On Mar 7, 5:29 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> 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
> >>> 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.
> But it is not valid to infer from this, that mathematics is *about*
> 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.
Yes, but even the symbols =, +, x, *, are notations that are
substitutes for words. Eg. Equals, addition or union, multiplication.
The operational notations are words used to describe the formulation
of the 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.
Yes. Then it is Ok to use it for that. eg. 1stness, 2ndness, 3rdness
in sport races gives a quality of feeling to the participants,
> > 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.
It is the “lived experience” that is reality as I understand.
The condition of the universal environment is influenced by an event
at a point in time of the evolutionary process. eg. Certain
qualitative conditions existed in Oct. 1066 in Britain. Also,
9/11/2001. In nature: January in central Europe exudes certain
environmental qualitative conditions.
> > 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.
Duration of time is quantitative. Existing conditions in the duration
You state: “Quality is more 1p” but it is not exclusive to 1p. Humans
observe and have empathy for others qualitative conditions and
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