The logic of Buddhist philosophy

In case anyone is turned off by the expectation of wishy-washy flim-flam, it&#x27;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.<p>I assume that what&#x27;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&#x27;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.<p>In particular, you are not allowed to delete or duplicate elements&#x2F;propositions&#x2F;types (corresponding to physical processes that cannot arbitrarily create or destroy particles, the &quot;no deletion theorem&quot; and &quot;no cloning theorem&quot; of quantum information theory), so functions of the type<p><pre><code> duplicate :: a -&gt; (a, a) </code></pre> and<p><pre><code> delete :: a -&gt; () </code></pre> 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.

<i>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.</i><p>Immediately I thought of Category Theory as this statement is a not terrible expression of what CT tries to teach. I&#x27;ll immediately recommend the paper Numbers Can Be Just What They Have To (<a href="http://www.cwru.edu/artsci/phil/NumbersCanBeJustWhattheyHaveTo.pdf" rel="nofollow">http:&#x2F;&#x2F;www.cwru.edu&#x2F;artsci&#x2F;phil&#x2F;NumbersCanBeJustWhattheyHave...</a>) for more exploration.<p>Briefly, while CT is usually &quot;bootstrapped&quot; off having a notion of objects <i>and</i> 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 <i>the relations they take with other objects</i>.<p>This is formalized in the Yoneda Lemma which, in a not terrifically generalized form, can be written<p><pre><code> forall a . (forall r . (a -&gt; r) -&gt; r) &lt;-&gt; a </code></pre> which is to say &quot;the collection of all ways to relate an object to other objects is isomorphic to the object itself&quot;.<p>So what&#x27;s the point? Well, as the paper linked above suggests, sometimes the &quot;intrinsic nature&quot; of things makes them very difficult. We&#x27;d often like to equate two things which &quot;ought to be the same&quot; but aren&#x27;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 &quot;extrinsic&quot; natures, their relations to other things.

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&#x27;s ironic he refers to &quot;Western orthodoxy&quot; 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.<p>I agree with the sentiment, however, that understanding paradox is extremely important to a person&#x27;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&#x27;t think the lesson here is to &quot;break the chains of Aristotelian logic&quot; (God forbid) but rather, well, reconcile it with the idea of paradox.

I would have enjoyed this article if it dropped the Buddhism and kept the math.<p>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&#x27;t add new functionality, they add succinctness. So it&#x27;s really strange to me to frame them as <i>totally different philosophies</i>.<p>For example, it is the case that self-referential statements don&#x27;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&#x27;t solve the problem of self-reference (consider &quot;This statement is not {}, is not {false}, is not {true}, is not {false,true}&quot;).

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.<p>What does this world feel like? Well, let&#x27;s assume we&#x27;ve formulated a proposition. In type theory syntax we&#x27;d write the body of the proposition `B` and give it a name `p` like so<p><pre><code> p : B </code></pre> Here p is just a symbolic name and B is some formal language expression which describes the proposition p.<p>It&#x27;s important to note that while we&#x27;ve immediately written this proposition but we&#x27;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!<p>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><pre><code> p : B p = proof1 -- note how this looks like a typed program now </code></pre> or we could construct a proof of its refutation<p><pre><code> notp : not B notp = proof2 </code></pre> 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.<p>What&#x27;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!<p>It also reflects the nature of (functional) programming (of a certain style) where we define the type we&#x27;re hoping to achieve and then work to create a program satisfying that type.<p>Note finally that Intutionistic Logic still holds that PNC is true. In particular, we can trivially prove the following proposition<p><pre><code> notPNC : forall prop . not (prop AND not prop) notPNC = &#x2F;\_ -&gt; \(p, np) -&gt; np p -- this is a legitimate proof term written in (System F) lambda calculus</code></pre>

Very interesting.<p>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&#x27;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: <a href="https://suite.io/matthew-bingley/1z8s2kx" rel="nofollow">https:&#x2F;&#x2F;suite.io&#x2F;matthew-bingley&#x2F;1z8s2kx</a><p>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&#x27;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.<p>Years of that experience, combined with things like Douglas Hofstadter&#x27;s work, made the apparent contradictions of Zen much easier for me to follow.<p>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 <i>one</i> right model, <i>one</i> 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.

For the benefit of non-Hindi&#x2F;Sanskrit speakers: the pronunciation of &quot;catuskoti&quot; starts with &quot;ch&quot; (as in &quot;chat&quot;) and not as in &quot;cat&quot;. &quot;chaet&quot; is the prefix signifying &quot;four&quot;.

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.<p>If koti means corner, there is no reason that &#x27;koti&#x27; should appear in a translation instead of corner otherwise you are giving it a special importance that distracts from the text&#x27;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&#x27;t contaminate the purpose of a translation.

Henk Barendregt (known for his work in lambda calculus and type theory) has good explanation of the apparent contradictions in tetra lemma.<p>Buddhist Phenomenology - 1.7 Explaining apparent contradictions:<p><a href="http://www.cs.ru.nl/~henk/BP/bp1.html#SECTION00027000000000000000" rel="nofollow">http:&#x2F;&#x2F;www.cs.ru.nl&#x2F;~henk&#x2F;BP&#x2F;bp1.html#SECTION000270000000000...</a><p>In other words: And Now for Something Completely Different...

The logic of Buddhist philosophy: emotional attachment to and&#x2F;or desire of impermanent things has the potential to result in dissatisfaction, as impermanent things are impermanent. It&#x27;s hardly rocket science. Desire nothing, and you&#x27;ll never never feel the dissatisfaction of not getting what you want. Be attached to nothing, and you&#x27;ll never feel the pain of losing something.<p>Some quotes by emperor Marcus Aurelius, of the Stoics, expressing a similar idea:<p>&quot;You have power over your mind - not over outside events. Realize this, and you will find strength.&quot;<p>&quot;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.&quot;

This made me think of an interesting way I have heard some people answer the question &quot;if God is omnipotent, then can he create a rock so heavy he wouldn&#x27;t be able to lift it and then lift it? If yes, he is not omnipotent, if no, he is not omnipotent!&quot; with a logical leap also hard to comprehend to western minds - he can do both, and that&#x27;s why he is considered omnipotent. He doesn&#x27;t need to follow human logic, hence the third option - creating a rock too heavy to lift and lifting it.<p>I am completely non-religious,but as a logical riddle it always fascinated me that there could be a &quot;third&quot; option.

&quot;An abhorrence of contradiction has been high orthodoxy in the West for more than 2,000 years.&quot;<p>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 &quot;Capital Volume 1&quot;:<p>&quot;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&quot;<p>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.

nagarjuna&#x27;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.<p>it&#x27;s similar to kant&#x27;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&#x27;s paradoxes, which have a rhetorical purpose: to confirm zeno&#x27;s teacher parmenides&#x27;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).<p>incidentally, i don&#x27;t mean to slag graham priest too much. after all, j.c. beall was my logic professor, and i&#x27;ll always fondly remember how he introduces every new step in a proof by saying, slowly, &quot;now holllld on, what about (etc).&quot; 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&#x27;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).<p><a href="http://www.thezensite.com/ZenEssays/Nagarjuna/Nagarjuna_and_Skillful_Means.htm" rel="nofollow">http:&#x2F;&#x2F;www.thezensite.com&#x2F;ZenEssays&#x2F;Nagarjuna&#x2F;Nagarjuna_and_...</a><p><a href="http://homepages.uconn.edu/~jcb02005/" rel="nofollow">http:&#x2F;&#x2F;homepages.uconn.edu&#x2F;~jcb02005&#x2F;</a><p><a href="http://www.amazon.com/Unshadowed-Thought-Representation-Language/dp/067400339X" rel="nofollow">http:&#x2F;&#x2F;www.amazon.com&#x2F;Unshadowed-Thought-Representation-Lang...</a>

An &quot;abhorrence of contradiction&quot; is necessary for him to even begin to express his having eschewed his former &quot;parochialism&quot;. To have said, &quot;abhorrence of contradiction&quot; he has demonstrated an abhorrence of contradiction -- in the very act of making his declaration.<p>The Principle of Non-Contradiction (PNC) means that every word in the sentence &quot;The line is straight&quot; has a specific meaning. &#x27;The&#x27; does not mean &#x27;any&#x27;, &#x27;all&#x27;, or &#x27;no&#x27;. &#x27;Line&#x27; does not mean &#x27;dandelion&#x27; or &#x27;doughnut&#x27;. &#x27;Is&#x27; does not mean &#x27;is not&#x27;. &#x27;Straight&#x27; does not mean &#x27;white&#x27;, 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. &#x27;Line&#x27; means &#x27;line&#x27;, but it also does not mean &#x27;not-line&#x27; — or &#x27;dog&#x27;, &#x27;sunrise&#x27;, or &#x27;monkey&#x27;.<p>If &#x27;line&#x27; 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 &#x27;line&#x27;. PNC means that each word, to have a meaning, must also not mean something. And so; anyone who argues against an &quot;abhorrence of contradiction&quot; must use PNC for that statement to even mean anything, thus undercutting his own argument.<p>----<p>&quot;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.&quot;<p>—George Boole, An Investigation of the Laws of Thought

(Just a quick note, don&#x27;t have time for more now.)<p><i>&quot;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.&quot;</i><p>The jump from Kant to Wittgenstein elides the step that was Schopenhauer, who did look East and said some cogent things.

I can appreciate the depth of research behind the article. The many-valued notions of logic are quite helpful. Here&#x27;s are two ways that I would distill the message for different audiences.<p>1. A computer science audience: Not all sentences have a computable boolean truth value. Here&#x27;s why. To find the truth value of the sentence &quot;This sentence is false.&quot;, you have to figure out the truth value of the following statement (call it X1): &quot;Whether or not this sentence is false depends on if X1 is true or false.&quot; 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.<p>2. To an educated, but non-technical, audience: Just because a sentence asserts something doesn&#x27;t mean there is any guarantee of the result being &quot;truth&quot; or &quot;falsehood&quot;. The truth value of this &quot;This sentence is false.&quot; is simply &quot;undecidable&quot; or &quot;ineffable&quot; -- pick a word. So, just live with the fact that not everything is true or false. Note: I&#x27;m <i>not</i> saying that the statement is really one or the other but we just can&#x27;t figure out which (as in Schrödinger&#x27;s cat); I&#x27;m saying that neither &quot;true&quot; or &quot;false&quot; makes any sense for that kind of self-referential sentence.<p>This really isn&#x27;t mind-blowing. Many articles write up these &quot;paradoxes&quot; as if they are insurmountable. They aren&#x27;t.<p>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.<p>There is no contradiction in Dickens writing &quot;It was the best of times and it was the worst of times.&quot; in my opinion. This is just a literary device to show contrast eloquently, because saying &quot;In some regards, it was the best of times. In other regards, it was the worst of times.&quot; is not as memorable or striking.

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.

It&#x27;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.

I&#x27;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.

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&#x27;t Siddharta read the IEEE 1164 standard?

Could someone explain why Priest, in discussing the &#x27;four corners&#x27;, presents the Hasse diagram with {F} at the bottom? Why would it not be {}? I&#x27;m not too familiar with posets, but it seems the order matters, right?

Nature is to have no nature, taken literally that is a contradiction, but isn&#x27;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 &quot;nature&quot; isn&#x27;t true essence but our interpretation of what we think essence is?<p>Jesus for instance freely admitted he taught in parables, and so everything was not to be taken word for word literally. Doesn&#x27;t make it any less true, but when interpreted literally you can come to some incorrect conclusions.

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 <i>meaning</i> seems important, too. &#x27;2020 will be a rainy year.&#x27; does not have meaning (yet). Pretty soon, though, the universe will reach a certain point where that statement starts to accumulate verity &amp; falsity. Maybe 2020 will be a peak monsoon season in the Eastern Hemisphere; verity++. Maybe it&#x27;ll be a record drought in North America, too; falsity++. This is not a 1-dimensional spectrum.<p>Seems like meaning is some sort of vector norm over || &lt; verity, falsity &gt; ||. It should be easy to imagine scenarios all across this unit square for &#x27;2020 will be rainy&#x27;: (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.<p>This seems heavily reliant on <i>human interpretation</i>, but trying to extract &quot;intrinsic truthiness&quot; will always rely upon some global context telling you what the rules are. &#x27;2 = 3&#x27; is absolutely true, depending on what you think the rules are.<p>&#x27;Correctness&#x27; seems to correspond to (verity - falsity), which is why ( .9, .9) is certainly <i>meaningful</i> but doesn&#x27;t improve on the correctness of saying 2020 is rainy.<p>I have a haunting feeling GEB talks about this, though I never finished reading yet.

&gt; If something is ineffable, i, it is certainly neither true nor false.<p>Wouldn&#x27;t it instead be the case that it&#x27;s simply not expressible inside a given formalism (or other form of expression)?

&quot;The only correct view is the absence of all views.&quot; - Thich Nhat Hanh (Thay)

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&#x27;s works. <a href="http://kalaya.org/" rel="nofollow">http:&#x2F;&#x2F;kalaya.org&#x2F;</a><p>Unfortunately foreigners most of his work is in sinhala. And only foreigners learn that language is germans,russians,chines and japanes diplomats.

Could the &#x27;easterners&#x27; 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 &#x27;thing&#x27; there.. it is a perceptual grouping of a set and series of events. Nevertheless, functionally there very much is a tornado. &#x27;It&#x27; 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&#x27;t have to think in terms of the objects in someone else&#x27;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. &#x27;my anger&#x27;.

I can&#x27;t remember the last time I read an an article and it&#x27;s discussion on HN that I enjoyed this much.

How the hell are there this many people here who buy this hogwash?<p>&gt;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.<p>Are you kidding me? This article isn&#x27;t even about formalizing non-boolean logic. It&#x27;s thinly veiled religious propaganda, artificially ascribing mathematical formality to a mystical religion.<p>And yes, statements are either true or false. If you can&#x27;t say a statement will be either true or false (you don&#x27;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.

Its strange that he brings Nagarjuna in when discussion sunnyata as this was already clearly spelled out in the sutta&#x27;s themselves. Two books that discuss this very well are <a href="http://www.amazon.com/Concept-Reality-Early-Buddhist-Thought/dp/9552401364" rel="nofollow">http:&#x2F;&#x2F;www.amazon.com&#x2F;Concept-Reality-Early-Buddhist-Thought...</a> and <a href="http://www.amazon.com/The-Magic-Mind-Exposition-Kalakarama/dp/9552401356" rel="nofollow">http:&#x2F;&#x2F;www.amazon.com&#x2F;The-Magic-Mind-Exposition-Kalakarama&#x2F;d...</a>

Interesting thread, though I could not understand all of it (tongue in cheek). I&#x27;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:<p><a href="http://jugad2.blogspot.in/2010/06/bhaskaracharya-and-man-who-found-zero.html" rel="nofollow">http:&#x2F;&#x2F;jugad2.blogspot.in&#x2F;2010&#x2F;06&#x2F;bhaskaracharya-and-man-who...</a>

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.

This is an awesome article.<p>So much of our daily life in the west rests directly on fundamental assumptions we make about reality. I believe it&#x27;s mind expanding to have those base assumptions challenged from time to time.

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).

This is nice. I&#x27;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?

That&#x27;s quite fascinating - reading the Pali canon as a teenager I got so used to the catuskoti.

His argument is self-defeating. Ultimately, it amounts to: &quot;There is no such thing as truth.&quot; But that is a statement about the truth.<p>The law of noncontradiction is one of several axioms that are presupposed by any proposition. Such axioms can&#x27;t be &quot;proven,&quot; because any proof would presume their correctness, but it is proper to accept them.

Very interesting article -- I&#x27;m only surprised Gödel didn&#x27;t make an appearance.

Do you think the Buddha borrowed some of his philosophy from the Stoics?

Can some enlightened soul give me a TL;DR version of this text?? :D

Does anyone know any good books with similar stuff in it?

jaxytee: fyi, you are shadowbanned; there&#x27;s no contact info on your profile, and your previous comments suggest no reason for the shadowbanning.

Well that was amazingly well-written and informative...

Fascinating essay. I enjoy and appreciate the references to Buddhist (&quot;Eastern&quot;) philosophies given that the paradoxical thinking is what most of us attribute to it.<p>What is the catch with Aeon? There don&#x27;t seem to be ads, paywalls, subscriptions, or other monetizing strategies, but the content seems fantastic. Is it charitable intellectualism?

But the Law of Non-Contradiction does hold.<p>And it&#x27;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).<p>Moreover, to exist is to have a particular identity, to have a nature, to be something.<p>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.<p>If this kind of thinking were to get &quot;popular,&quot; 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).

This article is kinda missing the point. The &quot;empty&quot; 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&#x27;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.