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Jan
7
comment Does the mathematics of physics require impure set theory?
Fair enough, thanks for the input. I'll ask about this at Math.SE.
Jan
7
comment Does the mathematics of physics require impure set theory?
@NickKidman I'll admit that I don't have a clear conception of what the "primitive relations of physics" are. I was hoping to get some guidance and plausible examples here. I suppose a rough characterization of what I have in mind are the primitive (undefined) relations of fundamental physics. Obviously this is somewhat cagey, but hopefully it is clear enough to elicit some helpful suggestions? Should this be a separate question ("What are the primitive relations of fundamental physics?")?
Jan
5
awarded  Commentator
Jan
5
comment Does the mathematics of physics require impure set theory?
Thanks for the reference by the way, very helpful.
Jan
5
comment Does the mathematics of physics require impure set theory?
Also, do you have any thoughts on differences like these between pure and impure set theories? If the theories really are "synonymous" then shouldn't the metatheoretic results coincide?
Jan
5
comment Does the mathematics of physics require impure set theory?
Your question is essentially an answer to my question. I was curious as to whether impure set theory was indispensable. You are saying that any theory that could plausibly be a foundations for mathematics would suffice for physics. So, no one theory is strictly required and no impure set theory in particular is required.
Jan
5
comment Does the mathematics of physics require impure set theory?
Hmm, very interesting. I stand corrected! Has there been any discussion of this paper in the literature that you know of?
Jan
5
comment Does the mathematics of physics require impure set theory?
I agree with your second point, and do not favor this reductionist attitude. I'm just trying to approach this from the standpoint of someone who favors reduction for reasons of simplicity of theory, since that is who I am attempting to respond to.
Jan
5
comment Does the mathematics of physics require impure set theory?
Impure set theory cannot be interpreted in terms of pure set theory. Well, if by that you mean "there's no real difference" then you're wrong. They have different primitives and impure set theory can only be "interpreted" within pure set theory by adding an additional theoretical primitive, the predicate "is a urelement". But once you do that, you haven't interpreted impure set theory within pure set theory, you've simply turned pure set theory into impure set theory!
Jan
4
comment Does the mathematics of physics require impure set theory?
No problem with the delay. Would you say that it is the prevailing sentiment among physicists that mathematics merely models physical phenomena and is not somehow more intricately bound up in the phenomena themselves? Do you know of any physicists who have voiced an opinion on the matter in print? If the answer is "Sorry, I don't know", that is perfectly fine. I don't want to abuse your generosity here, it just seems like your attention is the only that I've attracted with this question. Thanks again for your input! It's nice to hear what people in overlapping disciplines think.
Jan
3
awarded  Supporter
Jan
3
comment Does the mathematics of physics require impure set theory?
Oh no worries! Thanks for any help at all that you can provide. I am a philosopher/logician by trade and am woefully under-informed with respect to physics. So I appreciate any assistance in better understanding this topic.
Jan
3
comment Does the mathematics of physics require impure set theory?
I'm currently reading a paper where the author assumes that physics requires set theory, and in particular impure set theory. He then proceeds to argue for a set-theoretic construal (as opposed to mereological) of physical geometry and defends it on the grounds that it is simpler (in just the sense you describe in the second paragraph) than its mereological counterpart. I was skeptical of his claim that impure set theory was indispensable to physics and it seems that you think my suspicions are right.
Jan
3
comment Does the mathematics of physics require impure set theory?
The second and third paragraphs ("The...options.") provide exactly the sort of information I am looking for. Do you know of any papers that discuss what you describe in those paragraphs? The reason I'm interested in this is that there is a common argument in the Philosophy of Mathematics (the area I work in), the "Indispensability Argument" which argues that we must accept mathematical entities because they play an indispensable role in our best theory of the world (assumed to be something like fundamental physics). -> see next comment
Jan
3
awarded  Student
Jan
3
comment Does the mathematics of physics require impure set theory?
If further clarification is needed, let me know. Also, I hope this question is appropriate for this forum.
Jan
3
asked Does the mathematics of physics require impure set theory?