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Mathematical Ontology

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Posted by Luis Hamburgh on September 8, 2001 18:39:59 UTC

ALL,

Reading through these threads, I see that many people ascribe metaphysical *meaning* to the focus of their posts. (I'm referring specifically to the idea that mathematical entities are not simply a human invention, but rather an innate aspect of reality.) This treatment of any scientific discussion will invariably decay into a "my dogma is better than your dogma" discussion.

Is it not the nature of science to maintain a tentative hold on belief, no matter how tried-and-true said belief may be?

I think the tendency to pursue 'meaning' comes from a sense within each of us that, if I can't show what a thing *means,* then I shouldn't rely on it so heavily (perhaps this urge stems from the need to validate a fragile ego -- "I know how things *really* are..." etc.). But this tendency leads to a logical dead end, at which point one must either (a) believe without further probing, or (b) accept that we cannot know 'meaning' without forsaking the very tentative nature scientific inquiry requires.

Our empirical and logical means have achieved tenfold the success rate of any other system of study. This success is possibly the biggest reason many people see maths as 'real,' but I see this way of thinking as a quantum leap over logic (pun intended). Some would use set theory to tout mathematics as independent of its objects, and therefore metaphysical, but an indepth examination of the issue reveals that set theory is wholly dependent upon the mathematics it supports. I.e., it is not independently logical. Again, we're heading down the road to absurdity.

Any argument for maths as metaphysical will boil down to an ontological one -- that is, an argument whose premise is specifically created so as to elicit its predetermined conclusion (it's the SAP all over again).

Thanks,

-LH

P.S. - Obviously I see the 'irony' someone might highlight thus: "Your belief that belief is only tentative is just as dogmatic as is my belief that some beliefs are innate," but this scenario would only serve to illuminate my bigger message: ascribing 'meaning' to our observations is akin to bending these observations and their foundations into logical Möbius strips.

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