Münchhausen trilemma • Hacker News Board

Re: Münchhausen trilemma

#41

Post by clairity » Fri, May 11, 2018, 3:39 PM UTC

sp332 wrote: post #21

JepZ wrote: 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 a…

i believe that point is nicely encapsulated in gödel's incompleteness theorem (which is primarily about number systems, but analogous here nonetheless).

Re: Münchhausen trilemma

#42

Post by SilasX » Fri, May 11, 2018, 3:40 PM UTC

Angostura wrote: post #24

DanielBMarkham wrote: post #17

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?

https://en.wikipedia.org/wiki/Abductive_reasoning

Re: Münchhausen trilemma

#43

Post by dmreedy » Fri, May 11, 2018, 4:02 PM UTC

SideburnsOfDoom wrote: post #29

jrog wrote: post #25

Earlier quoted context omitted.

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 responsib…

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.

Re: Münchhausen trilemma

#44

Post by the_af » Fri, May 11, 2018, 4:09 PM UTC

bmm6o wrote: post #40

the_af wrote: post #30

Earlier quoted context omitted.

> 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 not even that they aren't held consistently. Honestly, nobody (outside of philosophy papers) lists out their axioms and derives beliefs. They have beliefs and "reverse engineer" the supporting axioms, and don't particularly care if the axioms required for one position conflict with the ones required for another.

Agreed, I don't think people really debate emotionally charged issues from first principles. I think it's an error to think of this as a matter of logical axioms. That's not how people (usually) debate.

Re: Münchhausen trilemma

#45

Post by gjm11 » Fri, May 11, 2018, 4:21 PM UTC

thanatropism wrote: post #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…

You're welcome to use the word "trilemma" however you prefer, but it is definitely not wrong to use it to mean "choose one out of three" as here. E.g., here is the OED's definition: "A situation, or (in Logic) a syllogism, of the nature of a dilemma n., but involving three alternatives instead of two." (The OED gives a number of citations, all of which appear to be pick-one-of-three rather than pick-two-of-three.)

The generalization to budgets seems to me to fit better with pick-one-of-three than with pick-two-of-three, too. You're picking p study, q social, r sleep -- and the restriction is p+q+r=1. Picking one out of three corresponds to points like (1,0,0) which are in that simplex. On the face of it, picking two out of three corresponds to points like (1,1,0) which are not. (You could take (1/2,1/2,0) if you like, but that's no longer an extremization; if that, why not (1/3,1/3,1/3)? "X, Y, Z, pick any three.")

Separately, I'm having trouble seeing how your married/single/smart/hot/nice thing actually has the structure of a simplicial complex. In a simplicial complex there are three ways (aha! a trilemma!) in which a 1-simplex can relate to a 2-simplex. They can simply be disjoint; it seems clear you don't intend that. They can share a vertex; that would mean identifying "married" (from the 1-simplex) with one of {smart,hot,nice} (from the 2-simplex), and again surely you don't want that. Or the 1-simplex can be a face of the 2-simplex, so that {single,married} correspond to two of {smart,hot,nice}. Again, surely you can't mean that. But what do you want? It seems like you want to identify one end of your 1-simplex with the whole of your 2-simplex, and the dimensions are wrong.

Re: Münchhausen trilemma

#46

Post by munificent » Fri, May 11, 2018, 4:39 PM UTC

sidyapa wrote: post #36

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

I believe it's roughly "MOON-chow-zen", though the "OO" is more like the "oo" in "book".

Re: Münchhausen trilemma

#47

Post by jrog » Fri, May 11, 2018, 4:42 PM UTC

SideburnsOfDoom wrote: post #29

jrog wrote: post #25

Earlier quoted context omitted.

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 responsib…

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.

Re: Münchhausen trilemma

#48

Post by Maybestring » Fri, May 11, 2018, 5:09 PM UTC

the_af wrote: post #44

bmm6o wrote: post #40

Earlier quoted context omitted.

It's not even that they aren't held consistently. Honestly, nobody (outside of philosophy papers) lists out their axioms and derives beliefs. They have beliefs and "reverse engineer" the supporting axioms, and don't particularly care if the axioms required for one position conflict with the ones required for another.

Agreed, I don't think people really debate emotionally charged issues from first principles. I think it's an error to think of this as a matter of logical axioms. That's not how people (usually) debate.

Its obvious that logic isn't a good model for how people form and change opinions. (I just feel that it isn't)

So... what's the state of the art?

Re: Münchhausen trilemma

#49

Post by dmreedy » Fri, May 11, 2018, 5:25 PM UTC

bmm6o wrote: post #40

the_af wrote: post #30

Earlier quoted context omitted.

> 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 not even that they aren't held consistently. Honestly, nobody (outside of philosophy papers) lists out their axioms and derives beliefs. They have beliefs and "reverse engineer" the supporting axioms, and don't particularly care if the axioms required for one position conflict with the ones required for another.

What is a belief but an axiom? A prior that must be assumed, as it cannot be proven within the system.

I will definitely concede that the logic people use on a day-to-day basis is much fuzzier than an analytic might prefer, and that there's much greater allowance for contradiction (see the phenomenon of Cognitive Dissonance). But I do think that most people argue from their own first principles, consciously or not. There are rare cases where you can convince someone of something when you discover and correct a logical flaw they have made. More often than not, though, a 'logical argument' is a veiled battle of dogma; both participants are moderately rational, and share the same rules of logic, but their axioms are so alien to eachother that what is plain as day to one is a violation of human decency to another. I'd reckon that in reality, it's rare that two people are actually even arguing about the same thing, even though they may be using some of the same words.

Re: Münchhausen trilemma

#50

Post by lifeformed » Fri, May 11, 2018, 5:26 PM UTC

bmm6o wrote: post #40

the_af wrote: post #30

Earlier quoted context omitted.

> 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 not even that they aren't held consistently. Honestly, nobody (outside of philosophy papers) lists out their axioms and derives beliefs. They have beliefs and "reverse engineer" the supporting axioms, and don't particularly care if the axioms required for one position conflict with the ones required for another.

Very true. In fact, I don't think people even start out with "beliefs". They start out with feelings. The emotional response is the equivalent to an axiom, and is abstract and formless. They must use their life experiences to form a reasoning to justify why they feel a certain way, and that is their "belief". This justification is rarely entirely accurate, it's just an approximation filtered through their own biases and reasoning capabilities.

When I have an argument, I find it most productive to first seek out to understand how the other person feels. Peoples' feelings are rarely "incorrect", and usually align with my own feelings at some fundamental level, although perhaps with different intensities. I then try to work with them to put our brains and experiences together to find a more solid understanding for why we feel that way.