Because there are actors who 1. do not adhere to philosophical principles, yet are still on the battlefield of debate and philosophy, 2. because there are no clear measurable results like Math or sciences have. So there are people calling themselves philosophers applying "logic" as they please, and selecting evidence as it fits their version best in order to make arguments. There is for example postmodernist subjectivity: There is no objective truth, only subjective truth. Well, that's quite a big, objective claim about the objective state of truth. It's contradictory - doesn't matter.

And if truth is only subjective, so why then can't I subjectively claim there is objective truth - along with all people who do as well? This tiny logical issue didn't stop postmodernists from further spreading into academia and arts, and expanding into politics, media and finally society itself. I bet they claim to be philosophers - even though they effectively abandoned the concept of objectivity, objective truth and logic itself.

Science and philosophy use the same "logical tools" used by mathematicians in their arguments. The key-point is that mathematics uses clearly "regimented" Language, defined concepts, clearly stated axioms. Only a part of (mainly Western) philosophy agree on the "deductive approach" to philosophical arguments.

And only a restricted part of the part above tried to adopt the "Euclidean" approach; see e.g Spinoza's Ethics.

What is stopping philosophy? Good sense, I hope. " epitome of epistemic foundationalism and argument held to the highest standard.". Just as often it is a way of hiding. To the mathematician working a problem, this is a natural process to him within the limits. But, more broadly, it can become an approach to the world that is a kind of hiding from the world.

Why should philosophy adhere to epistemic foundationalism if it has shown that epistemic foundationalism is incoherent? Why should we pretend that concepts and the world stand in a formal relation if we already know that this is too simple a picture? Why do you ignore the fact that mathematics itself has shown its inherent limits when coming to self-reference and self-description? It all comes down to: Because it does not work that way and things tend not to be just the way we define them to be. Formalism is dead, really.

It should be noted that ridiculous mistakes happen in mathematics too (e.g. sometimes authors with massive reputation write incomplete arguments but nobody dares to challenge them). A person who is now a Chicago politician has published a thoroughly wrong paper in a top-3 journal. Sometimes entire fields are developed on shaky bases (e.g. parts of symplectic topology). The conclusion is math is not perfect either.

You have issues with consistency. What are proofs by definition? Aren't the sense verifiable like all sciences? I never heard of a non physical proof. Science like math can provide wrong information when it comes to reality. Extraneous roots prove that. Why two solutions when you KNOW the negative answer is false? You followed the rules & derived one wrong answer them try to say it never happened. You derived two answers then picked the real one. Your axioms are just guess work & the audacity to change the definition of older philosophic terms in logic go beyond belief.

Mathematics is applied philosophy. xkcd.com/435

@PhilipKlöcking what are the inherent limits when it comes to self-reference and self-description? I am quite surprised to hear that formalism is dead, especially now, in the golden age of computer science and quantum mechanics.

The epistemological foundations of mathematics are extremely murky, with the same approximate complexity and difficulty as "big" metaphysical topics as realism versus nominalism versus constructivism.

Mathematical proofs prove a conjecture given a set of axioms which go unchallenged. Philosophy is arguing about the axioms.

@Battle I don't think that word means what you think it means...

@thedarkwanderer - Depends on how far you go. First you question the "(meta)narrative of history" - which is silly given how many do the same anyway. There are 3 typical steps: Recognize that people differ in views, cultures and morals (does not require a genius to recognize that); nobody is objectively correct (which is a far stretch, but sure - you can make a valid point with that); and therefore we need to tolerate all views (which is plain insane). The pattern is this: Weaken logic, ethics, objectivity and truth until you get your way with enabling irrationality, hedonism and violence.

Somewhat relevant: en.wikipedia.org/wiki/Münchhausen_trilemma If you will try to have your philosophy completely provable you will end up there, every time.

You still fail to mention Mathematical Logic requires axioms, assumptions or definitions to work. This is a problem in Epistemology. The question that will be thrown in your face is "Why did you start there? Why not somewhere else?" This is like saying GOD was always there. Why start there? How did GOD get there? Well the BIG BANG has the same issue. There was always a singularity then some gasses came along & an explosion occured. Well if there was nothing how did the explosion occur? How did the singularity get there? See you have to start somewhere. I will as WHY THERE though.

Please don't keep responding to answers in your post. This is supposed to be a question, not an essay.

Hi user40358 and welcome to Philosophy SE!! I agree with @Eliran. Your several edits and added bullet points might make it harder for someone who happens across your question to understand it without reading all the answers first. And the context of some of the answers may be lost as well after several edits. If you want to comment on specific answers asking for clarification, you should do so using the "add a comment" feature underneath the answer you wish to respond to. If you want to ask another more specific question about any of your bullet points, you should ask a new question.

@AdamSharpe Okay, sorry about that. I thought it was a good idea to keep everything in one place. I'm not a people person so you're probably right about that.

Raven Paradox :)