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Münchhausen trilemma

en.wikipedia.org

21–30 of 80 posts

Re: Münchhausen trilemma

#21
post #4

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 theref…

You can accept an axiom for the sake of arguemnt and do some reasoning from it without really agreeing with it. You can evaluate the form of an argument without necessarily thinking that it's true or false.

The Munchhausen trilemma explains why you need axioms at all. If you could put forward an argument that didn't need further support (interrupting the "ad infinitum"), then you wouldn't necessarily agree with the argument but you could at least accept it as a self-contained idea. But we can't even get that far. Proofs that aren't either circular or endless must rest on some other statements that we can't prove.

Re: Münchhausen trilemma

#22
post #18

Earlier quoted context omitted.

> 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.

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 c…

Very interesting concept, thanks for providing this link!

We could also apply this terminology to startups: precocial startups are profitable and self-sustaining soon after their launch. Superprecocial startups would be so right away.

Re: Münchhausen trilemma

#23

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

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.

Re: Münchhausen trilemma

#24

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 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…

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 prac…

I've no idea what abduction means in this context, and neither does my dictionary. Can anyone help?

Re: Münchhausen trilemma

#25

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 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…

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.

Re: Münchhausen trilemma

#26

Earlier quoted context omitted.

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 prac…

I've no idea what abduction means in this context, and neither does my dictionary. Can anyone help?

Take the facts, and form the simplest theory that explains them. At least that's my take on it in this context.

Re: Münchhausen trilemma

#27
post #10

Earlier quoted context omitted.

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 stand…

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 i…

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?

Re: Münchhausen trilemma

#28
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

Re: Münchhausen trilemma

#29
post #25

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 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…

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 conclusi…

> 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"

Re: Münchhausen trilemma

#30
post #25

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 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…

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 conclusi…

> 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.

Do note that often in this kind of controversial topics, the axioms are not held consistently by a given side (or the actual axioms are hidden and differ from the stated ones). For example, "it's always wrong to end a life [except when bombing abortion clinics | except when it's a death row immate]". Then the ad hoc provisions start, "oh, I meant an innocent life" ("but how can a nonsentient being be called innocent in any meaningful way?"), etc, etc. The debate then becomes anything but grounded on well defined axioms.

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