## Can you prove anything in philosophy?

If I might reinterpret your question lightly, do you mean to ask whether from the premises and toolings of philosophy-defined however you will-can we derive anything which could be construed as a "truth of the universe" with absolute confidence more akin to the sorts of confidences we gain from empirical science or mathematics?

If so, then this is a very interesting question! We'll have to take a moment to talk about proof and evidence and belief though in a technical sense.

There are a few models of epistemology here we might want to discuss. First, is the human notion of belief. Many formal models for this exist, but we might conversationally say that humans believe X for reasons like (a) they directly observe X with their own eyes and trust that they're not broken, or (b) they hear about an observation of X from someone else whom they trust to inherit data from, or (c) they are told that they should believe X by someone else that they trust to inherit belief from, or (d) X is implied by a "pattern of the world" which they've come to believe in due to a "preponderance of evidence", or (e) X is implied because the opposite, not X, cannot be believed for some of the reasons listed above, or, finally, (f) X follows from some other beliefs {Y1, Y2, ...} according to some rules of logic that the person believes are meaningful.

There are more models, but these will do. In particular, we'll discard (a) out of the common belief that philosophical things are not directly observable. We'll discard (b) and (c) since these don't usually constitute "proof" by any measure and we might demand a greater burden of proof to believe a philosophical justification. The interesting ones are (d), (e), and (f).

Reason (d) is pretty much the engine of hypothetical science and human pattern matching-let's call it extrapolation. There are strong reasons to not trust extrapolation, but it's both often trusted anyway and more importantly often used as the engine of inquiry. We begin with (d) and then use (e) and (f) to get to real belief.

Reason (e) is usually a strengthening of reason (d)-although that may be weird-and is a major component of statistical and scientific knowledge. It can be hard, e.g., to directly prove that Compound A makes rats live longer since for all we know they could be living longer just by chance. Instead, we often try to prove that there's no possible way they could be living longer by chance... and so we're now forced to believe it's Compound A.

Reason (f) is the tool of mathematical logic and gets quite complex. The reasoning is that it relies upon the person a priori believing some fundamental things (assumptions or axioms) along with trusting a set of logical rules (of which there are many and of which they do not always lead to the same conclusions). But that said, you can write conclusions of absolute certainty atop this foundation when you choose.

So after this exploration we come to something interesting. The notion of what "proof" means is actually sort of fuzzy. How do we apply it to philosophy.

Well, that's really large again but this time just because Philosophy itself is large! For instance, a branch of philosophy I quite like to study is epistemology and logic. This branch is pretty nearly fully adopted into mathematics these days though and operates almost entirely on principles of mathematical logic (what we called (f) above). Many, many of its ideas are well-proven.

But even in this field, and this is the reason it's not just entirely a mathematical notion, we bump into things which are dissatisfyingly unprovable. For instance, the basic question of mathematical logic might be "what exactly are the best choices of logical rules and axioms?"

This wouldn't be an interesting question except that different choices of those actually lead to what appear to be different answers about the world entirely. To make matters worse, they're often different in ways that are subtle enough that no human intuition (reasoning pattern (d) from above) can guide us.

For instance, they often end up being questions about infinity and how it behaves or if it even really exists. Our mathematical axioms presuppose or are driven to need its existence-or the existence of something very much like it-but true infinity is outside of human perception. Nothing can guide our intuition and we're forced to accept certain consequences of this logic even as they become increasingly strange.

So how do we answer that question from before-"what set of axioms and rules is best"? Or worse, say we have an answer, how can we prove it? How can we take our reasoning and transport it to someone else so that they must believe it as well?

And the answer is that nobody knows. Nobody is even sure if that's a reasonable question to ask. It's crisp and clear in terms of our willingness to try to ask it... but there might just not be anything there at the end of the day. Some are willing to believe that these rules and axioms are just language games we play with ourselves because-most of the time-they do about the right thing with respect to the world.

But again, these are dissatisfying results.

So how can we go further? At this point, things become deeply philosophical. For this particular sub-sub-branch of philosophy the typical approach is to try to just strip away assumptions to the greatest degree we can. The idea is not so different from reasoning system (e) above. If you want to prove "X" you can get some distance be eliminating as many risks of someone showing "not X" as you can. In this case, each assumption has a chance of being show to be wrong and so if you hoist your entire logic from the barest set of assumptions it becomes maximally unassailable.

To give a flavor for this, you will hear about people hypothesizing that mathematics is language which arises from foundational concepts like There Are At Least Two Things And We Can Tell Them Apart and the actually quite troubling one of I Or At Least Somebody Is Allowed To Make Choices About Things. These are pretty foundational-you'd have a hard time arguing they're not true. But, then, of course, the entire field is people doing just that.

So this is where we sit, somehow unsatisfied. Our arguments are ultimately arguing only weakly for the Ultimate Veracity of our Big Question and are under constant onslaught as people try to kill them.

But that's a kind of proof in and of itself, you know? It's not absolute, it's more evolutionary. These ideas are the ones which have survive enormous onslaught over the last century or two at least. Their stickiness attests to their power.

More than that, even when these ideas fall they don't fall apart completely. They end up differing only on aesthetic or extremely subtle points. Important as all hell to those in the know, but perhaps immaterial to almost everyone else.

So it's a kind of "proof" or at least evidence we've not yet discussed-the proof of the last man standing.

But to be fair now we have to spin back around and look at science. It works upon the principle of evidence and disproof, but is that really the engine that drive science forward?

I'd argue: no, it's not. And I'm not the first.

Science, as an act, is actually not even designed to arrive at the right answer. It's methods are at best "probably correct" when they arrive at proof. That's just the mechanism.

Science does not work in isolation. A single experiment is at best a biased coin flip away from being wrong. Science only works when we see it as Science As A Human Effort.

Because over time, the ideas which appeared to be proven are eventually defeated and we, as a society, evolve toward greater truth. This is what happened when Einstein refined Newton's laws. Newton was "right enough" for a while, but his ideas were eventually defeated. I think today it's generally believed that Einstein's will be too one day.

So, really, for all its fanfare, science is itself also driven by the proof of the last man standing.

Where does this leave us? Well, hopefully I've shattered your ideas about proof in a big way. As it turns out, evidence and belief and proof are not and almost never ultimate things. They're just as relative as the rest of the ideas of philosophy.

And I hope I've also introduced an area of philosophy which, unlike its cousins of Ethics and Aesthetics, has some right to believe that it could arrive at an Ultimate Truth. I also hope I've suggested well enough that it appears to have failed at this and appears that it always will.

So maybe it's not worth judging Ethics so harshly.

The final thing to leave on is the idea of what "proof" even is. I've used it a lot without really defining it. I explored "belief" and suggested what "evidence" might mean, but proof is absent.

So here's a definition: "proof is a process by which you communicate belief". It's not too different from "convincing".

The thing that's important about this is that it makes "proof" into a social, a communicative process. Even mathematicians are incredibly communicative and, in their way, social. Mathematics arises out of the wide community of mathematicians talking about their ideas and trying to convince one another of them!

So there's really a lot to say for the commonalities of even the spaciest bits of Philosophy and even the most technical arenas of mathematics. What we seek when we seek "proof" is efficient ability to convince someone else-even your worst critic. Mathematicians have avenues which give them very efficient proof which is both compact and highly effective. Philosophers lack this mechanism-but it doesn't mean they employ a significantly different arsenal.

Participation in philosophical discussion is itself a neighbor of proof. It's inefficient and expansive compared to mathematics... but, at least to some, it's just as fun.

Yes, I can prove we need to teach it. I submit this question as proof. (Sorry OP)

Is this question intended to ask:

- Is philosophy capable of producing proof?

Or

- Can philosophy prove all possible propositions?

We live in a complicated world, The current election cycle, Brexit, the banking crisis and the risk of another all trace back to the inability of people to employ reason.

We need to put logic back in the curriculum.

Accordingly to a given theory Yes (...). In a theory you have some premises. Those, united to logic statements make the Theory. Anything that makes that theory true are part of the theory and are proven statements. If you have a different theory, different premises and statements that make the theory logically true are the proven statements of that different theory.

Did you check here?

Can you prove anything in philosophy?