# TheAncientGeek comments on Excluding the Supernatural - Less Wrong

37 12 September 2008 12:12AM

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

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

Comment author: 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: 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: 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: 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: 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: 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: 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: 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: 14 December 2016 08:37:59PM 0 points [-]

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.

It's not clear to me how your reply is relevant. But by your own criteria, in what sense do these areas consist of 'knowledge' if there are no obvious axioms? In what sense is something known if it's not true? Do you mean knowledge in a sense that I would accept?

Regardless of the obviousness of axioms for a particular area of knowledge – doesn't an area of knowledge accept – at least implicitly – a number of axioms? It sure seems to me that, in practice, every area of knowledge simply accepts many claims as axioms because it's impossible to reason at all without assuming something. For example, every area assumes that people exist, that the relevant object(s) of study exist, that people can gather evidence somehow of the objects of study, that the universe is not arbitrary and capricious 'magic', etc.

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.

That's not true (ha)! Certainly God's existence is incredibly distinctive in so far that God has definite attributes and there is some correlation between those attributes and the universe we can observe. If there is no such evidence it's not clear in what sense God 'exists'.

What I've yet to glean from your comments is how 'absolute truth' is any different than 'green sound'. They're both short phrases but neither seems to refer to anything.

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.

The argument in which I've been participating is whether 'absolute truth' is coherent in principle. A means of distinguishing it from some other potential kind of 'truth' would certainly help me better understand what you seem to be trying to communicate.

The means of distinguishing them is just the kind of argument we are having now. Of course, that is not particularly algorithmic.

What's not "particularly algorithmic"? I don't think you've provided a means of distinguishing between absolute truth and other truths. Did I miss it or miss them? I'd be curious if you could offer any potential means in any form.

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.

You did? You simply asserted that most people conflate 'truth' and 'absolute truth' but I disagree. For one reason, I can't distinguish between people believing something to be an 'absolute truth' and believing something to be an 'axiom'.

But let's assume that most people believe things to be 'absolutely true' and yet, somehow, someone convinces them of the non-existence of absolute truth. What exactly causes the 'world to be turned upside down' for these people? That, because they think all truth is 'absolute truth' and that they're now convinced that the latter doesn't exist that therefore nothing is true? If they think nothing is true would that also include the belief or claim that 'absolute truth does not exist'?

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.

Your entire argument seems like an attempt at a 'sophisticated' justification of radical skepticism. So I'm not sure how I can possibly accept or decline either of those axioms. On what grounds would I do so or not do so?

What you seem to be trying to sidestep tho is a number of claims or beliefs that are required for the scenario you described above to even be sensible:

1. There is a thing 'you'.
2. There is a thing 'me'.
3. That there are things 'the natural numbers'.
4. There are things 'dollars' quantified using 'natural numbers'.
5. That the things 'you' and 'me' could possibly be related such that one of us 'owes' the other some number of 'dollars'. x. ...

Those claims, those beliefs, are what seem like required axioms. Because without assuming they're true it's not clear in what sense one can believe anything, let alone engage in written communication about something.

It's pretty clear you're acting as-if you believe I exist and that I can engage in an argument or discussion with you. It's pretty clear that there is a 'you', tho the details of your person are largely unknown to me, e.g. whether you're really a number of distinct people.

There is no "ideal philosophy student of perfect emptiness" on which 'absolute truth' could possibly be bestowed. By the way, that post to which I just linked covers all the reasons why the idea of 'absolute truth' is not even wrong.

You and I were both bootstrapped as minds with already existing 'axioms', tho really none of them are incapable of being revised or replaced.

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

Okay, everything completely sidesteps the Münchhausen trilemma because it's not actually a trilemma, because there is no absolute perfect truth of which anyone is capable of knowing.

Or, nothing involves a "compromise nature of truth" – because there's only one 'truth', it's built on evidence, and it's all bootstrapped by evolution and history.

From the end of the linked post, A Priori:

Perhaps you cannot argue anything to a hypothetical debater who has not accepted Occam's Razor, just as you cannot argue anything to a rock. A mind needs a certain amount of dynamic structure to be an argument-acceptor. If a mind doesn't implement Modus Ponens, it can accept "A" and "A->B" all day long without ever producing "B". How do you justify Modus Ponens to a mind that hasn't accepted it? How do you argue a rock into becoming a mind?

Brains evolved from non-brainy matter by natural selection; they were not justified into existence by arguing with an ideal philosophy student of perfect emptiness. This does not make our judgments meaningless. A brain-engine can work correctly, producing accurate beliefs, even if it was merely built - by human hands or cumulative stochastic selection pressures - rather than argued into existence. But to be satisfied by this answer, one must see rationality in terms of engines, rather than arguments.

The Münchhausen trilemma has been around for awhile and yet truth is just as true as ever. No one is bothered by it in practice. It's an empty argument.

Comment author: 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.