On 3/8/2012 1:43 PM, Bruno Marchal wrote:

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

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 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.Hmm... OK.In logic they are symbol associated with axioms and rules, and theyhave (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), ....}.

Dear Bruno,

`I could not resist! So they are infinite after all! Umm, where did`

`I see the idea of representing things as equivalence classes... LOL! I`

`wrote of that a while back... Whatever... My apologies, I am in a good`

`mood and being my normal sarcastic self.`

“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 themind of the machine winning the competition, or in the mind of themachines members of the jury, than in the ordering relation itself.

`Are these not equivalent in the Platonic sense? After all, we are`

`considering universal machinery that ignores any kind of local gauge`

`symmetry.`

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.OK. That is the reality of subjective experience, but we can bet thereis something independent of that reality, and which might beresponsible for that reality.

`It seems to me that any one that would bet against that "there is`

`something independent of that reality" would be a sucker or a solipsist`

`or some superposition thereof! How does this tie into 1p indeterminancy?`

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, manyqualitative conditions can happen, assuming digital mechanism.

`Wait a second, does not digital mechanism assume a fixed`

`substitution level?`

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. BrunoDuration of time is quantitative. Existing conditions in the duration are qualitative.I doubt this. I would bet that if time can be quantitative, andobjectively measured by different observers, the duration notion ismore qualitative, and subjective.

`How can a "measure of change" be anything but quantitative? Given`

`that we are seriously considering that all of our 1p and 3p tropes are,`

`literally, nothing more than numbers and relations between them, what`

`else is there?`

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.

`It could be that "qualities" are just spectral ranging over local`

`gauges... THink of how we can associate even an infinite field of`

`continuous transformations with a single point using fiber bundles. I`

`strongly suspect that this is exactly equivalent to "infinite`

`computations running through each 1p"...`

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