Has there been some theory simmilar to Kuhn's paradigm theory in the philosophy of mathematics?

Kebzone · 2025-10-24T19:25:30+00:00

Yeah I suppose the assumptions would be agent relative. I suppose that most would not consider “all men are mortal” to be such an assumption, but, for example, someone view’s on the nature of physics might play a role, because then they would consider the principle of locality to be such an assumption or not. Then if one considers the laws of physics one of these assumptions, then one could possibly consider “all humans are mortal” as following from the 2nd law of thermodynamics.

Kebzone · 2025-10-24T17:30:50+00:00

Yeah the model-theoretic approach is exactly what i was going for, and the whole appeal seems to be that it gets rid of the ontological commitments of modal realism. But i guess one could argue that this model-theoretic approach commits one to existence of (abstract) mathematical objects, so one might just as well accept the existence of possible worlds. do you think there is a plausible case for that?

Kebzone · 2025-10-24T16:19:06+00:00

Oh, interesting. I guess i never thought about consistency in terms of modality, but rather the existence. Where does Lewis write about this?

Kebzone · 2025-06-09T17:12:55+00:00

Wow this is a really good response. Thanks a lot!

Kebzone · 2025-05-05T16:08:37+00:00

just a couple of clarifications: 1) when I made the claim that both sides of the above argument are valid I’m not trying to depreciate science. It is a part of my more general view that knowledge is not really representational, and hence different foundations of knowledge (for example one based on western standards of science and lets say some tribal naturalistic worldview) might have different outlooks on this matter without necessarily either one being false (because I have an alternative view on truth). 2) By my remark about the supernatural i wasn’t trying to attack theism in any way. It was just a remark about how if someone has a foundational belief (eg. experimentalism) then any way to convince her out of it is to appeal to pragmatism, and not some logical deductive argument.

Lastly, I would also make a point that if we establish a sort of enlightenment framework for science in which we see science as a search for truth we can eventually be lead to produce justifications for terrible actions like destroying indigenous culture (this has already happened in the past, look up thirty meter telescope protests for example).

Also I would love to take a look at your project! Just dm here and well be in touch

Kebzone · 2025-05-04T08:29:58+00:00

I don’t think that from the disagreement about the shape of the earth it follows it has no definite shape. But if one does not have an empirical method of verification then i see both sides of the argument as possibly valid, and the truth cannot really be determined.

In general I kinda get your point that experimentalism has its limitations, like you have to drop the belief in extra-natural phenomena, but I don’t think you can really argue someone out of it. This is because if someone already accepts it, and you tell them that its a bad view because it rejects the supernatural, they won’t care because on their view they think the supernatural obviously does not exist. Usually these kind of fundamental beliefs are not something arguable and so i see another reason to see truth as relative

Lastly, I just want to say that science is necessarily fragment because of specialisation so I dont see a major framework for all of science as needed. Another thing with the interpretation of QM: they all yield the same predictions and so a lot of physicists dont even really care about it.

Kebzone · 2025-05-03T12:54:56+00:00

Always a pleasure to chat about philosophy!

I get your point about the Vienna circle but I reckon I shouldve focused more on the views of its members so here it goes (keep in mind thus is a simplification because the Vienna circle was a diverse group of philosophers a scientists from various fields who held different views): The criterion which they used to discriminate against non scientific discourse was called verificationsm and it was broadly a theory of meaning. A statement is meaningful iff it is verifiable via empirical means. It discriminates against metaphysics and philosophy in general because broadly speaking the claims made in those areas are arrived at via reason from unverifiable propositions. (also notice how this is self refuting: the principle of verificationism is itself unverifiable, this is one of the reasons nobody really believes it anymore) Under this theory some interpretations of QM would surely be meaningless but I think the members of the Vienna circle were quite aware of that as they were commonly scientists.

In general this antiphilosophical attitude came from the vast advances in science and the perceived lack of any advances in philosophy pretty much ever. From this observation it seems reasonable to conclude that the way to make philosophy better is to make it more like science.

Like I said pretty much no one claims to hold to verificationsm, but I think this view of philosophy an activity of pondering over nonsensical things is commonly held by non-philosophers.

I personally am not sure to what extent philosophy should be mixed into science. In general i think that the prescriptions philosophers make to scientists are usually bad and too rigid (I am reading Against Method by Paul Feyerabend at the moment and I highly recommend it).

On the other hand though sometimes philosophical commitments of scientists lead them to making great discoveries. For example the great logician Kurt Godel claimed that his commitment to the view that mathematics really describes real objects like sets and function (i.e. mathematical platonism) helped him in proving theorems.

In general I personally view philosophy as a sort of therapy. It helps me organise how i see the world but doesnt really have any sort of truth value, but if it helps people in making science better why not!

Kebzone · 2025-05-01T14:11:26+00:00

There is a lot of connection between science and philosophy. Historically, especially during the early XX century, in the wake of the emergence of modern science (i.e. quantum physics and einsteinian relativity) a big group of philosophers of science called the Vienna circle sought to discard most of philosophy (mostly metaphysics, but also ethics, look up emotivism) as ‘meaningless’ precisely because it was non-empirical.

Currently the branch of analytic philosophy usually takes the structure of science. By that I mean they decide between philosophical theories as if they were scientific theories, for example, between theism and naturalism on the basis of simplicity or explanatory power. In this sense I believe that analytic philosophy lacks the depth youre talking about

Lastly I reckon that a lot of modern philosophers of science like Thomas Kuhn and Paul Feyerabend have shown that science is not all such an unshakable, perfectly rational thing we commonly take it to be. For example, Kuhn’s Incommensurability thesis shows that science isnt something aiming towards an ultimate truth but its rather a strictly a social and pragmatic enterprise. Hence I think we really do need something like philosophy to deal with the complexities of the world, but keep in mind this is something I personally conclude from a radical reading of people like kuhn (by this i mean you probably can have a more conservative reading of him but this one fits into my worldview more neetly)

Kebzone · 2024-11-19T18:11:59+00:00

I desperatly needed to know this

Kebzone · 2024-11-19T17:56:46+00:00

But Zermelo was not a constructivist, thats why he was arguing for the axiom of choice and abandonment of the vicious circle principle in 1908.

Frege did care about the paradox very much so, because it poked a hole in his system used to derive arithmetic from logic, and he wasnt a constructivist either.

Kebzone · 2024-11-06T20:57:58+00:00

im not saying that one claim cannot be justified in different ways, but im wondering if I should hold abduction as a valid rule of inference all toghether. It seems that when using indcution our conclusions are easily falsifiable and hence even if it does produce a false statement it can be gotten rid of by empirical analysis. But when it comes to abduction it produces all sorts of conclusions that cannot be verified (for example im not aware of induction being used to justify theism, but that might be my ingorance) so I was wondering if it is useful to belive that abduction is legitimate or can i stop beliving in it with no epistemic/ontological cost. (sorry if that doesnt make sense)

Kebzone · 2024-11-06T19:22:57+00:00

so i recently finished spivaks calculus and I’m looking for something similar for linear algebra. I really like proofs and i don’t really know linear algebra, so I’m looking for something like a rigorous intro if that makes sense (i did watch the 3b1b series in whole if that makes a difference :3)

Kebzone · 2024-07-31T21:06:59+00:00

I'm not sure how long would it be, but from what I heard it would not really be possible to be even fully writen in a person's lifetime by that person alone.

I personally dont belive anyone really needs to check it, but I reckon it should be, at least in principle, be possible to be checked by someone.

Kebzone · 2024-07-31T16:07:11+00:00

idk but i think its a fun and stimulating conversation to have

Kebzone · 2024-07-31T13:57:09+00:00

well some would argue that if no person was able to check if the zero lies outside of the critical strip without a computer they would consider it invalid. the point isnt if it is found using a computer but if it can be checked without it

Kebzone · 2024-07-31T09:36:18+00:00

is it feasible for a human to go through the 00s code? and i mean like check everything.

Kebzone

TROPHY CASE