10 ms·

Münchhausen trilemma

156 points by lainon 8y ago

humanrebar 8y ago
In the situations where Münchhausen trilemma is applicable, people tend to use a version of abductive reasoning, which is finding the simplest narrative or explanation that fits the known facts. https://en.wikipedia.org/wiki/Abductive_reasoning https://en.wikipedia.org/wiki/Abductive_reasoning It's important to keep the Münchhausen trilemma and abductive reasoning in mind when discussion controversial issues where one side feels they have proof and the other side is ignorant or duped. Often the difference is something like whether emergent behavior or a conspiracy feels like a simpler explanation.
- Fnoord 8y ago
  Seems to be the same principle as Occam's razor [1] or am I missing something? [1] https://simple.wikipedia.org/wiki/Occam%27s_razor https://simple.wikipedia.org/wiki/Occam%27s_razor
  - xelxebar 8y ago
    In spirit, yes. However, it gets more interesting if we try to make Occam's Razor more precise with something like Solomonoff induction, then it get's trickier to decide in practice what "simpler" actually means. Even if we're able to reduce our competing models to Turing machine implementations, we're only able to calculate their complexity relative to some defined collection of models, which in turn depends on what kind of low-level logical formalism we're using. In practice, of course, we can't parse out all these formal details for every decision, but I think it's helpful to at least be aware of the inherent problems with naive Occam's Razor.
  - paulific 8y ago
    Occam's razor is better thought of as a method of choosing between alternative explanations of the same observed phenomena. It suggests choose the one that requires the least unproved theoretical scaffolding to support it. It is not really "accept the simplest explanation" but more like "do not create complex theories unless they explain the facts better than the simple ones."
- pron 8y ago
  The validity of abductive/inductive reasoning is itself subject to the trilemma.
  - humanrebar 8y ago
    First, inductive reasoning is different than abductive reasoning. Second, the goals of abductive reasoning are different than philosophical or mathematical proof. Often we need to make decisions on incomplete information, and it's a philosophy to help one do so. For example, juries are supposed to make a decision based on a preponderance of evidence or beyond a reasonable doubt. Convictions would be rare if the standard were incontrovertible truth.
    - pron 8y ago
      Of course, but the whole point of the trilemma is that absolute knowledge of absolute truth is impossible, not that we cannot axiomatically accept the utility of partial, approximate knowledge. Also, while abductive reasoning is (a bit) different from inductive reasoning, they have the same underlying epistemological justification. In discussions of epistemology you often don't see abductive reasoning mentioned, as it falls under the general framework of inductive reasoning.
      - blueprint 8y ago
        Well if absolute knowledge of absolute truth is impossible are you able to suggest a truth that could even be considered absolute? If not, bit of dangerous statement, isn't it?
        pron 8y ago
        That's the trilemma.
        blueprint 8y ago
        Uh, no it's not. You start with a statement then you go about trying to analyze it....? Ok.
- DanielBMarkham 8y ago
  We should teach abduction and Bayesian reasoning as part of a normal education. Epistemology overall is more of a collegiate/post-grad subject, but we have to provide some kind of foundation in epistemology. Otherwise we end up with a lot of kids who have tied their self-worth to knowing "science", but it's more of a slogan and catch-all phrase than something they can continue to build on. (Aside from the actual practice of whatever scientific field they end up in. Even then, we see in several fields epistemological problems rearing their heads -- and the leading practitioners clueless about what to do about it. Usually re-inventing the wheel in some ad-hoc fashion.)
  - Angostura 8y ago
    I've no idea what abduction means in this context, and neither does my dictionary. Can anyone help?
    - letsgetphysITal 8y ago
      Take the facts, and form the simplest theory that explains them. At least that's my take on it in this context.
    - SilasX 8y ago
      https://en.wikipedia.org/wiki/Abductive_reasoning https://en.wikipedia.org/wiki/Abductive_reasoning
- jrog 8y ago
  Really good point on controversial issues. I think opposing sides of current hot topic issues (take your pick, gun control, abortion, pronouns) start with a different set of axioms. Axiomatic differences can lead of vastly different conclusions, both with sound logical reasoning. Eg. If you take as axioms that it is always wrong to end life, and life begins at conception, abortion is wrong is a sound logical conclusion.
  - SideburnsOfDoom 8y ago
    > Eg. If you take as axioms that it is always wrong to end life, and life begins at conception, abortion is wrong is a sound logical conclusion. yes, and you'd also end up with an outright ban on civilian ownership of automatic weapons, amongst other safety measures. But you don't often see those two together. I think that the axioms are a layer or two below that, and might involve concepts like "individual responsibility" and "greater good"
    - dmreedy 8y ago
      Agreed; it seems likely that the axiom system of the typical pro-life defender[0] is closer to "It's always wrong to end an innocent life"; this requires the inclusion of a set of axioms defining innocence (and thus probably invoking some combination of free will, and an absolute moral axis. A convenient framework for this includes a soul). This way you preserve the ability to defend yourself, to take the life of an enemy soldier, etc, while still being able to justify a pro-life position. It also allows for the death sentence for murderers. --- 0. there are, of course, different sets of axioms that arrive at superficially similar conclusions. For example, the category of pacifist that believes that any loss of life is not justifiable; this kind of person will reject both abortion and ownership of weapons, war, etc.
    - jrog 8y ago
      It could also be that either side of these debates are unknowingly using abductive reasoning for how they feel about a stance that conflicts. Perhaps the proposed axioms come after to explain how people feel about controversial issues. Funny enough, this conversation could also be a form of abductive reasoning. We're inferring that people are using abductive reasoning because people often hold conflicting moral views, though using abductive reasoning wouldn't necessarily guarantee conflicting views.
- stcredzero 8y ago
  abductive reasoning, which is finding the simplest narrative or explanation that fits the known facts. The problem there, is figuring out what "simplest" means. To many people, "God" seems like the simplest explanation for the universe, even though what the word implies is very complex. It's the same phenomenon as people who say, "Scientists can't explain magnets, the liars!" Magnets seem like a magical extra, but it turns out that electromagnetism is a fundamental. It's a rock sitting on a tabletop that's complex and turns out to need explanation. https://www.youtube.com/watch?v=fwMSaCrcAmM https://www.youtube.com/watch?v=fwMSaCrcAmM
- jaclaz 8y ago
  Still, Occam's Razor (or lex parsimoniae) : https://en.wikipedia.org/wiki/Occam's_razor https://en.wikipedia.org/wiki/Occam's_razor tends to be a valid approach, generically speaking.
JepZ 8y ago
I wonder why they argue that way, when it seems obvious that you need some common ground to start reasoning at all. As we all start living in this world without any knowledge, all knowledge has been formed by the things we experience. And therefore, many of us agree to argue based on our (measurable) experiences (e.g. scientists). Others prefer to add beliefs which are wildly subjective (hard to reproduce) and therefore cause a lot of inconsistencies. But in the end, it always comes down to the point where you need a common set of truths to start an argument. Otherwise there is no point in arguing at all.
- blackbrokkoli 8y ago
  It's not as easy as that. First we don't start from zero. If you would build a robot with all human senses but erased hard drive it wouldn't do anything, ever. Second, while applied in RL, science might be labeled as "objective" and therefore be superior for, let's say, building a bridge. But on a very basal level, we're subjectively agreeing on what "scientific" is, or rather based on non-proofable paradigms, which is what the article is about
  - gerbilly 8y ago
    > First we don't start from zero. There is strong evidence that humans, and most animals are born with built in knowledge and expectations about the world.
    - boxy310 8y ago
      I found it simply fascinating when I learned that Blue Wildebeests are born knowing how to stand within minutes of their birth, and within a day can outrun adult hyenas: "Extremely precocial species are called "superprecocial". Examples are the Megapode birds, which have full flight feathers and which, in some species, can fly on the same day they hatch from their eggs. Another example is the Blue Wildebeest, whose calves can stand within an average of six minutes from birth and walk within thirty minutes; they can outrun a hyena within a day." [1] https://en.wikipedia.org/wiki/Precocial https://en.wikipedia.org/wiki/Precocial
cousin_it 8y ago
The question "why should claim X be trusted?" indeed runs into infinite regress and has no well-founded answer. But the modified question "why should claim X be trusted by creature Y?" can have a well-founded answer, based on facts about creature Y.
- blackbrokkoli 8y ago
  Why is that? You would rely on the third option, basing on axioms, no?
  - cousin_it 8y ago
    Axioms accepted by creature Y.
arf 8y ago
Let the set M = {circular, regressive, axiomatic} to be the set of "unsatisfying" arguments that may be used to prove any truth. Let the mapping J: powerset(M) -> <schools-of-thought-in-meta-epistemology> to map some subset of M to a theory of justification such that the believers in said theory only find usage of some combination of the said subset to be "acceptable". Then: J({}) is in {Skepticism} J({circular}) is in {Coherentism} J({axiomatic}) is in {Foundationalism} J({regressive}) is in {Infinitism} J({axiomatic, circular}) is in {Foundherentism} J(M) is in {Quietism} Is there an x where x is in the powerset of M, such that J(x) is {}? Or literally every possible position can be the foundation of a philosophical paper?
- tunesmith 8y ago
  J({circular, regressive}) is twoyearoldism. Where they ask why incessantly and don't care if you lead them in a circle. J({regressive, axiomatic}) seems contradictory, so maybe that's {}.
  - arf 8y ago
    On J({regressive, axiomatic}): Well, the regular formulation of "Infinitism" is that S is justified to believe P_1 on the basis of P_2 and P_n on the basis of P_n+1. J({regressive, axiomatic}) just defines a limit i.e. S is justified to believe P_1 on the basis of P_2 and P_n on the basis of P_n+1 such that lim_(k->infinity) P_k = P_x where x is not a natural number. You have to say x is not a natural number, because if it were, J's output would have been "foundationalism" and P_x then would be a "self-evident" belief - to use Chisolm's terminology. P.S. If anyone thinks that this is an abuse of mathematics, I agree. But, its usage is compatible with that of philosophers e.g. Goldman's Causal theory of knowledge literally uses a recursive formulation of belief formation where the base case is "self-evident", I just unwrapped the tail call and wrote it as a loop!
subroutine 8y ago
I feel like a better, formal proof of this concept is Gödel Incompleteness, given this lemma, if true, would in turn invalidate itself.
- adrianmonk 8y ago
  Seems like a wash to me. It wouldn't invalidate itself any more than it would invalidate other alternatives to it.
- jerf 8y ago
  The problem with using math to address this is that it very subtly ends up begging the question. Math has an answer to the trilemma: Math is based on axioms. The question of whether math corresponds to anything in the real world is a separate question from the mathematics itself. Godel's theorem is thus based on mathematical axioms, but the trilemma questions the axioms themselves. No structure built on the axioms can prove the axiomatic formulation is correct. Godel's incompleteness is an important part of math history about how that was finally proved so hard that modern mathematics now deeply accepts that non-uniqueness of axioms, but again, this is all happening at a level too high to help us with the trilemma. So no, the trilemma can not be solved or even particularly refined by feeding it to mathematics. "From whence mathematics?", it asks. If you are going to play philosophical games with the trilemma, a better approach is simply to feed it to itself. If the trilemma is true, then we can't be confident that we've properly read it, because it cuts away the foundation we are using to communicate. If any of us have successfully extracted even a portion of understanding about the trilemma from the reading of this text, we must be sharing a certain very basic amount of rationality to get that far, even if we can't nail down where that rationality came from exactly. You could then proceed to say that this basic shared rationality is de facto usable as a foundation. But that still doesn't answer the question of where it comes from.
thanatropism 8y ago
That's not a true trilemma. A trilemma is a "choose two out of three". Therefore a trilemma is always depicted as a triangle where the vertices are the things you would like to have and the edges are the possible combinations. A trilemma is an extension of the concept of a dilemma, which is "choose one out of two" . Example: [good, fast, cheap]: you can have good and fast, but it's going to be expensive. Or good and cheap, but it's going to take longer. Courtesy of Jason Kottke[0], some more simple trilemmas: Elegant, documented, on time. Privacy, accuracy, security. Have fun, do good, stay out of trouble. Study, socialize, sleep. Diverse, free, equal. Fast, efficient, useful. Cheap, healthy, tasty. Secure, usable, affordable. Short, memorable, unique. Cheap, light, strong. ---- Ultimately the generalization of a trilemma is a (3-)budget. I will show this. An n-lemma is "choose (n-1) out of (n)". Geometrically/topologically the things you would want in a n-lemma corresponds to the vertices in an (n-1)-simplex. A dilemma is represented as a 1-simplex, i.e. a line segment with each alternative as one end. In this case alternatives are points and so are the choices; in the 3-case alternatives the choices are segments. I'll leave you to imagine 4 and 5-lemmas geometrically. An n-simplex can be defined in a n-dimensional vector space as the region of points whose coordinates sum to 1. So for example a 2-simplex (a triangle) is the set of points (x,y,z) such that x+y+z = 1. In a n-lemma, only vertices are allowable choices -- i.e. x,y,z must be all either 0 or 1. In an n-budget, we can have partial allocations -- rather than have to choose two out of study-socialize sleep (i.e. sleep deprivation, loneliness or failing classes), I can spend my finite time as P% study, Q% social, R% sleep. Note: we can still represent budgets as points inside (n-1)-simplices. Of course, some trilemmas are not easily seen as extremizations of budgets. In some cases this will be because certain alternatives are fully binary (either you have floating exchange rates); in others, it's because we need to think a little more about the trade-offs (cheap, light, strong) -- we need to think harder about how lightness works against strongness. --- We can next imagine how to model slightly more complicated decision structures as n-lemmas. For example, I might have to decide between being married or single (each with its delights) and single people might have to decide between intelligence, looks and agreeableness. (This is terribly sexist but presumably very beautiful people don't have the same pressures to be smart and carve a space for themselves; and people who are intelligent and hot are full of themselves. Bear with me please). In this case we've connected a 1-simplex (married or single) to a 2-simplex. This is known as a simplicial complex, and it turns out we can (roughly oversimplifying) rebuild topology from the ground up by chaining simplices like that. So the choose-one-out-of-three "trilemma" in the OP isn't a trilemma at all. It's some decision structure that arises out of a complex of dilemmas. Possibly because every choice is connected to every choice, it even has the geometric contours of a triangle, but a hollow one, one where the segments are not connected. Therefore it doesn't generalize as a budget. What is the trade-off structure then? What is the finite thing that makes having everything impossible? What are these people talking about? [0] https://www.kottke.org/05/04/pick-two https://www.kottke.org/05/04/pick-two
md224 8y ago
It recently occurred to me that epistemology is essentially a hermeneutics of experience, which is to say: all of our non-trivial beliefs about ourselves and the world (including this very statement) are simply interpretations of what we perceive. This realization, while surely obvious to some, was very clarifying for me. Edit: Judging from the downvote I got, I guess some people don't share my interpretation of epistemology. C'est la vie.
sidyapa 8y ago
A tangent, how is Münchhausen actually pronounced ? Curious to know.
- jacquesm 8y ago
  With a sharp 'u' and the au like ou in the English word 'loud'.
  - sidyapa 8y ago
    Thank you.
- munificent 8y ago
  I believe it's roughly "MOON-chow-zen", though the "OO" is more like the "oo" in "book".
- elefantastisch 8y ago
  https://en.oxforddictionaries.com/definition/munchausen,_baron https://en.oxforddictionaries.com/definition/munchausen,_bar... https://forvo.com/word/m%C3%BCnchhausen/ https://forvo.com/word/m%C3%BCnchhausen/
akkartik 8y ago
I'm reminded of the chapter "Two-Part Invention" in Douglas Hofstader's "Gödel, Escher, Bach - An Eternal Golden Braid". https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achi...
TimTheTinker 8y ago
To me, this is a great illustration that there's no other coherent place to start any form of discussion, reasoning, or belief than with axioms (or assumptions). Regressive and circular arguments only shift the problem. I believe that if one is looking for truth in a big-picture sense (religious or philosophical), the best approach is to evaluate various existing systems of axioms/assumptions and apply a twofold test to each: (1) correspondence to reality and (2) internal consistency. It's a given that applying the first test requires stepping into the subjective, since one must honestly apply it to personal experience.
- tunesmith 8y ago
  Combine it with Hume's Guillotine and you realize that all "should" conclusions really just start with moral "value" axioms. So then you can make a distinction between people that reason correctly from values that are different than yours, and people that reason badly from their axioms. And you can also make a distinction between philosophies that are based off of unprovable beliefs (which is fine), and philosophies that are anti-factual (which isn't). I like to define the former as religion and the latter as ignorance, but unfortunately there are a lot of the latter that claim it's religion.
- romwell 8y ago
  I heavily disagree; axioms are never a good place to start, nor, historically, they ever were a starting place. Working mathematicians do a lot of mathematics and constructions before stopping to look and say: "OK, we can distill this rich theory down to this small set of axioms". Geometry has been quite developed before Euclid's axioms, and number theory took its sweet millenia before Peano's axioms were developed. On a more modern side, a lot of topology has been produced before people decided to write down a list of axioms for homology, which all the different homology constructions satisfied. The point is that understanding almost always precedes formal reasoning, language follows ideas, and rigid systems arise on a fertile soil of messy experiments - mental or physical. If you look at the history of science and mathematics, nothing was ever built up from the formulas and axioms (criminally contrary to the way these subjects are taught). There is an underappreciated beauty in our ability to argue about, reason with, and make use of concepts that we haven't even really defined. Everyone knew Newton's Calculus was full of holes, and people used it for centuries before coming up with solid definitions of limits, derivatives and integrals - the most fundamental concepts of the subject! And on that note, people used real numbers for a long time before having the formal machinery to define them. Zeno didn't have the axioms to resolve his paradox. Didn't stop anyone from using these weird objects in reasoning and practice. ---------------------------------------------------- TL;DR: never start with axioms, end with them.
ethn 8y ago
To be clear this trilemma is only a problem for rationalists, like Hans Albert. This problem doesn't exist for German Idealists like Kant or Schelling or even the empiricists. You escape the problem of infinite regression through acknowledging that the only thing real is experience, which lends you to the haven of relative objectivity, which is that of which modern science has become. You would think that the conjurer of the paradox would have shifted to empiricism or idealism—maybe my faith in people betrays me.
- Karrot_Kream 8y ago
  Yes, but so many tech people see themselves as rationalists or at least rational utilitarians, and I'm going to guess most of this forum does as well. Given that so many tech people see themselves this way, diving into the trilemma (and discussing how Idealists or empiricists moved past it) is important and probably eye-opening for many.
- smallnamespace 8y ago
  Isn't this taking the 'axiomatic' path? > through acknowledging that the only thing real is experience This seems like the key axiom for idealists/empiricists. Of course that leads you to many other details and questions (namely, which experiences?)
  - beaner 8y ago
    It is an observed axiom, rather than an "accepted" axiom, which the article implies is the only kind.
    - bryananderson 8y ago
      Why does observing something mean that something is true? If you keep asking questions, at some point you must get to either an accepted axiom, a circularity, or infinite regress.
      - beaner 8y ago
kazinator 8y ago
Those three options are not "equally" unsatisfactory. In fact, the axiomatic option is almost always entirely satisfactory. The marvel and utility of an axiomatic foundation cannot be categorically compared to the absurdity of regressing ad infinitum or going in circles.
- stochastic_monk 8y ago
  Much like how theorists could take the axiom of choice after the Gödel incompleteness theorems. Sure, it causes inconsistencies, but you can’t get anywhere without them.
- sdenton4 8y ago
  Well, depends who you ask. One could argue that axiomatic foundations in geometry made it take much longer to discover hyperbolic geometry. (One could view the axiomatic approach as a stand-in for truncating all of the required infinite proof below a well-established line.)
dwaltrip 8y ago
I find the concept of paradigms, as described by Kuhn, to be a much better model for truth and knowledge than axioms or series of "proofs" chained one after the other.

156 points by lainon 8y ago

In the situations where Münchhausen trilemma is applicable, people tend to use a version of abductive reasoning, which is finding the simplest narrative or explanation that fits the known facts. https://en.wikipedia.org/wiki/Abductive_reasoning https://en.wikipedia.org/wiki/Abductive_reasoning It's important to keep the Münchhausen trilemma and abductive reasoning in mind when discussion controversial issues where one side feels they have proof and the other side is ignorant or duped. Often the difference is something like whether emergent behavior or a conspiracy feels like a simpler explanation.

Fnoord 8y ago
Seems to be the same principle as Occam's razor [1] or am I missing something? [1] https://simple.wikipedia.org/wiki/Occam%27s_razor https://simple.wikipedia.org/wiki/Occam%27s_razor
- xelxebar 8y ago
  In spirit, yes. However, it gets more interesting if we try to make Occam's Razor more precise with something like Solomonoff induction, then it get's trickier to decide in practice what "simpler" actually means. Even if we're able to reduce our competing models to Turing machine implementations, we're only able to calculate their complexity relative to some defined collection of models, which in turn depends on what kind of low-level logical formalism we're using. In practice, of course, we can't parse out all these formal details for every decision, but I think it's helpful to at least be aware of the inherent problems with naive Occam's Razor.
- paulific 8y ago
  Occam's razor is better thought of as a method of choosing between alternative explanations of the same observed phenomena. It suggests choose the one that requires the least unproved theoretical scaffolding to support it. It is not really "accept the simplest explanation" but more like "do not create complex theories unless they explain the facts better than the simple ones."
pron 8y ago
The validity of abductive/inductive reasoning is itself subject to the trilemma.
- humanrebar 8y ago
  First, inductive reasoning is different than abductive reasoning. Second, the goals of abductive reasoning are different than philosophical or mathematical proof. Often we need to make decisions on incomplete information, and it's a philosophy to help one do so. For example, juries are supposed to make a decision based on a preponderance of evidence or beyond a reasonable doubt. Convictions would be rare if the standard were incontrovertible truth.
  - pron 8y ago
    Of course, but the whole point of the trilemma is that absolute knowledge of absolute truth is impossible, not that we cannot axiomatically accept the utility of partial, approximate knowledge. Also, while abductive reasoning is (a bit) different from inductive reasoning, they have the same underlying epistemological justification. In discussions of epistemology you often don't see abductive reasoning mentioned, as it falls under the general framework of inductive reasoning.
    - blueprint 8y ago
      Well if absolute knowledge of absolute truth is impossible are you able to suggest a truth that could even be considered absolute? If not, bit of dangerous statement, isn't it?
      - pron 8y ago
        That's the trilemma.
        blueprint 8y ago
        Uh, no it's not. You start with a statement then you go about trying to analyze it....? Ok.
DanielBMarkham 8y ago
We should teach abduction and Bayesian reasoning as part of a normal education. Epistemology overall is more of a collegiate/post-grad subject, but we have to provide some kind of foundation in epistemology. Otherwise we end up with a lot of kids who have tied their self-worth to knowing "science", but it's more of a slogan and catch-all phrase than something they can continue to build on. (Aside from the actual practice of whatever scientific field they end up in. Even then, we see in several fields epistemological problems rearing their heads -- and the leading practitioners clueless about what to do about it. Usually re-inventing the wheel in some ad-hoc fashion.)
- Angostura 8y ago
  I've no idea what abduction means in this context, and neither does my dictionary. Can anyone help?
  - letsgetphysITal 8y ago
    Take the facts, and form the simplest theory that explains them. At least that's my take on it in this context.
  - SilasX 8y ago
    https://en.wikipedia.org/wiki/Abductive_reasoning https://en.wikipedia.org/wiki/Abductive_reasoning
jrog 8y ago
Really good point on controversial issues. I think opposing sides of current hot topic issues (take your pick, gun control, abortion, pronouns) start with a different set of axioms. Axiomatic differences can lead of vastly different conclusions, both with sound logical reasoning. Eg. If you take as axioms that it is always wrong to end life, and life begins at conception, abortion is wrong is a sound logical conclusion.
- SideburnsOfDoom 8y ago
  > Eg. If you take as axioms that it is always wrong to end life, and life begins at conception, abortion is wrong is a sound logical conclusion. yes, and you'd also end up with an outright ban on civilian ownership of automatic weapons, amongst other safety measures. But you don't often see those two together. I think that the axioms are a layer or two below that, and might involve concepts like "individual responsibility" and "greater good"
  - dmreedy 8y ago
    Agreed; it seems likely that the axiom system of the typical pro-life defender[0] is closer to "It's always wrong to end an innocent life"; this requires the inclusion of a set of axioms defining innocence (and thus probably invoking some combination of free will, and an absolute moral axis. A convenient framework for this includes a soul). This way you preserve the ability to defend yourself, to take the life of an enemy soldier, etc, while still being able to justify a pro-life position. It also allows for the death sentence for murderers. --- 0. there are, of course, different sets of axioms that arrive at superficially similar conclusions. For example, the category of pacifist that believes that any loss of life is not justifiable; this kind of person will reject both abortion and ownership of weapons, war, etc.
  - jrog 8y ago
    It could also be that either side of these debates are unknowingly using abductive reasoning for how they feel about a stance that conflicts. Perhaps the proposed axioms come after to explain how people feel about controversial issues. Funny enough, this conversation could also be a form of abductive reasoning. We're inferring that people are using abductive reasoning because people often hold conflicting moral views, though using abductive reasoning wouldn't necessarily guarantee conflicting views.
stcredzero 8y ago
abductive reasoning, which is finding the simplest narrative or explanation that fits the known facts. The problem there, is figuring out what "simplest" means. To many people, "God" seems like the simplest explanation for the universe, even though what the word implies is very complex. It's the same phenomenon as people who say, "Scientists can't explain magnets, the liars!" Magnets seem like a magical extra, but it turns out that electromagnetism is a fundamental. It's a rock sitting on a tabletop that's complex and turns out to need explanation. https://www.youtube.com/watch?v=fwMSaCrcAmM https://www.youtube.com/watch?v=fwMSaCrcAmM
jaclaz 8y ago
Still, Occam's Razor (or lex parsimoniae) : https://en.wikipedia.org/wiki/Occam's_razor https://en.wikipedia.org/wiki/Occam's_razor tends to be a valid approach, generically speaking.

JepZ 8y ago

I wonder why they argue that way, when it seems obvious that you need some common ground to start reasoning at all. As we all start living in this world without any knowledge, all knowledge has been formed by the things we experience. And therefore, many of us agree to argue based on our (measurable) experiences (e.g. scientists). Others prefer to add beliefs which are wildly subjective (hard to reproduce) and therefore cause a lot of inconsistencies. But in the end, it always comes down to the point where you need a common set of truths to start an argument. Otherwise there is no point in arguing at all.

blackbrokkoli 8y ago
It's not as easy as that. First we don't start from zero. If you would build a robot with all human senses but erased hard drive it wouldn't do anything, ever. Second, while applied in RL, science might be labeled as "objective" and therefore be superior for, let's say, building a bridge. But on a very basal level, we're subjectively agreeing on what "scientific" is, or rather based on non-proofable paradigms, which is what the article is about
- gerbilly 8y ago
  > First we don't start from zero. There is strong evidence that humans, and most animals are born with built in knowledge and expectations about the world.
  - boxy310 8y ago
    I found it simply fascinating when I learned that Blue Wildebeests are born knowing how to stand within minutes of their birth, and within a day can outrun adult hyenas: "Extremely precocial species are called "superprecocial". Examples are the Megapode birds, which have full flight feathers and which, in some species, can fly on the same day they hatch from their eggs. Another example is the Blue Wildebeest, whose calves can stand within an average of six minutes from birth and walk within thirty minutes; they can outrun a hyena within a day." [1] https://en.wikipedia.org/wiki/Precocial https://en.wikipedia.org/wiki/Precocial

cousin_it 8y ago

The question "why should claim X be trusted?" indeed runs into infinite regress and has no well-founded answer. But the modified question "why should claim X be trusted by creature Y?" can have a well-founded answer, based on facts about creature Y.

blackbrokkoli 8y ago
Why is that? You would rely on the third option, basing on axioms, no?
- cousin_it 8y ago
  Axioms accepted by creature Y.

arf 8y ago

Let the set M = {circular, regressive, axiomatic} to be the set of "unsatisfying" arguments that may be used to prove any truth. Let the mapping J: powerset(M) -> <schools-of-thought-in-meta-epistemology> to map some subset of M to a theory of justification such that the believers in said theory only find usage of some combination of the said subset to be "acceptable". Then: J({}) is in {Skepticism} J({circular}) is in {Coherentism} J({axiomatic}) is in {Foundationalism} J({regressive}) is in {Infinitism} J({axiomatic, circular}) is in {Foundherentism} J(M) is in {Quietism} Is there an x where x is in the powerset of M, such that J(x) is {}? Or literally every possible position can be the foundation of a philosophical paper?

tunesmith 8y ago
J({circular, regressive}) is twoyearoldism. Where they ask why incessantly and don't care if you lead them in a circle. J({regressive, axiomatic}) seems contradictory, so maybe that's {}.
- arf 8y ago
  On J({regressive, axiomatic}): Well, the regular formulation of "Infinitism" is that S is justified to believe P_1 on the basis of P_2 and P_n on the basis of P_n+1. J({regressive, axiomatic}) just defines a limit i.e. S is justified to believe P_1 on the basis of P_2 and P_n on the basis of P_n+1 such that lim_(k->infinity) P_k = P_x where x is not a natural number. You have to say x is not a natural number, because if it were, J's output would have been "foundationalism" and P_x then would be a "self-evident" belief - to use Chisolm's terminology. P.S. If anyone thinks that this is an abuse of mathematics, I agree. But, its usage is compatible with that of philosophers e.g. Goldman's Causal theory of knowledge literally uses a recursive formulation of belief formation where the base case is "self-evident", I just unwrapped the tail call and wrote it as a loop!

subroutine 8y ago

I feel like a better, formal proof of this concept is Gödel Incompleteness, given this lemma, if true, would in turn invalidate itself.

adrianmonk 8y ago
Seems like a wash to me. It wouldn't invalidate itself any more than it would invalidate other alternatives to it.
jerf 8y ago
The problem with using math to address this is that it very subtly ends up begging the question. Math has an answer to the trilemma: Math is based on axioms. The question of whether math corresponds to anything in the real world is a separate question from the mathematics itself. Godel's theorem is thus based on mathematical axioms, but the trilemma questions the axioms themselves. No structure built on the axioms can prove the axiomatic formulation is correct. Godel's incompleteness is an important part of math history about how that was finally proved so hard that modern mathematics now deeply accepts that non-uniqueness of axioms, but again, this is all happening at a level too high to help us with the trilemma. So no, the trilemma can not be solved or even particularly refined by feeding it to mathematics. "From whence mathematics?", it asks. If you are going to play philosophical games with the trilemma, a better approach is simply to feed it to itself. If the trilemma is true, then we can't be confident that we've properly read it, because it cuts away the foundation we are using to communicate. If any of us have successfully extracted even a portion of understanding about the trilemma from the reading of this text, we must be sharing a certain very basic amount of rationality to get that far, even if we can't nail down where that rationality came from exactly. You could then proceed to say that this basic shared rationality is de facto usable as a foundation. But that still doesn't answer the question of where it comes from.

thanatropism 8y ago

That's not a true trilemma. A trilemma is a "choose two out of three". Therefore a trilemma is always depicted as a triangle where the vertices are the things you would like to have and the edges are the possible combinations. A trilemma is an extension of the concept of a dilemma, which is "choose one out of two" . Example: [good, fast, cheap]: you can have good and fast, but it's going to be expensive. Or good and cheap, but it's going to take longer. Courtesy of Jason Kottke[0], some more simple trilemmas: Elegant, documented, on time. Privacy, accuracy, security. Have fun, do good, stay out of trouble. Study, socialize, sleep. Diverse, free, equal. Fast, efficient, useful. Cheap, healthy, tasty. Secure, usable, affordable. Short, memorable, unique. Cheap, light, strong. ---- Ultimately the generalization of a trilemma is a (3-)budget. I will show this. An n-lemma is "choose (n-1) out of (n)". Geometrically/topologically the things you would want in a n-lemma corresponds to the vertices in an (n-1)-simplex. A dilemma is represented as a 1-simplex, i.e. a line segment with each alternative as one end. In this case alternatives are points and so are the choices; in the 3-case alternatives the choices are segments. I'll leave you to imagine 4 and 5-lemmas geometrically. An n-simplex can be defined in a n-dimensional vector space as the region of points whose coordinates sum to 1. So for example a 2-simplex (a triangle) is the set of points (x,y,z) such that x+y+z = 1. In a n-lemma, only vertices are allowable choices -- i.e. x,y,z must be all either 0 or 1. In an n-budget, we can have partial allocations -- rather than have to choose two out of study-socialize sleep (i.e. sleep deprivation, loneliness or failing classes), I can spend my finite time as P% study, Q% social, R% sleep. Note: we can still represent budgets as points inside (n-1)-simplices. Of course, some trilemmas are not easily seen as extremizations of budgets. In some cases this will be because certain alternatives are fully binary (either you have floating exchange rates); in others, it's because we need to think a little more about the trade-offs (cheap, light, strong) -- we need to think harder about how lightness works against strongness. --- We can next imagine how to model slightly more complicated decision structures as n-lemmas. For example, I might have to decide between being married or single (each with its delights) and single people might have to decide between intelligence, looks and agreeableness. (This is terribly sexist but presumably very beautiful people don't have the same pressures to be smart and carve a space for themselves; and people who are intelligent and hot are full of themselves. Bear with me please). In this case we've connected a 1-simplex (married or single) to a 2-simplex. This is known as a simplicial complex, and it turns out we can (roughly oversimplifying) rebuild topology from the ground up by chaining simplices like that. So the choose-one-out-of-three "trilemma" in the OP isn't a trilemma at all. It's some decision structure that arises out of a complex of dilemmas. Possibly because every choice is connected to every choice, it even has the geometric contours of a triangle, but a hollow one, one where the segments are not connected. Therefore it doesn't generalize as a budget. What is the trade-off structure then? What is the finite thing that makes having everything impossible? What are these people talking about? [0] https://www.kottke.org/05/04/pick-two https://www.kottke.org/05/04/pick-two

md224 8y ago

It recently occurred to me that epistemology is essentially a hermeneutics of experience, which is to say: all of our non-trivial beliefs about ourselves and the world (including this very statement) are simply interpretations of what we perceive. This realization, while surely obvious to some, was very clarifying for me. Edit: Judging from the downvote I got, I guess some people don't share my interpretation of epistemology. C'est la vie.

sidyapa 8y ago

A tangent, how is Münchhausen actually pronounced ? Curious to know.

jacquesm 8y ago
With a sharp 'u' and the au like ou in the English word 'loud'.
- sidyapa 8y ago
  Thank you.
munificent 8y ago
I believe it's roughly "MOON-chow-zen", though the "OO" is more like the "oo" in "book".
elefantastisch 8y ago
https://en.oxforddictionaries.com/definition/munchausen,_baron https://en.oxforddictionaries.com/definition/munchausen,_bar... https://forvo.com/word/m%C3%BCnchhausen/ https://forvo.com/word/m%C3%BCnchhausen/

akkartik 8y ago

I'm reminded of the chapter "Two-Part Invention" in Douglas Hofstader's "Gödel, Escher, Bach - An Eternal Golden Braid". https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achi...

TimTheTinker 8y ago

To me, this is a great illustration that there's no other coherent place to start any form of discussion, reasoning, or belief than with axioms (or assumptions). Regressive and circular arguments only shift the problem. I believe that if one is looking for truth in a big-picture sense (religious or philosophical), the best approach is to evaluate various existing systems of axioms/assumptions and apply a twofold test to each: (1) correspondence to reality and (2) internal consistency. It's a given that applying the first test requires stepping into the subjective, since one must honestly apply it to personal experience.

tunesmith 8y ago
Combine it with Hume's Guillotine and you realize that all "should" conclusions really just start with moral "value" axioms. So then you can make a distinction between people that reason correctly from values that are different than yours, and people that reason badly from their axioms. And you can also make a distinction between philosophies that are based off of unprovable beliefs (which is fine), and philosophies that are anti-factual (which isn't). I like to define the former as religion and the latter as ignorance, but unfortunately there are a lot of the latter that claim it's religion.
romwell 8y ago
I heavily disagree; axioms are never a good place to start, nor, historically, they ever were a starting place. Working mathematicians do a lot of mathematics and constructions before stopping to look and say: "OK, we can distill this rich theory down to this small set of axioms". Geometry has been quite developed before Euclid's axioms, and number theory took its sweet millenia before Peano's axioms were developed. On a more modern side, a lot of topology has been produced before people decided to write down a list of axioms for homology, which all the different homology constructions satisfied. The point is that understanding almost always precedes formal reasoning, language follows ideas, and rigid systems arise on a fertile soil of messy experiments - mental or physical. If you look at the history of science and mathematics, nothing was ever built up from the formulas and axioms (criminally contrary to the way these subjects are taught). There is an underappreciated beauty in our ability to argue about, reason with, and make use of concepts that we haven't even really defined. Everyone knew Newton's Calculus was full of holes, and people used it for centuries before coming up with solid definitions of limits, derivatives and integrals - the most fundamental concepts of the subject! And on that note, people used real numbers for a long time before having the formal machinery to define them. Zeno didn't have the axioms to resolve his paradox. Didn't stop anyone from using these weird objects in reasoning and practice. ---------------------------------------------------- TL;DR: never start with axioms, end with them.

ethn 8y ago

To be clear this trilemma is only a problem for rationalists, like Hans Albert. This problem doesn't exist for German Idealists like Kant or Schelling or even the empiricists. You escape the problem of infinite regression through acknowledging that the only thing real is experience, which lends you to the haven of relative objectivity, which is that of which modern science has become. You would think that the conjurer of the paradox would have shifted to empiricism or idealism—maybe my faith in people betrays me.

Karrot_Kream 8y ago
Yes, but so many tech people see themselves as rationalists or at least rational utilitarians, and I'm going to guess most of this forum does as well. Given that so many tech people see themselves this way, diving into the trilemma (and discussing how Idealists or empiricists moved past it) is important and probably eye-opening for many.
smallnamespace 8y ago
Isn't this taking the 'axiomatic' path? > through acknowledging that the only thing real is experience This seems like the key axiom for idealists/empiricists. Of course that leads you to many other details and questions (namely, which experiences?)
- beaner 8y ago
  It is an observed axiom, rather than an "accepted" axiom, which the article implies is the only kind.
  - bryananderson 8y ago
    Why does observing something mean that something is true? If you keep asking questions, at some point you must get to either an accepted axiom, a circularity, or infinite regress.
    - beaner 8y ago

kazinator 8y ago

Those three options are not "equally" unsatisfactory. In fact, the axiomatic option is almost always entirely satisfactory. The marvel and utility of an axiomatic foundation cannot be categorically compared to the absurdity of regressing ad infinitum or going in circles.

stochastic_monk 8y ago
Much like how theorists could take the axiom of choice after the Gödel incompleteness theorems. Sure, it causes inconsistencies, but you can’t get anywhere without them.
sdenton4 8y ago
Well, depends who you ask. One could argue that axiomatic foundations in geometry made it take much longer to discover hyperbolic geometry. (One could view the axiomatic approach as a stand-in for truncating all of the required infinite proof below a well-established line.)

dwaltrip 8y ago

I find the concept of paradigms, as described by Kuhn, to be a much better model for truth and knowledge than axioms or series of "proofs" chained one after the other.