On 07 Mar 2012, at 18:36, Pzomby wrote:

On Mar 7, 5:29 am, Bruno Marchal <marc...@ulb.ac.be> wrote: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 thedifferencebetween description (theories) and their interpretations (in from of mathematical structure). As you mention the notion of cardinal, a discovery here made bylogicians is that the notion of cardinal is relative. A set canhave ahigh 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.

Hmm... OK.

`In logic they are symbol associated with axioms and rules, and they`

`have (standard) semantics, for exemple the mathematical "meaning" of +`

`is given by the set {(0,0,0) (0, 1, 1), (1,0, 1) (1,1,2) .... (6,7,`

`13), ..., (1, 23, 24), ....}.`

“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.htmlAre 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, observers/bettors.

`OK. But I would say the "quality" of being the first is more in the`

`mind of the machine winning the competition, or in the mind of the`

`machines members of the jury, than in the ordering relation itself.`

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 moreakin with the human conception of quality as being a livedexperience.But what you say might make sense in some other contexts.It is the “lived experience” that is reality as I understand.

`OK. That is the reality of subjective experience, but we can bet there`

`is something independent of that reality, and which might be`

`responsible for that reality.`

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.

`Once universal numbers are in relation with other one, many`

`qualitative conditions can happen, assuming digital mechanism.`

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 ofnotion.Quality is more 1p, and can be handled at the meta-level by modal logic, or by (often non standard) logics. BrunoDuration of time is quantitative. Existing conditions in the duration are qualitative.

`I doubt this. I would bet that if time can be quantitative, and`

`objectively measured by different observers, the duration notion is`

`more qualitative, and subjective.`

You state: “Quality is more 1p” but it is not exclusive to 1p. Humans observe and have empathy for others qualitative conditions and states.

I agree. 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.