r/todayilearned • u/Coverlesss • 2h ago
TIL about the Münchhausen trilemma - The philosophical argument that all attempts to prove something true eventually rely on circular logic, endless regress, or an unsupported assumption.
https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma384
u/Fetlocks_Glistening 2h ago
Can you prove that?
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u/CommieLoser 2h ago
If you’re okay with circular logic, endless regresses or unsupported assumptions, then yes, yes I do.
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u/snidemarque 2h ago
Square logic and limited ingresses only. I’m cool with wild assumptions tho.
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u/tomrlutong 2h ago
No, but Godel could.
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u/Bardfinn 32 2h ago
Goedel couldn't. Even Goedel's assertions and proofs - ALL mathematical and logical proofs - rely on axioms - statements which are simply assumed to be fundamentally true
The problem that this philosophy argument brings up is that axioms are unexamined assumptions
Which has some utility, when you're criticising how a given proof is solid when i.e. assuming the Axiom of Choice, but utterly intractable / has not been attempted to be formulated when substituting in the Axiom of Determinism for the Axiom of Choice.
Which is relevant to Goedel's most (in)famous proofs
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u/Zomburai 2h ago
Compelling, but I feel like they're unfinished
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u/PersonalTrick6900 2h ago
This is honestly a bit of a mind-bender. The more you think about it, the harder it gets to explain how we know anything for sure. Definitely going down a rabbit hole with this one.
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u/WellHung67 2h ago
Isn’t it solved with axioms? Things you take to be true without proof and then build on that? Unsupported assumption yes but you gotta start somewhere. Math does if
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u/kaleb42 2h ago edited 2h ago
Axiom are just another way to say "we assume this is true" so it doesn't actually solve the dilemma because the dilemma is pointing out that you are at some point making an assumption which is an axiom
Axioms are the foundational assumption which is what this dilemma is pointing out
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u/weeddealerrenamon 2h ago
Eventually you just have to say "this is good enough for me"... how can I prove that everything I sense is real, and I'm not a brain in a jar or a dream or something? I can't, but I have to get on with my life, so I'm going to assume reality is real and go to work
It's kinda like "all models are wrong, but some models are useful"
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u/sevenut 2h ago
Everybody knows that axioms are good enough. That's why they exist. The rest of it are questions for people like philosophers, not you or me.
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u/Covid19-Pro-Max 2h ago
You know you are allowed to be a philosopher?
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u/Solid_Wind_3234 45m ago
Unfortunately, I was barred from philosophizing after the incident in Cairo. I can speak no further on the subject.
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u/WackaFrog 52m ago
Following this line of thinking and applying morals to it, we eventually end up at Existential Nihilism, which is kind of built upon similar ideas.
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u/joppers43 36m ago
That’s the same way I feel about the argument for whether free will exists or not. It’s impossible to know for sure if free will truly exists, but it sure feels like it does and it’s useful to say that it does, so that’s good enough for me.
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u/hapaxgraphomenon 2h ago
This is the epistemological equivalent of declaring that “we hold these truths to be self-evident”
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u/Autodidact420 2h ago
Certain truths are self evident tbh.
The fact that at least something exists in some sense to briefly perceive that it exists in some sense (you/me) necessarily implies that in some sense the perceiver exists to perceive. It may rely on axioms that things are remotely sensical but it seems like a fairly self evident truth to me.
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u/WellHung67 2h ago
No it could be you are a brain in a vat imagining all this
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u/Autodidact420 2h ago
A brain in a vat is still a thing perceiving something.
Something exists, even if it is not what I sense. This is different than the brain in a vat, and it’s the foundational ‘I think therefore I am’ except I’ve loosened it up to be clear that the ‘I’ and the ‘think’ are both vague. But something is, or I wouldn’t exist in any capacity.
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u/BrineFine 2h ago edited 2h ago
For sure, but then truth is still internally validated. It becomes contingent on our mutual agreement on the axioms rather than something strictly outside ourselves.
Not really a problem though because not many serious people are going to bat for rejecting the law of non-contradiction or excluded middle.
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u/KingoftheMongoose 2h ago
According to Munchhausen trilemma, after circular proofs and regressive poofs, the third option for validating anything is relying on dogmatic arguments, which are the basic accepted axioms/assumptions that you are describing.
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u/jcw99 16 2h ago
Welcome to level two of this mess...
The only way you can use axioms to prove that something is true, is to have at least one axiom in your system that is false.
See:
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
https://en.wikipedia.org/wiki/Tarski's_undefinability_theorem
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u/heyitjoshua 1h ago
In any comprehensive, consistent mathematical system, there will always be true statements that cannot be proven using the system's own rules. That is to say, a system of axioms cannot prove itself, there must be at least one true statement that is only provable with a different set of axioms
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u/plastic_alloys 39m ago
When you study philosophy you find that nearly everything becomes a language problem and even defining the key words in the theory becomes a major issue even if unintended. In general, the philosopher will not address this, so it opens up the entire theory to criticism and pulling it apart.
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u/Fantastic_Puppeter 2h ago
Meh…
What we experience in the world is highly consistent over time. Every time we throw a pebble in the air, it will fall. Every day the sun rises and sets. Etc.
The assumption of “The universe obeys a set of laws that are independent of time, location, and the observer” gets pretty obvious pretty fast.
The rest comes quite naturally from there.
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u/reddorickt 1h ago
You have not yet abstracted the thought.
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u/Fantastic_Puppeter 1h ago
I fear you are only looking for questions instead of answers.
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u/Turtleneck420 1h ago
Yes, but those are still assumptions. The only thing we can know for certain is that you(the self, the observer) exist in this exact moment. Everything else could be an illusion, we can't really prove anything else. Your memories could be an illusion, do they feel like your perception of now?
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u/Fantastic_Puppeter 1h ago
Meh…
Not to say you are _wrong_, but those questions can be answered satisfactorily.
Your perceptions _are_ what you know about the world. They are highly consistent. Therefore, you lose nothing and gain everything by assuming that the physical world does exist “outside of you” and behaves consistently. And it does work as you can see in all the scientific progress we’ve made.
That’s it.
The initial question was relevant and it was answered. It does highlight a core assumption (existence of physical laws) that has proven reliable for about 250 years.
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u/powerscunner 2h ago
Logic is a formal system and is incomplete, so sayeth Godel.
If you want actual truth, you'll never get it because truth comes from logical propositions which are formal systems and are by definition incomplete.
This is why I prefer measurements over truth. Measurements are way better than truth because they don't change with conditions. You can interpret measurements, give them names, but calling a kilogram in 1G heavy or light may be true or a lie depending on how strong you are, and yet regardless of the truth, the kilogram in 1G always weighs a kilogram in 1G.
That's not the truth, that's a measurement.
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u/Catshit-Dogfart 1h ago
Also, measurements are limited by the tools we have to take the measurement. Same with perception of reality.
What you measure might not be "true" because your measuring tool isn't capable of being truly accurate, and by the same token what you perceive with your senses might not be true either. Heck of it is, neither of these can ever be perfect, and therfore never entirely true.
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u/RolliFingers 2h ago
Idk, I'm going to need someone to explain the inherent assumption, circular logic, or regressive explenation necessary to prove 1+1=2.
Hell, it can be done without using words at all.
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u/hellomondays 1h ago
Circular reasoning would the definition of 2 as 1+1, we know 1+1 equals 2 because 2 1's put together is 2. Then the regression involved in proving the peano axioms that this math relies on. 1+1=2 is only true within the framework of the assumption of "that's how math works".
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u/RolliFingers 1h ago edited 1h ago
Okay, and trying to discuss here, not argue...
Can't I just put one rock down, then a second rock next to it, and then there are two rocks? It seems like the language part is the part that is subject to these principles.
Quantity and arithmatic existed before the concepts that explain them, and quantity is inherent in itself.
It seems to me that someone doesn't need to know what the context is behind the syllables "one" and "two" and "plus" and "equals" to understand the enherent fact that two single items grouped together are two items (or even that two separate items are two separate items).
Maybe I'm just looking at this too broadly (maybe not broadly enough)?
Edit: I am also definitely not a mathmatician.
Edit 2: Apparently whether or not quantity is inherent in and of itself is a much deeper philosophical debate that I didn't realize existed (and after briefly reading up on the points of view, I feel I agree more with the "inherent" crowd, as opposed to the "relational" crowd).
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u/Coady_L 1h ago
Fellow non-mathematician joining in the fun. I think about it as trying to explain math to an alien. Our way of thinking about one rock plus one rock may look very different to them. They may see a loosely organized cloud of 5.2 zillion atoms being put next to a 4.2 zillion atom cloud. Are you saying 9.4 zillion? It gets down to how you attach words to things, and that's limited by what you can perceive. We can get down to the atomic scale and there's still nuance that could lead to misunderstanding (disagree about truth).
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u/slvrbullet87 47m ago
But that is a problem with defining what you are looking at/for.
Its the difference between asking how many cars are in the parking lot vs the weight of metal in the cars in the parking lot.
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u/rsclient 57m ago
Weird counter example: computer integer arithmetic is "modulo": when you get to a high enough value, it wraps around. So if you've got an 8-bit value, the next number after 255 is 0, not 256.
Computers also do floating point math; the most common is called "double" which uses a 64-bit number. For very large numbers, adding a 1 no longer changes the number (it happens at about 253, IIRC).
And to really blow your mind: Lord Whitehead spent years proving that 1+1=2. The end result, the Principia Mathematic is a three-volume work.
This is part of the charm of math: some things which are really obvious, actually aren't when you get super rigorous
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u/LampyBoy 1h ago
How do you define 2? The sum of 1+1?
Any chain of justification will inevitably fall into one of the three camps defined by the dilemma.
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u/RolliFingers 1h ago
What if I do it by putting one rock next to another and pointing?
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u/LampyBoy 1h ago
Same issue, just with rocks 😅
You’re saying 1+1=2 because 1+1=2
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u/Silver-Elk-4239 21m ago
But that's neither a definition nor an argument. Not an axiom either. It's an observation. Something the titular paradix seems to conveniently leave out, because it is the fourth way out.
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u/creepy_doll 1h ago
It comes down to some philosophy and a handful of truisms that we work off. If those can’t be accepted nothing can.
The scientific method also is generally very good for getting things that are in all likelihood mostly right though they often still require some refinement.
We’ve gotten very good at figuring out things to a good enough state. One where things mostly work. Our understanding of physics and math are good enough that we can build massive structures. There are little details missing still but we’re not in a bad state of knowing
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u/peperonipyza 1h ago
Eh, anyone in the scientific community knows that it’s a given that nothing can be known at a 100% certainty. Do the best we can with the scientific method.
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u/marmot_scholar 24m ago
Yep it's pretty cool. We don't actually know anything for sure...if "for sure" means genuinely 100% for sure, with NO way to doubt something. But we know many things for a 90%, 95%, 99%, or 99.99% certainty...
There are several responses to this paradox, but I like the one called "hinge epistemology". (Epistemology is the study of knowledge and how we know things, and this is the term in philosophy, but a lot of people probably already figured out what I'm about to say with common sense)
Hinge epistemology notices that there are certain beliefs that cannot be doubted in practice, because the act of knowing, doubting, or communicating depends on those beliefs. So the basic act of thinking about the world depends on them like a door depends on its hinges.
For example, we do science based upon the assumption that there are regular laws or habits in our observations of nature. The philosopher Hume noticed that we can't justify that: if we say that the future is going to resemble the past because it has always resembled the past...in the past o__0 ; well, then we just used circular logic! However, if you try to believe "there are no regularities in nature at ALL, every single moment is completely random", you can't. There's nothing you can expect from that, no action you can take to prepare for it, and it seems to be instantly proven wrong because you don't suddenly fall through the floor.
Another hinge proposition is that your memory works most of the time. We know that our memory does NOT, in fact, always work. But you can't *generally* doubt your memory or think that it's always wrong, because that doesn't involve any specific beliefs or actions, and if it was true you wouldn't know what thought you were finishing. It's just an empty statement.
So, it's not that we know these "hinges" to a 100% certainty, not at all. But it doesn't make sense to doubt them. This is similar to axioms, but it's not the same.
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u/GooseQuothMan 20m ago
"I think, therefore I am". That's like the only thing you can know for sure. That you exist and you experience qualia.
Granted, from my perspective, I don't know if you actually think and experience things. Even if I had a perfect brain scan of your brain, I'd need to assume that the brain scan I see is a real thing and not some elaborate illusion.
Hell, even our thoughts might not be something that we ourselves do, just a thing that happens to us and we observe.
Having said all that though, how useful is it to think all that? If we are to participate in our "shared reality", I'd say not very, outside of philosophical debates. I mean - what's the point of thinking about most things not being provable when you need to boil some pasta for ten minutes? It's still going to be crunchy if you stop cooking it too early, regardless.
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u/amc7262 1h ago
To go in a different philosophical direction:
If the evidence we have points to something being true, and our assumption that it is true allows us to live our lives without hindrance, does it really matter if it isn't true.
Does the truth really matter more than perception of what is the truth?
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u/LightlySaltedPeanuts 1h ago
That seems to be the obvious takeaway. But it’s actually that since we can never know anything for certain, we can never be certain something is a bad idea to be thrown away. It means all information is equally relevant, despite what humans like to perceive.
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u/FreshmeatDK 8m ago
That is an unfortunate misconception. Just because nothing can be proved absolutely true, it can be quite trivial to prove something false, while other things cannot easily be proved so. While you can always take the "it is all an hallucination"-route, given almost any fact you accept to be true, a lot of other things (the world, causality, logic, and with a stretch some scientific statements) will be true as well.
"It is as true as your smartphone".
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u/_PaddyMAC 2h ago
Dig deep enough asking "why and how" and eventually you'll reach "because that's just the way it is."
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u/Sir-Lucy 37m ago edited 27m ago
no, you dig deep enough and get "because it isnt any way at all"
"That which depends upon conditions is empty of an intrinsic reality, what could be more amazing than this discovery"- Tsong khapa
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u/PugnansFidicen 1h ago
Perhaps I am missing something, but I thought logicians had basically settled this ages ago?
Endless regress traps you forever - if there is not even one single statement that can be accepted as true without proof, it'll never end.
Circular logical may seem appealing - if you can construct a self-referential system of logic with enough interlocking "supports", it may appear strong. But there are still unsupported assumptions that must be true in order for this to work. And if those assumptions are overly complex, they are less likely to be true.
So we converge on accepting unsupported assumptions, which we call axioms, and focus on keeping those axioms as simple and obvious as possible. Aristotle took this approach, so it's hardly new.
We may not be able to prove that 0 is a natural number, or that 1 is the successor of 0, but those axioms seem simple and self evident enough that we can fairly confidently build a system of arithmetic around them and construct proofs within that system that tell us useful things about the natural numbers.
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u/MartyMcBird 17m ago
It's settled, but with concessions. In an ideal world Godel is wrong and we live in a logical utopia and sing kumbaya. But we'll just have to settle with our axioms.
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u/Fit_Log_9677 2h ago
Ironically this is why the Catholic Church asserts there is no conflict between faith and reason.
All reason requires faith in the truth of certain prior axioms.
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u/BobertMcGee 1h ago
The faith that a catholic uses to arrive at belief in Jesus and the assumptions a logician or mathematician uses while constructing, say, ZF set theory or the foundations of logic, are not at all the same and to conflate the two is an incredibly dishonest way to address this topic.
The foundations of logic are evidently true and can be demonstrated with a venn diagram. The same can not be said for any axiom that leads to “Jesus is real”.
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u/shotgunocelot 53m ago
Anything that involves past events cannot be proven in the same way as something concrete like "1+1=2" because they are untestable and therefore unverifiable, but that doesn't we can't determine something with a high degree of probability based on available data. We have a high probability of correctly knowing what day Washington crossed the Delaware due to the amount of data and the recency of said data, but we have lower confidence in knowing what year Cleopatra was born. You can't "prove" either one though.
Regardless, most historians and scholars do agree that the historical Jesus existed, they just don't agree on his divinity. Obviously, neither can actually be proven
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u/BobertMcGee 51m ago
I’m fine with high degrees of certainty. We don’t have that for basically any fact about the life of Jesus, and the foundations of logic have the highest degree of certainty possible. Just because we can’t know anything 100% doesn’t mean every claim is equivalently likely.
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u/Heavy_Quiet8287 4m ago
Are foundations of logic evidently true? we have multiple systems which often say different things and work with different rules. Para-consistent logic comes to mind. The distinction you seem to be pointing out is that of necessary(deductive) and contingent(inductive) logic. The issue is, many people have claimed to deductively prove god(whether or not they have is a separate discussion.) So at the end of the day, if you’ve accepted the premise(axiomatic or synthetic) that god exists, you can of course do the same sort of logic as math/philosophy/etc using god as an object.
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u/Honest_Relation4095 2h ago
That's not surprising. For literally any explanation you have to assume a certain base or some axioms. Functions require inputs.
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u/spikebrennan 2h ago
So nothing is true.
Is everything permitted?
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u/Epistemite 2h ago
At worst this means nothing is known, not nothing is true. Skepticism, not nihilism.
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u/AnthropicSynchrotron 2h ago
That does not follow. We can't prove x is true, but x might still be true.
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u/Blenderhead36 1h ago
I mean, if you take a solipsistic worldview, then, no, nothing can ever be proven. To which I would say that that makes said worldview useless, because it means you can never know anything.
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u/Overthinks_Questions 1h ago
I feel like this is true when working with logic as a theoretical, but there's a pretty obvious way out of anything involved is empirically observable. Instead of relying on an unsupported assumption, you rely on empirical evidence.
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u/Retikle 1h ago edited 1h ago
but there's a pretty obvious way out of anything involved is empirically observable.
Most of us are absolutely unconscious to the fact that a vast proportion of what we assume to be 'empirically observable' is actually subject to preconceptions and interpretations.
For instance, we say "I saw it with my very eyes", but if you have two eyes, what you actually see is two slightly different worlds (one through the right eye, and one through the left eye) -- worlds in which objects constantly shift between sharp boundaries and blurry merging, and periodically disappear completely ever few seconds.
There is also an apparent third world, interpolated in 3D between the left and right images. And another thing we never notice: these 'worlds' always have a sort of fuzzy area at the periphery, beyond which there's not even darkness, but just... indistinct and boundless 'nothing'. (Try to perceive what is beyond or behind your peripheral vision, and you can become aware of this aspect of the 'world' you think is provable by seeing.)
What we are really saying with "I saw it with my own eyes" is that we assume an external, continually existing world of separate objects, and we assume that our senses support that belief. But this is an interpretation, not evidence; and even the notion of sharp boundaries between objects doesn't withstand scrutiny, since a boundary always belongs to both objects that are apparently bounded, and is revealed to be less and less distinct the closer you zoom in on it.
This is not even to mention all the visual aberrations, mirages, hallucinations, dreams, visualizations that -- if not for our premade assumptions -- have equal standing among visual experiences.
In fact, it is difficult to establish the existence of any externally existing reality that could be apprehended by empirical observation: we (most of us) only have at best a working hypothesis that there's an external world. Mystics, on the other hand, experience a nonduality between apparent subject ('me', the witness) and object ('that', the thing experienced).
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I feel like this is true...
Facts over feelings, friend. ;)
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u/Silver-Elk-4239 1m ago
Nobody sane actually operates on base assumption like that. You operate on empirical evidence, treating the world based on the sum of incoming data. You then make assumptions based on previous observations, sure, but the driver of those assumptions are empirically gathered datapoints provided by your sensory inputs.
Your ear gets the raw data about trembling air, then your brain proceeds to make assumptions on how to intepret that wave etc.
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u/TaftIsUnderrated 2h ago
Gödel's incompleteness theorems says this is even true of math.
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u/MegaIng 2h ago
No? That theorem is about the fact that no matter what, there are true statements that you cannot prove. But those statements probably aren't relevant at all for most things you want to prove.
Math needing axioms, i.e. "unsupported assumptions" has never been in contention AFAIK. That's something that annoys philosophers, not mathematicians. (although which axioms you accept is a very different beast)
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u/GreedyParfaitt 2h ago
Mathematical proofs are absolute GIVEN the axioms, but the axioms themselves aren’t proven within the system. They’re foundational assumptions, which is exactly what the trilemma identifies. Gödel’s incompleteness theorems don’t “prove” the Münchhausen trilemma, but they reinforce the idea that even mathematics has limits on self-justification.
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u/subwooferofthehose 2h ago
To make sure I understand the concept, it's axiomatic that 2 follows 1, and therefore 1+1=2?
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u/Bardfinn 32 2h ago
in logic and math, no
over 100 years ago two mathematicians wrote the Principia Mathematica, an enormous three volume treatise to prove logically from axioms that 1 + 1 = 2.
An example of an axiom is the statement
x = x2
u/limasxgoesto0 1h ago
It's true that this did happen, but 1+1=2 might as well have been an axiom beforehand as mathematics couldn't have been done without it, and even now if it'd have never been proven we'd be operating under the assumption that it's true
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u/Bardfinn 32 1h ago
You're thinking of arithmetic (operations on natural numbers). Mathematics is much more vast
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u/limasxgoesto0 32m ago
Uhh yeah obviously it is. I have a degree in math so I'd like to say I have some idea if what I'm talking about. And why would it stop at natural numbers? Subtracting one positive number from another is equivalent to adding a positive and a negative number. Multiplication is also defined in terms of addition, with division being its inverse and bringing rational numbers into the mix.
In every field of mathematics, the use of addition is assumed to work and never given a formal proof when one studies it. You can't add matrices in linear algebra if the elements of it can't add. You can't find the limit of a sequence if the idea of addition doesn't work. All of geometry relies on arithmetic. Even defining addition on integers as a field in abstract algebra doesn't work without the assumption.
If mathematicians weren't using 1+1=2 as an axiom before it was actually proven, which means ANY arithmetic operation as corollary, then how can any field of mathematics that involve any operation ever function? Fermat's last theorem has a plus sign. The proof that there are infinite primes involves plus signs.
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u/redopz 2h ago
To get into the weeds I am pretty sure 1+1=2 was proven mathematically true, but it required multiple books of work to do so and they didn't go any further.
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u/subwooferofthehose 1h ago
Forgive me, I phrased that poorly. What i meant is:
Axiom: 2 follows 1
Because we accept that axiom, 1+1 therefore equals 2
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u/MegaIng 1h ago
I would phrase it "we define 2 as the next natural number after 2. Therefore 1+1 = 2". So yes, you are correct, although in parlance "2 follows 1" is not an Axiom but a definition of notation (we define what the symbol 2 means).
The actual underlying axioms are more complex, lookup ZF-Set theory.
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u/BurnieTheBrony 1h ago
This is why some of the "proof" stuff just feels so divorced from reality that I wonder how useful it even can be.
I got one ball in each hand. I put em both in my right hand. I got two balls in my right hand. 1+1=2
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u/rsclient 51m ago
You are simultaneously completely right (there's a lot of weeds in mathematics) while also being wrong from a strictly economic point of view.
All of internet security depends on things like the diffie-helman key exchange. The key exchange lets two computers send encryption keys to each other. The exchange can be completely observed by anyone, and yet at the end, only the two original computers get the keys, and nobody else can figure them out.
It's all done with a previously-obscure branch of mathematics that had no known value. But as it turns out, that one discovery is worth trillions of dollars to the economy every year.
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u/reddorickt 1h ago
Getting that far into the weeds in mathematical minutia is almost never practical to an average person's experience.
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u/reddorickt 1h ago
The first complete proof of 1 + 1 = 2 (no mathematical axioms) was famously hundreds of pages long.
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u/MegaIng 1h ago
Sorry, I still don't see the relation between Gödel's incompleteness theorem and the Münchhausen trilemma, except that they both talk about unprovable statements.
Neither implies the other, nor do they talk about the same kinds of unprovable statements.
One of them says "we always need Axioms". The other says "Axioms can never be enough". These are almost polar opposite statements.
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u/GreedyParfaitt 52m ago
They’re not necessarily the same argument, and I don’t think Gödel’s theorem “proves” the Münchhausen trilemma. The connection is more-so that both highlight limits on self-justification in formal systems. They’re addressing different problems, but there’s overlap in the broader idea that a system can’t completely ground itself using only its own internal resources.
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u/Menolith 2h ago edited 1h ago
Math needing axioms, i.e. "unsupported assumptions" has never been in contention AFAIK
IIRC, making a self-consistent system which didn't have to rely on outside axioms was a big part of what drove Russell to work on Principia Mathematica (which Gödel later pulled the rug on). Even in school, he didn't like how Euclidean geometry had to rely on axioms, especially the famously fickle fifth one.
The brand of math they also dealt with is cutting pretty close to philosophy, so Russell definitely was annoyed by the topic.
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u/MegaIng 1h ago
Well sure, he wanted all his axioms to be obvious and have as few as possible, but I don't think he wanted to actually eliminate the axioms themselves? After all, "the empty set exists" is an axiom, i.e. an unsupported assumption, even if few people would contest it (although they do exists).
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u/thissexypoptart 2h ago
Further proof that math is invented not discovered imo
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u/hapaxgraphomenon 2h ago
You would have trouble posting this comment on the internet from your phone if math was just invented and not discovered
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u/KingSpork 2h ago
A foundational aspect of logic (which is just a form of math) is that it always begins from a set of assumptions. Since everything is filtered through our subjective experience so there’s no way to be sure about anything anyway. This could all be a dream. There’s no way to tell. So then logic/math becomes a tool you can use within your subjective reality, but ultimately, it can’t prove that your experience of reality is objectively real. At the end of the day, the universe must be accepted on faith.
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u/GobertGrabber 2h ago
“I think therefore I am.” Seems to refute this argument.
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u/GreedyParfaitt 2h ago
Not really. Descartes argued the cogito is a properly basic belief that doesn’t need further justification. Whether you accept that is another debate, but it’s still a foundational assumption, not an escape from the trilemma.
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u/Ofabulous 48m ago
I thought his point with that was that there’s loads of properly basic things we can’t take as facts (eg I am awake, I am not a brain in a vat), but “I think therefore I am” is irrefutable as to think requires being in some form, even if the form itself can’t be certain
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u/Silver-Elk-4239 8m ago
Thay doesn't follow. There is no assumption in perception. Raw signals to your brain are the base data upon which you build assumptions, but they are not assumptions themselves.
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u/donach69 2h ago
No, there's an implicit assumption, at least partially from how our language is structured, that thinking requires a subject
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u/GooseQuothMan 15m ago
I'd say it just tells us that because we experience things, thoughts etc, what we can deduce from that is that we exist. Not much else.
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u/Avandalon 1h ago
Isn’t that a tautological argument itself tho?
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u/GreedyParfaitt 1h ago
Yeah, sort of. It argues that every attempt at ultimate justification eventually bottoms out somewhere. The debate isn’t whether there’s a foundation, it’s what that foundation is and whether it can be justified without becoming circular.
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u/naliron 2h ago
Sticking your hand in a fire will prove that it is hot.
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u/awfulworldkid 2h ago
in this case, "something that seems to be hot and burns you actually is hot" is your unsupported assumption; it's obviously true, but you can't actually prove it
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u/Bundabar 2h ago
Hot relative to you. It’s not hot relative to the sun. It’s actually quite cold in that respect.
You assumed it’s hotness.
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u/Silver-Elk-4239 11m ago
Well yes, the speaker said hot and followed it up with no qualification. This obviously means hot by the speaker's standards. This is as expected and works as intended.
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u/kaleb42 2h ago
You can move your hand through a candle quickly and it won't burn you. Does this prove that a candles flame isn't hot? Or would that just prove that hot is relative? Or that you must stick your hand in a flame for an amount of time to prove it's hotness? What if you stick your hand in a fire but have a glove that offers some protection does that now mean the flame is Or isn't hot?
You are still making an assumption that if your hand touches fire you will know it's hot. In the candle example this proves that your assumption is not universally true.
Even now I made an assumption that you meant by putting your hand in fire means that you're getting burned.
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u/wercooler 2h ago
You assume you can trust that the nerves in your hand are real, and that they are giving you legit information about the world.
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u/GooseQuothMan 7m ago
I could use some electrodes to make you feel cold instead. I could use some different electrodes to make you see fire where one isn't, and make you not see fire where one is.
It's all subjective experiences that can't conclusively prove anything.
We have to function on assumptions and belief.
But almost everyone anyway acts as if the world around us is a fact, which is why this is mostly philosophy and not a way to live (unless one wants to become some starving monk).
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u/dormidary 2h ago
The first word in my comment is "The". Which of the three options is that statement relying on?
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u/ruggedtextile 2h ago
Unsupported assumption: Your sentence should be read left to right. Without that axiom the sentence is false.
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u/dormidary 2h ago
That and the "what is a word" answer both seem like just socially constructed rules of communication so we understand each other. Is that really the stuff this theorem is getting at? That doesn't seem like a very important point if so.
Maybe it's that I'm relying on the unsupported assumption that I'm observing the sentence correctly - I guess that would make sense.
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u/ruggedtextile 2h ago
Yes, those socially constructed rules are axiomatic in this context. And I agree being pedantic about them is not particularly interesting in the context of social communication. It’s slightly more interesting in the context of formal logic / provability. But not really. Just philosophers creating knots to tie themselves in.
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u/BrineFine 2h ago
Most contemporary epistemology is concerned with the relationship between communicative language and reality, not thought and reality.
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u/TheBanishedBard 2h ago
This is where the God of the Gaps finds his niche among people who believe in both science and religion. (Fundamentally, they are incompatible but that's neither here nor there). The idea is that eventually, at the bottom of all scientific and logical inquiry there exists a question without an answer, an effect without a cause. God is a convenient answer to that problem. To take the example to a logical end point: the big bang. What caused it? We can't know because there's no way to observe it. It's not a scientific question. So believers often use God to fill in what cannot be explained by science. The difficulty is that God gets smaller and smaller and his nature changes as science fills in the gaps previously placeholdered by god, which isn't particularly divine of him. Going back to the big bang, it reduces God to a singular action, a spark that gave birth to the universe... And then what? Did he just set the gears and cogs in motion and watched? Still not compatible with the god of scripture.
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u/GreedyParfaitt 1h ago
I think you may be misunderstanding where the argument is coming from. The issue isn’t that science will eventually reach a point where we don’t know the answer and then we insert God as a placeholder. That would be a God-of-the-Gaps argument. The deeper question is whether science, logic, and rational inquiry themselves depend on some underlying foundation that they can’t justify from within their own framework. The question isn’t “what caused the Big Bang?” but “why is there a rational order to reality that allows us to discover truths about it in the first place?” A theist would argue that God isn’t an explanation for a gap in our knowledge, but the foundation that makes knowledge itself possible.
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u/GooseQuothMan 1m ago
But then you're redefining god to something that's more of a phenomenon than god. You could call it fate instead, perhaps. Why would you pray to it, or try to influence it in anyway? It doesn't make much sense to me. Seems like some word play.
And if you insert like any religion lore in to the argument, it just becomes incredibly silly, why would some fundamental concept, framework or maybe reality itself become a human?
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u/ghotier 2h ago
How is this distinct from the concept of sophistry?
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u/CorrosiveMynock 2h ago
Because sophistry is about superficial plausibility and deceptive presentation. The Münchhausen trilemma says all claims asserting truth fail, even our very best proofs such as what we get from mathematics and deductive logic.
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u/HarrumphGuffaw 2h ago
Which is a deceptive way to appeal to absolute knowledge. Which is sophistry and fallacious.
There is something here! If you keep digging and redefining you can’t get to an absolute that we can observe and define.
This concept is fundamentally about human limitations and not a refutation of the concept of truth.
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u/CorrosiveMynock 1h ago
I'd say it is about the refutation of the concept of absolute truth. Ironically the Münchhausen trilemma was coined and popularized by Hans Albert and Karl Popper who were advocates for Fallibilism and Critical Rationalism. They leaned into the necessity to treat all knowledge as provisional, open to revision, and subject to critical testing. It is definitively NOT about justifying nihilism and just because absolute foundations do not exist, does not mean some arguments aren't better than other ones.
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u/BrineFine 2h ago
This is a foundational problem in epistemology and sophistry is a set of rhetorical practices.
If your point is that running in circles with speculative metaphysics and epistemology is itself sophistry, yeah I think so too.
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u/Fun-Negotiation5510 2h ago
This is very interesting. Thanks for sharing, my friend.
I'll now look at it more thoroughly now :)
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u/bblade2008 2h ago
Arguments like this make people ignore philosophy. If you are going to argue useless nonsense and pretend like we can't figure anything out, there's really no point in listening to you.
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u/klauskervin 14m ago
I feel like half the people here have never read any philosophy at all. Most deal with this exact question at the start of their theories/books. Plato's Republic goes on for quite awhile about this very concept.
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u/Talinn_Makaren 2h ago
Philosophy is about contemplating shit. Making the naive and gullible listen to a message is the realm of advertising.
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u/Sbatio 2h ago
It’s always “we can’t know anything” until you offer to test the theory with sex stuff.
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u/FaufiffonFec 1h ago
A magician once told me he would fuck my wife and then disappear. And he did.
You're onto something.
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u/JacksGallbladder 1h ago
Thus we accept that our definition of "true" is some combination of mathmatic accuracy, consensus of peers, or a consistently repeatable outcome.
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u/flp_ndrox 1h ago
I seem to remember in HS geometry learning that all geometry was based on axioms or things assumed to be true. IDK why anything else would be any different.
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u/bobbi21 1h ago
Well.. duh? This is like lesson 1 in philosophy and logical reasoning in general. You always have to start with some assumption/axiom and build from there.
Even in pop culture you get the standard descartes i think therefore i am as the base assumption to build the rest of his philosophy (an assumption that has many flaws in it imo. All you can really say is “i”. My thoughts could be created by some other entity entirely. Maybe im a dream figment in some eldritch monsters head. I might not be thinking. Something else could be thinking through me. Even the “i” is hard to know how to define since split brain experiments show that a single brain is kind of made of many individual consciousnesses, mainly the left and right brain operate independently and talk to each other to form your current thoughts. If split, they happy continue their own thoughts independent of each other. So even the “i” has caveats. All you can say is that there is something that i think of as i that observes thoughts of some sort. Which isnt much of a basis)
So yeah, this is basic philosophy.
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u/Tregavin 1h ago
I don't know. Maybe, but still you can minimize the faulty logic more than other arguments. Like one argument boils down to one assumption which is likely correct compared to another argument which is based on 1000s of wildly unsupported claims... These two stances are not equal. They are arguably equally as true by proof, but you are still better to support the first.
Another comparison is how technically there is no pure definition of words which doesn't rely on some circularly defining words. It's a fun math proof but it is true that any definition of a word at some point boils down to some word being used to describe itself circularly. That doesn't mean words have no definitions, or that a wrong definition is equally as valid as another. it just means that sometimes you have to just go outside to see what the color red is. You can't purely describe it by reference.
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u/Inside_Ad_7162 59m ago
Don't make me quote Thoreau! Let's just say if I stick a trout in a gallon of milk, it may be circumstantial, but I dont need to prove it's there.
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u/fauxfilosopher 34m ago
All comes back to my ontological feeling that all knowledge stems from intuition. Infinite regression otherwise.
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u/OnionsAbound 12m ago
I think Socrates came before Munchhausen, but perhaps he formalized the logic.
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u/Buttman_Poopants 2h ago
See, here I thought I didn't like philosophy because I just wasn't smart enough to understand it! But actually, philosophy is dumb!
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u/TheComplimentarian 2h ago
Philosophy major here!
This is a question of deductive logic, which is like math, except that math works in the real world, and deductive logic really doesn't. (This is obviously a simplification: Geometry rocks deductive style proofs.)
The second main kind of logic is inductive. Inductive is messy real-world shit. It's percentages, basically. Calculus. Most math proofs are inductive...The limit as X approaches infinity...
With a lot of deductive logic, you try to reduce the argument to a tautology or a contradiction, which is to say, something that's always true or always false.
With induction, you try to get as close to a right answer as possible, while accepting that the real world sucks and you're only ever going to get close.
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u/blankford 2h ago
TLDR; this is what you experience when a 6 year old kid just keeps asking you "why?"