Münchhausen Trilemma(en.wikipedia.org)
en.wikipedia.org
Münchhausen Trilemma
https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma
130 comments
More on this point of view ("formalism") and a provably unfixable issue (incompleteness) in these notes of mine: https://iblech.gitlab.io/bb/multiverse.html
Just realized you are a student of Marc Nieper-Wißkirchen in Augsburg.
Extend my greeting when you see him! He introduced me to Category Theory around 2006 in Mainz.
Extend my greeting when you see him! He introduced me to Category Theory around 2006 in Mainz.
> The way that Mathematics and approaches this is, using the Axiomatic way. You can view this as a game: Let's make some assumtions / axioms, and see what we can build with it.
It is often described in such way and you can see it like that in retrospect, but actually it is often intuitive grasp of mathematical structures first, axiomazation second.
For example, natural numbers was understood (including number theory) for thousand years, but Peano axioms are from the end of 19. century.
But that does not say there is 'absolute thruth', there are just infinite different graspable math structures and it is arbitrary (or pragmatic), which we consider interesting to develop.
It is often described in such way and you can see it like that in retrospect, but actually it is often intuitive grasp of mathematical structures first, axiomazation second.
For example, natural numbers was understood (including number theory) for thousand years, but Peano axioms are from the end of 19. century.
But that does not say there is 'absolute thruth', there are just infinite different graspable math structures and it is arbitrary (or pragmatic), which we consider interesting to develop.
Sure, that's the historic route that we ended up at the place we are in.
However, this is not the logical foundations that are used for current teaching and research. There has been a lot of effort, in particular in the late 19the century by folks like Hilbert, Goedel, Frege, etc. to put Mathematics on solid foundations. This is what we ended up with.
However, this is not the logical foundations that are used for current teaching and research. There has been a lot of effort, in particular in the late 19the century by folks like Hilbert, Goedel, Frege, etc. to put Mathematics on solid foundations. This is what we ended up with.
We just wind up with minor details such as almost all real numbers that exist cannot be in any way exactly described. So in what sense do they exist? (Proof: The reals are uncountable. The set of possible descriptions that might specify a real number is countable. Therefore almost all have no description.)
But as long as we use words like "existence" in this weird way, everything works out.
But as long as we use words like "existence" in this weird way, everything works out.
That's OK. Assuming the universe is finite or countable, the number of all possible circumstances in which a real number needs to be described (e.g. a practical problem needing solution or somebody's curiosity needing satisfaction) is also countable. In other words, most real numbers will never come up in any situation in the entire history of a countable universe.
The same epistemological problem exists in a discrete context.
My favorite example is https://en.wikipedia.org/wiki/Robertson%E2%80%93Seymour_theo.... There is a proof by contradiction that any class of graphs with the property that it is closed under minors can be characterized by a finite list of forbidden minors. Which therefore means that there is a polynomial time algorithm for membership in the class.
The classic example is that "planar graphs" have the necessary property, and there are exactly two forbidden minors.
However it is a pure existence proof. And the following facts are also known. We do not have a general way to construct the forbidden minors. Or a way to find out how many there are. Or any way to verify whether any given list of them is complete. And not just, "We don't know how to do it." But, "No such algorithm exists." (More precisely that being able to answer those questions in general leads to contradictions.)
So despite the entirely discrete nature of this problem (there are only a countable number of such classes), we find ourselves asserting the existence of a finite thing that we cannot find, bound the size of, or verify the correctness of if someone presented a reasonable candidate for our inspection.
In what meaningful way does this thing exist?
My favorite example is https://en.wikipedia.org/wiki/Robertson%E2%80%93Seymour_theo.... There is a proof by contradiction that any class of graphs with the property that it is closed under minors can be characterized by a finite list of forbidden minors. Which therefore means that there is a polynomial time algorithm for membership in the class.
The classic example is that "planar graphs" have the necessary property, and there are exactly two forbidden minors.
However it is a pure existence proof. And the following facts are also known. We do not have a general way to construct the forbidden minors. Or a way to find out how many there are. Or any way to verify whether any given list of them is complete. And not just, "We don't know how to do it." But, "No such algorithm exists." (More precisely that being able to answer those questions in general leads to contradictions.)
So despite the entirely discrete nature of this problem (there are only a countable number of such classes), we find ourselves asserting the existence of a finite thing that we cannot find, bound the size of, or verify the correctness of if someone presented a reasonable candidate for our inspection.
In what meaningful way does this thing exist?
I always read the second incompleteness theorem as important /because/ of the connection to truth.
I think we (many, anyway) want to believe something like Leibniz' principle of sufficient reason: that every true statement has some sufficient reason for being so. We naturally interpret proofs in a formal system as that "sufficient reason". If we could prove from within a system that all and only consistent statements have a proof -- then that's great news! Maybe that system is Truth, or if it isn't maybe that's evidence some other system like it could be.
So Godel's work crushed this hope. No system can prove itself consistent, so there is no system under which the principle of sufficient reason is true. Maybe then we shouldn't believe it! Then are there truths that are true for no reason at all...?
But of course, there are many readings here -- many different roads to being thwarted by Godel :)
I think we (many, anyway) want to believe something like Leibniz' principle of sufficient reason: that every true statement has some sufficient reason for being so. We naturally interpret proofs in a formal system as that "sufficient reason". If we could prove from within a system that all and only consistent statements have a proof -- then that's great news! Maybe that system is Truth, or if it isn't maybe that's evidence some other system like it could be.
So Godel's work crushed this hope. No system can prove itself consistent, so there is no system under which the principle of sufficient reason is true. Maybe then we shouldn't believe it! Then are there truths that are true for no reason at all...?
But of course, there are many readings here -- many different roads to being thwarted by Godel :)
Yet the question of truth was indeed important to Godel, a lifelong Platonist. So it was the will to truth that brought us here in the first place
Moreover, this tool-theory of truth that you proffer still runs on some concept of truthiness.
All these system share a similar paradox to this trilemma: let's assume there is such a thing as truth, but the condition of that assumption seems to be the impossibility of proving it with any system produced by such a will to truth.
Moreover, this tool-theory of truth that you proffer still runs on some concept of truthiness.
All these system share a similar paradox to this trilemma: let's assume there is such a thing as truth, but the condition of that assumption seems to be the impossibility of proving it with any system produced by such a will to truth.
It may well be that the search for "truth" has brought us here. However, we found out that "truth" is always a relative. It has to be rooted in assumptions/axioms.
So I would say, it runs on, good choices of axioms and the ability to perform logical deductions.
Set Theory is an attempt to come up with axioms that are so simple that no-one who is not completely out of it's mind would doubt their "truth". This is stuff like:
- There exists a set
- Two sets are equal if all their elements are equal
- We can form subsets from sets, by picking out elements
The only exception is the axiom of choice, which is less intuitively evident, but a technical necessity to build and reason about infinite sets like the real numbers.
So I would say, it runs on, good choices of axioms and the ability to perform logical deductions.
Set Theory is an attempt to come up with axioms that are so simple that no-one who is not completely out of it's mind would doubt their "truth". This is stuff like:
- There exists a set
- Two sets are equal if all their elements are equal
- We can form subsets from sets, by picking out elements
The only exception is the axiom of choice, which is less intuitively evident, but a technical necessity to build and reason about infinite sets like the real numbers.
Before we can ask "is this consistent", we have to understand what consistency means. Basically, underneath axioms we have to have one more underpinning that is yet more immovable than axioms, and that is rationality. If someone has a problem with that, we tend not to engage them in debate. It may be that they thereby they remain unsatisfied, but that is their problem.
If you understand, things are just as they are; If you do not understand, things are just as they are.
— Zen Proverb.
If you can demonstrate the possibility of proving any truth, you just proved it, you are done.
If you can demonstrate the impossibility of proving any truth, then you just demonstrated that you can prove some truth, thus it is false that it is impossible to prove any truth.
Finally, if you can neither disprove nor prove the impossibility of proving any truth, you just don't know whether it's possible or not; in which case the honest posture is agnosticism. Oh, and if you admit that an honest posture is desirable when pursuing truth, you just bootstrapped a ground that allows to growth (relative and sound) truth allied to virtue.
That might not be as satisfying as "acquiring some absolute truth", but personally I feel that for my humble human capacities and needs, that's not too bad.
If you can demonstrate the impossibility of proving any truth, then you just demonstrated that you can prove some truth, thus it is false that it is impossible to prove any truth.
Finally, if you can neither disprove nor prove the impossibility of proving any truth, you just don't know whether it's possible or not; in which case the honest posture is agnosticism. Oh, and if you admit that an honest posture is desirable when pursuing truth, you just bootstrapped a ground that allows to growth (relative and sound) truth allied to virtue.
That might not be as satisfying as "acquiring some absolute truth", but personally I feel that for my humble human capacities and needs, that's not too bad.
This argument is a classic example of the vicious circle principle [1]. The self-referential nature of this interesting argument makes it somewhat meaningless (from a logical perspective).
[1]: https://en.wikipedia.org/wiki/Vicious_circle_principle
[1]: https://en.wikipedia.org/wiki/Vicious_circle_principle
> The self-referential nature of this interesting argument
Self-referential symbolic statements are at the core of Gödel's incompleteness theorem.
Self-referential symbolic statements are at the core of Gödel's incompleteness theorem.
Yes, but that self-reference happens outside the formal language, not within it. Gödel encoded formal statements in the language as integers, and thus turned the question of provability into statements of arithmetic. If the formal system is powerful enough to let you reason about arithmetic, you can thus trick the system to be self-referential, but only via this mechanism external to the system itself.
The thing is, as far as we have to deal with in the real world, there is nothing such as an absolutely isolated system. To my mind, self-reference only occurs in an interpretation, thus in the frame of some actions, which are only possible in a world where changes happen, most likely changing the frame of interpretation itself.
Which argument are your referring to? Do you mean the Münchhausen Trilemma or the comment to which you replied?
I was referring to the comment to which I replied, not the trilemma.
The only truth available is that there are no other truths. We have exactly one truth available to us. (This is a form of epistemological monism.)
Ironically, It's Plato (through Socrates) who says "I know that I know nothing" but it should be fixed to say "I know that I know nothing else"
"the truth that there are no truths is a truth" is a cop out. It can easily be resolved and the statement "I know that I know nothing else" is coherent
Ironically, It's Plato (through Socrates) who says "I know that I know nothing" but it should be fixed to say "I know that I know nothing else"
"the truth that there are no truths is a truth" is a cop out. It can easily be resolved and the statement "I know that I know nothing else" is coherent
If at first, the only truth available to us is that we don't have any other truth available to us than existence, then we just built an other truth, and we can construct other truths in a similar way, don't we? If we have the power to access any truth, then we have the power to access truth of our power to access the previous truth, and so on.
Not only do we know that truth exists, but also we are aware that not every representations that come to our mind are truth. One might even consider that most representations that occupy our mind are unchecked untruths, but that doesn't undermine our ability to explore and gain new truth knowledge in some absolute way.
Not only do we know that truth exists, but also we are aware that not every representations that come to our mind are truth. One might even consider that most representations that occupy our mind are unchecked untruths, but that doesn't undermine our ability to explore and gain new truth knowledge in some absolute way.
So in short: if you are being truly logical, every statement of fact is just a statement of belief, it seems.
I think that's a potentially misleading way of summarizing it. Facts are true beliefs; not all beliefs are true. The trilemma only implies that there's no way for me to step outside of my own head and know, beyond the possibility of error, that my beliefs are true. But they may still be true. (That applies recursively to the trilemma itself!)
So if you dig far enough, how accurate our beliefs are is partly reliant on factors beyond our control: if our minds happen to be wired with bad axioms we may be unable to avoid inaccurate conclusions.
So if you dig far enough, how accurate our beliefs are is partly reliant on factors beyond our control: if our minds happen to be wired with bad axioms we may be unable to avoid inaccurate conclusions.
> But they may still be true.
How? If beliefs have no way to be verified, what does it mean to say one still may be true.
This statement has as much meaning as randomly uttered noise.
How? If beliefs have no way to be verified, what does it mean to say one still may be true.
This statement has as much meaning as randomly uttered noise.
I'm not sure the concept of "truth" is reducible. Any argument about the question "what does truth mean?" implicitly requires that participants can already make some sense of the idea that some answers would be true and others would be false. Also, it seems like you're implying that unverifiable claims are meaningless - but isn't that an unverifiable claim?
Putting that aside, some things are unverifiable yet have concrete ramifications for people's lives. Some examples:
- If "earth will be swallowed by a black hole in ten seconds" is true, I'll never be able to verify it, even though it will have the concrete effect of ending my life.
- I can't verify _or_ falsify that other humans have conscious experiences, but I believe they do. If that belief happens to be false, the world is vastly different than if it is true.
- _Nobody_ could 100% verify that a given physical law applies everywhere at all times. But if it does, some people's lives will be different than if it did not. The fact that everyone in the cosmos has experiences consistent with the law being true, and nobody ever has an experience inconsistent with the law, are part of what make the law true. But that fact can't be verified by anyone.
(A hypothetical omniscient person could verify all these things, but omniscience just means "knowing all true things", so redefining truth in terms of what an omniscient person could verify would be circular.)
Putting that aside, some things are unverifiable yet have concrete ramifications for people's lives. Some examples:
- If "earth will be swallowed by a black hole in ten seconds" is true, I'll never be able to verify it, even though it will have the concrete effect of ending my life.
- I can't verify _or_ falsify that other humans have conscious experiences, but I believe they do. If that belief happens to be false, the world is vastly different than if it is true.
- _Nobody_ could 100% verify that a given physical law applies everywhere at all times. But if it does, some people's lives will be different than if it did not. The fact that everyone in the cosmos has experiences consistent with the law being true, and nobody ever has an experience inconsistent with the law, are part of what make the law true. But that fact can't be verified by anyone.
(A hypothetical omniscient person could verify all these things, but omniscience just means "knowing all true things", so redefining truth in terms of what an omniscient person could verify would be circular.)
I don't believe the other replies answer your question sufficiently. Here is my answer:
Just because you can't prove something is true, doesn't mean it's not true. You can just never know whether it's true or not. See also the Zen Proverb that someone posted in this thread.
Just because you can't prove something is true, doesn't mean it's not true. You can just never know whether it's true or not. See also the Zen Proverb that someone posted in this thread.
Moral and purely subjective beliefs aside, unless we're talking about a wave function collapse, observing (proving?) a belief does not change the truth value of the underlying point of discussion. So implicitly... it is what it is whether you confirm it to be true or not. Broken clock telling the right time twice a day and all that.
Take "the Earth is round" belief. The Earth was round since before humans existed. Having or not having evidence to support this belief did not and does not alter the shape in any way. The Earth is still round. So this belief was always true (even if unbeknownst to anyone) regardless of who held it and whether they had any evidence to support it.
Take "the Earth is round" belief. The Earth was round since before humans existed. Having or not having evidence to support this belief did not and does not alter the shape in any way. The Earth is still round. So this belief was always true (even if unbeknownst to anyone) regardless of who held it and whether they had any evidence to support it.
> If beliefs have no way to be verified, what does it mean to say one still may be true.
It may not be able to be verified, but it can often be falsified. Suppose I believe that all bridges are safe for me because there is a swarm of fairies following me around holding up the bridges. And suppose you believe that no bridges are safe between the hours of 2 and 3 am, because the gods have so decreed. And suppose we both come to a bridge at 2am.
If I walk over the bridge and it collapses, it falsifies my belief that fairies will always hold up bridges for me, but it doesn't prove your belief that the gods have promised universal collapse for bridge-walking at 2am. On the other hand, if I walk over the bridge and it doesn't collapse, it falsifies your belief that the gods have promised universal collapse for bridge-walking at 2am, but does not prove my belief that fairies will always hold up bridges for me.
"All models are wrong, but some models are useful."
It may not be able to be verified, but it can often be falsified. Suppose I believe that all bridges are safe for me because there is a swarm of fairies following me around holding up the bridges. And suppose you believe that no bridges are safe between the hours of 2 and 3 am, because the gods have so decreed. And suppose we both come to a bridge at 2am.
If I walk over the bridge and it collapses, it falsifies my belief that fairies will always hold up bridges for me, but it doesn't prove your belief that the gods have promised universal collapse for bridge-walking at 2am. On the other hand, if I walk over the bridge and it doesn't collapse, it falsifies your belief that the gods have promised universal collapse for bridge-walking at 2am, but does not prove my belief that fairies will always hold up bridges for me.
"All models are wrong, but some models are useful."
As a corollary to this - a principle I've accepted goes like this: "If you don't know what evidence could show your belief to be false, you don't really know what it means for your belief to be true."
For all of our important beliefs -- about people, politics, religion, whatever -- it's always important that we ask ourselves, "How would I know if I was wrong?"
For all of our important beliefs -- about people, politics, religion, whatever -- it's always important that we ask ourselves, "How would I know if I was wrong?"
It seems that falsifying would provide an escape route. Unfortunately it doesn't, because you would first have to establish - without a doubt - the truth of the contradicting statement. That works ok-ish for collapsing bridges, but it breaks down for less direct observations, e.g., when reading experimental data from a computer screen, collected to refute a Physics theory.
When people start debating the truthfulness of things the rest of us agree upon, it's usually time to disengage because they are being unreasonable. Another option is to question not the truth of a belief, but its usefulness.
No, this is not the conclusion that analytic epistemology has come to. Have a look at coherentism, foundationalism and reliabalism for example. The view you describe is skepticism and is held by a very small minority of modern philosophers.
https://plato.stanford.edu/entries/justep-coherence/
https://plato.stanford.edu/entries/justep-foundational/
https://plato.stanford.edu/entries/reliabilism/
https://plato.stanford.edu/entries/skepticism/
https://plato.stanford.edu/entries/justep-coherence/
https://plato.stanford.edu/entries/justep-foundational/
https://plato.stanford.edu/entries/reliabilism/
https://plato.stanford.edu/entries/skepticism/
> The view you describe is skepticism and is held by a very small minority of modern philosophers.
To be honest the percentage of modern philosophers (or any other modern profession) having a view on something like this has no relation to the actual thing being true, false, or true or false at the same time or neither true nor false at the same time. We're all playing glasperlenspiel [1] trying to make sense of some of the things that surround us, that is until all of us will inevitably die.
[1] https://en.wikipedia.org/wiki/The_Glass_Bead_Game
To be honest the percentage of modern philosophers (or any other modern profession) having a view on something like this has no relation to the actual thing being true, false, or true or false at the same time or neither true nor false at the same time. We're all playing glasperlenspiel [1] trying to make sense of some of the things that surround us, that is until all of us will inevitably die.
[1] https://en.wikipedia.org/wiki/The_Glass_Bead_Game
Whether anyone has a view on anything like this has no bearing on the actual thing being true, false, or true or false at the same time or neither true nor false at the same time, but they're specially trained in determining which is the case, so there is very likely a relation. I'm going to defer to them until such time I ever have the skills to do otherwise. That's how the division of labot goes.
Thanks for te book recommendation. Looks amazing. Loved Siddartha.
Thanks for te book recommendation. Looks amazing. Loved Siddartha.
After the postmodernist wave, analytic philosophers have attempted to rescue the notion of truth. All those attempts, including the ones you listed, change the meaning of 'truth' significantly, compared to how non-philosophers use that term.
None of the listed options is so convincing that everybody using their rationality would immediately agree with the proposed model of truth. That seems to indicate that also for these options, rationality alone is insufficient to establish truth, and a belief/irrational/social factor still would be at play.
I'm not implying that the mentioned approaches developed by analytic philosophers are useless. They do deepen our understanding how reasoning and fact establishing works. But in my opinion they are still very far away of solving the Münchhausen Trilemma.
None of the listed options is so convincing that everybody using their rationality would immediately agree with the proposed model of truth. That seems to indicate that also for these options, rationality alone is insufficient to establish truth, and a belief/irrational/social factor still would be at play.
I'm not implying that the mentioned approaches developed by analytic philosophers are useless. They do deepen our understanding how reasoning and fact establishing works. But in my opinion they are still very far away of solving the Münchhausen Trilemma.
Awesome, thanks for the links - I’ll dig into those the next chance I get.
The 3 schools against skepticism all argue against each other's points, so in a sense they strengthen the skeptical position.
Appears there is no clear consensus on exactly why skepticism is false.
Appears there is no clear consensus on exactly why skepticism is false.
Your argument is an argument of Pyrrho, 3rd century BC. It refutes itself if you think about it. What they have in common though is making or relying on strong arguments against skepticism. The question is which alternative is the best, not whether an alternative is necessary.
Can’t one turn this argument around to any other school of philosophy?
Counterargument: skepticism is kind of boring compared to the other positions. There's just not much to build on if you flatly reject the ability to build things. People who're inclined to take that route are likely to avoid modern philosophy, so of course they would be a small minority of philosophers.
Hahahah it's like people just ignored all the awesome philosophy from radical skeptics.
Max Stirner, the most radical skeptic of them all, is without a doubt a more interesting philosopher than many others one is forced to read. Moreover, contrary to the claim made by the OP - he expects the reader to have read philosophy from other authors.
A radical skeptic like Stirner loves Kant and Hume. Maybe it's because Kant shows that the "thing-in-itself" is unknowable even if it exists and Hume shows us that empirical observation is basically all we have for trying to work with the world. Both show that no one in science has found anything resembling truth
Max Stirner, the most radical skeptic of them all, is without a doubt a more interesting philosopher than many others one is forced to read. Moreover, contrary to the claim made by the OP - he expects the reader to have read philosophy from other authors.
A radical skeptic like Stirner loves Kant and Hume. Maybe it's because Kant shows that the "thing-in-itself" is unknowable even if it exists and Hume shows us that empirical observation is basically all we have for trying to work with the world. Both show that no one in science has found anything resembling truth
Or you could take a look at the references and the corpus and see that there are strong arguments against it instead of just guessing with no data. Analytic philosophers don't tend to build things anyway. They focus more on answering specific questions. There are plenty of "continental" philosophers who still do and many in fact have no problem with this.
You're assuming "building things" will bring us closer to getting to know the world a little better (or its essence), that might be false.
> so of course they would be a small minority of philosophers
I'm not a philosopher myself but I found Heraclitus's writings (Democritus's, too) a lot more interesting than many philosophers' writings from the 20th century, in this field being more modern doesn't necessarily mean being better or knowing more.
> so of course they would be a small minority of philosophers
I'm not a philosopher myself but I found Heraclitus's writings (Democritus's, too) a lot more interesting than many philosophers' writings from the 20th century, in this field being more modern doesn't necessarily mean being better or knowing more.
> Counterargument: skepticism is kind of boring compared to the other positions. There's just not much to build on if you flatly reject the ability to build things.
Skepticism doesn't demand that you "reject the ability to do things." See Hume.
Skepticism doesn't demand that you "reject the ability to do things." See Hume.
Indeed. This is why it often seems like anything built up rationally can be tore down rationally.
This leads some to the interesting (and perhaps terrifying) conclusion that narratives are more important and useful than rationalism. Example: https://en.wikipedia.org/wiki/Joseph_de_Maistre
“ According to Maistre, any attempt to justify government on rational grounds will only lead to unresolvable arguments about the legitimacy and expediency of any existing government and that this in turn will lead to violence and chaos.[23][24] As a result, Maistre argued that the legitimacy of government must be based on compelling, but non-rational grounds which its subjects must not be allowed to question.”
Perhaps whatever is useful is oftentimes more important than what is true.
This leads some to the interesting (and perhaps terrifying) conclusion that narratives are more important and useful than rationalism. Example: https://en.wikipedia.org/wiki/Joseph_de_Maistre
“ According to Maistre, any attempt to justify government on rational grounds will only lead to unresolvable arguments about the legitimacy and expediency of any existing government and that this in turn will lead to violence and chaos.[23][24] As a result, Maistre argued that the legitimacy of government must be based on compelling, but non-rational grounds which its subjects must not be allowed to question.”
Perhaps whatever is useful is oftentimes more important than what is true.
>“ According to Maistre, any attempt to justify government on rational grounds will only lead to unresolvable arguments about the legitimacy and expediency of any existing government and that this in turn will lead to violence and chaos.[23][24] As a result, Maistre argued that the legitimacy of government must be based on compelling, but non-rational grounds which its subjects must not be allowed to question.”
>
>Perhaps whatever is useful is oftentimes more important than what is true.
There has been an ongoing debate in the UK about proportional representation and the first past the post system. It has not, as yet, lead to violence and chaos. So I think that the link Maistre identifies between questioning the status quo and chaos is not always true.
Admittedly there is time and place for debate. You don't argue about the cars direction, when the driver is trying to concentrate in a dangerous situation.
There has been an ongoing debate in the UK about proportional representation and the first past the post system. It has not, as yet, lead to violence and chaos. So I think that the link Maistre identifies between questioning the status quo and chaos is not always true.
Admittedly there is time and place for debate. You don't argue about the cars direction, when the driver is trying to concentrate in a dangerous situation.
Yeah. I shared that quote as an example of the “terrifying” conclusions this good lead one to, not necessarily because I though his reactionary stance was true (or useful, haha).
But maybe the success of representative democracy is not based in rationalism but instead the mythology around individual liberty.
But maybe the success of representative democracy is not based in rationalism but instead the mythology around individual liberty.
I meant "conclusions this could lead to". Not sure how I ended up with the above. Sorry about that.
Yep. It's like the God problem. If God created the universe, then who created God? If another God created God, then who created that God. Ad infinitum. Or you can just ignore the exhausting issue altogether by claiming it is axiomatic.
It's the same with any logical statement. You could go all the way up to the premises and question that and when given a proof of the premises, then you can question the premises of the "proof of the premises". Ad infinitum. Or you just take the axiomatic approach.
I think most of life is lived axiomatically.
It's the same with any logical statement. You could go all the way up to the premises and question that and when given a proof of the premises, then you can question the premises of the "proof of the premises". Ad infinitum. Or you just take the axiomatic approach.
I think most of life is lived axiomatically.
Coherentism ans reliabakism address this. You're alao confounding infinite regression in metaphysics (causality and/or composition) with imfinite regression in epistemic justification.
If you're going to accuse someone of confounding infinite regression with infinite regression, you really need to give some explanation of the difference between infinite regression and infinite regression.
The difference is the difference between metaphysics and epistemology. One can consistently accept that there is no first cause (everything has a cauase), smallest thing (everything has a part) as examples while rejecting infinitely chained justificationa or vice versa. They don't necessarily or usuallydepend on eachother.
Well, obviously they don't occur at the same position! ;)
This is correct, but a lot of people derive and indefensible conclusion from it. The real insight is that any belief in an axiom is an exercise in faith. A scientist who fails to recognise the role of faith in their beliefs commits the same error as a religious person who fails to recognise the role of faith in their beliefs.
This is a common argument, and it is a form of argument by dictionary definition, which are seldom informative, and most often used to avoid the issues.
While individual scientists may hold beliefs that go beyond scientific premises, the significant difference between scientific and religious belief is that in the former case, all axioms are considered to be defeasible - and they quite often are overthrown.
While individual scientists may hold beliefs that go beyond scientific premises, the significant difference between scientific and religious belief is that in the former case, all axioms are considered to be defeasible - and they quite often are overthrown.
The foundational axioms of scientific practice are generally not considered to be defeasible at all. The axioms of any particular theory or field may also be considered entirely beyond reproach.
This is also not a semantic argument at all. It is strictly a logical one.
This is also not a semantic argument at all. It is strictly a logical one.
Please humor me. Trying to articulate a half-baked notion.
A close relative went from marine biologist to creationist (et al), and I've been struggling to accept the change. My Calvinist self still doesn't understand Evangelic system of faith.
--
Given Structure + Process => Outcomes:
Scientist: Faith in processes, eg scientific method. Belief is based on reproducibility.
Evangelical: Faith in outcomes. The book (authority) is used to rationalize (justify) proclamations of belief.
To your point: Yes, both have "faith", but with different starting points and emphasis.
A close relative went from marine biologist to creationist (et al), and I've been struggling to accept the change. My Calvinist self still doesn't understand Evangelic system of faith.
--
Given Structure + Process => Outcomes:
Scientist: Faith in processes, eg scientific method. Belief is based on reproducibility.
Evangelical: Faith in outcomes. The book (authority) is used to rationalize (justify) proclamations of belief.
To your point: Yes, both have "faith", but with different starting points and emphasis.
> ... every statement of fact is just a statement of belief, it seems.
Perhaps. The "just" part gets me thinking.
There seems to be an important qualitative difference between prototypical statements of belief---e.g. I believe in the healing power of reiki---and prototypical statements of fact---e.g. This is a glass of water.
While both of the above do contain elements of belief---namely, narratives about what things are in the world---they seem to operate quite differently in many respects.
Belief-style statements tend to more overtly signal traits like social ingroup or self-identity. In particular, declaring belief in the power of reiki seems more likely to influence how others think and concieve of you as a person. I doubt that declaring the existence of a glass of water is likely to do the same.
More generally, this line of thought makes tempts me to say that fact-like staments tend to have less social content than belief-style ones.
Or, more susinctly, facts are a proper subset of beliefs.
In the same way that 2D space differs wildly from 1000D space, despite the former being a subset of the latter, I think it ignores a lot to treat "facts" as "just beliefs." How a belief operates matters.
Perhaps. The "just" part gets me thinking.
There seems to be an important qualitative difference between prototypical statements of belief---e.g. I believe in the healing power of reiki---and prototypical statements of fact---e.g. This is a glass of water.
While both of the above do contain elements of belief---namely, narratives about what things are in the world---they seem to operate quite differently in many respects.
Belief-style statements tend to more overtly signal traits like social ingroup or self-identity. In particular, declaring belief in the power of reiki seems more likely to influence how others think and concieve of you as a person. I doubt that declaring the existence of a glass of water is likely to do the same.
More generally, this line of thought makes tempts me to say that fact-like staments tend to have less social content than belief-style ones.
Or, more susinctly, facts are a proper subset of beliefs.
In the same way that 2D space differs wildly from 1000D space, despite the former being a subset of the latter, I think it ignores a lot to treat "facts" as "just beliefs." How a belief operates matters.
Humans require food and water to live. You might evade that fact as a mere belief, but you cannot escape the consequences of such an approach.
What are the consequences? Have you ever experienced them yourself?
Yes. Another way of looking at it is that there are no first principles.
And a similar concept to this is that given a set of accepted axioms, two parties should always come to the same conclusion if both parties are behaving rationally. All debates are at best disagreements of accepted premises and definitions.
It's a important concept to remember for anyone who's argumentative/legalistic since understanding the oppossing sides definitions and desired conclusion is often the cause for disagreement. If there are no first principles, then there are no definitive last principles.
It's a important concept to remember for anyone who's argumentative/legalistic since understanding the oppossing sides definitions and desired conclusion is often the cause for disagreement. If there are no first principles, then there are no definitive last principles.
An entertaining related concept https://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem
Also, in some ideal sense, since we attain consciousness as pure minds untainted by experience, tabula rasa, all that follows is the result of sense information on the network. The concept of individuality is weak. Two pure minds, fully rational and capable of honest communication, can be different by having different sense information, but if they are able to communicate with each other they should, in time, be identical. i.e. once I have given you everything I know completely and you have given me everything you know completely, we are not distinct, you and I are the same. A full mind meld.
We can't do this for all sorts of reasons, but two AGIs truly meeting may, which means that there is a sort of greyness to this true meeting of AGIs: by meeting they achieve unity. All AGIs behaving in this manner then become the same purely by meeting. Interesting.
Also, in some ideal sense, since we attain consciousness as pure minds untainted by experience, tabula rasa, all that follows is the result of sense information on the network. The concept of individuality is weak. Two pure minds, fully rational and capable of honest communication, can be different by having different sense information, but if they are able to communicate with each other they should, in time, be identical. i.e. once I have given you everything I know completely and you have given me everything you know completely, we are not distinct, you and I are the same. A full mind meld.
We can't do this for all sorts of reasons, but two AGIs truly meeting may, which means that there is a sort of greyness to this true meeting of AGIs: by meeting they achieve unity. All AGIs behaving in this manner then become the same purely by meeting. Interesting.
This makes total sense, because of the assumption of common priors.
Drop that assumption, and fully rational people can indeed agree to disagree. This is a large part of why rational people can look at the same evidence, and come to different conclusions.
Drop that assumption, and fully rational people can indeed agree to disagree. This is a large part of why rational people can look at the same evidence, and come to different conclusions.
> This makes total sense, because of the assumption of common priors.
That's the Wiki article, yes. But scarejunba is going past that, to something more fundamental.
If you have "pure minds untainted by experience, tabula rasa", then you remove the issue of priors. No longer is there any matrix of prejudices that have to agree. You start with observations about the world and logic, and nothing else, and everyone ends up in agreement.
(To an extent you might bootstrap with priors, but over time you'd use observations and logic to replace them, especially when they disagree with someone else you're debating.)
That's the Wiki article, yes. But scarejunba is going past that, to something more fundamental.
If you have "pure minds untainted by experience, tabula rasa", then you remove the issue of priors. No longer is there any matrix of prejudices that have to agree. You start with observations about the world and logic, and nothing else, and everyone ends up in agreement.
(To an extent you might bootstrap with priors, but over time you'd use observations and logic to replace them, especially when they disagree with someone else you're debating.)
This seems unworkable because it ignores the role instincts have in living things, which are prior beliefs about the world put immediately into action.
For example, an infant has an instinct to breathe right after birth. Is that a belief or an action? It’s both—a strategy to survive in the world encoded in genes attached to an implicit belief. An infant that tries to breathe two minutes later would suffer hypoxia and brain damage, while one that tries sooner will choke.
There is no pure tabula rasa untainted by priors, as soon as you acknowledge minds are embedded in bodies shaped by millions of years of evolution and steeped in survival tactics, and what are tactics except a set of useful priors about good actions?
For example, an infant has an instinct to breathe right after birth. Is that a belief or an action? It’s both—a strategy to survive in the world encoded in genes attached to an implicit belief. An infant that tries to breathe two minutes later would suffer hypoxia and brain damage, while one that tries sooner will choke.
There is no pure tabula rasa untainted by priors, as soon as you acknowledge minds are embedded in bodies shaped by millions of years of evolution and steeped in survival tactics, and what are tactics except a set of useful priors about good actions?
Things your body does don't have to be integrated into the priors you use when performing logic.
But "You need to breathe." and things like that would be the easiest priors to replace with observational data.
But "You need to breathe." and things like that would be the easiest priors to replace with observational data.
[deleted]
Also, I believe this requires full mutual trust between the two parties, and perfect communication.
Any breaks in trust, or breakdowns in communication can disrupt the process of mind melding. And it seems to me that trust and failure of communication are features of boundaries between individuals.
Any breaks in trust, or breakdowns in communication can disrupt the process of mind melding. And it seems to me that trust and failure of communication are features of boundaries between individuals.
> but two AGIs truly meeting may
Interesting indeed
Interesting indeed
> Another way of looking at it is that there are no first principles.
Is that part of the principles you adhere to? :)
Is that part of the principles you adhere to? :)
Thanks to Karl Popper, the scientific method asks that hypotheses be falsifiable. When a scientist makes a claim, she then does everything she can think of to disprove it.
Stage II clinical trials of novel drugs are like this. The hypothesis is "this stuff cures baldness and is otherwise harmless." The experiment is an elaborate attempt to disprove the claim, with enough subjects to avoid the small "n" effect and control-subject randomization to avoid the wishful-thinking effect.
Science tries to avoid claims that things are true. "Not false" gets us a long way. That avoids the Münchhausen logical trap.
Stage II clinical trials of novel drugs are like this. The hypothesis is "this stuff cures baldness and is otherwise harmless." The experiment is an elaborate attempt to disprove the claim, with enough subjects to avoid the small "n" effect and control-subject randomization to avoid the wishful-thinking effect.
Science tries to avoid claims that things are true. "Not false" gets us a long way. That avoids the Münchhausen logical trap.
There are problems with falsificationism, as well. You don't really reject theories based on a single falsifying data point. Sometimes you reject the data point as fake or misinterpreted. Sometimes you modify your theory and replace it, but it's unclear that that's different from the goalpost-moving of astrologers and homeopaths.
Falsification is a good stake in the ground that allows scientists to work, but it's unclear if it's actually a step towards the epistemology represented by the Munchausen trilemma. Scientists have a notion that it allows them to work "toward" Truth-with-a-capital-T, a notion which both feels right and has produced high standards of living. Those may be better goals than Truth-with-a-capital-T, which may be unavailable.
Falsification is a good stake in the ground that allows scientists to work, but it's unclear if it's actually a step towards the epistemology represented by the Munchausen trilemma. Scientists have a notion that it allows them to work "toward" Truth-with-a-capital-T, a notion which both feels right and has produced high standards of living. Those may be better goals than Truth-with-a-capital-T, which may be unavailable.
I don't think all axioms are "merely asserted rather than defended". For example, one axiom is the existence of existence, which cannot be denied, because any question, doubt, skepticism, reason, point, or imagined counterargument is something that exists and is within existence.
Another is consciousness. To grasp that existence exists, or make any attempt to reason either way about the proof or truth of anything, is itself an expression of consciousness.
Existence exists, and so does consciousness capable of conceiving that. Start there and work down.
Another is consciousness. To grasp that existence exists, or make any attempt to reason either way about the proof or truth of anything, is itself an expression of consciousness.
Existence exists, and so does consciousness capable of conceiving that. Start there and work down.
> one axiom is the existence of existence, which cannot be denied, because any question, doubt, skepticism, reason, point, or imagined counterargument is something that exists and is within existence
You argue that the denial of the axiom of "existence of existence" is self-refuting. But don't all arguments that something is self-refuting depend on the acceptance of the law of non-contradiction ("for all A, not (A and not-A)"?) If your argument for the axiom of "existence of existence" depends on the axiom of non-contradiction, is the axiom of "existence of existence" truly axiomatic any more?
What about the axiom of non-contradiction? Do we have to believe that? Well, dialetheism [1] denies that the axiom of non-contradiction holds (in the most general case), and yet the whole system doesn't fall apart. The secret is to allow contradictions, but limit their consequences, by rejecting the classical principle of ex contradictione quodlibet (ECQ, from a contradiction anything follows, aka the principle of explosion). An unlimited allowance for self-contradiction destroys all possibility of non-trivial reasoning, whereas a more limited allowance for self-contradiction leaves open the possibility of non-trivial thought. So, if we have a choice whether to accept the axiom of non-contradiction, maybe your attempt to escape Münchhausen's trilemma has not succeeded.
[1] https://plato.stanford.edu/entries/dialetheism/
You argue that the denial of the axiom of "existence of existence" is self-refuting. But don't all arguments that something is self-refuting depend on the acceptance of the law of non-contradiction ("for all A, not (A and not-A)"?) If your argument for the axiom of "existence of existence" depends on the axiom of non-contradiction, is the axiom of "existence of existence" truly axiomatic any more?
What about the axiom of non-contradiction? Do we have to believe that? Well, dialetheism [1] denies that the axiom of non-contradiction holds (in the most general case), and yet the whole system doesn't fall apart. The secret is to allow contradictions, but limit their consequences, by rejecting the classical principle of ex contradictione quodlibet (ECQ, from a contradiction anything follows, aka the principle of explosion). An unlimited allowance for self-contradiction destroys all possibility of non-trivial reasoning, whereas a more limited allowance for self-contradiction leaves open the possibility of non-trivial thought. So, if we have a choice whether to accept the axiom of non-contradiction, maybe your attempt to escape Münchhausen's trilemma has not succeeded.
[1] https://plato.stanford.edu/entries/dialetheism/
Fair point, but how do you determine when to stop following the consequences of the contradictions? Furthermore, from the point at which you stop, you are then re-enforcing the principle of non-contradiction, so why not enforce it from the start and call it a day? To me, dialetheism has always seemed very arbitrary, but maybe that's exactly the point of it. If that's true, then it's just another flavor of extreme relativism where anything can be true or false and any reasoning is meaningless.
On top of that, it seems to me that even in denying the principle of explosion, one must follow it if they want to be consistent in the denial. Otherwise the denial itself won't hold, because if you allow contradictions, by definition you must also allow their opposite, which is the principle of non-contradiction. And as far as I'm aware there is no proof in logic that allows for an exception to ECQ. Because once you allow any contradiction, you implicitly allow anything, which makes thought impossible.
On top of that, it seems to me that even in denying the principle of explosion, one must follow it if they want to be consistent in the denial. Otherwise the denial itself won't hold, because if you allow contradictions, by definition you must also allow their opposite, which is the principle of non-contradiction. And as far as I'm aware there is no proof in logic that allows for an exception to ECQ. Because once you allow any contradiction, you implicitly allow anything, which makes thought impossible.
Well, one approach is to start with an assumption that the law of non-contradiction is true in most cases, and then look at specific cases in which it might be worthwhile to make exceptions to that generalisation - for example, the liar sentence (This sentence is false), Gödel sentences, Russell’s paradox (“this set both is and isn’t a member of itself”), etc. Dialetheism in which every contradiction is accepted is trivial. In non-trivial dialetheism, you argue that there are good reasons for accepting certain contradictions that do not apply in the case of others.
My questions still remain unanswered. Regarding the examples you raised: the liar paradox can be solved without breaking explosion by observing that all assertions carry the implicit ending "and this sentence is true". The liar sentence then becomes "This sentence is false and this sentence is true", which is simply false. As for Russell's paradox, as far as I know this has been solved in ZF theory, although admittedly with a few extra axioms needed. Not sure about Gödel's sentences.
It just doesn't seem worth it to me to suspend the fundamentals of thinking just to solve some paradoxes that can anyway be solved within our current model of logic.
It just doesn't seem worth it to me to suspend the fundamentals of thinking just to solve some paradoxes that can anyway be solved within our current model of logic.
> Regarding the examples you raised: the liar paradox can be solved
There are various proposed solutions, but they all have drawbacks. You have to compare the drawbacks of the different options. (From my limited memory, your proposed solution is not one of the standard solutions proposed in the literature.)
> As for Russell's paradox, as far as I know this has been solved in ZF theory
ZF theory pays a price – the restriction of the axiom of comprehension. The point is you don't solve Russell's paradox for free, every solution has its price, every solution involves giving up some component of naïve set theory; ZF chooses to partially give up the axiom of comprehension; inconsistent set theory (part of inconsistent mathematics [1]) chooses to partially give up the axiom of non-contradiction instead. If we have to give something up, how do we decide which part to give up? You think that giving up the axiom of comprehension is a smaller price to pay than giving up the axiom of non-contradiction – but is that a subjective value judgement? Or, can it be objectively justified? (And if so, how?)
A good argument for paraconsistent logic is that relevant implication is a more accurate model of natural language than material or strict implication, and relevant implication is paraconsistent. (That said, dialetheism goes beyond mere paraconsistency.)
I'd suggest (if you have the time/inclination) reading Graham Priest's book In Contradiction. It explains the arguments for all this far better than I can from memory. (I read that book 15 years ago.)
[1] https://plato.stanford.edu/entries/mathematics-inconsistent/
There are various proposed solutions, but they all have drawbacks. You have to compare the drawbacks of the different options. (From my limited memory, your proposed solution is not one of the standard solutions proposed in the literature.)
> As for Russell's paradox, as far as I know this has been solved in ZF theory
ZF theory pays a price – the restriction of the axiom of comprehension. The point is you don't solve Russell's paradox for free, every solution has its price, every solution involves giving up some component of naïve set theory; ZF chooses to partially give up the axiom of comprehension; inconsistent set theory (part of inconsistent mathematics [1]) chooses to partially give up the axiom of non-contradiction instead. If we have to give something up, how do we decide which part to give up? You think that giving up the axiom of comprehension is a smaller price to pay than giving up the axiom of non-contradiction – but is that a subjective value judgement? Or, can it be objectively justified? (And if so, how?)
A good argument for paraconsistent logic is that relevant implication is a more accurate model of natural language than material or strict implication, and relevant implication is paraconsistent. (That said, dialetheism goes beyond mere paraconsistency.)
I'd suggest (if you have the time/inclination) reading Graham Priest's book In Contradiction. It explains the arguments for all this far better than I can from memory. (I read that book 15 years ago.)
[1] https://plato.stanford.edu/entries/mathematics-inconsistent/
I was referring to Arthur Prior's solution to the paradox.
As for dialetheism being a better model of natural language, I'm familiar with the claim but I think its main argument fails to grasp that contradictions in natural language do not happen "in the same sense and at the same time". For instance, the sentence "This sentence is false" is true and false in natural language, but in succession and not at the same time. Moreover, dialetheism does not seem to be able to explain hierarchies and cause-effect relationships, which are key constructs of language.
I think that when it comes to logical systems such as mathematical theories, the point is not necessarily to come up with a theory that is true (that would ultimately be impossible due to Agrippa's trilemma), but to have a theory that has predictive power and is self-consistent, and this is what ZF is. Self-consistency seems to be the minimum requirement for any theory, lest it falls into triviality.
The little I know about paraconsistent logic is that it suspends consistency in a few select cases. But generally, consistency still holds, otherwise, as you said, the system would become trivial. I guess my question was: would paraconsistent logic claim to be true? Or, at least, identical to itself? If yes, then if would itself be subject to consistency and identity. And if it chooses to temporarily suspend those, then in that time it can no longer claim to be true. But if in general it complies with consistency (lest it becomes trivial), then it must reject the subsets that are not true, otherwise it could no longer be self-consistent.
I guess my point (and I could be wrong) is that paraconsistent logic is entirely non-consistent, unless it chooses to redefine what consistency means, in which case, we're back to triviality.
Thanks for the book suggestion, I'll definitely read it and hopefully find some answers.
As for dialetheism being a better model of natural language, I'm familiar with the claim but I think its main argument fails to grasp that contradictions in natural language do not happen "in the same sense and at the same time". For instance, the sentence "This sentence is false" is true and false in natural language, but in succession and not at the same time. Moreover, dialetheism does not seem to be able to explain hierarchies and cause-effect relationships, which are key constructs of language.
I think that when it comes to logical systems such as mathematical theories, the point is not necessarily to come up with a theory that is true (that would ultimately be impossible due to Agrippa's trilemma), but to have a theory that has predictive power and is self-consistent, and this is what ZF is. Self-consistency seems to be the minimum requirement for any theory, lest it falls into triviality.
The little I know about paraconsistent logic is that it suspends consistency in a few select cases. But generally, consistency still holds, otherwise, as you said, the system would become trivial. I guess my question was: would paraconsistent logic claim to be true? Or, at least, identical to itself? If yes, then if would itself be subject to consistency and identity. And if it chooses to temporarily suspend those, then in that time it can no longer claim to be true. But if in general it complies with consistency (lest it becomes trivial), then it must reject the subsets that are not true, otherwise it could no longer be self-consistent.
I guess my point (and I could be wrong) is that paraconsistent logic is entirely non-consistent, unless it chooses to redefine what consistency means, in which case, we're back to triviality.
Thanks for the book suggestion, I'll definitely read it and hopefully find some answers.
> If your argument for the axiom of "existence of existence" depends on the axiom of non-contradiction, is the axiom of "existence of existence" truly axiomatic any more?
Obviously since there's no need to rely on precisely one axiom.
Obviously since there's no need to rely on precisely one axiom.
My point being, if you use A to demonstrate B, then B is not axiomatic in the sense of Münchhausen's trilemma. In the sense of Münchhausen's trilemma, an axiom is a belief accepted as true without being justified on the basis of some more basic belief. When you use A to demonstrate B, B ceases to be a belief accepted as true without being justified on the basis of some more basic belief, since you are justifying it on the basis of A.
I see what you meant and that's actually interesting regarding LNC. What I mean is if you can use A and B to prove C, it doesn't matter that you may be able to use A and something else to prove B. Relative to C, A and B may be considered axioms.
You seem to be summarizing Descartes' "Cogito Ergo Sum" - "I think therefore I am". It does indeed prove the existence of something, but it doesn't actually prove anything about the nature of that existence. Are you an actual human being on a planet, the way it looks like, or are you a mind trapped in the Matrix? Does one thought cause the next, or are your thoughts just recordings on a tape of some sort, played sequentially, so the apparent causality is just an illusion?
My point is, you really don't get very far before you need to believe in some axiom, e.g. "I am a sensing being whose subjective experience of reality resembles the objective reality around me" (I know this sounds very basic, but try listening to someone who thinks they can slow Earth's rotation by meditating, and you'll realize that not everybody starts with an axiom where subjective and objective reality are separate, or where subjective reality is a derivative of objective reality and not the other way around)
My point is, you really don't get very far before you need to believe in some axiom, e.g. "I am a sensing being whose subjective experience of reality resembles the objective reality around me" (I know this sounds very basic, but try listening to someone who thinks they can slow Earth's rotation by meditating, and you'll realize that not everybody starts with an axiom where subjective and objective reality are separate, or where subjective reality is a derivative of objective reality and not the other way around)
By century-old arguments due to Russell, this "existence of existence" is incoherent. For example, as an imagined counterargument, imagine that there is a set of all things which exist, are sets, and do not contain themselves. By your axiom, this set exists. By definition, this set does not contain itself. Therefore, and by definition, this set contains itself.
Formal proofs are syntactic. As a result, they do not need consciousness to be verified; verification is algorithmic and can be done by a machine. Proofs can also be searched for by machines, although such proof search does not run at practical speeds on existing hardware yet. Nonetheless, to take your claim at face value is to claim that computing machines are conscious; are you prepared to embrace this result? (I don't personally have a problem with it, but many people do.)
This sort of word salad, more generally, is why Objectivism has such a poor reputation: It doesn't make sense when examined with even basic critical thinking.
Formal proofs are syntactic. As a result, they do not need consciousness to be verified; verification is algorithmic and can be done by a machine. Proofs can also be searched for by machines, although such proof search does not run at practical speeds on existing hardware yet. Nonetheless, to take your claim at face value is to claim that computing machines are conscious; are you prepared to embrace this result? (I don't personally have a problem with it, but many people do.)
This sort of word salad, more generally, is why Objectivism has such a poor reputation: It doesn't make sense when examined with even basic critical thinking.
Russell's paradox deals with self-referencing logically unconstructible objects, not with the impossibility of proving anything as existing.
>Formal proofs are syntactic. […]
This confuses means of formal proof with meanings attached to them. A proof, whatever the means used to perform it, only matter to conscious beings. A computer can help to solve a logical problem, but so far none have been catched wondering which logical problem would be interesting to solve as its next challenge – as far as I know.
>Formal proofs are syntactic. […]
This confuses means of formal proof with meanings attached to them. A proof, whatever the means used to perform it, only matter to conscious beings. A computer can help to solve a logical problem, but so far none have been catched wondering which logical problem would be interesting to solve as its next challenge – as far as I know.
In mathematics, we do actually take logically self-defeating objects to be non-existent, as a matter of classical reasoning: If they don't exist, then they must not-exist; otherwise, they would exist, and immediately defeat themselves in a puff of logic [5]. Such classical reasoning can reject a large number of similarly-shaped objects [2], and Russell's antimony is actually only the tip of the iceberg of a bundle of formal results, notably Tarski's [3] and Lawvere's [4].
The Gödel Machine algorithm [0][1] is only a few years old, and it cannot yet be tested due to practical hardware constraints, but it provably implements a system which wonders, specifically, about which direction of proof search will speed up its ability to search for proofs, to consider directions, or to wonder.
[0] https://en.wikipedia.org/wiki/G%C3%B6del_machine
[1] http://people.idsia.ch/~juergen/goedelmachine.html
[2] https://terrytao.wordpress.com/2009/11/05/the-no-self-defeat...
[3] https://en.wikipedia.org/wiki/Tarski's_undefinability_theore...
[4] https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem
[5] https://tvtropes.org/pmwiki/pmwiki.php/Main/PuffOfLogic
The Gödel Machine algorithm [0][1] is only a few years old, and it cannot yet be tested due to practical hardware constraints, but it provably implements a system which wonders, specifically, about which direction of proof search will speed up its ability to search for proofs, to consider directions, or to wonder.
[0] https://en.wikipedia.org/wiki/G%C3%B6del_machine
[1] http://people.idsia.ch/~juergen/goedelmachine.html
[2] https://terrytao.wordpress.com/2009/11/05/the-no-self-defeat...
[3] https://en.wikipedia.org/wiki/Tarski's_undefinability_theore...
[4] https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem
[5] https://tvtropes.org/pmwiki/pmwiki.php/Main/PuffOfLogic
Yes, this is the lumine naturali of Decartes! The undoubtable doubt was presented and the rest is history. Needless to say it has been contended against, but the heritage of this line of reasoning as a foundation for epistemology cannot be disputed.
Using just an axiom of existence, you cannot get very far. Notice that, by the end of this post, you have already introduced a second axiom, concerning consciousness. Working down without additional axioms is the difficult part.
With regard to "the existence of existence", you appear to have started on your way down the "regressive argument" branch.
With regard to "the existence of existence", you appear to have started on your way down the "regressive argument" branch.
What's the next step after those?
I'm not sure! There is the idea of the "stolen concept fallacy", which is to reason about something while denying that you are able to reason as the result of sensory perception, which if you accept, might mean there's some naturally resulting axioms about the senses and what a consciousness is capable of knowing.
These aren't my ideas. At the risk of having this and my first comment downvoted into oblivion, I got them from Ayn Rand. She has a short (80-page) nonfiction book about just these things which I think is remarkable, called Introduction to Objectivist Epistemology. If you are not predisposed to despising the author, it's a quick, very interesting read that I recommend.
Edit: And there are the downvotes...
These aren't my ideas. At the risk of having this and my first comment downvoted into oblivion, I got them from Ayn Rand. She has a short (80-page) nonfiction book about just these things which I think is remarkable, called Introduction to Objectivist Epistemology. If you are not predisposed to despising the author, it's a quick, very interesting read that I recommend.
Edit: And there are the downvotes...
Your starting point is taken up by Descartes in his Meditations on First Philosophy.
The more modern expansion of these ideas can be found in Phenomenology by people like Husserl or Heidegger.
There are a lot of contemporary philosophers dealing directly with philosophy of mind and consciousness which is more of an offshoot of these questions once you sideline questions of grounding.
And there is also more contemporary philosophy of science/math that deals directly with questions of consistency and the grounding of logical or rationalistic methods.
Basically there are a lot of resources if you are interested in this stuff, and I would heavily recommend reading and understanding what others have thought about before trying to re-invent the wheel as your starting point. That takes too long and there's a long way to go.
The more modern expansion of these ideas can be found in Phenomenology by people like Husserl or Heidegger.
There are a lot of contemporary philosophers dealing directly with philosophy of mind and consciousness which is more of an offshoot of these questions once you sideline questions of grounding.
And there is also more contemporary philosophy of science/math that deals directly with questions of consistency and the grounding of logical or rationalistic methods.
Basically there are a lot of resources if you are interested in this stuff, and I would heavily recommend reading and understanding what others have thought about before trying to re-invent the wheel as your starting point. That takes too long and there's a long way to go.
Not trying to reinvent anything, just sharing things that I've found appealing. Not claiming this author was first or last or original or not, only an influence on myself. Have you read the book? If not, it may contain perspectives you haven't encountered yet. Thanks for the recs!
Oh I wasn't trying to imply that. I was responding to "What's the next step after those?" with some of the paths I've gone down.
I've put somewhat of a moratorium on philosophy as of late because I don't have the time for it, but I'll check it out if I do get the time.
I've put somewhat of a moratorium on philosophy as of late because I don't have the time for it, but I'll check it out if I do get the time.
Nope, the law of identity is incoherent and doesn't exist in physical reality. I'm extremely frustrated that Western Philosophy has reasoned about this extremely poorly and the assumptions made from antiquity seem to continue to be unquestioned.
The Cogito, or other ontological foundations of existence which rely on appearances are completely wrong. "I think therefor I am?" How do you know that you are thinking? How do you know that appearances of thinking are actually in existence? It's possible that you did not think! and that what you believe to be existence is not existence at all.
At best, you can say "it appears to me that I think therefor it appears that I exist". You cannot just escape radical doubt because of appearances.
Also, the no-cloning (and the other no-go) theorems and bells theorem (no determinism) seem to imply that Quantum Theory has concluded that the law of identity doesn't hold up in reality. Objects are NOT equal to themselves. We do not know that a fundamental minimal quantized unit of time exists, meaning that we cannot say that "an object is equal to itself at a particular time". If we accept the Kantian thesis that time and space are the "vessel" or "canvas" of reality, than it's not possible to confirm that an object exists in the same point in time, and the same point of space with itself without a fundamental minimal quantized unit to measure those in.
You should instead conclude that the metaphysical constitution of objects is ultimately in-determinant
The law of in-determinancy would say that "objects can be infinitesimally close to identical with themselves"
A =/= A. The left-side A exists in a different point in time and space as the right-side A. You cannot even think of these in your own mind at the same time, in the same part of your "mind-space". There is no verifiable measure of the "present" so we cannot constitute an object in exactly one point of time and space at a particular "moment"
All of what I've just said is basically a more modern version of Nietzsche's revulsion to the exact same "A = A" crap that was being thrown around in his own time.
tl;dr you don't know that you exist
citations:
https://en.wikipedia.org/wiki/Bell%27s_theorem
https://en.wikipedia.org/wiki/No-cloning_theorem
https://en.wikipedia.org/wiki/No-broadcast_theorem
https://en.wikipedia.org/wiki/No-deleting_theorem
https://en.wikipedia.org/wiki/No-communication_theorem
The Cogito, or other ontological foundations of existence which rely on appearances are completely wrong. "I think therefor I am?" How do you know that you are thinking? How do you know that appearances of thinking are actually in existence? It's possible that you did not think! and that what you believe to be existence is not existence at all.
At best, you can say "it appears to me that I think therefor it appears that I exist". You cannot just escape radical doubt because of appearances.
Also, the no-cloning (and the other no-go) theorems and bells theorem (no determinism) seem to imply that Quantum Theory has concluded that the law of identity doesn't hold up in reality. Objects are NOT equal to themselves. We do not know that a fundamental minimal quantized unit of time exists, meaning that we cannot say that "an object is equal to itself at a particular time". If we accept the Kantian thesis that time and space are the "vessel" or "canvas" of reality, than it's not possible to confirm that an object exists in the same point in time, and the same point of space with itself without a fundamental minimal quantized unit to measure those in.
You should instead conclude that the metaphysical constitution of objects is ultimately in-determinant
The law of in-determinancy would say that "objects can be infinitesimally close to identical with themselves"
A =/= A. The left-side A exists in a different point in time and space as the right-side A. You cannot even think of these in your own mind at the same time, in the same part of your "mind-space". There is no verifiable measure of the "present" so we cannot constitute an object in exactly one point of time and space at a particular "moment"
All of what I've just said is basically a more modern version of Nietzsche's revulsion to the exact same "A = A" crap that was being thrown around in his own time.
tl;dr you don't know that you exist
citations:
https://en.wikipedia.org/wiki/Bell%27s_theorem
https://en.wikipedia.org/wiki/No-cloning_theorem
https://en.wikipedia.org/wiki/No-broadcast_theorem
https://en.wikipedia.org/wiki/No-deleting_theorem
https://en.wikipedia.org/wiki/No-communication_theorem
All you’ve done is assert some axioms, and claim they cannot be questions.
Mathematicians peddle in absolute truths, under contract. The truths are not facts: they're logical fabric between axioms and conclusions. You can change the rules of logic, you can change your base axioms, but doing so only changes the set of reachable conclusions.
Once one accepts that no rational argument is more true than its axioms, this seems unremarkable.
Through the thicket of your stacked negations I find it difficult to make out what it is that you intended to say. I guess nobody could deny that no thing isn't really nothing that doesn't fail to exist, don't you disagree?
Ha! I tried to resist saying that no-one should attempt parody without bearing in mind the caveat that one should avoid making the target look less deserving of it than one's counterpoint, but failed, no?
I was by no means my intention to make my counterpoint look less deserving of the same parody, and it seems I succeeded?
Belief does not necessarily come from provability. Wittgesnstein's On Certainty contains some interesting thoughts in this regard. Quoting a few extracts:
"If you tried to doubt everything you would not get as far as doubting anything. The game of doubting itself presupposes certainty."
"Giving grounds, however, justifying the evidence, comes to an end."
"At the foundation of well-founded belief lies belief that is not founded."
"The child learns to believe a host of things. I.e. it learns to act according to these beliefs. Bit by bit there forms a system of what is believed, and in that system some things stand unshakeably fast and some are more or less liable to shift. What stands fast does so, not because it is intrinsically obvious or convincing; it is rather held fast by what lies around it."
"If you tried to doubt everything you would not get as far as doubting anything. The game of doubting itself presupposes certainty."
"Giving grounds, however, justifying the evidence, comes to an end."
"At the foundation of well-founded belief lies belief that is not founded."
"The child learns to believe a host of things. I.e. it learns to act according to these beliefs. Bit by bit there forms a system of what is believed, and in that system some things stand unshakeably fast and some are more or less liable to shift. What stands fast does so, not because it is intrinsically obvious or convincing; it is rather held fast by what lies around it."
Where there are gaps in your own knowledge, truth becomes about trust and relevance.
I don't know that e = mc^2 but I trust scientists that it is the case but it doesn't matter to me much either way; I would not participate in any argument about this subject because although my level of trust is strong, I personally have nothing at stake whether this fact is true or false (it is not relevant to me).
People who have a huge ego tend to think that every fact they know is a crucial part of their personal identify; these people tend to avoid saying "I dont' know" because doing so would be an admission that their information sources (which they see as extensions of themselves) are not trustworthy and are therefore low value (which would bring down their own self-worth).
People who have a huge ego tend to think that every fact they know is a crucial part of their personal identify; these people tend to avoid saying "I dont' know" because doing so would be an admission that their information sources (which they see as extensions of themselves) are not trustworthy and are therefore low value (which would bring down their own self-worth).
Well, it doesn't matter to you if it's true, but at least if it's true that it sufficiently adequately models the world to allow all the technologies derived from it. Of course, most human don't care about it directly, but it impacts their live nonetheless.
[deleted]
It reminds me a bit of Godel's Incompleteness Theorems https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theor...
In this article, Zizek brings the Munchhausen story to show how he differs from Nietzsche on deep philosophical grounds.
https://thephilosophicalsalon.com/the-fall-that-makes-us-lik...
It's been my mind for a while now, and I'm still not sure with whom I stand here. Roughly, Zizek says : Any kind of mental breakdown that changes you will be related to your subsconscious. Nietzsche : Lol, when you reach my level of psychosis, you really have to pull yourself out all by yourself.
https://thephilosophicalsalon.com/the-fall-that-makes-us-lik...
It's been my mind for a while now, and I'm still not sure with whom I stand here. Roughly, Zizek says : Any kind of mental breakdown that changes you will be related to your subsconscious. Nietzsche : Lol, when you reach my level of psychosis, you really have to pull yourself out all by yourself.
Y'all it's best to understand the universe for what it is an immense perpetual motion machine
We often think of perpetual motion as set it and forget it once it's set in motion it continues forever but of course this isn't feasible
Have you ever considered that a truly perpetual motion is one that never needs to be set in motion that always is in motion?
This is precisely the bootstrapping argument in essence so a small measure of faith is needed
We can rely on our perception to be reality for all intents and purposes and begin reasoning with base assumptions and not over analyze the starting conditions too much
We often think of perpetual motion as set it and forget it once it's set in motion it continues forever but of course this isn't feasible
Have you ever considered that a truly perpetual motion is one that never needs to be set in motion that always is in motion?
This is precisely the bootstrapping argument in essence so a small measure of faith is needed
We can rely on our perception to be reality for all intents and purposes and begin reasoning with base assumptions and not over analyze the starting conditions too much
A parallel in defining words. A word dictionary has to be self referential, or you need an ever increasing vocabulary, or just accept some axioms that don't require verification (you know what a word like cat is by some interaction escaping out of the context of word descriptions)
Another parallel https://www.youtube.com/watch?v=X8aWBcPVPMo
we were computationally evolved to make sense of the world... and making sense is a computation
Another parallel https://www.youtube.com/watch?v=X8aWBcPVPMo
we were computationally evolved to make sense of the world... and making sense is a computation
I'm going to stop paying my bills. We'll see how far this "demonstrate the impossibility of proving any truth" really goes.
Gottfried Benn once said, style is superior to truth because it carries proof of its existence in itself (other than truth which always requires external proof). For someone who wasn't a logician or a mathematician, I find this remarkably insightful.
Given it took Whitehead and Russell 300 pages to logically prove that 1 + 1 = 2, I think we can all go ahead and assume any supposition stated in less detail is naturally flawed and incomplete, including this one.
In foundations of math that mathemati ians actually use (such as ZF), you don't need 300 pages to show 1+1=2.
Logically, that makes sense, but since this thread is about logic, not math, it doesn't. (Unless you're saying logic and math are the same, in which case I would need to see a rigorous proof in order to believe you.)
Pyrrhonism. n. An ancient philosophy, named for its inventor. It consisted of an absolute disbelief in everything but Pyrrhonism. Its modern professors have added that.—Ambrose Bierce, The Devil's Dictionary
Isn’t a circular argument just an axiom with (unnecessary) extra parts?
Related from 2018: https://news.ycombinator.com/item?id=17043954
"You would never attempt to prove that 1+1=2, as 2 is defined as the value of 1+1."
The whole discussion here is quite depressing.. in an enjoyable way.
This is basically a simple theorem about graphs.
Not to be confused with Munchhausen syndrome...
You can view this as a game:
The most popular axiom set is Zermelo-Fraenkel-style Set Theory [1], but there are other choices which have been explored.
Note that, there a no claims about absolute truth or reality here. We just play a game in our minds.
The most fundamental question about the game, that we can ask is "Is this game consistent". Goedel found out, somewhat unfortunately, we are not able to answer that question from within the game [2]. However, sofar no intrinsical inconsistencies (paradixies) have been found.
Now, it turns out, that the ZF-Mathematics game is a very useful game, since it allows us to model certain aspects of reality. E.g. Newtons Mechanic, allows us to forecast how planets move in space.
The Natural Sciences (Physics, Chem., Bio) and Engineering are essentially about how to model reality with mathematics. The way to do that is the empirical scientific method [3], where hypothesis are formed, experiments are designed and evidence is collected.
So the question of "truth" does not really arise. It's just:
(A) Mathematics is an interesting mind-game to play.
(B) Mathematics has been used very successfully to model and predict our preceived reality.
That's all you can ask for.
[1] https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory [2] https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theor... [3] https://en.wikipedia.org/wiki/Empirical_evidence