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Kenny comments on Excluding the Supernatural - Less Wrong

37 Post author: Eliezer_Yudkowsky 12 September 2008 12:12AM

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Comment author: Kenny 22 May 2013 12:01:16PM 1 point [-]

Funny that you use mathematics as an analogy to something being argued as irreducible, as mathematics is all reducible to fundamentally simple components. And one could even argue that mathematics is 'reducible' to simple physical systems; it's not like you're claiming that every other non-ontologically-fundamental concept or category is Platonically supernatural. What makes the patterns of mathematics special?

Comment author: TheAncientGeek 12 June 2016 10:19:10AM 4 points [-]

Mathematics doesn't escape the Munchausen Trilemma...how do you justify your axioms?

Comment author: Kenny 24 November 2016 05:43:20PM 0 points [-]

Mathematics, the thing that humans do, completely side-steps the trilemma. There's no need to justify any particular axiom, qua mathematics, because one can investigate the system(s) implied by any set of axioms.

But practically, e.g. when trying to justify the use of mathematics to describe the world or some part thereof, one must accept some axioms to even be able to 'play the game'. Radical skepticism, consistently held, is impractical, e.g. if you can't convince yourself that you and I are communicating then how do you convince yourself that there's a Munchausen Trilemma to be solved (or dissolved), let alone anything else about which to reason?

Comment author: TheAncientGeek 25 November 2016 06:30:57PM 1 point [-]

Mathematics, the thing that humans do, completely side-steps the trilemma. There's no need to justify any particular axiom, qua mathematics, because one can investigate the system(s) implied by any set of axioms.

There's a need to justify axioms if you are going to regard your theorems as true. Game-playing formalism amounts to that, but it is not "mathematics" per se, it is a rather radical take on mathematics.

But practically, e.g. when trying to justify the use of mathematics to describe the world or some part thereof, one must accept some axioms to even be able to 'play the game'.

Which then gets back to the trilemma.

Radical skepticism, consistently held, is impractical, e.g. if you can't convince yourself that you and I are communicating then how do you convince yourself that there's a Munchausen Trilemma to be solved (or dissolved), let alone anything else about which to reason?

Even if I have reason to reject radical scepticism, that doesn't mean I have a solution to the Trilemma.

Comment author: Kenny 28 November 2016 06:51:47PM 1 point [-]

There's a need to justify axioms if you are going to regard your theorems as true. Game-playing formalism amounts to that, but it is not "mathematics" per se, it is a rather radical take on mathematics.

I just don't feel that this a real practical problem to be solved – I don't have any relevant intuitions about why it would be.

In particular, it doesn't seem like the many interesting results relating to the axiom of choice (AC) – or even more specifically results pertaining to what can or cannot be proved assuming the axiom is true, or not so assuming – are "game-playing formalism". It just doesn't seem to me like it's a particularly useful notion that we must decide, once and for all, whether AC is true or not.

What do you or would you, personally, mean by believing that Euclidean geometry is not true? To me it seems like it's true by default, i.e. 'it' is just all the things implied by its axioms. Whether it's a useful theory with respect to understanding the universe we inhabit is a separate question (and it certainly seems to be the case to me that it is). What then is left by wondering still whether it's 'true'?

But practically, e.g. when trying to justify the use of mathematics to describe the world or some part thereof, one must accept some axioms to even be able to 'play the game'.

Which then gets back to the trilemma.

I don't follow you. If we "must accept some axioms to even be able to 'play the game'" then it seems like, at least practically, the trilemma is solved by accepting the 'axiomatic argument', i.e. "accepted precepts".

Comment author: TheAncientGeek 05 December 2016 04:49:01PM *  1 point [-]

particular, it doesn't seem like the many interesting results relating to the axiom of choice (AC) – or even more specifically results pertaining to what can or cannot be proved assuming the axiom is true, or not so assuming – are "game-playing formalism".

I can make no sense of that, because taking something as true only in relation to an axiom whose truth is itself unknown is precisely what game playing formalism means. You seem to simultaneously asserting and denying he same thing.

What do you or would you, personally, mean by believing that Euclidean geometry is not true?

GPF mean Euclidean isn't true in any sense other than being a valid deduction from arbitrary premises,..for instance, that it isn't true in the sense of corresponding to the territory, and that it isn't true in the sense of being derived from non-arbitrary premises. As it happens, our best physics tells us that the universe does not have Euclidean geometry, so truth by correspondence is out, and we also know that the Euclidean axioms are not the only self -consistent axiom set, so the axioms of Euclidean geometry look arbitrary. All that being the case, Euclidean geometry is either false simpliciter, or true only in the diluted sense allowed by GPF.

It' is just all the things implied by its axioms.

Again, you seem to be agreeing with the substance of GPF while rejecting the label.

Whether it's a useful theory with respect to understanding the universe we inhabit is a separate question (and it certainly seems to be the case to me that it is). What then is left by wondering still whether it's 'true'?

If it were true in a full-strength sense, that would be an example of something that has evaded the Muchausen Trilemma.

then it seems like, at least practically, the trilemma is solved by accepting the 'axiomatic argument', i.e. "accepted precepts".

I think you are missing something important. The Trilemma doesn't just mean you have to choose between three methods of justification, it means you have to choose between three bad methods. If you can only say that something is true relative to some arbitrary axioms, then you can't say it is true in an absolute sense.

Comment author: Kenny 05 December 2016 06:56:47PM 0 points [-]

our best physics tells us that the universe does not have Euclidean geometry

How do you know that? How could I know that? Is either of our knowledge of this 'true'?

I don't understand how we're having this conversation if we don't both consider some things true and even agree that some of the same things are true.

Again, you seem to be agreeing with the substance of GPF while rejecting the label.

Yeah, that seems to be the case. Is the label not pejorative? Is it not intended to exclude the substance to which it refers by mockery?

If it were true in a full-strength sense, that would be an example of something that has evaded the Muchausen Trilemma.

I don't know why this would be interesting in and of itself. Assuming anything could be "true in a full-strength sense" and something was 'true in that sense', what would that mean?

I think you are missing something important. The Trilemma doesn't just mean you have to choose between three methods of justification, it means you have to choose between three bad methods.

It seems like you're trying to push some kind of imagined reductio ad absurdum but I refuse to play your game! I pronounce the Trilemma dissolved by virtue of the 'axiomatic argument' not being a bad method for justifying truth, actual mundane truth not 'absolute truth'.

If you can only say that something is true relative to some arbitrary axioms, then you can't say it is true in an absolute sense.

I agree and I freely admit that nothing is true in an absolute sense. I don't even know what that would mean. What could possibly be true – and expressible in a language made and used by humans – "in an absolute sense"?

Could you explain to me what the difference would be between something that is merely 'mundanely true' and something that is 'absolutely true'?

What would be different about the world if something was 'absolutely true'? What would be different if we knew that something was 'absolutely true'? And even if something was absolutely true how could we ever trust that we could know it was 'absolutely true'?

Comment author: TheAncientGeek 05 December 2016 07:24:29PM *  1 point [-]

I don't understand how we're having this conversation if we don't both consider some things true and even agree that some of the same things are true.

I am not asserting that nothing is true.

Is the label not pejorative? Is it not intended to exclude the substance to which it refers by mockery?

No and no.

I don't know why this would be interesting in and of itself. Assuming anything could be "true in a full-strength sense" and something was 'true in that sense', what would that mean?

Prinicpally that its truth doesn't depend on arbitrary assumptions.

I pronounce the Trilemma dissolved by virtue of the 'axiomatic argument' not being a bad method for justifying truth, actual mundane truth not 'absolute truth'.

Most people think of mundane truth as absolute truth. The relative truth offered by GPF is a rather idiosyncratic taste.

I agree and I freely admit that nothing is true in an absolute sense. I don't even know what that would mean. What could possibly be true – and expressible in a language made and used by humans – "in an absolute sense"?

It's meaning is a straightforward reversal of "in a relative sense". If the one is comprehensible, so is the other.

Of course, you might be using "I can't see what absolute truth would mean" to mean "I can't see how absolute truth can be obtained"....

Could you explain to me what the difference would be between something that is merely 'mundanely true' and something that is 'absolutely true'?

I never used the phrase "mundanely true", so I don't have to explain it. As I have explained, the popular notion of truth is absolute, not relative, so the Munchausen Trilemma, if irresolvable, has the momentous implication that people can't have the only kind of truth they believe in.

Comment author: Kenny 05 December 2016 07:50:36PM 0 points [-]

Is the label not pejorative? Is it not intended to exclude the substance to which it refers by mockery?

No and no.

That seems unlikely. Describing something as 'game-playing' seems to be clearly implying that it's not serious, and therefore unworthy of serious consideration. How do you know it's not pejorative? Or were you merely asserting that you are not using it pejoratively?

I don't know why this would be interesting in and of itself. Assuming anything could be "true in a full-strength sense" and something was 'true in that sense', what would that mean?

Prinicpally that its truth doesn't depend on arbitrary assumptions.

I'm still confused. If a truth doesn't depend on "arbitrary assumptions" what makes it different than an "arbitrary assumption"? If you're familiar with mathematics, what would a sketch of a 'constructive proof' of an absolute truth look or seem like?

Presumably, something "true in a full-strength sense" would not depend on "arbitrary assumptions". If it depends on no other truths it seems equivalent to an axiom. Do you disagree? If you do disagree, can you help me understand how a truth like this could exist? Could you describe anything about such a truth that would be different than other truths?

I pronounce the Trilemma dissolved by virtue of the 'axiomatic argument' not being a bad method for justifying truth, actual mundane truth not 'absolute truth'.

Most people think of mundane truth as absolute truth. The relative truth offered by GPF is a rather idiosyncratic taste.

Let's ignore most people. I don't think of mundane truth as absolute truth. If you're not arguing that they're the same, what are you arguing?

I agree and I freely admit that nothing is true in an absolute sense. I don't even know what that would mean. What could possibly be true – and expressible in a language made and used by humans – "in an absolute sense"?

It's meaning is a straightforward reversal of "in a relative sense". If the one is comprehensible, so is the other.

So there's nothing else distinctive about absolute truth other than it 'not being relative'? That seems pretty uninteresting.

Of course, you might be using "I can't see what absolute truth would mean" to mean "I can't see how absolute truth can be obtained"....

Of course you might have written:

Mathematics doesn't escape the Munchausen Trilemma...how do you justify your axioms?

but you didn't actually mean anything by it. You haven't committed to claiming that mathematics is false; just that they're not 'absolutely true'. You haven't provided any means of distinguishing 'absolute truth' from any other kind other than claiming that the former is the complement of the latter among the set of all truths (or something similar).

You haven't offered any reason to care about 'absolute truth' or any ideas about the benefits acquiring such truths would render; nor any constructive, even-minutely-specific details about how one would acquire them.

I never used the phrase "mundanely true". As I have explained, the popular notion of truth is absolute, not relative, so the Munchausen Trilemma, if irresolvable, has the momentous implication that people can't have the only kind of truth they believe in.

I'm not arguing for any popular notion of truth. I claim truth is not absolute and cannot be.

Is there anything left to discuss?

Note that my original comment to which you replied was about mathematics being reducible, not absolutely true (or otherwise).

Comment author: TheAncientGeek 05 December 2016 08:11:55PM *  0 points [-]

That seems unlikely. Describing something as 'game-playing' seems to be clearly implying that it's not serious, and therefore unworthy of serious consideration. How do you know it's not pejorative? Or were you merely asserting that you are not using it pejoratively?

Principally the latter, I suppose, although I don;t think it is particularly perjoritive in any case.

Prinicpally that its truth doesn't depend on arbitrary assumptions.

I'm still confused. If a truth doesn't depend on "arbitrary assumptions" what makes it different than an "arbitrary assumption"? If you're familiar with mathematics, what would a sketch of a 'constructive proof' of an absolute truth look or seem like?

There are any number of areas of knowledge where the axioms aren't at all obvious.

Presumably, something "true in a full-strength sense" would not depend on "arbitrary assumptions". If it depends on no other truths it seems equivalent to an axiom.

Consider an observation. Is that an axiom?

So there's nothing else distinctive about absolute truth other than it 'not being relative'? That seems pretty uninteresting.

And there's nothing distinctive about God's existence other than it's being the opposite of God's non-existence. You seem to be associating momentousness with complexity.

You haven't provided any means of distinguishing 'absolute truth' from any other kind other than claiming that the former is the complement of the latter among the set of all truths (or something similar).

The means of distinguishing them is just the kind of argument we are having now. Of course, that is not particularly algorithmic. If you are running on the implicit assumption that nothing is meaningful unless it has very precise, algorithmic truth conditions, then that could do with being made explicit.

You haven't offered any reason to care about 'absolute truth'

I have in fact explained why the non existence of absolute truth would turn the world upside down for billions of people.

Consider use of arbitrary axiom in arguments with real-world implications:

Axiom1: You owe me a whole number sum greater than $99. Axiom2: You owe me a whole number sum less than $101. Conclusion: You owe me $100.

So.. do you owe me that money? Arbitrary axioms are relatively safe in mathematics, because it is abstract..they are pretty disastrous when applied to the real world.

I'm not arguing for any popular notion of truth. I claim truth is not absolute and cannot be.

Is there anything left to discuss?

Yes: whether you are correct.

Mathematics does not "compeltely" sidestep the Munchausen Trillema, because completely sidestrepping it would not involve a compromise nature of truth!

Comment author: Dacyn 26 November 2016 01:22:22AM 0 points [-]

The investigation of the systems implied by a set of axioms also requires some assumptions. For example, one must assume that any axiom implies itself, i.e. P -> P. Once this axiom is accepted, there are a great number of logical axioms which are equally plausible.