nothing at all. Game theory is a branch of mathematics.But "language" says something. It says mathematics is about description.Mathematicians search what is language independent, and description independent. They don't like when a result depends on the choice of a base. Mathematics is more about structures and laws. Math uses languages, but is not a language, even if it can be used as such in physics. But there is more to that.Bruno: “Cardinal” numbers with values appear to necessarily use language to describe the unit being measured or quantified (tons, kilos, etc.)? Quantitative description.

OK.

`But it is not valid to infer from this, that mathematics is *about*`

`description.`

`On the contrary, mathematicians reason on "models" (realities,`

`structures), and they use description like all scientists.`

`mathematical logic is the science which study precisely the difference`

`between description (theories) and their interpretations (in from of`

`mathematical structure).`

`As you mention the notion of cardinal, a discovery here made by`

`logicians is that the notion of cardinal is relative. A set can have a`

`high cardinality in one model, and yet admit a bijection with N in`

`another model.`

“In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc.” http://mathworld.wolfram.com/OrdinalNumber.html Are the “ordinal” numbers actually adjectives describing the relational position in a sequence (first, second,…one-ness, two-ness etc.)?

They can be used for that. But they can be much more than that.

Are numbers (ordinal) necessarily qualitative descriptions?

`Perhaps. In the comp frame, I prefer to ascribe the qualities of`

`numbers, by the possible computational relation that they have with`

`respect to their most probable universal environment. This is more`

`akin with the human conception of quality as being a lived experience.`

`But what you say might make sense in some other contexts.`

Numerals symbolize number position (as in particular instants in the sequence of the continuum of time).

`OK. But that's quantitative for me, or at least a "3p" type of notion.`

`Quality is more 1p, and can be handled at the meta-level by modal`

`logic, or by (often non standard) logics.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.