
Münchhausen trilemma - lainon
https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma
======
humanrebar
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.

~~~
jrog
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.

~~~
the_af
> _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.

~~~
bmm6o
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.

~~~
the_af
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.

~~~
Maybestring
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?

~~~
dmreedy
It's been out of favor since Derrida, but I think Structuralism is due for
another pass in the limelight. An extreme subjectivism about reality, shaped
by the stimuli you are exposed to. These external stimuli are what define your
axioms, and from there, you use the same (fuzzy, bad, and prone to inducing
contradctions) logic as everyone else. It provides a compelling model for why
people have difficulty reconciling their opinions; they're not even talking
about the same things, just using the same words, the same signs.

------
ethn
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.

~~~
smallnamespace
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?)

~~~
ethn
No, Experience is forced upon you, it is neither an assumption or something
discovered through reason.

Additionally, words like "real", "exists" or "reality" only have meaning in
this way, otherwise it would be impossible to understand them since
understanding is only through terms of experience.

However, it's important to note that idealists aren't naive realists, they
acknowledge that what they see is created by their own sensory organs. That
is, there is the not-object that cannot be discussed or learned about further
than the knowledge obtained from the negative predicate of the object—hence
why you can only see one side of a coin or why your experience can change
through hallucinatory drugs.

The not-object is also necessary for communication between individuals, where
the inter-subjective experience must be mapped to do so.

~~~
smallnamespace
> Experience is forced upon you, it is neither an assumption or something
> discovered through reason.

Why? _That_ claim must be justified by reference to other truths, or taken
itself as an assumption. So doesn't the trilemma still apply, but at one more
remove?

Note that 'assumption' does not necessarily mean an arbitrary statement, but
includes statements that we consider self-evident, e.g. 'something exists'.

~~~
omon
It doesn't have to be explained why, it is. The why would be a separate
question requiring reasoning. Things can be true without an explanation as to
why they happen. It's not an assumption as experience is not a choice, in fact
experience is a prerequisite to then be able to assume (as well as to reason).

------
arf
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
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
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!

------
TimTheTinker
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.

~~~
romwell
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.

~~~
TimTheTinker
I'm talking about different sorts of axioms than those that science and math
work towards.

For example, any discussion between 2 people depends on mutually accepting
basic assumptions such as:

    
    
        - I and you are persons. We exist.
        - The words we speak and hear have meaning.
        - The words you hear are the words I spoke, and vice versa.
    

We can't even have a meaningful, coherent discussion without assuming things
like that.

We also can't live a meaningful, coherent life without basic assumptions about
origin, meaning, morality, and destiny. Everyone has them, and unless we're
careful, they're easy to catch like the cold from folks we hang around.

A coherent, truthful worldview is essential. The test for truth
(correspondence to reality and internal consistency) _does_ provide us a way
of comparing religions and philosophies (and ruling out the obviously false
ones). Once we do arrive at a coherent worldview that best corresponds to
reality and is internally consistent, we have to _assume_ it and derive our
beliefs and practices from it without proof (i.e. faith). (BTW, we all have a
worldview, but we haven't all subjected our worldview to the truth test.)

Everyone has faith: it's required to accept the axioms of one's worldview.

------
JepZ
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
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
> 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
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)

~~~
raphael_l
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.

~~~
peterwwillis
Aside from drug dealers there are few superprecocial businesses. The only
reliable way to form such a business is to provide something everyone needs
and nobody has, like water in the desert.

------
kazinator
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.

~~~
sdenton4
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.)

------
md224
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.

------
akkartik
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_Achi...](https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles)

------
cousin_it
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
Why is that? You would rely on the third option, basing on axioms, no?

~~~
cousin_it
Axioms accepted by creature Y.

------
sidyapa
A tangent, how is _Münchhausen_ actually pronounced ? Curious to know.

~~~
jacquesm
With a sharp 'u' and the au like ou in the English word 'loud'.

~~~
sidyapa
Thank you.

------
dwaltrip
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.

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

~~~
jerf
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
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)

~~~
gjm11
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.

