{ } = the empty set = philosophy? :smile:

philosophy ≠ 1

$philosophy \equiv huh? (mod \infty)$

Make a distinction. Call it the first distinction."

https://en.wikipedia.org/wiki/Laws_of_Form

Can you use math to describe philosophy? — Huh

"God exists since mathematics is consistent, and the Devil exists since we cannot prove it" ~André Weil

Can you use math to describe philosophy? — Huh

Unsolved; yet: ~[X=~X], therefore X.

Can you use math to describe philosophy? — Huh

Philosophy = ∞

Can I? Not a chance, no!

I can use math to count my toes!

You might like to read this piece on mathematical phenomenology

Words like "congruence", "symmetry", "asymmetry", "equality", "function", and loads of other words with mathematical meaning do pop up frequently in philosophical discourse.

Words like "congruence", "symmetry", "asymmetry", "equality", "function", and loads of other words with mathematical meaning do pop up frequently in philosophical discourse. — TheMadFool

They may bear mathematical significance, but is their invocation necessarily in a mathematical context?

Even if they aren't (strictly), though - one can always endeavor to quantify philosophical communication.

First-order predicate calculus, for example, was derived from a quantification of propositional logic - which, in turn, is sentential (quintessential of any mode of discourse).

They may bear mathematical significance, but is their invocation necessarily in a mathematical context? — Aryamoy Mitra

To me, yes. All the words I listed can be made precise with math and thereby hangs a tale.

To me, yes. All the words I listed can be made precise with math and thereby hangs a tale. — TheMadFool

Wait - isn't that tremendously ambitious? Words themselves can be made precise, but the sentences they're placed in are far more subjective. In order to express a qualitative construct, in a mathematical model - it's almost paramount that one first find an intermediary, that allows the entirety of the construct to be amenable to quantitative manipulation.

Propositional logic, for example, acts as an equivalent intermediary (between generic, philosophical statements and First-order logic).

Furthermore, several mathematical edifices are exclusionary to quantitative discourse.

For instance, Functions pertain to continuous variables across domains, that are mapped onto (quantitative) output spaces. Under what circumstance, might one be able to repurpose them to philosophical conveyance?

Well, I'm only guessing at this point but your objections seem to have its roots in a weltangschauung that, true or false, gives math a kind of privileged status which I presume is that of math as some kind ultimate Tertön but I'm taking a different approach, an approach which treats math as only one of many facets to reality, comparable in more ways than just that of being different windows to the world.

Well, I'm only guessing at this point but your objections seem to have its roots in a weltangschauung that, true or false, gives math a kind of privileged status which I presume is that of math as some kind ultimate Tertön but I'm taking a different approach, an approach which treats math as only one of many facets to reality, comparable in more ways than just that of being different windows to the world. — TheMadFool

That may be, but I was merely seeking to reassert the epistemic character of Mathematics, as a discipline. It's not as though two, distinctive modalities can be integrated seamlessly (and there are few modalities less comparable, than that of purely subjective Philosophy, and Mathematics).

I do concur with you, on the front that it's one of many facets to reality; I solely believe that mitigating the chasms it shares with other facets of reality, is not a straightforward objective.

That may be, but I was merely seeking to reassert the epistemic character of Mathematics, as a discipline. It's not as though two, distinctive modalities can be integrated seamlessly (and there are few modalities less comparable, than that of purely subjective Philosophy, and Mathematics).

I do concur with you, on the front that it's one of many facets to reality; I solely believe that mitigating the chasms it shares with other facets of reality, is not a straightforward objective. — Aryamoy Mitra

Well, I was contemplating how we maybe able to both numericize and geometrize philosophy because we do to talk of philosophical "landscapes" and, for me, that's an open invitation for mathematicians to get involved in philosophy. In addition, the divine is closely linked to the concept of infinity; philosophy, my friend, is a mathematician's paradise.

Well, I was contemplating how we maybe able to both numericize and geometrize philosophy because we do to talk of philosophical "landscapes" and, for me, that's an open invitation for mathematicians to get involved in philosophy. In addition, the divine is closely linked to the concept of infinity; philosophy, my friend, is a mathematician's paradise. — TheMadFool

That's an enthusing idea, but what does numericizing and geometrizing Philosophy entail, precisely? We can't ascribe predetermined quantities to abstract ideas, mediate them, and pretend we're ingeniously resolving a confluence between two, disparate epistemologies.

On the notion of Infinity: that's certainly a mathematically inclined concept. Its converse (infinitesimals) was of significance, if I'm not mistaken, in Newton's Calculus - prior to being discounted in exchange for Limits. Nonetheless, the mathematical Infinity is rigorously constrained to an array of mathematical consequences, and doesn't trivially extend outside them.

Mathematicians may be (but often aren't) predisposed to undertaking philosophical discussions - but solely in a fashion, that is adherent to quantitative frameworks. Aside from Kurt Gödel, very few others (to my knowledge) have willfully lent themselves to that cause; David Hilbert might constitute an exception.

Hilbert's Program may be the most consecrated (and valuable) mathematical interpretation of a philosophical edifice, in that it rigidifies several constructs of finitary reasoning, consistency and meta-logic.

It isn't as though the chasms that separate quantitative and qualitative disciplines are untraversable, either; it's only that they should (ideally) be traversed with forethought, and two-sided significance.

Ernst Mach, for instance - a proponent of the famed Mach's principle, was commemorated for path-breaking discoveries in both Physics and Philosophy.

Mathematicians may be (but often aren't) predisposed to undertaking philosophical discussions - but solely in a fashion, that is adherent to quantitative frameworks. — Aryamoy Mitra

Topological ideas don't necessarily have a quantitative context. The concept of what continuous means in continuous transformations has been discussed at length in this forum.

For instance, Functions pertain to continuous variables across domains, — Aryamoy Mitra

Not necessarily. A basic definition lies in set theory and may be discrete.

Philosophy = ∞ — javi2541997

:up:

Topological ideas don't necessarily have a quantitative context. The concept of what continuous means in continuous transformations has been discussed at length in this forum. — jgill

I'm not familiar with topological spaces, but they are a counterexample to the (otherwise) quantitative norm that several mathematicians witness.

For instance, Functions pertain to continuous variables across domains,
— Aryamoy Mitra

Not necessarily. A basic definition lies in set theory and may be discrete. — jgill

I'm certain that you're of the expertise, to contend that. I wasn't rigorously defining Functions; I was merely referring to what they pertain to, in other areas of Mathematics (in my understanding). Aren't domains of continuous variables and images the two, conceptual schemes at the forefront of most individual's minds - when apprised of a 'function'? Once again, I might be mistaken.

Again you're doing what's unthinkable to the ordinary man - willingly, voluntarily, slipping into the straitjacket of logic and math; the men in white coats don't even have to lift a finger for this one.

Of course your view of me is exactly the opposite - I'm taking subjects like logic and math which many luminaries have gone to great lengths to perfect as precise, well-organized, crystal clear mental constructs that seem almost muraculously suited for making sense of and describing the world and violating or intending to violate every possible meticulously formulated rule in them.

Again you're doing what's unthinkable to the ordinary man - willingly, voluntarily, slipping into the straitjacket of logic and math; the men in white coats don't even have to lift a finger for this one. — TheMadFool

It's not as though I'm exalting mathematicians to an unassailable pedestal, and insulating them from the haphazard thoughts of the 'ordinary man'. I'm solely positing this singular, epistemic question:

How does one interweave two, dichotomous frameworks, without first fixating over their rarefied drudgeries (by perhaps, slipping into their 'straitjackets')?

If I still can't perceive the heart of your rationale, do contemplate re-formulating the argument.

Of course your view of me is exactly the opposite - I'm taking subjects like logic and math which many luminaries have gone to great lengths to perfect as precise, well-organized, crystal clear mental constructs that seem almost muraculously suited for making sense of and describing the world and violating or intending to violate every possible meticulously formulated rule in them. — TheMadFool

That's not necessarily my stance (insofar as it's not a caricature); I only feel that your endeavors to unify (or integrate) Philosophy and Mathematics, can be slightly more adherent to the circumstantial strictures of the latter. If refraining from rule-breaking is a covenant, or prerequisite to that end (not a theme, that I can righteously impart assertions on) - then an insistence on that front, might be wise.

It's not as though I'm exalting mathematicians to an unassailable pedestal — Aryamoy Mitra

Yes you are but I'm not sure whether you're doing it knowingly or unwittingly. Every time I try to build a bridge between philosophy and mathematics as I've tried my best to do in my previous posts, you immediately start pointing out how either this or that is flawed in my work. Of course I value your criticism and my impression of you is that you're more than qualified to critique matters such as this but, in my humble opinion, many great, productive interactions between disciplines involve a good deal of compromise and that usually involves relaxing the rules, ignoring differences that may even involve sweeping frank contradictions under the rug, and embarking on a cooperative venture that requires, in this case, math to meet philosophy halfway. Does this not seem reasonable?

Yes you are but I'm not sure whether you're doing it knowingly or unwittingly. Every time I try to build a bridge between philosophy and mathematics as I've tried my best to do in my previous posts, you immediately start pointing out how either this or that is flawed in my work. Of course I value your criticism and my impression of you is that you're more than qualified to critique matters such as this but, in my humble opinion, many great, productive interactions between disciplines involve a good deal of compromise and that usually involves relaxing the rules, ignoring differences that may even involve sweeping frank contradictions under the rug, and embarking on a cooperative venture that requires, in this case, math to meet philosophy halfway. Does this not seem reasonable? — TheMadFool

I'm a naive 17-year old, who couldn't fathom attending an hour-long undergraduate Mathematics lecture, sans being utterly stupefied and overwhelmed. Terming me 'qualified' (in any respect), is almost certainly unwarranted. In all honesty, you're of a far greater credence than I am (especially in Philosophy); if I didn't feel so fervently with regards to this (perceived) incongruence, however, I wouldn't have remarked on it.

Yes, one can (and perhaps should) neglect their intrinsic differences momentarily; but can we acknowledge how that might unravel (from a practical perspective)? Even if one is willing to compromise on either end, where does one seek a middle-ground between the two? Your motive is fully reasonable; it's solely the pathway to that motive, to which I seek a more profound rumination.

Mathematics bears a specific utility: undertaking abstractions of quantitative (spatial and variable) constructs, and thoroughly evaluating them. Contrarily, Philosophy witnesses its own sustenance in evaluating qualitative ideas. I'd love to be apprised of an ignorance on this subject, but it's hard to envision how the two might be methodically amenable to one another - as they manifest themselves today. I'm not casting aspersions on a 'rule-breaking' paradigm; I'm stating that the underlying fabrics on which their rules are woven, are incomparable.

If an immersion was necessary, one might elect to redefine their fabrics in a manner that wasn't impermanent. For instance, part of why Hilbert was as aberrant a mind as he was (whilst still overshadowing his adversaries on canonical fronts), was that he was willing to transcend the historical (and then demonstrably incomplete) axiomatization of mathematical fields, by instituting a self-referential Metamathematics. Aside from Gödel, very few others were as introspective as he was; and even then, he's likely to have been philosophical in reassessing Mathematics, as opposed to have architected a philosophical edifice within Mathematics.

In reiteration, I'm not eminently setting ablaze a (hypothetical) wedding between Philosophy and Mathematics; I'm merely inquiring (in a critical fashion) whether one might be pragmatic, and foreseeable in their current forms.

Well, if it doesn't make sense to you then it doesn't. I, on the other hand, see opportunity where you see incompatibility. I see a very profitable synthesis where you see irreconcilable conflict. All that aside, I must impress upon you that from what I can glean from your posts, you're a very knowledgeable 17 year old. By my standards, those are 17 years well spent. Ergo, given your insightful reservations on my proposal of a union between philosophy and math, I suppose that makes you the right person for the job of doing exactly that. In my humble opinion, a man who wants war knows exactly what peace is, right?

Well, if it doesn't make sense to you then it doesn't. I, on the other hand, see opportunity where you see incompatibility. I see a very profitable synthesis where you see irreconcilable conflict. — TheMadFool

Of course - some of my misgivings may stem from overly fixating on their idiosyncrasies, and ceasing to gauge the landscapes they really are. It's likely that remaining embroiled in them for a longer time, will loosen those perceptions.

All that aside, I must impress upon you that from what I can glean from your posts, you're a very knowledgeable 17 year old. By my standards, those are 17 years well spent. Ergo, given your insightful reservations on my proposal of a union between philosophy and math, I suppose that makes you the right person for the job of doing exactly that. — TheMadFool

Thank you. I'm still learning of course; only the primitive foothill in a portrait whose horizon remains unseen.

In my humble opinion, a man who wants war knows exactly what peace is, right? — TheMadFool

Exactly; and wonderfully reminiscent of Orwell too.

Exactly; and wonderfully reminiscent of Orwell too. — Aryamoy Mitra

Well, kindly show us the way then. How can we marry philosophy with math?

Well, kindly show us the way then. How can we marry philosophy with math? — TheMadFool

First and foremost, I'd like to concede that there already exists a concrete, formalized Philosophy of Mathematics, that illuminates how philosophical concerns underpin set-theoretic, axiomatic and abstract Mathematics (quintessential of the hypothetical interrelations you've been suggesting).

For an unequivocal integration, nevertheless (do apprise me if you disagree), a Mathematics of Philosophy should be discovered (that is to say, the redirection of mathematical constructs to philosophical matters, as opposed to the converse). I don't bear any expertise on this dichotomy, but if there were any straddling edifices - they're likely be characterized by:

1) Non-Quantitative Approaches (with the exception of 2) - wherein abstract entities - inclusive of the natural numbers, can be mediated and extended, but without a quantitative rigor (certain sub-fields of Mathematics may accord this liberty);
2) Propositional Quantification (already a hallmark of first-order logic - wherein sentential arrangements (eg: syllogisms) can be thoroughly evaluated with a (sparingly selected) group of quantitative paradigms, and their ramifications made amenable to philosophical explication.

I'm certain that there are other, mathematical objects that can be intertwined with philosophical thought - but they remain elusive.

Once more, it's not that I believe Mathematics and Philosophy are fated to be distant - it's only that they don't (at first glance) share an interlap, with the majority of their territories.

Thank you. It appears that either I'm a very bad referee/judge - ever ready to look the other way when rules are being violated or I'm criminally oriented - I don't mind bending/breaking the rules.

Nevertheless, I feel math can be applied to philosophy and all it takes is to quantify many of the underlying principles of philosophy and I'm fairly certain such is possible. Take for instance the notions of compatibility/incompatibility of ideas/systems of beliefs. Even as a non-mathematician I can imagine a scale starting from 0 to 2, with 0 being incompatible, 2 being compatible and 1 being somewhat compatible. You get the idea, right.

Plus, now is a good time I suppose to pull out the big guns: utilitarianism and the felicific calculus (Google will take you to the relevant sources). This is just a sample by the way, there maybe a lot more areas in philosophy that may have been mathematized. Which reminds me, science, a fully mathematized subject, began as natural philosophy.