Erm... I don't think philosophy is based on axioms. Argumenting is based on assumptions or else on premises.

Math is based on axioms, and math is a branch of philosophy. But not the entire body of philosophy is math.

I have to apologize, but I did not read the link. I fear there may be something untowardly there. I am very careful not to get a bug. A bit of a mask on my browser.

Looked up The Trilemma. It's an economic theory. That is not quite the same as philosophy.

Looked up The Trilemma. It's an economic theory. — god must be atheist

A trilemma is a kind of argument. The top Google result for the word is about an economic argument, but OP is talking about the Munchhausen trilemma, aka Agrippa's trilemma, an epistemological argument, showing that beliefs are justified either by chains of argument that terminate eventually in unquestioned assumptions or axioms (foundationalism), circular arguments (coherentism), or chains of argument that go on forever never reaching any bottom (infinitism).

The OP's link seems to take it that foundationalism is the only viable of those three alternatives, and therefore that all beliefs are based on axioms.

@Darkneos, this trilemma is a good reason to reject justificationism entirely in favor of critical rationalism. The short version is: instead of saying that people should reject every belief until it can be justified from the ground up -- which as this trilemma shows either results in infinite regress, circularity, or appeal to something entirely unjustified being taken as unquestionable -- we should merely permit tentative belief in anything that has thus far survived falsification. So in a disagreement, neither side is wrong by default until they can prove themselves right. Either side is possibly-right, until the other side can show some reason why they must be wrong.

So instead of starting with a blank slate and trying to find some base certainty to build up from -- since we can't ever do that, without just assuming something to be certain by fiat, as an axiom -- we start with an infinite space of contrary possibilities, and slowly weed out the ones we find to be impossible, forever narrowing down the range of remaining possibilities but never pinning down exactly one conclusive one.

Well who cares, as long as you both agree with X, whether or not X is actually the case. For the purposes of discussion, it is. And you can get plenty done what way. Everything, really.

How can we call anyone right or wrong when our justifications reach a dead end? — Darkneos

You could try and explain wny you think such a thing, which here, you've patentlly failed to do, other than pointing to some offlink.

How can we call anyone right or wrong when our justifications reach a dead end? — Darkneos

Obviously, one does not simply carry on with life when someone is wrong.

The short version is: instead of saying that people should reject every belief until it can be justified from the ground up -- which as this trilemma shows either results in infinite regress, circularity, or appeal to something entirely unjustified being taken as unquestionable -- we should merely permit tentative belief in anything that has thus far survived falsification — Pfhorrest

Here we go again.

If the triemma shows something, it justifies something. Therefore the trilemma is a justification for believing that there are no justifications for beliefs.

I still don't understand these philosophers that just don't get the contradiction they make in asserting that knowledge is inherently flawed.

So in a disagreement, neither side is wrong by default until they can prove themselves right. Either side is possibly-right, until the other side can show some reason why they must be wrong. — Pfhorrest

If one is possibly right, they are possibly wrong at the same time. To be right, one must make all possible wrongs and learn from them.

Relying on sense perceptions for a theory of knowledge, the realist has to argue, “apples are red if I perceive them to be red, and I perceive the apple to be red; therefore, apples are red”. This is circular reasoning, as it appeals to sense perception to verify something found in sense perception. — WHAT IS THE MÜNCHHAUSEN TRILEMMA?

Ah, the direct realist specialty. Things are as we perceive them because we say they are.

If one is possibly right, they are possibly wrong at the same time. To be right, one must make all possible wrongs and learn from them. — Harry Hindu

Sounds a lot like the falsificationism Pfhorrest advocates: dismiss beliefs as and when they become untenable.

I think the OP has value and my response is more about pragmatism. In mathematics we have axioms, in philosophy a priori knowledge and assumptions, in science we have laws (which are empirical rather than ab initio).

The progress of mathematics and science has been to take those fundamentals and look for new fields in which they can be derived. An axiom in algebra might be a conclusion in set theory; a law of chemistry is a prediction in QED.

The effects are that a given axiom is buttressed on both sides and that the most fundamental axioms tend to become fewer in number and simpler (not always, but usually). Ever more fundamental beliefs tend to refine higher level beliefs, which is to say they give the opportunity to falsify those beliefs.

It is really a mixture of justificationism (the belief has explanatory power), coherentism (the belief can in turn be explained, or is fundamental), and falsificationism (the belief has not been ruled out) that whittles down the number of viable beliefs.

Worst case scenario is that we don't have a viable, explanatory, coherent narrative at all. Next worst is that we have too many, i.e. we have multiple competing theories with incompatible axioms and each are coherent and viable, which only helps in avoiding untrue, incoherent and meaningless beliefs. Third worst is we come up with exactly one and it's wrong but we never find out.

Does not Descartes's cogito cover this? In the sense that one may claim that something is known - leaving aside for that moment the what it is that is known? This, or this else bares its teeth:

If the triemma shows something, it justifies something. Therefore the trilemma is a justification for believing that there are no justifications for beliefs.

I still don't understand these philosophers that just don't get the contradiction they make in asserting that knowledge is inherently flawed. — Harry Hindu

How can we call anyone right or wrong when our justifications reach a dead end? — Darkneos

It's not a matter of right or wrong because this is intuitive, but it should give pause to consider to what is knowable. That's the real question here.

The Munchhausen trilemma is, as far as I can tell, an insurmountable barrier to knowledge. None of the options avaiable are satisfactory in any sense of that word. Nonetheless, I recall a professional philosopher making a big deal of what he called self-evident truths, truths, propositions, that are so obvious that they have no need for arguments to prop them up. If self-evident truths are real and if they do exist in the issues philosophy deals with, they would be the fourth and perfectly legit alternative to the Munchhausen trilemma.

yeah you clearly don’t get it which is fine but don’t assume it’s unclear when everyone else understands.

That being said I still repeat how do we move on to knowledge. I mean axioms sound like a pretty terrible way to go. “This is true because we say it is”? If we are to go the route of falsification then we are really screwed because an external world or other minds can’t be falsified or proven so the how can we verify anything at all? Ethics would be an issue too as that is more or less just personal opinion and not really facts.

I just feel like the trilemma shows how useless philosophy ends up being and why the pyrrhonists preached what they did

Science is true because it works, and it works because it's true. Simples!

That doesn’t sound very reassuring

If the triemma shows something, it justifies something. Therefore the trilemma is a justification for believing that there are no justifications for beliefs.

I still don't understand these philosophers that just don't get the contradiction they make in asserting that knowledge is inherently flawed. — Harry Hindu

Nobody here is saying that "knowledge is inherently flawed", we're saying that knowledge doesn't operate the way justificationists say it does, because if it did then the Munchhausen trilemma would in turn show that knowledge is impossible, which is exactly the kind of contradiction you're talking about. That contradiction is thus reason to reject the possibility of justificationism.

To be right, one must make all possible wrongs and learn from them. — Harry Hindu

Yes, that's exactly what I'm saying. By default everything and its negation might be right and might be wrong; then knowledge comes from determining which things are definitely wrong, and thus narrowing the range of things that might still be right.

In contrast, the justificationist assumption underlying the Munchhausen trilemma is that by default everything is wrong, until knowledge is built by showing something to be definitely right, and then building up from there. But the Munchhausen trilemma, running from that assumption, thereby shows that knowledge thus-understood is impossible, a contradiction (you can't know that you can't know anything), and thus a reason to reject understanding knowledge in that way, i.e. to reject justificationism.

Yes, that's exactly what I'm saying. By default everything and its negation might be right and might be wrong; then knowledge comes from determining which things are definitely wrong, and thus narrowing the range of things that might still be right. — Pfhorrest

But how do you do that without justification? The point about the trilemma is that everything is ultimately based on three unsatisfying assumptions. Usually to determine what is wrong we have to justify it, we can't just say someone is wrong. But if all justifications fall back to those three points then one could argue there is no right or wrong because everything has arbitrary beginnings.

You can show something is wrong regardless of external premises, via reductio ad absurdum. If assuming the thing itself leads to contradictions, then you have reason to discard it, without appeal to anything else.

This trilemma is precisely such a reductio for justificationism itself: if you assumed justificationism was true, the trilemma that follows from it would prove that it’s impossible to ever justify anything, a contradiction with your initial assumption; so you must reject justificationism.

If we want empirical evidence to be able to falsify things too, we just need to show that anti-empiricism leads to a similar absurdity, which I think can be done. Disregarding empirical evidence is then thereby ruled out, so aside from internal self-consistency a belief has to be consistent with empirical observation as well or else your belief system as a whole will have an inconsistency.

From there science proceeds as normal, and philosophy can sit back and just watch.

I like this trilemma thing. I am indebted to you, PfHorrest, for enlightening me.

I don't think it has a refutation. But it does not need a fefutation for humans to continue operating with reason.

Human experience is based on belief. Socrates pointed out first the difference between knowledge and make-belief; and he said there is knowledge, in the form of Ideals, but humans haven't reached the way to uncover them yet.

The trilemma is a way of showing how humans can't reach rational knowledge.

But we do NOT need rational knowledge. As long as we have assumptions that we say are given; in other words, there are things we accept as true, whether they are or not; we have a mode to operate, and to apply our reason.

So what if we are wrong. We are most likely wrong in our knowledge. There is no way to check that. But does false knowledge bother us any? No, instead, it eggs us on to gain more false knowledge. And the conglomeration of false knowledge gives us a world view that works for us, and we can even make predictions based on our false world views.

In this sense, the falsity is not a problem; the problem is only that we know it is falsity. In and by itself, falsity never bothered anyone any. In the middle ages they believed a set of superstitions; in the ancient times humans believed a yet different set of superstitions; in the times before that, there was yet another world of superstitions that formed human's world view.

I am quite sure we are living in yet another age of superstition, but just like the persons in the middle ages, in ancient times, and before, we are not made aware of it. We are not aware of our mistakes, we can only say that we are probably wrong, and most likely wrong in our claims of how this bloody thing, the universe, works.

I love this trilemma. It solves nothing, but it points at how we should get comfortable in our ignorance and set of false beleifs.

You can show something is wrong regardless of external premises, via reductio ad absurdum. If assuming the thing itself leads to contradictions, then you have reason to discard it, without appeal to anything else. — Pfhorrest

In the first half of this proposition you are explaining how we show something is 'wrong', but what you actually demonstrate is something which seems to you to be 'absurd' and which provides, for you, 'reasons' to reject it.

Are you claiming that what is 'wrong' is synonymous with what you personally find absurd or objectionable?

Are you claiming that what is 'wrong' is synonymous with what you personally find absurd or objectionable? — Isaac

No, and you should know that already, because we've been around this merry-go-round many times before and if it didn't sink in the first million times I'm not wasting my time going over it with you again.

Let me Google that for you: reductio ad absurdum.

you should know that already, because we've been around this merry-go-round many times before and if it didn't sink in the first million times — Pfhorrest

Ah. Are you referring to the discussion in which literally everyone involved was pointing out how you were wrong but you insisted you were right regardless?

So how come it's the case that it's me who doesn't 'get' your argument and not you who doesn't 'get' everyone else counter argument? Tell me, what's most likely - that you're a unique genius who nobody understands, or that you've made a mistake which you don't understand?

I don't think it has a refutation. But it does not need a fefutation for humans to continue operating with reason. — god must be atheist

As long as we have assumptions that we say are given; in other words, there are things we accept as true, whether they are or not; we have a mode to operate, and to apply our reason. — god must be atheist

:up:

Are you referring to the discussion in which literally everyone involved was pointing out how you were wrong but you insisted you were right regardless? — Isaac

I'm referring to many previous discussions in which you repeatedly, and I think willfully, misinterpret "reductio ad absurdum" as "reducio ad something-I-subjectively-don't-like", rather than the technical meaning in which "absurd" means "self-contradictory".

But you seem to be referring to one specific discussion in which everyone kept bringing up things I didn't disagree with and then acting like that somehow proved something against my position that already included within it the things that they were saying.

So how come it's the case that it's me who doesn't 'get' your argument and not you who doesn't 'get' everyone else counter argument? — Isaac

Because I already agreed with what "everyone else" was saying, so it can't be that I was somehow failing to be persuaded by their arguments, since I wasn't disputing the conclusions.

It reminds me of arguing for libertarian socialism only to be met with right-wingers presenting arguments against the state as reasons why not to adopt socialism. Yeah, I already agree with those arguments against the state... that's why I'm not a state socialist, but a libertarian one. No amount of arguments against the state could change my mind about the state, because I already agree with the conclusion of them, and am already anti-state. If you think that those are arguments against my position, it's you who fails to understand what my position even is.

Tell me, what's most likely - that you're a unique genius who nobody understands, or that you've made a mistake which you don't understand? — Isaac

I never claimed to be a unique genius. Almost all of my positions are ones that much better-credentialed people than me also support. In this case, aside from the obvious philosophers like Karl Popper, Ernest Gellner, and Hans Albert, you've also got legal scholars like Reinhold Zippelius, physicists like David Deutch, biologists like Hans Krebs, and the one I expect you'll like most, neurophysiologists like John Eccles.

But yeah, when it comes to discussing a topic in which I majored summa cum laude with easy straight-As, putting me in the top twentieth of people who have BAs on the topic, on an anonymous internet forum where over two thirds of people don't even have a BA in it at all, yeah I'm leaning statistically toward it being other people not understanding me rather than vice versa.

I'm referring to many previous discussions in which you repeatedly, and I think willfully, misinterpret "reductio ad absurdum" as "reducio ad something-I-subjectively-don't-like", rather than the technical meaning in which "absurd" means "self-contradictory". — Pfhorrest

Then why did you direct me to a Wiki definition in which the first paragraph states reductio ad absurdum to be "the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction"? I've bolded the 'or'. One or the other, not that the two are being treated as technically the same thing.

If you want to use that BA of yours to teach me something about the technical meaning of philosophical terms, then it would help if you directed me toward definitions which actually support the claim you're making.

you seem to be referring to one specific discussion in which everyone kept bringing up things I didn't disagree with and then acting like that somehow proved something against my position that already included within it the things that they were saying. — Pfhorrest

This ^ characterisation of the discussion is the thing I'm talking about. Everyone else was saying that this wasn't what was happening and that your posts had meaningful problems of the sort we described, you were saying that this was exactly what was happening and we were all wrong in thinking otherwise. It is the characterisation of our objections as being "the things you were saying and already agreed with" that was your error in that thread. They were not the things you were already saying, you simply didn't understand the difference.

Almost all of my positions are ones that much better-credentialed people than me also support. In this case, aside from the obvious philosophers like Karl Popper, Ernest Gellner, and Hans Albert, you've also got legal scholars like Reinhold Zippelius, physicists like David Deutch, biologists like Hans Krebs, and the one I expect you'll like most, neurophysiologists like John Eccles. — Pfhorrest

No. You think your positions are ones that much better-credentialed people than you also support. It is possible for you to be wrong about that (which is something people better qualified than me have tried to demonstrate also). That you think your arguments are supported by these writers is not de facto evidence that they in fact are. But you seem (in common with a worrying number of people here) to have some trouble distinguishing between things seeming to you to be the case and things actually being the case.

Notwithstanding that, all of those writers are themselves critiqued and opposed by a slew of similarly well-credetialed people, so their support alone doesn't lend authority to your arguments, it just helps us understand where they're coming form. As far as an indication of who has misunderstood whom, they're useless.

when it comes to discussing a topic in which I majored summa cum laude with easy straight-As, putting me in the top twentieth of people who have BAs on the topic, on an anonymous internet forum where over two thirds of people don't even have a BA in it at all, yeah I'm leaning statistically toward it being other people not understanding me rather than vice versa. — Pfhorrest

Really? Then I suggest you take a serious look at the stratification of your samples. Within a couple of paragraphs I can tell quite easily f I'm talking to someone who has some knowledge of the topic or not. The idea that ten pages into a discussion you're still assuming your interlocutors are drawn from the full population who responded to that survey is rather worrying.

Then why did you direct me to a Wiki definition in which the first paragraph states reductio ad absurdum to be "the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction"? I've bolded the 'or'. One or the other, not that the two are being treated as technically the same thing. — Isaac

I directed you to a Google search, as a rhetorical device indicating that you should understand these things already if you're going to take the high horse that you always do.

But to follow up on the very first reference in that Wiki article that is the top result:

Proof by Contradiction

An indirect method of proof that attempts to prove a claim by proving that the opposite will lead to a contradiction. For that reason, the method is also known as “reductio ad absurdum” — or “reduction to absurdity” in Latin. — The Definitive Glossary of Higher Mathematical Jargon

Yeah, it is sometimes used more loosely than that (as the second reference in the Wiki article states), but it should be clear from context to anyone fluent in English who isn't looking to maliciously misinterpret me that I'm meaning the sense equivalent with proof by contradiction, because I'm explicitly talking about contradictions.

If you want to use that BA of yours to teach me something about the technical meaning of philosophical terms, then it would help if you directed me toward definitions which actually support the claim you're making.

See above, but also: I'm not really trying to teach you anything here, I'm trying to disengage from conversation with you, because you've long since demonstrated that you're not interested in an honest and charitable conversation but in scoring some kind of imaginary internet debate points.

But I can't resist one last snip:

No. You think your positions are ones that much better-credentialed people than you also support. — Isaac

One of the aforementioned people, Hans Albert, is the originator of the trilemma that is the topic of this thread, and he introduced it specifically as an argument for critical rationalism. In arguing for critical rationalism here, I'm pretty much just explaining what the point of the argument the OP is talking about is.

Yeah, it is sometimes used more loosely than that (as the second reference in the Wiki article states) — Pfhorrest

Where in that article does it say that the 'absurd' definition is 'more loose'? It just seems to reiterate exactly the conclusion I reached from the wiki. As does every other reference I followed, apart from the one single reference you cherry-picked (from mathematics, not philosophy) to try and prop up your untenable argument.

should be clear from context to anyone fluent in English who isn't looking to maliciously misinterpret me that I'm meaning the sense equivalent with proof by contradiction — Pfhorrest

I took both definitions as being possible. I don't see how that's malicious or uncharitable.

I said...

Are you claiming that what is 'wrong' is synonymous with what you personally find absurd or objectionable? — Isaac

...which you've neatly avoided having to answer by side-tracking into this attempt to recast your inability to raise a counter-argument as some kind of stance against my cantankerousness.

Both absurdity and contradiction are senses which you personally might have of two propositions and which others might disagree with. So I'll ask again. Are you suggesting that what you personally find absurd or contradictory is the measure of what is actually wrong?

Both absurdity and contradiction are senses which you personally might have of two propositions and which others might disagree with. — Isaac

Are you suggesting that logical contradiction or consistency is only a matter of subjective opinion? Or merely that people can sometimes wrongly assess whether or not something is contradictory? Many of your responses across this forum seem to rest on implicitly conflating those two kinds of things: "You might be wrong, therefore there are no correct answers at all".

Yes, people can be wrong. (And yes, I am a person... complete the syllogism in your head, we all get your obvious point.) People can even add up numbers incorrectly. That doesn't mean that there is no correct answer to the question of what is the sum of two numbers, or that everything else that depends upon the sum of two numbers is completely subjective too.

Things either are contradictory or they're not. People can assess whether they are or not incorrectly, but "you might be doing it wrong" is the most inane argument against anything that I can imagine. Get back when you can point out a specific thing someone's doing wrong. Meanwhile, the mere possibility of doing it wrong doesn't make the entire endeavor pointless or futile.

see "The meaning of life & greek mythology".

Are you suggesting that logical contradiction or consistency is only a matter of subjective opinion? — Pfhorrest

I would say that's the case yes, I agree with Ramsey that logic is simply a mode of thought, not an objective fact about the world, and as such is prime to some subjective variation. But that's not my argument here, rather it is...

merely that people can sometimes wrongly assess whether or not something is contradictory — Pfhorrest

...even under the view where contradiction is an objective fact, it is still possible for epistemic peers to disagree about what is and what is not contradictory.

Things either are contradictory or they're not. People can assess whether they are or not incorrectly, but "you might be doing it wrong" is the most inane argument against anything that I can imagine. Get back when you can point out a specific thing someone's doing wrong. Meanwhile, the mere possibility of doing it wrong doesn't make the entire endeavor pointless or futile. — Pfhorrest

This would all be relevant if the 'incorrect', or 'wrong' we were talking about were, like your example with the sum, the goal. In that example, there is a 'right' answer regardless of the propensity for some to miscalculate.

But that's not what your claim is here. It's not simply that some things are right and others wrong and that we should strive to reject the wrong, leaving the viable options for what is right. I agree entirely with that claim.

What you do here is additionally claim an objective method for doing so. That the 'wrong' can be identified by determining that it is contradictory, and that such an identification carries normative weight. That's not the same as the maths sum example at all. Instead of talking about whether the answer could possibly be right (regardless of the potential for miscalculation), you're talking about how we know whether the answer is right. A completely different proposition to the mere declaration that there is a right answer.

Say you have a proposition, and you 'feel' it's wrong. Later you compare it to another (necessary) proposition and you 'feel' it leads to a contradiction. How is your first 'feeling' made objective by your second? You could be wrong in either case, in either case we might agree that there is a 'right' answer out there somewhere...

What is it about the status of feeling there's a contradiction that gives it this authority over any of your other feelings about the proposition in question?