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LINK The logic of Buddhist philosophy goes beyond simple truth | Aeon Essays

FTA: Buddhist thought, and Asian thought in general, has often been written off by Western philosophers. How can contradictions be true? What’s all this talk of ineffability? This is all nonsense. The constructions I have described show how to make precise mathematical sense of the Buddhist views. This does not, of course, show that they are true. That’s a different matter. But it does show that these ideas can be made as logically rigorous and coherent as ideas can be. As the Buddha may or may not have said (or both, or neither): ‘There are only two mistakes one can make along the road to truth: not going all the way, and not starting.’

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I read this when first released, excellent.


Calling the Mulamadhyamakakarika cryptic is an understatement, IMO, but I don't agree with the author's interpretation of the verse cited at the beginning of the article:

"The nature of things is to have no nature; it is their non-nature that is their nature. For they have only one nature: no-nature."

The author interprets this in the context of formal logic and the law of the excluded middle, but I think it's clear enough from Nagarjuna's argument that this isn't his subject. In fact he relies on more or less standard modes of logical argumentation in the text, even if it's obscured by technical language and the poetic form.

I don't think Nagarjuna is concerned with logic or epistemology as much as he is concerned with ontology. The first part of the text is all about the "essence" of things (or their nature, as rendered above: you can relate this to Greek concepts of ousia, to some extent). The point is not to challenge the law of non-contradiction, but to challenge the idea that "things" have some essential nature, that there is something like an "essence" of tree-ness that lies within all trees, and so on. The lack of essence is the foundation of the doctrine of Sunyata, and it gives rise to his later work on interdependent origination (pratityasamutpada).

In Garfield's translation and commentary ([], he puts it like this:

"For Nagarjuna and his followers this point is connected deeply and directly with the emptiness of phenomena. That is, for instance, when a Madhyamika philosopher says of a table that it is empty, that assertion by itself is incomplete. It invites the question, Empty of what? And the answer is, Empty of inherent existence, or self-nature, or in more Western terms, essence (svabhava). To say that it lacks essence, the Madhyamika philosopher will explain, is to say, as the Tibetans put it, that it does not exist "from its own side" -- that its existence as the object that it is -- as a table -- depends not on it, nor on any purely nonrelational characteristics, but depends on us as well." (p. 89, cf. the discussion of svabhava here: []

So, calling the nature of a thing "non-nature" is -- despite the poetic language -- not intended to suggest both a state of truth and falsehood of a proposition at the same time, it's just a rejection of essentialistic ontology.

The way I see it, being is a consequence of, an emergent property of, interrelationship of a certain complexity. In and of themselves, things have nothing to them. You can take apart a table, and eventually all you get are probability distributions. Mere whisps of thought, and even these have no real substance to them. Space itself bloomed out of an impossible nothing.

The dualistic split into observer and observed creates the interaction. The interaction creates the split. However, for all their fictional character, the amplitude of some of these distributions is rather high.


Actually ineffability is also a Christian thing (see early mystics and monastics). It's called apophatic theology, and it holds that God has no attributes, no features, and cannot be known by the mind. It is similar to the idea of Brahman in the Hinduism that influenced Buddha. Paradoxes in Eastern though refer to a nonlinear way of knowing, one that is achieved through meditation and right action. It doesn't have to be "math" to be valuable. That desire for logical coherence is a Western disease (scientism).

Orbit Level 7 Dec 11, 2018

As someone who studied logic it is a very interesting read but it didn't really convince me that it makes sense or is useful. The problem I have with it is that it takes natural languages and tries to somehow fit it into a logical structure, which is always possible even with things that make no sense. The way I find more useful is to first look what the language could be used for and then construct it logically - like we did with formal logic and math - and skip the step where we look at natural languages, because paradoxes necessarily follow from them because of the way they are constructed. Do we want to say something about the world? Then we need the principle of the excluded middle (PEM). Do we want to analyze paradoxes? Then we can construct systems which might help us without PEM.
But we always have to keep in mind, when we reason and try to find out if something makes sense at all we presuppose PEM. The author of this article makes sentences that are either true or false. He doesn't describe this "Buddhist logic" with Buddhist logic, but with classical logic in mind. In fact no logical system makes sense without it. So the meta language is always classical. That seals the deal for me.

Dietl Level 7 Dec 3, 2018

Perhaps PEM is both true and not true. PEM is also indeterminate and also undefined.

An assertion that is true in a particular logical system is one that does not contradict the other assertions within that system which were previously determined to be true. But also the assertion must be derivable from the assumptions of that system. If the assertion contradicts then it is false with respect to that system. If derivable and harmonious it is true with respect to that system. If it is derivable and not harmonious the system is kaput. If it does not contradict but is not derivable the assertion is undecided or indeterminate. The assertion could also be undefined or meaningless with respect to the system.

Under a lot of different systems an assertion can be classified in a lot of different ways. Is there a universal or ultimate truth? I don’t know.

This is what I am thinking in regards to the article, but I could be off course. In any event, I am not very confident about verbal logic as it is bandied about.

@WilliamFleming I am deeply sceptical of assertions saying something is both true and not true. In my view it is nonsense. We are always presupposing classical logic when we reason. Nothing makes sense if we assume it's basic inciples are false. Up is down, down is up, good is bad, bad is red, pink is 15. If we kick out the principle of non-contradiction how would you even say if a sentence follows from a system. It all, including the things you say in your second paragraph, relies on the notion of contradiction.


Assumptions underlie every logical system. Within a specific system an assertion is either true or false but there may be no way of finding out which. The assertion could also be meaningless or undefined as in your “pink is 15”.

But change the assumptions and a true statement might become false and vice versa. Or it could become undecided or meaningless.

In our ordinary everyday lives we take for granted a lot of assertions and think they are true, and they are true in the context of our personal realities. Many of those assertions are meaningless in the context of modern physics.

I acknowledge your point. It's a bit of an semantics issue how you want to categorize certain statements. It makes sense to use a logical system where you can deal with undecided or meaningless statements but I would never say a statement is both true and false at the same time. That's where the line is crossed for me. But I still think it is worthwhile thinking about what would happen if you throw out the most basic logical assumptions. So I see value in excercises such as these.


If nothing else it’s fun to talk about.

"I am deeply sceptical of assertions saying something is both true and not true."
Are you deeply skeptical of quantum mechanics, where that gets said all the time with wave-particle duality and Schrodinger cat?

Thing is that LEM only applies if you have a truly dichotomous system, a true black and white and nothing else, a true 0 and 1 and nothing else.

However, there are many systems that are not dichotomous and thus LEM cannot be applied. Simplest of these is the trinary logic which can take the form of true, false, and undetermined. Claims of religions for example follow this pattern with the question "gods exist" being true (theist), false (atheist), or undetermined (agnostic).

You obviously only have a shallow understanding of both quantum mechanics and formal logic.
"True and not true" doesn't get said all the time. What does get said is that something is in a superposition of being decayed and not being decayed. This is based on the usual interpretation of quantum mechanics but it still doesn't render classical logic obsolete. The underlying formal system to describe quantum mechanics also relies on classical logic.
If LEM applies to something specific or not only relies on the definitions you use and what you want your system to be able to achieve. For instance you can make a definition in classical logic where existence and non-existence at the same time is impossible and we can discuss if this definition is a suitable describtion of the world but with quantum mechanics in mind you see that this description might be called into question and then you just adjust your definition of existence or use other terms to describe what is going on. And this is exactly what is being done in quantum mechanics, without throwing out classical logic.
Of course you could also use a multiple-value logic to avoid any of those confusions but in my view this is quite inelegant and since we use classical logic for reasoning because of the way we evolved those confusions will arise anyways. Especially with people like you or Chopra running around who want to talk about a subject where they only have superficial knowledge. Even your example of the religious claims is a shallow explanation of what is going on. You have to recognize that there are different layers to this question. One is about the claim about the existence of a god and another is about the believes about the existence of a god. Once you understand this you will see the problem yourself without me having to spell it out for you, I hope.

RE: ad hominems

"You obviously only have a shallow understanding of both quantum mechanics and formal logic."
My physics PhD in theoretical particle physics begs to differ, but let's not let that get in the way of both of use exposing our POV. smile009.gif

"Especially with people like you or Chopra running around who want to talk about a subject where they only have superficial knowledge."
Again with the ad hominem? smile002.gif Again... physics PhD here and I'll show you twice how your views are not in line with physicist in the next section.

RE: Quantum Logic is NOT classical logic and doesn't use LEM

""True and not true" doesn't get said all the time. What does get said is that something is in a superposition of being decayed and not being decayed."
I can easily rephrase this to be true and not true. Using spin, I can ask if an electron's superposition state is spin up? By superposition, the answer is both true, it is in a spin up, and false, it is not in a spin up. Hence, the notion that quantum mechanics doesn't lend itself to LEM is proven once and I'll prove it again

"The underlying formal system to describe quantum mechanics also relies on classical logic."
Nope. It uses quantum logic which is not classical logic.
But don't take my word for it, here is 't Hooft and Birkoff, and von Neumann on the subject, all much more knowledgeable about QM tahn you or I:

quantum mechanics is generally considered to be fundamentally incompatible with classical logic, [source: Gerard 't Hooftl, Journal of Physics: Conference Series, Volume 361, conference 1]

The object of the present paper is to discover what logic structures one may hope to find in physical theories that, like quantum mechanics, do not conform to classical logic
[source: Birkoff and von Neuman, The logic of quantum mechanics, the annals of mathematics, vol 37, no 4, 1936]

RE: trinary logic and theology
"One is about the claim about the existence of a god and another is about the believes about the existence of a god. Once you understand this you will see the problem yourself without me having to spell it out for you"
Doesn't matter; trinary logic applies to both ontology (existence) or epistemology (belief). In both cases, you can have a case where I claim existence or belief (theist), where I claim non-existence or unbelief (atheist), or where I claim I neither existence nor non-existence, belief nor unbelief... I simply claim that there isn't enough justification or information to make any claim whatsoever (agnostic)

First of all, you are right. The ad hominems were unwarranted. I shouldn't have made assumtions about your knowledge or lack of knowledge even though I had my reasons. But you constructed a big strawman out of my comments. I did not say quantum logic IS classical logic, so a lot of what you are saying are moot points. If you read carefully what I wrote you will see that I said "relies on" and that classical logic doesn't get "thrown out". What I meant was - and I also pointed that out earlier - was that classical logic is the underlying structure we use to formulate any formal system. You need to construct the language by first defining your symbols and what constitues a meaningful expression and then you decide upon the rules which govern how the symbols are used how inferences are made and so on. All those things even for many-valued systems rely on you defining things and making up rules which you do with classical logic in mind. I didn't want to make my comments too technical but the point I'm making is a metalogical point not necessarily about the systems itself.
Next point, when describing quantum mechanics in a many-valued system you could call the state of having spin up in a superposition true and not true but this goes against what is meant by something being true. You are misusing the word 'true' from our natural language and apply it to something which it does not respresent. Of course, you can change definitions all you like but this is what I meant by saying that it is an inelegant solution. 'True' carries a meaning and it leads to confusions in a field that is already unintuitive and weird. So yes, I stand by my earlier comment that I'm deeply sceptical, especially since we are only talking about the Kopenhagen interpretation and not about many-worlds for instance.
Lastly, concerning logic and religion you are just wrong. There is no use for many-valued logic here, because it doesn't apply. This only involves statements which are either true or false. "Do you believe in God?" Either you have a belief or you don't. There is no third option here. A belief involves accepting a statement to be true. Either you do or you don't "Do you know that there is a God?" This question again is not a question about the existence of a being but about your knowledge. If you don't have a justification for your belief then you don't know it. To summarize, you can either be a theist (have a belief in god) or an atheist (don't have a believe in god) and you can be an agnostic atheist (you have no justification to believe in god and you don't believe in god), agnostic theist (you have no justification to believe in god but you still believe in god), gnostic atheist and theist.

RE: quantum v. classical logic
But the point is that quantum logic doesn't rely on classical logic at all. It fails the distributive property of classical logic: (p and (q or r) = (p and q) or (p and r) and it is a multi-variate system (hillbert space) unlike classical which relies on the distributive property and is a dual variate system, binary true and false. It is the dual variate nature of classical logic that allows LEM to be valid and the multi-variate system that makes LEM invalid.

RE: truth
I am using "true" correctly since it's the answer to a question. If I ask "is the electron spin up?" and it is true that correlates to a reading on a gauge, say 10 uT (purely made up btw). If I then ask "is the electron spin down", it is true if that value might correlate to -10 uT. However, if I get a value of +10, then it is not true that the electron is spin down and if I get a value of -10, it is not true that it's spin up.

The fact that it's in superposition means that I will get a value of 0 because, in gross terms, it's adding up the +10 to the -10... eventhough there IS no zero value for electron spin. Put another way, a single electron that can only be spin up (+10) or only spin down (-10) is not showing to be neither with spin zero. This is superposition. This is what it means to be true (+10) and not true (-10) at the same time. Experiments confirm this behaiviour so it's more than just a mathematical "trick" but actual honest to goodness phenomenology.

RE: theology
I don't know what to say here if you only accept a binary vision of theology. Much like our differences with Quantum Mechanics, if you are wed to the notion that a person either has to believe or not believe and there is no other possibility (much like many claim that an electron has to be spin up or spin down and there is no other possibility despite evidence to the contrary), then there is nothing that will convince you otherwise.

I disagree with a binary notion of belief and knowledge and live my life with the more advanced non-binary version. I live my life as an agnostic neither believing nor unbelieving, neither knowing or not knowing. That you say can't be so is clearly in conflict with what I, do every day, in every discussion on the subject.

RE: agnostic/gnostic atheist/theist
And I don't agree with an agnostic atheist either since they are basing a belief on non-existence not knowing... a stance I find epistemologically unsatisfying. Same with the agnostic theist... they are basing a belief on existence based on not knowing. This whole "atheism as belief" is a relatively new concept... started with Andrew Flew in 1972. It hasn't gained much traction in the philosophical world and only atheists (like american atheists) who want to profess belief even while admitting they don't have knowledge for that belief, have widely adopted that. Me personally, I find that distinction unsatisfactory...

RE: quantum v. classical logic
We have to agree to disagree here. The argument you give here doesn't really adress what I'm saying. It's a bit of a technicality so I understand if it's not easy to see the difference.
RE: truth
Saying that you are using it correctly doesn't make it so. But this is just semantics. If that's your definition of truth so be it. On your example you make an additional assumption. From "measuring a value of +10" it doesn't logically follow to "not also measuring a value of -10". This is a key misunderstanding of classical logic of yours. It can deal with things that are not black and white, this depends on your definitions and assumptions. When you have a shirt that is white, it doesn't logically follow that it is not also black. Look at this argument.

  1. The shirt is white.
  2. The shirt is black.
  3. Black is not white.
    Therfore: The shirt is white and the shirt is not white. (Contradiction)

This is probably the wrong argument that you have in your head. The problem lies in assumption 3. You interpret it like you can just exchange the term however you like but when you say "Black is not white" it is not clear what is meant. Either you mean "The color black is not the same as the colour white", which is a true statement. But there you should see that the argument doesn't hold anymore. Or you mean "Something being black implies that it is not white". Which is false but the only way to come to the wrong conclusion.
I'm not sure if I can be any clearer.
RE: theology and agnostic/gnostic atheist/theist
When using a language you should want it to represent reality in a clear way. That's why it would be important to use it in a consistent way and to make distinctions where necessary.
Let's imagine neurology advances to a point where we can read people's minds. Scientists measure a pattern in the brain that implies that the person believes in a god. Meaning if and only if the pattern is there a person believes in god. So the scientists either measure the pattern or they don't. The pattern is in the brain or it isn't. What do you think they would measure in your brain? Would the pattern be there or wouldn't it be? I hope you won't be arguing that in an agnostic's brain they would measure a superposition between the pattern being there and not being there because you know that that would be ridiculous, right?

"We have to agree to disagree here."
That's fine.
But please note that you are not disagreeing with me but with established physicsts who pioneered and established quantum mechanics. They have conclusively established, through experiments, that classical logic cannot be applied to results in the quantum world.

Thus I encourage you to read the papers I have cited above and further to google "quantum vs classical logic" to see how physicists and philosophers reject the notion of quantum logic relying on classical logic. (wikipedia, the stanford encylopedia of philosophy, and the internet encyclopedia of philosophy are all good resources on this subject)

"Therfore: The shirt is white and the shirt is not white. (Contradiction)"
You established in 1 that the shirt was white and you established in 2 that the shirt was black. Then by 3 you established that black is not white. Hence

1 X= a
2 X = b
3 a = - b
C X = -b and b


1 X = a and b
2 a = -b
C X = -b and b

Clearly in classical logic that is false because classical logic follow LEM and thus X cannot be both true ( b ) and false (-b) at the same time. This is precisely why quantum logic is not classical logic because an object can be true (spin up) and false (not spin up) at the same time; i.e. it doesn't follow LEM.

"From "measuring a value of +10" it doesn't logically follow to "not also measuring a value of -10""
But it does. The real numbers (i.e. measurements) do obey classical logic insofar as positive and negative are the only two options available. Thus if a number isn't positive, it must be negative. This is the same as the odd, even duality: if a number isn't odd, it must be even. LEM is present when speaking of the true dichotomy of positive/negative and odd/even in the real numbers.

Gonna split this up as these are two related, but distinct, conversations.

"So the scientists either measure the pattern or they don't"
We have to be careful with these hypotheticals. Whereupon you imagine a hypothetical where measuring one pattern identifies a person as a thiest and failing to find that pattern as an atheist... and thus there is no room for agnostics... I can imagine a completely different scenario.

They would measure one pattern for belief, say a sine wave. This would identify that person as a theist.
They would measure another pattern for non-belief, say a cosine wave. This would identify that person as an atheist.
They would measure yet another patter, say a square wave, if a person neither believes or doesn't believe,. This would identify a person as an agnostic (they could also get no measurement or measure random noise but my choice of a square wave will become clear below).

Let's take this out of the world of hypotheticals.
Let's ask a question and list the justification given for an answer, that question being "Do gods exist?"
If you were to answer "yes", you would list one set of justifications for why you think they do exist.
If you were to answer "no", you would list a different set of justifications for why you think they don't exist.
But, if you answer "I don't know", you would list a completely different set of justifications for why you don't know, from outright ignorance of the subject (hard agnosticism or ignosticism) to claiming that the data is inconclusive or unavailable right now (soft agnosticism).

Hence each position has it's own "pattern", that pattern being the justifications we give for our positions.

"I hope you won't be arguing that in an agnostic's brain they would measure a superposition between the pattern being there and not being there because you know that that would be ridiculous, right?"
Assume that the agnostic gives a square wave as per the discussion above.
According to Fourier decomposition, that square wave can be created as a superposition of sine (theist) and cosine (atheists). So no, not ridiculous at all if you are familiar with how superposition works.

And again, taking it out of hypotheticals, if the theist says they have convincing evidence for gods (sine wave) and the theist says they have convincing evidence for no gods (cos wave), an agnostic superposition (square wave) might look like the agnostic saying that neither evidence is convincing and thus doesn't accept either position.

Taking it out of theology, this is like one person saying that they are convinced you have a million dollars in the bank because you drive a nice car (theist), another saying that you don't have a million dollars in the bank because they've never seen you with a million dollars (atheist), and yet another saying they are not convinced that either argument is valid for claiming that you have a million dollars in the bank or not (agnostic)

That's the thing, I'm not disagreeing with what you or what the physicists are saying I'm disagreeing with how you interpret my words. You don't understand what I'm saying. I'm making a point and then you say something that does not adress my point.
In the rest of your comment you very clearly showed that you don't understand logic. I could explain all the fallacies, inaccuracies and misunderstandings again but I would just have to repeat points I already made that you just ignore. You would have to rigorously look at you own statements and try to find the hidden assumptions you are making but I see no willingness to do that on your part. I'm sorry, but you are wasting my time.

", I'm not disagreeing with what you or what the physicists are saying"
Then you agree that quantum logic doesn't rely on classical logic and that your previous claim was wrong because that is what I and the physicists are saying: quantum logic is non-classical logic.

After all, you can't say quantum logic relies on classical logic if quantum logic doesn't abide by the distributive property or LEM, two things necessary for classical logic and the point I and the physicists are making.
I don't think that is an interpretation of your words but rather a response to a direct quote from you.

"In the rest of your comment you very clearly showed that you don't understand logic."
This is a vacuous statement. It could be you that doesn't understand logic. Dunning-Kruger and all that. It could be that I'm completely correct and you lack the skill-set to understand why, especially since we are talking quantum logic and quantum physics, a field in which I spent many years getting my PhD in. Not everyone has that skill set and I get that.

Or I could be completely wrong but without your providing evidence to showcase my errors and allowing us to process that evidence together, none of us are the wiser.

Thus, why do you insist on judging my understanding instead of simply talking about my understanding even if you disagree with it?
Or simply walking away from the conversation if you don't want to talk about my understanding without making judgement upon it?

" I could explain all the fallacies, inaccuracies and misunderstandings again but I would just have to repeat points I already made that you just ignore"

If you could, you would. That you don't want to is another story entirely.

After all it's demonstrably true that I've not ignored ANY of your points as witnessed by my posting style of referencing exactly what you say and commenting on it... and I try and reference everything you say as my way of respecting you as my conversation partner in this discussion.
You may not agree with my response, and that is fine. But your accusation of my "ignoring" your points as a way to fuel your view of my not understanding logic is simply not true.

My reply did not take your second comment into consideration. I did not see it before posting. Here is my reply to that. You take my example and instead of answering you "imagine a completely different scenario". How is that not ignoriny my points?
"If you could, you would."
The thing is I already did. The refutation of your bad misreading of my shirt example is already in my comment. This is introductionary level logic and you say wrong things with great confidence like your "But it does" comment. When a sentence follows logically(!) from another it means it follows without any further assumptions. I say it doesn't logically follow and then you say "yes it does, with the following assumptions".
This is a conversation on a level I'm not willing to have anymore. You don't listen to what I'm saying and you make strawman arguments left and right. To continue with this madness for me would be having to repeat myself over and over again. Listen, I made all my relevant points if that is not enough to convince you I'm fine with that. It's not my duty to educate you on logic, you would have to do that yourself if you were willing.

You said you were skeptical of systems that do not use LEM.

I provided ample evidence that such non-classical systems exist in formal logic and are applicable to physics and theology and thus you need not be skeptical of them.

I can only lead your horse of skepticism to the river of evidence; I can't make you drink the water of truth.

You're killing me smile001.gif I really can't talk with someone like you. Maybe it's my fault but I don't have the patience. I feel like every sentence you write needs some major or minor corrections. But I don't want you to feel bad or think that I'm angry with you or something. All the things we discussed so far are really minor points. You're not arguing for eating babies being legalized or that there's a white genocide going on. So let stop here. I think you are wrong, you think I are wrong, maybe we both are. Maybe we are both wrong and not wrong. Doesn't matter. I still wish you a nice day!


That is a very interesting essay for me, and I am bookmarking it for future reference. The ideas merit further study.

I had to look up the word “ineffable”, but it is a familiar concept. Many questions or statements are simply meaningless from a higher perspective. Questions about immortality are ineffable because time is an artificial human construct.

“Is there an Ultimate Reality beyond the senses”? The question is grounded in our sensory world and has meaning only from that limited perspective. If I answer “yes”, all I am saying is that I don’t have the whole picture—that my perspective is symbolic only. Ultimate Reality is ineffable and can not be described, but I can make statements about my limited reality, or it seems that way to me. If I have been in a house with no windows all my life, it would seem logical to say, “These walls are the limit to my world. I know nothing of what is beyond, but I know there is a beyond. The beyond I define as that which is not contained by these walls”.

IMO the ego is a put-up job and we actually don’t exist in the way we think. Therefore any statement or question about ourselves has meaning only within our limited, symbolic reality.

Time has flown—gotta go.


Thanks for pointing out this article!

jerry99 Level 8 Dec 2, 2018
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