When I went to Uni a common pairing was "physics and philosophy". That was my chosen degree subject when I was in high school. I wanted to do particle physics.
In the end I loved (pure) maths more than philosophy so graduated with Theoretical Physics and Mathematics. There were probably a quarter of the physics students doing the Philosophy of Science module (the only things I remember covering were Aethers, Xeno's Paradox, maybe also the Realism of QM Interpretations [it was a couple of decades ago]).
One could just as easily say that mathematicians are natural philosophers clouded by rigid symbols that have no inherent meaning on their own. For every zag, a zig.
Alright, I’ll bite. I challenge your assertion that math is without objective meaning.
First I want to make an observation. Do you know the history of how the study of complex algebra/calculus came about? If so, I assume you will agree that it was initially a completely abstract thought experiment with no connection to anything in the “real” world.
Given your assertion that math is without meaning, it would seem to me that mathematical ideas that originate purely out of human imagination would just be arbitrary semantics.
Then how can it be that complex analysis only several decades after it was formulated turned out to be not only useful, but necessary to formulate the theory of quantum mechanics in a way that agrees with physical observation?
I can name numerous other examples of the same phenomenon; namely that a purely abstract mathematical idea is long after its formulation shown to be profoundly reflected in physical reality.
To me it seems obvious that the way these phenomena occur implies that part of the process by which humans use their imagination and reasoning to come up with abstract mathematical ideas, is more akin to using their intuition to map out objective ‘structures’ of logic (that are also reflected in the underlying structure of physical reality) than to simply play with semantics, as it seems you are asserting.
Tl;dr
Post modernist philosophers are fools and they should be ashamed. Qed
I agree with you that there are many incredible and useful insights based on mathematics and the equals sign, but the main point of contention is that not every mathematical truth has a co-responding physical phenomenon. Nor can we adequately explain how an equals sign works, or why it works. Mathematics and [im]material reality are not one-to-one and assuming that mathematics supersedes the imagination or is a superset of human language and expression negates human experience and renders our lives as secondary to "almighty math." Mathematics is a tool, would you agree? Philosophy is also a tool. Mathematics without a human user is like a video game without a player. I am not asserting that mathematics has no "objective meaning" it _only_ has objective meaning (because for every "object" we must have a "subject" namely, the observing consciousness).
I'm always up for a discussion on this topic, because I find it very interesting and I think there is a major (dare I say it) metaphysical point here that is overlooked by mainstream intellectuals. However I've argued with enough post-modernists online over the years (which is usually like arguing with a wall) that I might have become a bit snarky- sorry about that, I appreciate the graceful tone in your response.
I agree that the symbolic language we call mathematics and reality are not one-to-one as you say. But the fact that we can use abstract reasoning around these symbols to uncover new ways of understanding of the physical world, especially in cases like the one I lined out in my example, implies to me that there must be some objective reality that is in some way captured by these symbols, in a way that plain philosophy cannot.
So to answer your question, I agree that math is a tool, but I think in some sense it also more than a tool. I believe it can also be seen as a map into a platonic reality, and that there is some element of our mind that is able to observe this realm which allows us to draw the map (using mathematical symbolic language) and come to an agreement about how it should be drawn. And that elements of this platonic realm are for some mysterious reason also reflected in the structure of our physical reality.
Nietzsche solved philosophy; everything since has been quibbling over semantics, there is no original thought anymore. Whereas physics’ Nietzsche was Newton, and there have been continuous advances since his time.
Maybe in the sense the Von Braun solved rocketry. I agree that everything that has come since have been refinements to Nietzsche's developments (dare I say models) but those refinements have brought about the real-world application of philosophy more than Nietzsche ever did.
See Mao, or Popper, or even though I can't stand the guy Chomsky.
Nietzsche and Wittgenstein worked to show many (most) of then current philosophical problems weren't. Bias and language were such a big part of problems that when substracting them, they were rendered hollow. So the subject, as it was until XIX century, could very well be called a problem and yes, it was solved.
Sure, if you totally reframe the entirety of what it means "to solve philosophy" to mean what you said, then gaius's comment makes sense.
I'm not sure I agree that solving a lot of the then/now "problems" with philosophy is the same as solving the entire field of philosophy. Especially since it requires mobile goalposts.
Also, it's a hilarious and an absurd claim "x Solved Philosophy" because that's like saying "Tony Hawk solved the skateboard." Perhaps Tony Hawk is great at skateboarding, but you can never personally know what it's like until you try yourself. Philosophy is not something that can be solved by someone outside of yourself, not even Nietzsche can wipe away your ignorance, only you can do that for yourself.
No. I suppose when you say "nothing" you're talking about philosophical propositions, which can be mapped to computer programs. In which case we can note that (1) the vast majority of programs have never been generated before by any process and (2) the vast majority of possible programs cannot be reduced to simpler programs that might have been expressed earlier.
Who said anything about computers? The whole universe is in a constant state of Recycling. Remember that old adage "energy/matter cannot be created nor destroyed?"
I recall someone (Eliezer Yudkowsky?) writing an essay with the thesis that a couple of millennia of epistemology did not foresee the epistemic issues raised by quantum mechanics.