>>7771416 If you were to ask a chemist to explain something in biology, like a reaction in the body, in terms of pure chemistry, he could.
If you were to ask a physicist to describe a chemical reaction in terms of pure chemistry, he could.
If you were to ask a philosopher to prove something in modern mathematics (analysis, topology, abstract algebra, etc.) he'd have no fucking idea.
But I understand you. You know that you are a useless piece of shit so to give yourself you value you say that somehow *SOMEHOW* science and mathematics *SOMEHOW* come from philosophy in some really weird and made up way that makes you sound like you are right, but in reality you would never be able to prove a theorem yourself.
>>7771433 >Try to name me a philosopher who did ANY work in mathematics. The only rule is that he has to have been alive in the past 300 years. Being this ignorant you don't even deserve to be alive, please get the fuck out of science
>>7771440 >A philosopher studied math so it doesn't count THEN HOW THE FUCK DO YOU WANT THEM TO PROVE SOMETHING, ARE THEY JUST GOING TO PULL PROOFS OFF THEIR ARSES OR WHAT? The fact that mathematics is applied philosophy doesn't imply that if you know philosophy you automatically know math, the same way a mathematician needs to study in order to contribute to physics for example. THE FACT THAT TWO FUCKING THINGS ARE RELATED DOESN'T MEAN UNDER ANY CIRCUMSTANCES THAT IF YOU KNOW ONE YOU SHOULD KNOW THE OTHER ONE. Just try to understand that fucking pleb. Fucking moron, you deserve to die
>>7771448 >THEN HOW THE FUCK DO YOU WANT THEM TO PROVE SOMETHING
Well, isn't math applied philosophy? This means that in the Venn diagram of life, philosophy completely surrounds mathematics, right? So I can ask a philosopher about Complex Analysis and he will answer me no problem right?
>The fact that mathematics is applied philosophy doesn't imply that if you know philosophy you automatically know math
Then in what practical sense do you say that math is applied philosophy? If philosophers can't do math in the same way mathematicians can do physics then what is the fucking point? You are just jerking off your ego, fucking sperg.
> the same way a mathematician needs to study in order to contribute to physics
Applied Math PhDs who do research in physics and engineering methods only have that, a PhD in Mathematics.
>THE FACT THAT TWO FUCKING THINGS ARE RELATED DOESN'T MEAN UNDER ANY CIRCUMSTANCES THAT IF YOU KNOW ONE YOU SHOULD KNOW THE OTHER ONE.
This is not the case if you are literally anyone BUT a philosopher.
As I said, chemist can literally do biology. Physicist can literally do chemistry. Mathematician can literally do physics.
However, as I said in my initial post, philosophers can't do math.
So again, I ask you, in what practical sense do you exclaim that 'math is applied philosophy'?
Anyway OP, a quick googling has given me these names. It's pretty clear you're just baiting people, but perhaps these names will be useful to other people. >Alfred Tarski >Charles Sanders Peirce >Kurt Gödel >L. E. J. Brouwer >Alfred North Whitehead >Hilary Putnam >George Boole >Bernard Bolzano and many familiar ancient philosopher mathematicians that OP ruled out.
>>7771433 >I can name you various chemists who did work in biology, I can name you various physicists who did work in chemistry, I can name you various mathematicians who did work in physics. No you can't. Liar.
However, there is more to formal logic than plain predicate logic. Foundational systems of categorical logic and of type theory (which happens to have its roots in (Russell 08)) subsume first-order logic but also allow for richer category-theoretic universal constructions such as notably adjunctions and modal operators (see at modal type theory). That adjunctions stand a good chance of usefully formalizing recurring themes of duality (of opposites) in philosophy was observed in the 1980s (Lambek 82) notably by William Lawvere. Since then, Lawvere has been proposing (review includes Rodin 14), more or less explicitly and apparently (Lawvere 95) inspired by (Grassmann 1844), that at least some key parts of Hegel’s Logic, notably his concepts of unity of opposites, of Aufhebung (sublation) and of abstract general, concrete general and concrete particular as well as the concepts of objective logic and subjective logic as such (Law94b) have an accurate, useful and interesting formalization in categorical logic. Not the least, the concept and terminology of category, modality, theory and doctrine matches well under this translation from philosophy to categorical logic.
>>7771486 Lawvere also proposed formalizations in category theory and topos theory of various terms appearing prominently in Hegel’s Philosophy of Nature, such as the concept of intensive or extensive quantity and of cohesion. While, when taken at face value, these are hardly deep concepts in physics, and were not at Hegel’s time, in Lawvere’s formalization and then transported to homotopy type theory (as cohesive homotopy type theory), they do impact on open problems in fundamental physics and even in pure mathematics (see also at Have professional philosophers contributed to other fields in the last 20 years?), a feat that the comparatively simplistic mathematics that is considered in analytic philosophy seems to have little chance of achieving.
Lawvere 92: It is my belief that in the next decade and in the next century the technical advances forged by category theorists will be of value to dialectical philosophy, lending precise form with disputable mathematical models to ancient philosophical distinctions such as general vs. particular, objective vs. subjective, being vs. becoming, space vs. quantity, equality vs. difference, quantitative vs. qualitative etc. In turn the explicit attention by mathematicians to such philosophical questions is necessary to achieve the goal of making mathematics (and hence other sciences) more widely learnable and useable. Of course this will require that philosophers learn mathematics and that mathematicians learn philosophy.
Homotopy type theory as such (UFP 13) is a logic of types, of (mathematical) concepts (Martin-Löf 73, 1.1, Martin-Löf 90, p.1, Ladyman&Presnel 14). (References which recall that the modern “type” is a contraction of “type of mathematical concepts” include for instance also (Sale 77, p. 6).
With the univalence axiom for weakly Tarskian type universes included – which says that this essence appears properly reflected within itself – then its interpretation via categorical semantics is in elementary homotopy toposes (Shulman 12a, Shulman 12b, Shulman 14). These are the models of homotopy type theory. Conversely, homotopy type theory is the internal language of homotopy toposes, hence the latter are its “externalization”. This way homotopy type theory overlaps much with (higher) categorical logic. See at relation between type theory and category theory for more background on this.
Accordingly, since it is more immediately readable, we display mostly categorical expressions in the following, instead of the pure type theoretic syntax. Judgement
The earliest formulation of a logic of concepts is arguably Aristotle's logic, which famously meant to reason about the relation of concepts such as “human” and “mortal”. We consider now a natural formalization of at least the core intent of Aristotle’s logic in dependent homotopy type theory.
Formalizations of Aristotle’s logic in categorical logic or type theory has previously been proposed in (LaPalmeReyes-Macnamara-Reyes 94, 2.3) and in (Pagnan 10, def. 3.1). The formalization below agrees with these proposal in the identification of the Aristotlean judgement “All BB are AA” with the type-theoretic judgement “⊢f:B→A\vdash f \colon B\to A”, and with the identification of syllogisms with composition of fuch function terms.
>>7771468 pleb spotted. how does it feel to be pleb ?
>Have professional philosophers contributed to other fields in the last 20 years
http://philosophy.stackexchange.com/questions/9768/have-professional-philosophers-contributed-to-other-fields-in-the-last-20-years/9814#9814 Here is an example of philosophy helping a breakthrough in mathematics (in differential topology). The breakthrough happened last year, the philosophy that helped it come into existence happened 200 years ago, via a formalization suggested in the last two decades.
A long-standing open problem in differential topology and in mathematical physics was the definition of differential cohomology theories that are "twisted". This plays a role notably in quantum anomaly cancellation in quantum field theories, such as in the Freed-Witten-Kapustin anomaly in the worldvolume theory of the type II superstring, where it is twisted differential K-theory that is relevant. As this example shows, the question is of profound relevance for the foundations of our most advanced theories of fundamental physics. It was long known how to do the twist and the differential refinement separately, but their combination used to be elusive. The right framework was as much missing as it was known to be necessary.
It should be clear at least from the sound of the technical terms here that this is a question that involves messing with the very foundations of modern geometry. Topology, differential structure, homotopy theory, generalized cohomology, fundamental physics (string physics, hence perturbative quantum gravity if you wish) all intimately interact in differential cohomology theory. That should make it plausible that if you get stuck here with your formal mathematics, it might help after a while to step back, put on a philosopher's hat, and try to see if for a moment you might be helped by adopting more of a "natural philosophy" perspective to regauge your formal tools.
>>7771495 Lawvere discovered that in order to lay foundations for geometry of physics in the foundations of mathematics, it was surprisingly useful to read Hegel's metaphysics, the "Science of Logic" from 1813, if only one translated the notorious "unities of opposites" that structure this text into the formal concept of pairs of adjoint modalities (Lawvere called them: "adjoint cyclinders"). Indeed, in his famous and at the same time (I think it is fair to say) widely underappreciated "Some thoughts on the future of category theory" he follows Hegel, formally defines "categories of being" (mathematically, in category theory!) in which "nothing" and "being" combine to "becoming" in a genuine formalized precise mathematical sense, and suggests that these categories of being are where the foundations of the geometry of physics is to be looked for. Later he speaks instead of categories of "cohesion" to amplify the differential geometrical aspect more. Lawvere uses Hegelian terminology in much of his mathematics, and it seems clear -- preposterous as that may seem in the eyes of the anayltic philosopher -- that reading Hegel helped Lawvere develop the intuitionistic mathematics and the application of cohesive toposes. Indeed, once you follow Lawvere and accept that whenever Hegel speaks of his infamous dualities he is secretly (intuitively) describing an adjoint modality in intuitionistic type theory, then it feels a bit as if one can suddenly see the Matrix behind the mysterious string of greenish symbols, and Hegel's seemingly gnostic metaphysics suddenly reads much more like axioms for a practical axiomatic metaphics.
>>7771496 Nobody picked this up for years, because I think nobody recognized it. Then homotopy toposes (infinity-toposes) appeared on the scene (there is another story to be told here about the philosophy of constructivism causing a fantastic breakthrough in the foundations of mathematics via homotopy type theory, but this should wait for another post) and founding fundamental physics (in particular gauge theory) in (higher) topos theory became ever more compelling.
In any case, at some point it became clear that equipping an infinity-topos with the structure of a Hegelian "category of being" in the formal translation via Lawvere, hence making it a "cohesive infinity-topos", is the step necessary to obtain a working formal foundation for differential cohomology.
Indeed, last year Ulrich Bunke, Thomas Nikolaus and Michael Völkl realized (see here ) that the famous "differential cohomology diagram", which is a diagonally interlocking pair of two excact sequences of cohomology groups that has been postulated to be the very characteristic of differential cohomology, universally follows for every stable object in any "homotopy topos of Hegelian being and becoming", whence in every cohesive infinity-topos. And based on that more profound understanding of the foundations of differential cohomology, Uli Bunke and Thomas Nikolaus could now solve the problem of twisted differential cohomology. (This followup article should be out soon.)
To sum this up, I think one lesson is the following. Sure, once you have a formal system that formalizes what previously was "just" natural philosophy -- such as when Newton finally had his laws of motion nailed down -- then reasoning with that formal system will be far superior to what any philosphical mind un-armed with such tools may possibly achieve. But these formal systems -- our modern theories of mathematics and physics -- don't just come to us, they need to be found, and finding them is in general a hard and nontrivial step. Often once we have them they appear beautifully elegant and of an eternal character that makes us feel as if they had always been around in our minds. But they have not. And this is the point where philosophical thinking may have deep impact on the development of science, at that edge of science where the very formal mathematical methods that feel so superior to bare philosophical reasoning -- end.
In fundamental physics it is (or at least was in the 1990s) common to declare with a certain awe and also pride that quantum gravity, non-perturbative string theory and such like will force us to do things like "radically rethink the foundations of reality" or similar. Unfortunately, that rethinking has mostly been what I think is fair to call a bit naive. One cannot just talk about it. It needs both, a technical understanding of the core formal mathematics up to that very edge up to which we do understand the formal laws of nature, and a trained profound philosophical mind who can stand at that cliff, stare into the misty clouds beyond and suggest directions along which further solid ground of formalism might be found. Once it is found, true, then the philosopher should probably better step back and watch those mathematicians and physicist built a tar road over it and then run heavy truck load back and forth through what had been uncharted territory. But before that is possible, the new stable ground has to be found first.
I conclude with a personal note. Back as a kid I was thrilled by philosophy, but then got appalled by the philosophy that I was fed in school, turned to science instead and held views much like those exppressed by Aaronson above. Then the philosopher who profoundly changed my view of philosophy was David Corfield, philosopher of science and mathematics from University of Kent. His philosophical commentary and prodding as he watched me develop maths as in my recent "Homotopy-type semantics for quantization" have considerably helped and propelled some of these developments. I am thankful for that.
>>7771461 All of these studied mathematics. Of course they also did some philosophy, just like they also breathed, ate and walked. Would you in your disgusting ignorance and redditarded pseudo-intellectualism now claim that math is just applied eating, breathing and walking? You are a dumb piece of shit.
>>7771414 Andrei Rodin, section 5.8 Categorical Logic and Hegelian Dialectics of Axiomatic Method and Category Theory (arXiv:1210.1478), Springer 1914
Andrei Rodin (Submitted on 25 Sep 2012)
Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of heigher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hibert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in Categorical logic opens new possibilities for using this method in physics and other natural sciences.
>>7771668 All you people accomplished was nothing.
There was no philosopher that without specific training in mathematics was able to figure out something in math just from his philosophy knowledge.
All we have is pretty much Math/Philosophy double majors and when that is the case, the statement becomes trivially true. Not an interesting result.
>>7773595 I already explained why the ancient guys don't count.
Back then, math and philosophy were still pretty much the same. In fact, the only philosophers I respect are the ancient philosophers because back then that is all they had. They did a lot with what little they had. Nowasays, philosophers just want to avoid doing work by choosing an 'I have an opinion' degree and then trying to become a researchers.
What do philosophers even research? Their own opinion? Fucking pathetic.
>>7773682 >>When I say that Physics is applied math I mean it very literally. As in that is 100% the case and there is no dispute about it. Physics IS applied math. no mate, in physics, math comes only after you have identified the good parameters of your systems.
>>7771414 The symbols [math]\exists[/math] and [math]\forall[/math] were invented by a philosopher, and then *ahem* applied in mathematics. That's one of the most concrete examples.
But in general, pure mathematics is motivated by philosophical interest in the corresponding abstract characterization. It is philosophical insight that motivates the construction of new fields of mathematics.
>>7773682 In Physics observations are made, then mathematical formulas are created to represent the observations, or in other cases maths is used to check if observations are correct or to predict possible observations. That is different to applying maths which is entirely observation free and all knowledge is derived from already known/defined knowledge.
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