Tuesday, April 11, 2006
On maths as another religion, or the problems with Set Theory: Should You Believe?:
Most of the problems with the foundational aspects arise from mathematicians' erroneous belief that they properly understand the content of public school and high school mathematics, and that further clarification and codification is largely unnecessary. Most (but not all) of the difficulties of Set Theory arise from the insistence that there exist 'infinite sets', and that it is the job of mathematics to study them and use them.¶ 7:38 PM
In perpetuating these notions, modern mathematics takes on many of the aspects of a religion. It has its essential creed---namely Set Theory, and its unquestioned assumptions, namely that mathematics is based on `Axioms', in particular the Zermelo-Fraenkel 'Axioms of Set Theory'. It has its anointed priesthood, the logicians, who specialize in studying the foundations of mathematics, a supposedly deep and difficult subject that requires years of devotion to master. Other mathematicians learn to invoke the official mantras when questioned by outsiders, but have only a hazy view about how the elementary aspects of the subject hang together logically.
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Occasionally logicians inquire as to whether the current `Axioms' need to be changed further, or augmented. The more fundamental question---whether mathematics requires any Axioms---is not up for discussion. That would be like trying to get the high priests on the island of Okineyab to consider not whether the Divine Ompah's Holy Phoenix has twelve or thirteen colours in her tail (a fascinating question on which entire tomes have been written), but rather whether the Divine Ompah exists at all. Ask that question, and icy stares are what you have to expect, then it's off to the dungeons, mate, for a bit of retraining.
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Doesn't Putnam's quasi-empirical methods into mathematical "foundations" do just that?
BTW - I'm intrigued. Why suddenly a post unrelated to Heidegger? Or is their a Heideggarian angle I'm missing?
BTW - I'm intrigued. Why suddenly a post unrelated to Heidegger? Or is their a Heideggarian angle I'm missing?
Haven't read Putnam.
The angle is Badiou going on about Set Theory and ontology. That said, not everything must be Heidegger related. That's just the attraction that pulls in the surfers--and en-traps them, heh. On the other hand, keeping up on Heidegger content is pretty much all I usually have time for, so there we are.
The angle is Badiou going on about Set Theory and ontology. That said, not everything must be Heidegger related. That's just the attraction that pulls in the surfers--and en-traps them, heh. On the other hand, keeping up on Heidegger content is pretty much all I usually have time for, so there we are.
You ought read Putnam's work. It's widely reprinted in various readers. I did a post on it last year.
It's actually somewhat interesting if one considers it in terms of Heidegger's own thought on the mathematical in the 1930's. i.e. why do we chose the projective ontologies we do.
It's actually somewhat interesting if one considers it in terms of Heidegger's own thought on the mathematical in the 1930's. i.e. why do we chose the projective ontologies we do.
Just an other quick thought.
I think that if one expands Putnam's notion of quasi-empirical approaches to mathematics one ends up very much with Derrida's conception. Indeed Derrida's appeal to Godel ends up being the same. And I suspect a lot of what Derrida is getting at is the projective ontology of Heidegger in the 30's and in section 69 in B&T.
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I think that if one expands Putnam's notion of quasi-empirical approaches to mathematics one ends up very much with Derrida's conception. Indeed Derrida's appeal to Godel ends up being the same. And I suspect a lot of what Derrida is getting at is the projective ontology of Heidegger in the 30's and in section 69 in B&T.
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