The Half-life of Facts.

Rolling ones eyes seems to be the killer argument du jour... A2K is dropping to high school level. Next step is to make the L sign on your forehead. That will tell 'em!

Thomas, you suggest that in THIS discussion aggressive disagreement may be "inevitable." I agree, and I suspect it has less to do with personalities than with the fact that our "conflict" is between paradigms. I don't think argumentation across paradigms can ever be fruitful. In my academic days I was routinely asked to review articles submitted to journals. In my later years I came to refuse to review works that reflected paradigms differing from the one I favored. In other words I chose to review only those works that more or less shared my theoretical presuppositions. That way I could critique them for being adequate or inadequate examples of work that was at least "right-headed" in its foundations.

Wow, and you've only been here since what, May? All I have to say is that probably 90% of discussions and debates are based upon
Argumenta per Carborundum until people just drift away based upon either frustration or boredome.

All I mean is: rolling one's eyes is no argument where I come from. If that's found offensive, so be it.

It seems to me that all facts rely on context. The conditions under which water boils may not change, but it's not unlikely that the metric scale will become outdated, and in a few hundred years 100 degrees means absolutely nothing.

Similarly, the way we understand circles may change, and so our facts about them may change. But the relationship between the radius and the circumference of a circle cannot change if it is to remain a circle, so perhaps pi is better viewed as part of the definition of a circle, rather than a fact about nature.

Yes, I see mathematical principles as reflecting the nature of "human mind" more than of the rest of nature.

Perhaps we can call mathematics the least biased language we have. It is certainly the most precise, since everything depends on strict definitions, rather than the rather ambiguous definitions of words. That is not to say that numbers can't be ambiguous, but more and more I am learning that the descriptive power of mathematics is simply awesome.

Euclid Elements is the oldest unedited text. The facts contained in its 13 volumes is as true today as they were 24 Centuries ago.

Rap

Oh yeah? A few pages ago you seemed quite happy to argue with Joe, Setanta, Frank, Parados and me.

A minimal paradigm across all of philosophy is that one's thoughts ought to be logically coherent and somehow interesting. So when I think my correspondents fail to supply this minimum, I complain --- never mind the paradigm stuff.

And how fruitful have our efforts been?

That sounds like the conclusion regarding symbolic logic by the Viena School of logical positivism (including early but not later Wittgenstein). I don't know; I'm just sharing my tentative impressions.
But it does seem to me that even the most unambiguous of denotations of mathematics can be ultimately biased, but in a manner different from the ambiguous connotations of normal language.

Very. I feel much better now.

Regarding the ontological status of mathematics, reference to the literature yields a formidable amount of technical discussion from the idealism of Platonic forms to the functionality of non-Eucldean geometry. One core issue is the status of set theory since it underpins both logic and the coherence of other mathematical structures. (I have already suggested problems with set theory earlier in this thread regarding measurement, and the nature of set membership in terms of "agreed properties").

From this, it seems to follow for me, that if metalinguistic levels of analysis (aka mathematics) are themselves problematic, then demands for "logic" at the normal level of language can be classed as secondary or even vacuous. And for me, the import of post-modernist philosophy is that it embraces such a conclusion and attempts to illustrate its consequences by means of deconstructive analysis of various issues. ( A good example of this for those interested, is Derrida's analysis of the impossibility (aporia) of "genuine hospitality").

So those here who demand "logical arguments" and "dictionary definitions" are not merely operating on a different paradigm, but are unaware of the intricacies of paradigmatics per se. And such awareness is surely central to a separation of philosophical from non-philosophical discussion.

I do not know much about set theory. But it seems to me that if mathematical facts have being or existence, their ontological status is similar to that of the hole in a donut.

No, they don't have a similar status. In fact, a hole in a donut is part of a mathematical fact called torus:

One could also say that torus is a mathematical description of a shape that is commonly found in nature. Donuts, tubes and rings of all sorts have ontological status. Torus, we could say, is merely a description of certain attributes shared by all these objects.

I don't agree with this. The diameter of a circle has a specific relationship to its circumference. It doesn't matter if we call it pi or bluto. We could define pi as equal to 1 and change all the other numbers. The relationship is still there.

Yes, and that is what the mathematics refers to. The relationship. It is the most precise and concise way we have to describe the spatial relationships that characterize a circle.

And we wonder why politicians, who are also humans, cannot find a way to agree...or at least have meaningful discussions in order to at least attempt to solve problems.

Suppose the mathematical model called "torus" is used to describe a theoeretical entity such "a magnetic field" such that it generates or predicts new experimentally observed data. What does this say about the "reality" (ontological status) of either the field or its shape ? I would argue that what is going on is a functional contextual application of an abstract model which could easily be superceded by an another model in terms of increased predictive power in a redefined context. We are at the stage now in physics where quite abstract models which often resist visualization, are successfully predicting data.There seems to be no limit to such modelling.

Toruses (and circles) are relatively easy to mentally assign with status, because we use them all the time for day-to-day "objects". Their "reality" is carried by association with our daily "naive realism" . But if we attempt to assign such status to successful yet more complex models I suggest we need to re-think any usage of the terms "fact" or "reality".