Is mathematics a way of "doing" philosophy?

It is a form of systematizing entities in the world, so yes. Combined with modern advances in logic it can be quite useful and strong, but it is obviously a limited perspective - ahistorical, atemporal.

>philosopher Roger Scruton has questioned Badiou's grasp of the foundation of mathematics, writing in 2012:

>There is no evidence that I can find in Being and Event that the author really understands what he is talking about when he invokes (as he constantly does) Georg Cantor's theory of transfinite cardinals, the axioms of set theory, Gödel's incompleteness proof or Paul Cohen's proof of the independence of the continuum hypothesis. When these things appear in Badiou's texts it is always allusively, with fragments of symbolism detached from the context that endows them with sense, and often with free variables and bound variables colliding randomly. No proof is clearly stated or examined, and the jargon of set theory is waved like a magician's wand, to give authority to bursts of all but unintelligible metaphysics.[19]

>An example of a critique from a mathematician's point of view is the essay 'Badiou's Number: A Critique of Mathematics as Ontology' by Ricardo L. Nirenberg and David Nirenberg[20] , which takes issue in particular with Badiou's matheme of the Event in Being and Event, which has already been alluded to in respect of the 'axiom of foundation' above. Nirenberg and Nirenberg write:

>Rather than being defined in terms of objects previously defined, ex is here defined in terms of itself; you must already have it in order to define it. Set theorists call this a not-well-founded set. This kind of set never appears in mathematics—not least because it produces an unmathematical mise-en-abîme: if we replace ex inside the bracket by its expression as a bracket, we can go on doing this forever—and so can hardly be called “a matheme.”

Only for materialistic brainlets

How is mathematics ‘materialistic’?

Logic relations are not mathematical they're used by maths
A syllogism is not a mathematical statement it is a logical one

You are so wrong. Logic is the foundation of all math. True/false statements their combinations. Without logic, there is no math. Philosophy as a practice evolved from mathematical observations - I.e. there are patterns, therefore one can understand the world through these patterns. That’s why the inscription on the gate to Plato’s acedemy read, “Let no one ignorant of geometry enter.”

Why is Badiou so obsessed with mathematics? Is it a gimmick, autism, or does he actually develop some philosophy relevant to political struggle from it?

Well, in a matter-spirit paradigm, only matter could really be represented in some form by mathematics. If you have a suggestion on mathematizing spirit I'd be interested to hear your take on it, since I just pulled this out of my ass.

Grammar (Fundamental ontology) --> Logic --> Math

If math were completely self-referential, it would be sky-castles of enclosed logic puzzles and no one would care. The initial axioms of the system would entail endless fractal extensions of themselves into more and more baroque studies of patterns in prime numbers etc. And in fact these axioms are being interpreted and re-interpreted and are not "objective" at all, so it would still only be an illusion of conceptual determination from the initial axioms.

The problem is that math refers to material reality in a structural way that is ALSO DEFINED MORE DEEPLY BY GRAMMAR (FUNDAMENTAL ONTOLOGY).

So, instead of math remaining in its self-referential playhouse, various more fundamental grounds (originally, common-sense ideas about matter and mechanics, but now, very complex and rarefied versions of those common-sense notion which allow scientists to arrogantly presume they have escaped common-sense) are applied to "reality," in a way that allows mathematics to "couple" with those observations and mindlessly steer the ship, blind to the fact that fundamental ontology is grounding the possibility of such a steering to begin with, and therefore leaving fundamental ontology dormant and causing a runaway ship.

So a human being interacts with reality, with various notions which have not been examined. For example, he decides, "there are two objects here." Then he examines their "interactions," which also requires a priori notions. He seeks "regularity" in these notions (the concept of regularity being a priori, but also the forms and tests which regularity takes being a priori). Then he takes up mathematics, which "clicks into" the study of "regularities," encloses the assumptions in the self-referential playhouse of mathematical abstraction, and endlessly draws conclusions about those "objects" and their interactions. These are then translated back to the real world, back into more living language and culture, either in destructive ways (scientific materialism) or in badly broken ways (science's complete incapacity to understand the quantum realm or move beyond Einstein in their inquiries). The result is that human culture stagnates, being ontologically cut
off from and therefore unable to come closer to Nature, while the technical capacities of the species are increased in a badly stereotyped form, such as primitive retarded materialistic empiricist monkeys gaining access to zero-point cold fusion modules that allow the destruction of entire populations by a single retard who tweets Rick and Morty memes and owns half the productive relations of the entire planet.

Math is nothing other than an ossified tentacle of mankind's psychic ability for abstraction and conceptualization. Higher math would simply involve dissolving the tentacle, reabsorbing it into its ontological ground, and creating better tentacles that use the same faculties in the same ways but with much more broadly and reflectively.

if you think maths is invented: no
if you think maths is discovered: yes

I'm not sure if you're actually arguing about the proper ideas or just semantics

Strict logic is a core part of maths, but also of many other domains. This means logic is not limited to maths, so logical statements are not necessarily mathematical ones.

The act of saying A is B and B is C therefore A is C is not a mathematical statement it is a logical one from which one can derive mathematical truths or other forms of truth.

This user sort of explains it

>Logic is the foundation of all math.
That doesn't make it math

yes, when you talk about theoretical stuff like infinity