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The logic of Buddhist philosophy

• kirab 12y ago
  This is nice. I'm wondering how much our restricted thought environment (x can only be true or false) has hindered our development in the last thousands of years?
  • wfn 12y ago
    I'm wondering how much Aristotle's metaphysics of essence may have hindered certain paths of thought. :) You must admit, his base system is powerful and ever-penetrating (Descartes is probably a very good example, but it's only one of the more obvious ones...) Of course it's easy to say things like that, and harder to come up with a consistent (pun intended) metaphysical system on your own self. :)
    • vram22 12y ago
      Speaking of Descartes, I've always thought that the famous quote supposed to be by him, i.e. "I think, therefore I am": http://en.wikipedia.org/wiki/Cogito_ergo_sum http://en.wikipedia.org/wiki/Cogito_ergo_sum is (vaguely? :) wrong. Shouldn't it be: "I am, therefore I (can) think"?
      • wfn 12y ago
        Hmm. I don't think so, but, feel free to expand your opinion (why do you think it should be "I am, therefore I (can) think"? Maybe you have an interesting point to make?) Re: etymology, it's pretty much "think => exist." Re: conceptual level: well, one of the texts where this whole concept/causal-chain is introduced is in his "Meditations on First Philosophy"[1], in particular, in Meditation 2. Very (very) roughly (and from bad memory), the idea is that one can first start casting into doubt everything that there is (skepticism as a method) (this is Meditation 1.) When you abstract enough times, you can start doubting even the certainty of things which may seem true in themselves (this latter notion is an endless field of debate in itself; see e.g. Quine's "Two Dogmas of Empiricism"[2]) - cliche example is "2+2=4." Say there's a deceitful daemon: each time the thought "2+2" is produced, the daemon "intercepts" the answer and produces a "5". (Yes, I'm saying that Descartes may be one of the originators of the concept of a MitM, ha!) (Also, this doesn't work so well with mathematics, since again, one could say that mathematical statements are "analytically true", and it's simply not true that one may mistake a "5" for a "4". But imagine something more mundane: each time you think if there is a god, the daemon deceives you into thinking there isn't one; whatnot.) So now you generalize the doubt process enough to start doubting whether anything exists, what-so-ever. The point is not so much in thinking that there isn't anything, but in removing certainty from usual ontological assumptions (what (kinds of) things exist.) So now you're not certain if there is an "I": you are able to doubt it. But then Descartes says that this very process of certainty-removal requires an operation (he doesn't use these words, did I say this is extremely rough): namely, the "doubt" itself. "Doubts are to be had." Or, if you will (and closer to D. (I think)): if an evil daemon can cast into doubt even the existence of your own self - it it can deceive everything, etc. - there needs to be a something to be deceived. Or at the very least, the process of deception (or: of doubt) does happen (if you want to cast everything into doubt.) So if you doubt that anything exists and hence can not be certain of anything, then it so happens that this requires doubt "to happen." Hence "doubt exists." (He also says (I think) that, basically, "clearly since I am doubting right now, doubt does happen". A kind of phenomenological argument, which doesn't really stick with me, fwiw. He then starts using the notion of "clear and distinct perception", and that's where things go downhill imho (Meditation 3, a (kind of circular) proof of God, etc.) But I have few qualms about Meditation 2, and this includes cogito ergo sum.) (You could say that the only thing one can be certain of is that "there are thoughts" (not an "I"). I would agree with this. "Thinking exists." And since "thinking" would be, well, thinking this thought, it is certain that "thinking exists.") edited to include two paragraphs (this+next one): So now we (hopefully) have something that exists for certain; thoughts exist (or somesuch.) Descartes claims a bit more: this entity that does the thinking (there does need to be an agent which thinks those thoughts (is what he assumes, I guess)) - let us just say it is "I", who does the thinking/doubting - when we trace back the process by which we concluded that we are certain that it exists - involves us discovering that thinking/doubting definitely does take place. Hence "I think; I exist." (I suppose you could have a concept of an "I" that is simply instrumental (doesn't have independent substance (oof, this is dangerous/slippery territory)): thoughts can have relations, and related thoughts can be seen as "bundles", and this process producing continuing interrelated bundles is "the I doing the thinking." But, I'm not sure of this at all. Maybe D. would say that the deceiving daemon needs to deceive something, if it does actually do any deceiving; and if this does happen, then this "something" which is being deceived is (let us call it an) "I".) Now, to go from cogito ergo sum to proof of God and subsequent re-establishment of certainty about the whole world - that is something else. And I don't think that he does a very good job at it. (And this is "usually", "generally" agreed upon.) [1]: https://en.wikisource.org/wiki/Meditations_on_First_Philosophy https://en.wikisource.org/wiki/Meditations_on_First_Philosop... - which btw is an easier read than you might think, if you're curious enough! [2]: http://www.ditext.com/quine/quine.html http://www.ditext.com/quine/quine.html
        • vram22 12y ago
          >Hmm. I don't think so, but, feel free to expand your opinion (why do you think it should be "I am, therefore I (can) think"? Maybe you have an interesting point to make?) I did say "vaguely". Let me think about it a bit and then reply later tonight.
          • vram22 12y ago
            Ok, here's my attempt at an answer: Take his statement: "I think, therefore I am." My guess is that the way people interpret it is like this: Descartes is saying that he (notices that he) thinks, wbich (to him) implies that he must exist. The statement can be broken down like this: A, therefore B where A = "I think" and B = "I am". But if you look at it like this: the "I am" part is asserting that he exists, which according to him is a logical implication of "I think". But his asserting "_I_ think" itself implies that his "I" exists (whether it thinks or not). So the "I think" is like saying "I exist" (and am also thinking - my emphasis is on the "I"). So it seems like he is already assuming something is true ("I" exist/am), on the left side of the sentence, what he is trying to prove ("I am"), on the right side of the sentence. Note the difference in the two uses of quotes in the last sentence. Hope I've made my thinking :) clear.
            • wfn 12y ago
              Thanks for this. :) Indeed, I think I actually mostly agree with you. See my longer comment / explication of Descartes' argument (if it's an argument) above: I personally (also) think that "I think" already presupposes too much. What one might be able to argue is a lesser version of the thing, though: thinking, therefore, existing. ("thought exists" (whatever that actually means!)) > So it seems like he is already assuming something is true ("I" exist/am), on the left side of the sentence, what he is trying to prove ("I am"), on the right side of the sentence. ..so yeah, I think that the only safe thing for him to say at that point would have been "thoughts exist." Maybe this does sound lame, but in the context of Descartes' Meditations, it's about discovering that even though you can doubt everything, this does require (the process of ) doubting as such. Or: I can be deceived about everything there is in the world (so e.g. in actuality, there is no world as such); but who is being deceived? At the very least, there is (some kind of) thought happening. One might say that doubting requires an agent, etc., but really, this is already debatable. But in short: you're right, if one were to establish "I exist" (with an "I" having certain desirable properties), one could then say "I think", and that would have been less murky, indeed! Problem is, poor Descartes is not sure that he "exists": indeed, for him (and this is partly to do with the whole mentality present in Rationalism, and with the start of Modern philosophy (many people hold him to be the father of it)) thinking comes before existing. You will find many parallels of the latter around, scattered in various places; cf. "god thinks itself into being", etc. He kind of articulates one of the foundations of Rationalism as in the epistemology: thought shall be the ultimate and primary criterion for truth. But again, I agree, however, I would say that he could have stated a lesser version of his point (while not reversing the logical implication arrow): "thoughts exist." However, to go from that to re-establishment of certainty about the whole wide world would have been even more tough (and he was already having a hard time!) In summary, I think I understand where he's coming from, but one could say that his project (a kind foundationalist epistemology) had been doomed from the very beginning! > Hope I've made my thinking :) clear. Yeah, I think that was clear! Forgive me for my verbosity, and thanks for the explanation. I think it makes sense, and fwiw, I agree with the general gist of it.
  • andreasvc 12y ago
    The article doesn't make such a statement, and it would be quite a stretch. Although reasoning in science and mathematics is to some sense restricted to logic with binary truth values, this doesn't mean that we are also restricted to such a logic in everyday life.
  • im3w1l 12y ago
    A multi-valued logic (at least of the sort described in the article) is not stronger than a single-valued one. They can be transformed into one another. For instance lets say give the proposition "the sky is blue", the truth value (0.78, right here, right now), corresponding to being quite blue, but not necessarily always or everywhere. truth value(the sky is blue) = (0.78, right here, right now) Since a function is just a special case of a relation, we could say the sky is blue ~ (0.78, right here, right now) And a relation can be described as function from the composite space to {false, true}, where false denotes not related, and true denotes related. So we could transform the whole thing into truth value((the sky is blue, (0.78, right here, right now)) ) = true Now another question is which model is most convenient.
  • tel 12y ago
    It's been thrown away in some (growing) part of modern mathematics and has lead to the creation of automated provers as logic rejecting PEC and not PNC models lambda calculus. See my top level response in this thread for more detail.
• deleted 12y ago
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• jaxytee 12y ago
  I think boolean logic was a skillful starting place for human society. Now that we have a good understanding of "conventional" logic, we can begin to explore a more sublime logical framework.
• throwaway13qf85 12y ago
  In case anyone is turned off by the expectation of wishy-washy flim-flam, it's worth noting that Graham Priest may be a professor of philosophy, but is most well known for his work in logic, particularly in non-standard logics (i.e. not propositional or predicate logic) that allow non-boolean truth values, or weaken or remove some of the axioms of classical logic. I assume that what's relevant here will be his work on paraconsistent logics (which allow contradictions) but I think an equally interesting line of work is linear logics. It's of interest to computer scientists because of its relationship to linear type theory (in the same way that the Curry-Howard correspondence links type theory and classical logic) and because it has close relationships with quantum computing. In particular, you are not allowed to delete or duplicate elements/propositions/types (corresponding to physical processes that cannot arbitrarily create or destroy particles, the "no deletion theorem" and "no cloning theorem" of quantum information theory), so functions of the type duplicate :: a -> (a, a) and delete :: a -> () are not allowed in a linear type system. Practically, this means that many operations can be optimized by the compiler to in-place mutations, because it is guaranteed that there is only ever one reference to a particular object.
  • elbenshira 12y ago
    Don't immutable data structures give us most of the benefits? Clojure, for example, approaches this by preferring values over hidden, mutable state (e.g. classes). We see libraries like Om take advantage of the fact that comparing two complex structures (e.g. a hash map) is simply a reference equality test. http://clojure.org/state http://clojure.org/state http://swannodette.github.io/2013/12/17/the-future-of-javascript-mvcs/ http://swannodette.github.io/2013/12/17/the-future-of-javasc...
    • dllthomas 12y ago
      Immutable data structures give us many benefits, but linear types promise most of those plus safe mutability. Think of it as a compile-time proof that you'll be getting vector fusion style speed-ups.
    • deleted 12y ago
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• javert 12y ago
  But the Law of Non-Contradiction does hold. And it's very easy to save the PEM if you distinguish the value of a proposition (true or false) and the cognitive status of the proposition (certain, probable, possible, or arbitrary). Moreover, to exist is to have a particular identity, to have a nature, to be something. Thus, all of this work is utter hogwash. The professor who wrote this IS practicing mysticism and irrationality. He ought to be shunned by all actual philosophers. If this kind of thinking were to get "popular," Western civilization and science would collapse into skepticism and religion would take over again. Just as happened in the Middle Ages and at the end of the Islamic Golden Age (in the latter case, there never was a recovery).
  • mjburgess 12y ago
    1) Graham Priest is one of the most famous logicians of this century. 2) The LNC is an axiom it doesnt "hold", its either built into what you mean by identity or it isnt. Either way there is no non-circular "hold"ing. 3) Im sure the notions of truth, falsity and consistency are far too technical here for the lay person to get a serious grasp of but i'd be careful of rationalizing your own ignorance by projecting stupidity onto others.
    • javert 12y ago
      For 2, yes, the LNC is an axiom. What that properly means is that to deny it is a contradiction, because it must be assumed to deny it. In other words, you can't say "The truth is, there is no truth." Which is what Graham Priest is doing. 1 is an interesting observation, but has no bearing on the facts of the case: he is a fraud. 3: You should be ashamed to make a statement like this in an intellectual conversation. If you feel the need to bolster your argument with an unsubstantiated character attack like this, you must not feel that your argument is sound. No offense, but I'd flag your comment for #3, except it's not worth wasting moderators' time on.
      • kfnn 12y ago
        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.
• joelmichael 12y ago
  Paradox is not really so alien to Western philosophy, as this article initially suggests. It does end up referencing a number of modern Western philosophers, but the idea is older than that. It's ironic he refers to "Western orthodoxy" as being strictly anti-paradox, as traditional Christian theology is full of official paradoxes; a major example would be the doctrine that Jesus is simultaneously fully human and fully divine. Many were declared anathema for refusing this and other paradoxical doctrines. So rather than Western orthodoxy being unaware of paradox, it has insisted on it. The concept of the dialectic also touches on this idea of reconciling apparent contradictions, rather than defeating your opponent as one does in a debate, and this idea originates not truly with Hegel but spans all the way back to Socrates, and probably before. I agree with the sentiment, however, that understanding paradox is extremely important to a person's capability for nuance and understanding. If you insist on a simplified internal consistency, you will end up sacrificing (and demonizing) whole parts of your thought process rather than trying to reconcile them as having some truth. It can be a process of self-indoctrination purely to avoid the pain of confusion. Another way to think of paradox is simply rejecting false dichotomies in favor of a more complex and uncertain reality. I don't think the lesson here is to "break the chains of Aristotelian logic" (God forbid) but rather, well, reconcile it with the idea of paradox.
  • andreasvc 12y ago
    I don't think Christian theology makes the Western tradition any less anti-paradox, because the paradoxes of Christian orthodoxy are dogma, they do not give rise to a systematic treatment of paradoxes as described in the article.
  • CPLX 12y ago
    > Another way to think of paradox is simply rejecting false dichotomies in favor of a more complex and uncertain reality. That, as it so happens, is an excellent shorthand for Buddhism as well. Which I believe is a fruitful avenue for discussion, as the author does here.
  • Daishiman 12y ago
    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 faithful must abide to, since belief is an essential component to salvation in Christianity and relates to concrete actions and thoughts. Buddhist dogman in general, with the notable, extremely fuzzy, and highly opinionated exception of karma, does not have such a problem, since no particular belief system is considered critical for enlightenment, since all beliefs are delusion and only a direct experience with reality (the Deathless) is truly relevant.
• dusklight 12y ago
  This article is kinda missing the point. The "empty" is the undefined. That which has yet to exist, or never will. There is that which is uncountable, for example the number of corners in a circle. Just because it is a contradiction doesn't mean it is wrong -- maybe your models are wrong. The usefulness of eastern philosophy is to free yourself of preconceived ideas. I think it is obviously clear to everyone today that there are modes of thought that are far inferior to logic. I think it would be supremely arrogant to presume that logic is the best mode of thought that humanity will ever come up with. To try to shoehorn everything to fit into a logical framework feels akin to epicycles to me.
  • eludwig 12y ago
    >>The "empty" is the undefined. That which has yet to exist, or never will. The "empty" is the un-defined. Direct experience, that which can't be talked about, labeled or categorized. That (this) which has always existed, and always will. The void is that which can't be named. It's all around you! You can never leave it because it is you, stretching from your center in all directions. There are no contradiction here, because you need a logical layer over reality to have contradictions. Tat twam asi!
    • zorze 12y ago
      So true. To experience the un-manifested one has to just be actively aware: - listen to sounds/silence; - look at where you're looking out from; - feel the tickle of the body's energy. Bluntly said, you have to fucking shut-up! Here are some links to people that go directly to the essential: http://www.eckharttolle.com http://www.eckharttolle.com http://www.adyashanti.org http://www.adyashanti.org http://www.headless.org http://www.headless.org
      • deleted 12y ago
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  • andreasvc 12y ago
    Maybe it is missing your pet theory, but the article has a definite point and Priest argues it at length. You seem not to have grasped the article because you refer to logic as something singular that should not be deemed superior to other modes of thought, while the article demonstrates there are many different, mathematically rigorous conceptions of logic. Epicycles are a non-sequitur here, because there is not a particular proposition that you set out to prove with whatever explanation you can find. Rather the goal is to find a logic that does not break down when presented with paradoxes.
• kalaya 12y ago
  If you want to learn more about this catuskoti, meaning ‘four corners’ theories there are another one threekoti, meaning ‘three corners’ you need to check Prof. Nalin de silva's works. http://kalaya.org/ http://kalaya.org/ Unfortunately foreigners most of his work is in sinhala. And only foreigners learn that language is germans,russians,chines and japanes diplomats.
• awakened 12y ago
  "The only correct view is the absence of all views." - Thich Nhat Hanh (Thay)
  • vram22 12y ago
    That statement is false :)
• pepon 12y ago
  Can some enlightened soul give me a TL;DR version of this text?? :D
  • andreasvc 12y ago
    It is possible to give a rigorous mathematical definition of a logic that deals with contradictions and propositions that cannot be assigned a truth value. This has parallels with traditions in Buddhism and helps resolve paradoxes which are problematic for traditional Western logic (e.g., "this sentence is false").
    • pepon 12y ago
      Thanks a lot!! It looked like interesting but I am way too busy for such a long text.
      • dodders 12y ago
        But not too busy to read HN and post questions, it would seem...
• Strilanc 12y ago
  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-referential statements don't always have well-defined truth values and that allowing them to have values like {} and {false,true} is a fruitful way to think about it. But this approach can be grounded in two-valued logic (and vice versa), and it doesn't solve the problem of self-reference (consider "This statement is not {}, is not {false}, is not {true}, is not {false,true}").
  • pera 12y ago
    > I would have enjoyed this article if it dropped the Buddhism and kept the math. May I ask you why? Personally I enjoy reading about the origin of some particular idea/philosophy, even when it's purely anecdotal.
    • arkaeologic 12y ago
      Also, it's rather eye-opening to note how other cultures thought. This is best done by examining their religion or some other foundation ideology like Buddhism.
    • Strilanc 12y ago
      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 other system that we're not in, this would violate an axiom!". (If I thought this was a flaw in the article, instead of my opinion of it, I would have just said it was terrible instead of saying I didn't enjoy it. Its style just grates me sometimes.)
      • 12y ago
• nabla9 12y ago
  Henk Barendregt (known for his work in lambda calculus and type theory) has good explanation of the apparent contradictions in tetra lemma. Buddhist Phenomenology - 1.7 Explaining apparent contradictions: http://www.cs.ru.nl/~henk/BP/bp1.html#SECTION00027000000000000000 http://www.cs.ru.nl/~henk/BP/bp1.html#SECTION000270000000000... In other words: And Now for Something Completely Different...
• tremols 12y ago
  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 true meaning. Almost every translation of indian philosophy suffers from this fetish for the sanskrit language and as beautiful as sanskrit is, it shouldn't contaminate the purpose of a translation.
  • 1stop 12y ago
    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 (for example) nirvana, has a bunch of translations: awakening, calmness, relief, void/voidless, the light, nothingness, or (my favourite) phew. Because we don't have the context to properly describe that in the west (latin-germanic based languages), so we need a bunch of other concepts that kind of point at it.
    • kazagistar 12y ago
      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.
      • 1stop 12y ago
        ill defined in one language, doesn't mean ill defined in another. I'm saying language and culture are inextricably linked. And not 100% compatible with all other languages and cultures.
  • valarauca1 12y ago
• noisy_boy 12y ago
  For the benefit of non-Hindi/Sanskrit speakers: the pronunciation of "catuskoti" starts with "ch" (as in "chat") and not as in "cat". "chaet" is the prefix signifying "four".
• wfn 12y ago
  jaxytee: fyi, you are shadowbanned; there's no contact info on your profile, and your previous comments suggest no reason for the shadowbanning.
• ap22213 12y ago
  Could someone explain why Priest, in discussing the 'four corners', presents the Hasse diagram with {F} at the bottom? Why would it not be {}? I'm not too familiar with posets, but it seems the order matters, right?
  • throwaway13qf85 12y ago
    Intuitively, it is to indicate degree of 'truthiness'. Certainly false {F} is less truthy than either both true and false {T,F} and neither true nor false {}, which are in turn less truthy than certainly true {T}. The Hasse diagram indicates that there is no relationship between {} and {T,F} in terms of level of truthiness. More mathematically, you can think of the Hasse diagram as a lattice, with the meet and join operations being AND and OR. For example, we are used to thinking of the expression p AND q as being true if p is true and q is true. But what if we have four values: {}, {T}, {F} and {T,F}? The Hasse diagram tells us how to interpret expression like this - p AND q is the meet (greatest lower bound) of p and q, and p OR q is the join (least upper bound) of p and q. So for example, {F} AND {T} = {F} {F} OR {T} = {T} {F} AND {} = {F} {F} AND {T,F} = {F} {F} OR {} = { } {F} OR {T,F} = {T,F} {T} OR {T,F} = {T} {T} OR {} = {T} { } OR {T,F} = {T} // I think..! { } AND {T,F} = {F} { } OR { } = { } { } AND { } = { } The Hasse diagram in the article makes sure that expressions like this agree with our intuition in the cases where we have intuition for what the result should be, and give us a way to interpret expressions consistently when our intuitions fail us. We're used to seeing Hasse diagrams for subsets of a set S used to indicate inclusion, in which case you would have {} < {F}, but you can have a valid poset structure that's not based on inclusion.
• tel 12y ago
  If you only want to go partway to catuskoti, consider the intuitionistic logic of Heyting and Brouwer. This is the actual form of logic which has the Curry-Howard isomorphism with lambda calculus. In particular, it rejects PEM but not PNC. What does this world feel like? Well, let's assume we've formulated a proposition. In type theory syntax we'd write the body of the proposition `B` and give it a name `p` like so p : B Here p is just a symbolic name and B is some formal language expression which describes the proposition p. It's important to note that while we've immediately written this proposition but we've not established whether it is true or false. PEM would imply that the state we are in currently is unstable—p must be either true or false already! Intuititionistic Logic, however, admits that the state of almost all propositions is far closer to what p is now—neither proven nor refuted. This neither-true-nor-false state is natural and only through a process of communication and work can we move forward. For instance, we could construct a proof of p p : B p = proof1 -- note how this looks like a typed program now or we could construct a proof of its refutation notp : not B notp = proof2 But we might be incapable of either. It is unclear whether a program searching through the space of possible proofs would ever terminate, one might note. What's immediately nice about this system is that it can model internally the notion of an independent statement—all statements are assumed independent until proven otherwise even! It also reflects the nature of (functional) programming (of a certain style) where we define the type we're hoping to achieve and then work to create a program satisfying that type. Note finally that Intutionistic Logic still holds that PNC is true. In particular, we can trivially prove the following proposition notPNC : forall prop . not (prop AND not prop) notPNC = /\_ -> \(p, np) -> np p -- this is a legitimate proof term written in (System F) lambda calculus
• tel 12y ago
  Central to his teachings is the view that things are ‘empty’ (sunya). This does not mean that they are non-existent; only that they are what they are because of how they relate to other things. Immediately I thought of Category Theory as this statement is a not terrible expression of what CT tries to teach. I'll immediately recommend the paper Numbers Can Be Just What They Have To (http://www.cwru.edu/artsci/phil/NumbersCanBeJustWhattheyHaveTo.pdf http://www.cwru.edu/artsci/phil/NumbersCanBeJustWhattheyHave...) for more exploration. Briefly, while CT is usually "bootstrapped" off having a notion of objects and their relations, it becomes quickly obvious that focusing on the objects themselves is useless—they are given no emphasis in CT and thus wither away to being nothing at all. Instead, absolutely every interesting property of the objects must be expressed in the relations they take with other objects. This is formalized in the Yoneda Lemma which, in a not terrifically generalized form, can be written forall a . (forall r . (a -> r) -> r) <-> a which is to say "the collection of all ways to relate an object to other objects is isomorphic to the object itself". So what's the point? Well, as the paper linked above suggests, sometimes the "intrinsic nature" of things makes them very difficult. We'd often like to equate two things which "ought to be the same" but aren't because their intrinsic nature differs. If you work in standard mathematics (set theory) you run into this problem because everything is described as having an intrinsic nature derived from sets. If you work in CT-based math you have no such issue because objects fail to have intrinsic natures altogether. They only have their "extrinsic" natures, their relations to other things.
  • wfn 12y ago
    Ahh, very nice. While at it: here's a very nice etymological explanation of why the Ubuntu-Yoneda lemma is called the Ubuntu-Yoneda lemma: https://golem.ph.utexas.edu/category/2013/03/spivak_on_category_theory.html#c043578 https://golem.ph.utexas.edu/category/2013/03/spivak_on_categ...
    • tel 12y ago
      Haha! That's great! I'm going to keep that in mind from now on.
  • dietrichepp 12y ago
• logicchains 12y ago
  The logic of Buddhist philosophy: emotional attachment to and/or desire of impermanent things has the potential to result in dissatisfaction, as impermanent things are impermanent. It's hardly rocket science. Desire nothing, and you'll never never feel the dissatisfaction of not getting what you want. Be attached to nothing, and you'll never feel the pain of losing something. Some quotes by emperor Marcus Aurelius, of the Stoics, expressing a similar idea: "You have power over your mind - not over outside events. Realize this, and you will find strength." "If you are distressed by anything external, the pain is not due to the thing itself, but to your estimate of it; and this you have the power to revoke at any moment."
  • xmonkee 12y ago
    This is a rather gross oversimplification. What you state is true, and is in fact the essence of the first 2 noble truths, but that's hardly the meat of "the logic of buddhism". The hardest attachment is that to the self, and the hardest realization is that the self itself is impermanent. To have the "right view" of the self, one has to understand the illusory nature of phenomena and the paradoxial nature of awareness itself. Awareness, is one of those things about which none of the following can be said: 1) that is exists, 2) that is doesn't exist, 3) that is both exists and doesn't exist, and 4) that is neither exists nor doesn't exist. Buddhism is very simple, but at the same time it can take "many lifetimes" to achieve true understanding of it.
    • logicchains 12y ago
      The illusory nature of the self can also be explained relatively simply to anyone who's familiar with the justification problem[1]. What 'is' the self and what 'is not' the self? That requires a metric for deciding. But that metric in turn requires another metric to determine its validity, and so on ad infinitum. The concept of self is thus arbitrary, and hence logically meaningless. Wittgenstein expresses this idea far better than I do here, in his Tractatus[2]. This equally applies to all phenomena; any attempt to divide anything up into 'things' is ultimately arbitrary, as it relies on ultimately unsubstantiated metrics, and hence is without meaning. 1. http://en.wikipedia.org/wiki/Regress_argument http://en.wikipedia.org/wiki/Regress_argument 2. http://philosurfical.open.ac.uk/tractatus/tabs.html http://philosurfical.open.ac.uk/tractatus/tabs.html
• wpietri 12y ago
  Very interesting. It reminds me that I think an early start on programming made some Buddhist concepts easier for me to get. In particular for me there's a strong connection between using software to model the world and the Buddhist doctrine of emptiness, the notion that nothing exists in its own right: https://suite.io/matthew-bingley/1z8s2kx https://suite.io/matthew-bingley/1z8s2kx I started coding young, and over time I gradually came to see that any computational representation of the world was always false. The act of writing software was always an editing of the real world, a discarding of everything that wasn't apparently material to my particular purpose. Changing software was sometimes a recognition of ignorance or fallibility, but often showed me how changing purpose changed what the maximally useful model was. Years of that experience, combined with things like Douglas Hofstadter's work, made the apparent contradictions of Zen much easier for me to follow. I think that also primed me to be ready for the Agile movement. Early on, I had strong BDUF tendencies. But once I gave up believing that there was one right model, one right design, I lost my taste for BDUF. So when people claimed we could keep our software as flexible as our understanding, that was very exciting for me.
  • dj-wonk 12y ago
    In my experience, I have found that in some key Buddhist works that the apparent contradiction is a literary device for learning. I don't think that contradictions are intended to persist and represent a "finished" philosophy.
    • wpietri 12y ago
      Hm. I've seen some of that, for sure. But for me the contradictions also point out the long-term weakness of taking conceptual frameworks too seriously. Our conceptual models of the world, like our software models, are temporary structures that we use for particular purposes. Eventually, we throw them all away. The map is not the territory, and there is no perfect map, just the right one for the moment. Thus it is reasonable for Buddhists to advocate the end of Buddhism. E.g.: http://www.shambhalasun.com/index.php?option=content&task=view&id=2903Itemid=247 http://www.shambhalasun.com/index.php?option=content&task=vi...
• shawndumas 12y ago
  An "abhorrence of contradiction" is necessary for him to even begin to express his having eschewed his former "parochialism". To have said, "abhorrence of contradiction" he has demonstrated an abhorrence of contradiction -- in the very act of making his declaration. The Principle of Non-Contradiction (PNC) means that every word in the sentence "The line is straight" has a specific meaning. 'The' does not mean 'any', 'all', or 'no'. 'Line' does not mean 'dandelion' or 'doughnut'. 'Is' does not mean 'is not'. 'Straight' does not mean 'white', or anything else. Each word has a definite meaning. In order to have a definite meaning, a word must not only mean something, it must also not mean something. 'Line' means 'line', but it also does not mean 'not-line' — or 'dog', 'sunrise', or 'monkey'. If 'line' were to mean everything, it would mean nothing; and no one, including him, would have the foggiest idea what he means when he says the word 'line'. PNC means that each word, to have a meaning, must also not mean something. And so; anyone who argues against an "abhorrence of contradiction" must use PNC for that statement to even mean anything, thus undercutting his own argument. ---- "There exist, indeed, certain general principles founded in the very nature of language, by which the use of symbols, which are but the elements of scientific language, is determined. To a certain extent these elements are arbitrary. Their interpretation is purely conventional: we are permitted to employ them in whatever sense we please. But this permission is limited by two indispensable conditions, first, that from the sense once conventionally established we never, in the same process of reasoning, depart; secondly, that the laws by which the process is conducted be founded exclusively upon the above fixed sense or meaning of the symbols employed." —George Boole, An Investigation of the Laws of Thought
  • dllthomas 12y ago
    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 everything provable - but we're dealing with nontraditional logics that may have other ways of dealing with that.
    • 12y ago
• javert 12y ago
  His argument is self-defeating. Ultimately, it amounts to: "There is no such thing as truth." But that is a statement about the truth. The law of noncontradiction is one of several axioms that are presupposed by any proposition. Such axioms can't be "proven," because any proof would presume their correctness, but it is proper to accept them.
• simondedalus 12y ago
  nagarjuna's point is not that contradiction or many-valued logic can be tolerated. nagarjuna, who is addressing a specific set of buddhist logicians, is finding paradoxes in logic in an attempt to break those logicians clinging to logic, and (somewhat presciently in the history of buddhism) suddenly enlighten them. he, like most buddhists, is not making any ontological or metaphysical claims whatsoever. it's similar to kant's antimonies. he is not trying to assert contradiction exists, he is trying to point out why we need to countenance ideas like a distinction between noumina and phenomena. or like zeno's paradoxes, which have a rhetorical purpose: to confirm zeno's teacher parmenides's claim that the universe is one undifferentiated whole. see also plotinus, who does roughly the same thing (any real ontological difficulty posed by the paradox of plurality is uninteresting to them; they have a thesis and their statement of the paradox is for a purpose). incidentally, i don't mean to slag graham priest too much. after all, j.c. beall was my logic professor, and i'll always fondly remember how he introduces every new step in a proof by saying, slowly, "now holllld on, what about (etc)." the dialetheists will always hold a place in my heart. that said, i think godel did about all that need be done with the liar's paradox, and we ought to be wittgensteinians regarding language in the first place (words mean what they do in virtue of their being used by agents for a purpose; you cannot fully enumerate representational content of an utterance solely in virtue of its shape. all utterances are context sensitive. for more, see the almost unreadable but spot on work of charles travis, e.g. unshadowed thought). http://www.thezensite.com/ZenEssays/Nagarjuna/Nagarjuna_and_Skillful_Means.htm http://www.thezensite.com/ZenEssays/Nagarjuna/Nagarjuna_and_... http://homepages.uconn.edu/~jcb02005/ http://homepages.uconn.edu/~jcb02005/ http://www.amazon.com/Unshadowed-Thought-Representation-Language/dp/067400339X http://www.amazon.com/Unshadowed-Thought-Representation-Lang...
• personZ 12y ago
  Fascinating essay. I enjoy and appreciate the references to Buddhist ("Eastern") philosophies given that the paradoxical thinking is what most of us attribute to it. What is the catch with Aeon? There don't seem to be ads, paywalls, subscriptions, or other monetizing strategies, but the content seems fantastic. Is it charitable intellectualism?
  • grifpete 12y ago
    I LOVE the fact that you can download to read later!
• doxcf434 12y ago
  It's interesting that the west would write off eastern philosophy, as though the eastern philosophers were unaware of the seeming contradictions and that there may be a deeper reason for that.
  • feralmoan 12y ago
    I think by extension of the Platonic school of thought Western culture has become deeply ingrained in dichotomous thinking applying such constraints to all areas of life (beyond simple science and logic), whereas Eastern non-dualism supposes all things (existentially) being equal. Neither West or Eastern philosophies do a very good job of describing each others domain space and yet they share many similar concepts. Karma (Theoretical) vs Causality (Empirical) is a basic example - they're exactly the same but few Westerners and particularly those in academic circles would admit to such a thing as it undermines Western status quo.
• Uncompetative 12y ago
  Well that was amazingly well-written and informative...
• gambiting 12y ago
  This made me think of an interesting way I have heard some people answer the question "if God is omnipotent, then can he create a rock so heavy he wouldn't be able to lift it and then lift it? If yes, he is not omnipotent, if no, he is not omnipotent!" with a logical leap also hard to comprehend to western minds - he can do both, and that's why he is considered omnipotent. He doesn't need to follow human logic, hence the third option - creating a rock too heavy to lift and lifting it. I am completely non-religious,but as a logical riddle it always fascinated me that there could be a "third" option.
  • dj-wonk 12y ago
    This isn't as hard as some people make it out to be. If God has to obey logic and/or other laws, then of course, there are some limitations to his power. Could a dictator decide to set up a Constitution and limit his own powers? Of course. Having absolute powers means having the ability to limit your future power.
  • thyrsus 12y ago
    A rock too heavy to lift would be a rock inside the event horizon of a black hole, if one can stipulate that the rock still "exists". My own attitude toward paradoxes concerning God is that understanding is a gift - awesome in its comprehension of the universe from big bang to Planck length scale interactions. Nonetheless, the understanding given to us as finite beings will be incomplete and approximate. If we avoid every other end, dementia will eventually remove what little understanding we have. I hold that rejection of the gift of understanding - e.g., the six day materialist biblical interpretation - is a grave error. Nonetheless, I hold that entities (or sets of relations) exist for which I will never have a consistent or correct rational model - and that one of those is God. Other instances are my fellow humans, and even myself. It should go without saying, ignorance does not preclude fascination with, delight in, nor love for those beings.
• weatherlight 12y ago
  I can't remember the last time I read an an article and it's discussion on HN that I enjoyed this much.
• logfromblammo 12y ago
  Silly Buddhists. Everyone knows that there are nine possible logic values: false, true, unknown, uninitialized, irrelevant, indeterminate, weak false, weak true, and high impedance. Didn't Siddharta read the IEEE 1164 standard?
• ableal 12y ago
  (Just a quick note, don't have time for more now.) "The great lodestar of the German Enlightenment, Immanuel Kant, said that there are things one cannot experience (noumena), and that we cannot talk about such things. He also explained why this is so: our concepts apply only to things we can experience. Clearly, he is in the same fix as Nagarjuna. So are two of the greatest 20th-century Western philosophers. Ludwig Wittgenstein claimed that many things can be shown but not said, and wrote a whole book (the Tractatus), explaining what and why." The jump from Kant to Wittgenstein elides the step that was Schopenhauer, who did look East and said some cogent things.
  • KrisAndrew 12y ago
    Wittgenstein would say that the Buddha and Schopenhauer were playing a quite similar language-game.
    • ableal 12y ago
      He might say that, but I think "language-game" is not quite the right take. Anyways, to shore up my impression I looked up "Schopenhauer eastern philosophy" and hit a few things. The "Schopenhauer and Buddhism" piece by Peter Abelson ( at http://ccbs.ntu.edu.tw/FULLTEXT/JR-PHIL/peter2.htm http://ccbs.ntu.edu.tw/FULLTEXT/JR-PHIL/peter2.htm ) seems good: "When the tenets of Buddhism became known in Europe during the third and fourth decade of the nineteenth century, Arthur Schopenhauer was delighted with the affinity they showed to his own philosophy. Having completed his main work Die Welt als Wille und Vorstellung as early as 1818, he considered it an entirely new (and thus pure) expression of the wisdom once taught by the Buddha." I would have been gladder if the original article, by a professional philosopher, which I am not, had said something about this.
• jotux 12y ago
  I'm going to go meta here and say the hn discussion here is just fantastic. This is the reason I frequent hn and I wish more submissions would spur discussions of this quality.
  • visarga 12y ago
    Yes, guys, where have you all come from? There is just tech and politics talk for months, and then suddenly, religion and philosophy pops out - and everyone is talking at a very high level. How come?
• anuraj 12y ago
  Sankara (8th century CE) talks about two types of truth - 1) Kevala Satya (Absolute Truth) and 2) Vyavaharika Satya (Relative Truth) - He also says that people who are not one with the Absolute truth (One with God - liberated) can only discern the Relative Truth. He called this state - Maya (illusion). Looks like he was talking similar to Gorampa. To be noted is Sankara was extremely knowledgeable about Budhist thought - and is often called Abhinava Budha (Neo Budha) and was instrumental in propagating Neo Hinduism based on Adwaita (Non Duality) defeating the Budhist schools of the day using their own arguments.
• EGreg 12y ago
  Do you think the Buddha borrowed some of his philosophy from the Stoics?
  • neuralk 12y ago
    Actually it would be the reverse, since Buddha predates stoicism. Though it is possible Buddha was partially influenced by pre-Socratic Greek thought and, in turn, later Greek philosophers were influenced by Buddhism (to put it in perspective, Socrates was roughly contemporaneous with Buddha).
  • orasis 12y ago
    Its very important to understand, that unlike most Western philosophers, the Buddha's philosophy came as a side effect of his meditation and realization. When you realize the non-dual nature of reality, that the split between subject and object is an illusion, your entire conception of reality changes radically. This realization, which is beyond concepts, allows the generation of ideas that are completely outside "normal" frames of thinking. This present moment is not conceptual, it is real.
• dpweb 12y ago
  Nature is to have no nature, taken literally that is a contradiction, but isn't it possible that is not meant to be taken literally, but to illustrate for instance that everything we hold dear is really just a construct. What we call "nature" isn't true essence but our interpretation of what we think essence is? Jesus for instance freely admitted he taught in parables, and so everything was not to be taken word for word literally. Doesn't make it any less true, but when interpreted literally you can come to some incorrect conclusions.
• zenogais 12y ago
  "An abhorrence of contradiction has been high orthodoxy in the West for more than 2,000 years." Not necessarily so, just a particular branch of western thinking and tradition now widely called the analytic tradition. GWF Hegel and Karl Marx had philosophies that deeply and profoundly embraced contradictions. Neither tried to abolish them, but instead to embrace them. To quote Marx in "Capital Volume 1": "This is, in general, the way in which real contradictions are resolved. For instance, it is a contradiction to depict one body as constantly falling towards another and at the same time flying away from it. The ellipse is a form of motion within which this contradiction is both realized and resolved" In other words, contradictions are not resolved but given room to move within forms. This was a move deeply influenced by Hegel, whose Logic embraced contradictions and sought to sublate them in higher forms.
  • vidarh 12y ago
    In Marx case - at least in your example - he is not using "contradiction" in a formal logic sense. He is using it in the sense of the contradicting forces of dialectical contradictions. Marx specifically used different terms when referring to contradictions of formal logic.
    • grifpete 12y ago
      Exactly. (just posted same point.) Even those 'dialectical contradictions' are perhaps better described as opposing forces that set in train a dialectical resolution.
  • grifpete 12y ago
    For all the talk of Marx as having a philosophy that embraced contradictions I am a little sceptical of the way that this is frequently represented. Hegel certainly did have a philosophy that embraced contradiction and Marx certainly drew from his system as a mode of expression but his work was rooted IN the world and the kinds of contradictions he pointed out where not logical contradictions but rather opposing forces that demanded resolution.
• deleted 12y ago
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• arh68 12y ago
  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 || < verity, falsity > ||. 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.
• wwweston 12y ago
  > If something is ineffable, i, it is certainly neither true nor false. Wouldn't it instead be the case that it's simply not expressible inside a given formalism (or other form of expression)?
  • wyager 12y ago
    That is absolutely the case. If something is "ineffable", it's probably logically ill-defined, and we should treat anyone who tries to use something "ineffable" in formal argument as a mystic spouting hogwash.
    • muhuk 12y ago
      This seems like a valid argument to me. Could one of the downvoters perhaps care to point out the errors in it. Or is it just because of the word 'hogwash'?
      • wyager 12y ago
        I'm very concerned at the number of people on HN who seem to have bought into this religious mysticism disguised as math. That's one of the oldest tricks in the book.
        • muhuk 12y ago
          But logic is subjective and reason is impotent. What is the purpose of philosophy other than to protect us from acquiring knowledge about reality? We'd be defenseless without faith and mysticism.
    • orasis 12y ago
      This present experience is ineffable. Is this present experience hogwash?
• wyager 12y ago
  How the hell are there this many people here who buy this hogwash? >Nagarjuna often runs through the four cases of the catuskoti. In some places, moreover, he clearly states that there are situations in which none of the four applies. They don’t cover the status of an enlightened person after death, for example. Are you kidding me? This article isn't even about formalizing non-boolean logic. It's thinly veiled religious propaganda, artificially ascribing mathematical formality to a mystical religion. And yes, statements are either true or false. If you can't say a statement will be either true or false (you don't have to know which one), the statement is ill-defined. Non-binary logical systems are useful only insofar as they allow us to model uncertainty, not because they reflect the nature of reality.
  • muhuk 12y ago
    "The truth or falsehood of all of man’s conclusions, inferences, thought and knowledge rests on the truth or falsehood of his definitions." - Ayn Rand
• transfire 12y ago
  It is amazing how tangled men can get in their own thoughts and words. The concept of ineffable is nonsense from the outset. By the definition given, if something were truly ineffable, not a word has been spoken about it. What is being contorted here is the difference between the limitations of words to describe an experience, which is the Buddhist ineffable, and the idea of the unassailable noumena, which is the Reality that might be outside of any experience we can have. There is also nothing mysterious or limiting about Western logic. A statement is either true or false; or it is a contradiction (which generally means a premise was false), or indeterminate (which simply means that no one knows which it is).
• smithy44 12y ago
  Could the 'easterners' point be the avoidance of reification and the limitation and mental trapping that involves? For example, we say we see a tornado. But there is no essence of the tornado, no 'thing' there.. it is a perceptual grouping of a set and series of events. Nevertheless, functionally there very much is a tornado. 'It' has its conditions, states, and results. (But there is only the wind...) (And in some visions of physics, this goes all the way down to the vacuum.) Renaming for clarity of action is useful, but no new substances are generated by the act. (One doesn't have to think in terms of the objects in someone else's code nor in terms of the lumped matter discipline.) So if one can think outside of the perceptually given externally, how much more so might it be useful to do so in relation to internals, i.e. 'my anger'.
• vram22 12y ago
  Interesting thread, though I could not understand all of it (tongue in cheek). I'm going to lighten up the mood a bit by posting this link to a blog post I wrote a while ago - Bhaskaracharya and the man who found zero: http://jugad2.blogspot.in/2010/06/bhaskaracharya-and-man-who-found-zero.html http://jugad2.blogspot.in/2010/06/bhaskaracharya-and-man-who...
• grifpete 12y ago
  The bizarre states uncovered by quantum mechanics resulted in a million popular works trying to distill quantum reality into a world in which multiple states could coincide even at the macro level. We know that this is true at quantum scale, it has been a little harder to swallow at the level of everyday reality.
• funky_lambda 12y ago
  Does anyone know any good books with similar stuff in it?
• e12e 12y ago
  Very interesting article -- I'm only surprised Gödel didn't make an appearance.
• novalis78 12y ago
  That's quite fascinating - reading the Pali canon as a teenager I got so used to the catuskoti.
• novalis78 12y ago
  Its strange that he brings Nagarjuna in when discussion sunnyata as this was already clearly spelled out in the sutta's themselves. Two books that discuss this very well are http://www.amazon.com/Concept-Reality-Early-Buddhist-Thought/dp/9552401364 http://www.amazon.com/Concept-Reality-Early-Buddhist-Thought... and http://www.amazon.com/The-Magic-Mind-Exposition-Kalakarama/dp/9552401356 http://www.amazon.com/The-Magic-Mind-Exposition-Kalakarama/d...
• dj-wonk 12y ago
  I can appreciate the depth of research behind the article. The many-valued notions of logic are quite helpful. Here's are two ways that I would distill the message for different audiences. 1. A computer science audience: Not all sentences have a computable boolean truth value. Here's why. To find the truth value of the sentence "This sentence is false.", you have to figure out the truth value of the following statement (call it X1): "Whether or not this sentence is false depends on if X1 is true or false." Put that way, you can immediately see the circularity in computation. From a computer science perspective, there is no terminating condition. The function will never complete, so there is no computable boolean truth value. 2. To an educated, but non-technical, audience: Just because a sentence asserts something doesn't mean there is any guarantee of the result being "truth" or "falsehood". The truth value of this "This sentence is false." is simply "undecidable" or "ineffable" -- pick a word. So, just live with the fact that not everything is true or false. Note: I'm not saying that the statement is really one or the other but we just can't figure out which (as in Schrödinger's cat); I'm saying that neither "true" or "false" makes any sense for that kind of self-referential sentence. This really isn't mind-blowing. Many articles write up these "paradoxes" as if they are insurmountable. They aren't. All of this said, I think many philosophical writings, especially Buddhist writings, use contradiction as way of promoting thinking and careful decomposition of the essence of things. In short, complex things consist of parts that vary over time. So their components or transient values can seem to change or stand in contradiction. There is no contradiction in Dickens writing "It was the best of times and it was the worst of times." in my opinion. This is just a literary device to show contrast eloquently, because saying "In some regards, it was the best of times. In other regards, it was the worst of times." is not as memorable or striking.
  • abandonliberty 12y ago
    They like to make things seem as complicated as possible. It's like Aeon writers get paid by the word.
  • virtualwhys 12y ago
    > In short, complex things consist of parts that vary over time. So their components or transient values can seem to change or stand in contradiction. Forgot something, one's self is also transient. Given that the observer itself is constantly changing, mind blowing is possible.
• jqm 12y ago
  This is an awesome article. So much of our daily life in the west rests directly on fundamental assumptions we make about reality. I believe it's mind expanding to have those base assumptions challenged from time to time.