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

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

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.


“Cardinal” numbers with values appear to necessarily use language to
describe the unit being measured or quantified (tons, kilos, etc.)?
Quantitative description.

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

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.



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