The logic of Buddhist philosophy • Hacker News Board

Re: The logic of Buddhist philosophy

#101

Post by dpierce9 » Thu, May 08, 2014, 6:02 PM UTC

Strilanc wrote: post #63

dpierce9 wrote: post #53

Earlier quoted context omitted.

It is simply not true that multi-valued logics collapse into two-valued logics. While it is true that you can assign indeterminate statements {true,false} and call it a third value, logic is more than assignments of truth-values to statements, it is also rules of inference for that formal system. The rules of inference are the driving force behind paraconsistent logics and the rules of inference are very different. O…

They don't collapse into two-valued logics, but they can be encoded into two-valued logics in the same way that numbers can be encoded into sets. The simplest way to see this is to think of a computer. Its operation can be described by a function in two-valued logic, taking the bits making up the state of the CPU and memory as input then returning the next state. And you can write programs that do multi-value'd logic…

I agree that you can model a multi-valued logic system on a universal Turing machine but you are wrong to think that doing this is the same as mapping to classical logic. TMs do not intrinsically follow the rules of classical logic, rather, they obey classical logic (when they do) because they have instructions written into their head. Similarly, the marks on the tape do not intrinsically represent two-valued logic even if there are only two kinds of marks on the tape. This has nothing to do with succinctness or making Turing Machines better and everything to do with 'what do the marks represent?' and 'what is the best way to reason with the marks?' which are definitely interesting questions in my book.

Re: The logic of Buddhist philosophy

#102

Post by dllthomas » Thu, May 08, 2014, 6:10 PM UTC

shawndumas wrote: post #97

dllthomas wrote: post #50

Earlier quoted context omitted.

I don't see that every violation of the principle of noncontradiction trivially leaves definitions meaningless. Suggesting that a principle shouldn't be taken to hold in general doesn't mean that you have to violate the principle at every opportunity, just that there is some place it is (in whatever sense) correct to violate the principle. Of course, under traditional logics, accepting a contradiction leaves everythi…

by ' every violation' do you mean ' any violation', ' no violation', ' blue violation'... by 'every violation ' do you mean 'every observance ', 'every miss-fire ', 'every monkey '... you see, apart from the law of non-contradiction language is impossible.

You're being needlessly difficult to no good end. I am not dropping the law of non-contradiction in my comments here, where I speak about logics that drop non-contradiction.

And the point you're trying to make here ignores what I said. It is certainly the case that if you permit every violation of non-contradiction, whether or not it violates any other rule, you wind up with nonsense. In no way does that establish that nonsense follows from any violation of non-contradiction even in the face of other rules. I don't have deep enough knowledge to say one way or the other, but some mathematicians seem to think there are things of interest there and your superficial rejection does nothing to prove them wrong.

Re: The logic of Buddhist philosophy

#103

Post by dllthomas » Thu, May 08, 2014, 6:11 PM UTC

notdonspaulding wrote: post #98

dllthomas wrote: post #50

Earlier quoted context omitted.

I don't see that every violation of the principle of noncontradiction trivially leaves definitions meaningless. Suggesting that a principle shouldn't be taken to hold in general doesn't mean that you have to violate the principle at every opportunity, just that there is some place it is (in whatever sense) correct to violate the principle. Of course, under traditional logics, accepting a contradiction leaves everythi…

As someone not versed in nontraditional logics, can you give an entry-level statement or thought experiment that violates the principle of non-contradiction without leaving everything provable?

I'm also not particularly versed in nontraditional logics. I'm just leery of saying a mathematical structure can't be interesting or has no applications, when mathematicians seem to disagree.

Re: The logic of Buddhist philosophy

#104

Post by Daishiman » Thu, May 08, 2014, 6:13 PM UTC

tremols wrote: post #25

Much of the mysticism and misunderstandings about indian philosophy comes from a very bad habit in the translation of indian works where some words are left untranslated as to give them a magical-religious cool sounding sanskrit aura. If koti means corner, there is no reason that 'koti' should appear in a translation instead of corner otherwise you are giving it a special importance that distracts from the text's tru…

The problem is that a lot of those words are only a rough translation, and if you want to understand the concepts more profoundly then you're going to need something more to get by.

The Buddhist Mahayana concept of "emptiness" requires at the very least a few paragraphs to have a grasp, at best a couple of books on your belt. Same with "concentration" (samadhi), "insight" (vipassana), "life-energy" (prana), and so on and so forth.

To the uninformed reader they certainly add that confusion, but for someone versed in Eastern philosophy it's essential that the original concepts be preserved.

Re: The logic of Buddhist philosophy

#105

Post by simondedalus » Thu, May 08, 2014, 6:30 PM UTC

javert wrote: post #81

kfnn wrote: post #58

Earlier quoted context omitted.

The author himself wrote: The constructions I have described show how to make precise mathematical sense of the Buddhist views. This does not, of course, show that they are true.

> How can contradictions be true? What’s all this talk of ineffability? This is all nonsense. The constructions I have described show how to make precise mathematical sense of the Buddhist views. This does not, of course, show that they are true. That’s a different matter. But it does show that these ideas can be made as logically rigorous and coherent as ideas can be. No, they are nonsense. Nothing that claims that…

while i don't agree with priest either, your reasoning is bad.

the point is not to argue against how people define logic, or anything as arbitrary or seemingly self-defeating as that.

the point is to provide a functional logic in the face of the liar's paradox and the like. regardless of the motivations of individual philosophers, the work itself posits as motivations actual technical problems. the technical problems generally arise from self-reference, but (as you can see with varieties of incompleteness proofs as well) you don't need outright self-reference to get the truth of a statement resting on its negation.

yell all you want about rigor, the onus is on you to use conventional logic to resolve these tensions. again, i personally think that proponents of many-valued logic are misguided in their large scale view of truth functional representation (and i probably think the same of you!). however, i respect that they seek to defend it by solving problems rather than saying "hurr, 'this is a lie' just doesn't mean anything at all. and oh yeah, language is compositional, truth is correspondence, and i'll hear nothing saying otherwise!"

Re: The logic of Buddhist philosophy

#106

Post by splat » Thu, May 08, 2014, 6:41 PM UTC

muraiki wrote: post #89

Daishiman wrote: post #61

Earlier quoted context omitted.

I think the difference between the Christian and Buddhist approaches to the paradoxes is the fact that Christian theologists have spent centuries devising new doctrine that accomodates the contradictory statements in a sort of logical superstructure, whereas no such thing happens in Buddhist contradictions. Part of the reason why I suspect this is because Christian dogma ultimately reflects on concrete precepts that…

The approach in Eastern Christianity (pre-Great Schism groups such as the Orthodox, Coptic, and others) is generally that of Apophatic or Negative theology. "Leave behind the senses and the operations of the intellect, and all things sensible and intellectual, and all things in the world of being and non-being, that thou mayest arise by unknowing towards the union, as far as is attainable, with Him who transcends all…

There certainly have been similar approaches in Western Christianity. An explicit attempt at synthesizing Buddhist philosophy with Christianity was made by the Catholic monk Thomas Merton back in the 1960s. Moreover there has been a long mystical tradition in Western Christianity as well. Look to saints like John of the Cross and Thomas a Kempis among others. It’s more that there’s a difference in emphasis between the two churches. The Catholic Church has historically placed more of an emphasis on developing a scholarly, logical theology whereas the Eastern Churches have put more emphasis on theosis, or obtaining a vision of God (participating in a vision of God might be a better way of phrasing that). But neither sees either approach as being in conflict with the other.

I would also claim that the idea that salvation is a process of deification has also long been present in the Catholic Church, the idea of purgatory being one important example. Both Purgatorio and Paradiso from Dante’s Comedy also point toward this idea. But the notion of deification as being a process that continues through life and into death seems to be missing in many Protestant communities.

Re: The logic of Buddhist philosophy

#107

Post by kazagistar » Thu, May 08, 2014, 6:50 PM UTC

vinceguidry wrote: post #67

Strilanc wrote: post #29

Earlier quoted context omitted.

I subjectively don't find those philosophies interesting, and have a distaste for assigning single ideas to heterogeneous groups like "the west". Your mileage may vary. For example, I would consider myself western but I don't have any problem imagining systems with true, false, both and neither. You just treat them as anonymous values with particular operations, instead of getting stuck on "but if we were in this oth…

> I don't have any problem imagining systems with true, false, both and neither. You just treat them as anonymous values with particular operations, instead of getting stuck on "but if we were in this other system that we're not in, this would violate an axiom!". It's not quite that simple. We've built up entire codes of ethics and law and branches of mathematics with practical applications like computing that rely u…

> law

The law is about as non-binary as it gets. There are two states of the law: proven guilty, and not proven guilty. We say things like "innocent until proven guilty" but we all know and accept that reality does not work that way. There is no law of the excluded middle here.

EDIT: Actually, adding some excluded middle might make our law better and more fair. For example, cases could be dismissed if it is shown that a law is being applied selectively, forcing any "discrimination" to be written into law explicitly. For example, if tax code is more often enforced against the wealthy, or drug law against members of poor neighborhoods, that would have to be explicit, instead of systematically hidden, or else enforcement could be nullified.

As for computing, the reason we use binary logic is simple: weakening makes many problems more tractable. We spend all our time building abstractions and rules to limit what a programmer can express within certain bounds, to enable a compiler to better optimize it. If all we need for an application is boolean logic, then using other logics adds unnecessary power, and power leads to bugs.

Re: The logic of Buddhist philosophy

#108

Post by kazagistar » Thu, May 08, 2014, 7:09 PM UTC

1stop wrote: post #27

tremols wrote: post #25

Much of the mysticism and misunderstandings about indian philosophy comes from a very bad habit in the translation of indian works where some words are left untranslated as to give them a magical-religious cool sounding sanskrit aura. If koti means corner, there is no reason that 'koti' should appear in a translation instead of corner otherwise you are giving it a special importance that distracts from the text's tru…

I was under the impression this was done because the english translation loses some meaning or context. The idea that every concept can be translated is probably a false one. Ideas are built on cultures, cultures are described by language you can't change one without changing another. So when describing an idea generated by a culture, using a secondary idea and secondary culture, you will lose things. That is why (fo…

If a concept cannot be translated between languages, it seems likely that it cannot be translated properly between people either. Or do you mean directly translated? The concept of nirvana is ill defined if you cannot directly describe it, and can only point at it.

Re: The logic of Buddhist philosophy

#109

Post by KrisAndrew » Thu, May 08, 2014, 7:22 PM UTC

Strilanc wrote: post #15

I would have enjoyed this article if it dropped the Buddhism and kept the math. Alternate logics are interesting, but you tend to be able to reduce them into each other in the same way that universal turing machines can simulate each other. They don't add new functionality, they add succinctness. So it's really strange to me to frame them as totally different philosophies . For example, it is the case that self-refer…

I find the crossover between philosophy and mathematics/logic extremely interesting. I've read both of Wittgenstein's major works ("Tractatus Logico-Philosophicus" and "Philosophical Investigations") and found them very compelling. I tried to read Heidegger's "Being and Time", but it was beyond me at that point. I'll attempt it again next year maybe.

The essential point of the article is that systems without contradictions are not interesting. The contradictions create a point of discussion; a single, loose thread on the lapel of an otherwise perfectly tailored suit jacket. However, were you to don this suit and show up at a formal, elegant dinner party, everyone would see the flaw but no one would speak of it... at least not at the party. That would be gauche.

If you enjoyed the math, but not the Buddhism, you might enjoy "Philosophy of Arithmetic" by Husserl, or almost anything by Frege.

Re: The logic of Buddhist philosophy

#110

Post by arh68 » Thu, May 08, 2014, 7:38 PM UTC

Seems like statements can have both verity (truthiness) and falsity in varying quantities. They might sum to 0, 1, or anything at all. Whether a statement has meaning seems important, too. '2020 will be a rainy year.' does not have meaning (yet). Pretty soon, though, the universe will reach a certain point where that statement starts to accumulate verity & falsity. Maybe 2020 will be a peak monsoon season in the Eastern Hemisphere; verity++. Maybe it'll be a record drought in North America, too; falsity++. This is not a 1-dimensional spectrum.

Seems like meaning is some sort of vector norm over || ||. It should be easy to imagine scenarios all across this unit square for '2020 will be rainy': (0,0) is now, (1,0) means lots of agreed-to raining everywhere, ( .9, .9) is crazy weather, and ( .2, 1) means it was mostly dry that year.

This seems heavily reliant on human interpretation, but trying to extract "intrinsic truthiness" will always rely upon some global context telling you what the rules are. '2 = 3' is absolutely true, depending on what you think the rules are.

'Correctness' seems to correspond to (verity - falsity), which is why ( .9, .9) is certainly meaningful but doesn't improve on the correctness of saying 2020 is rainy.

I have a haunting feeling GEB talks about this, though I never finished reading yet.