• TheMadFool
    10.8k
    1. P; that is being.
    2. not P; that is not being.
    3. P and not P; that is being and that is not being.
    4. not (P or not P); that is neither being nor that is not being.

    These four statements hold the following properties: (1) each alternative is mutually exclusive (that is, one of, but no more than one of, the four statements is true) and (2) that all the alternatives are together exhaustive (that is, at least one of them must necessarily be true)
    — Wikipedia

    I first encountered the Catuskoti as Buddhist Nagarjuna's tetralemma. As the quote above states, given any proposition P only one of the 4 of the tetralemma will obtain and together they represent every possible "state" for P.

    If I were a skeptic, I would suspend judgement on every proposition made to me and made by me. In other words I would, if a true skeptic I am, negate all four component "states" for a given proposition P. To a skeptic given a proposition P, the following will describe his/her position:

    1. Not P
    2. Not Not P
    3. Not (P And Not P)
    4. Not Not (P Or Not P)

    Note that Nagarjuna's Not seems to possess a different meaning than the usual defintion of negation in first-order logic. By way of a clarification, Nagarjuna's Not doesn't, in fact can't, conform to the double negation rule: Not Not P = P. If it did then it leads to a contradiction. Does anyone have any idea regarding this point?

    Pyrrho the skeptic would've found Nagarjuna's tetralemma very useful, no?

    I seek your counsel.
  • Gregory
    3.7k
    Pyrrho doubted that he doubted, and so verged on relativism. I am not sure this is where the Tetralemma leads.
  • Wayfarer
    13.1k
    It was never put in those dry scholastic terms in the early Buddhist texts. Here is the origin of this whole thing: note how simple it is.

    Then the wanderer Vacchagotta went to the Blessed One and, on arrival, exchanged courteous greetings with him. After an exchange of friendly greetings & courtesies, he sat to one side. As he was sitting there he asked the Blessed One: "Now then, Venerable Gotama, is there a self?"

    When this was said, the Blessed One was silent.

    "Then is there no self?"

    A second time, the Blessed One was silent.

    Then Vacchagotta the wanderer got up from his seat and left.



    https://www.accesstoinsight.org/tipitaka/sn/sn44/sn44.010.than.html

    This was then developed into the principle that to say of (self and world, i.e. 'everything') 'it exists' is the 'error of eternalism'. To say of [...] 'it does not exist' is the error of nihilism. Instead, the task is to understand 'dependent origination' which is the means by which 'self and world' arise in the first place. But that, in turn, requires intense meditative absorption (samadhi). So it's not simply dry logical syllogisms.
  • Gregory
    3.7k


    I see the four corners as mind expanding, not dry
  • Wayfarer
    13.1k
    Sure, but expressed in syllogistic form, it is pretty scholastic. Agree that underlying insight is vital.

    Pyrrho the skeptic would've found Nagarjuna's tetralemma very useful, no?TheMadFool

    You know about Pyrrho and India, right?
  • Pfhorrest
    4.6k
    In classical logic, the latter two options are not possible, and also are equivalent: not(P or not-P) = (P and not-P) = FALSE

    In paraconsistent logics, something like (P and not-P) is permitted, in a sense, but not anything not(P or not-P).

    In intuitionistic logics, something like not(P or not-P) is permitted, in a sense, but not anything like (P and not-P).

    I’m not aware of any true paraconsistent intuitionistic logics that would permit both, but I recently had a thread about a way that something like both could be accommodated at the same time, all while never actually giving up the principle of bivalence that governs classical logics:

    The use of these mood functions also facilitates something superficially resembling the motivations for non-classical types of logic such as paraconsistent logics and intuitionist logics, without actually abandoning the principle that differentiates classical logic from them: the principle of bivalence. The principle of bivalence is the principle that every statement must be assigned exactly one of two truth values, "true" or "false", no more and no less. Intuitionist logics allow for statements to be assigned neither of those truth values, while paraconsistent logics allow for statements to be assigned both of them at the same time.

    With these mood functions, similar things can be constructed without actually violating the principle of bivalance, because there is nothing strictly logically prohibiting it being the case that neither is(P) nor is(not-P), if for example P were some kind of descriptively meaningless statement; it is merely necessary, to preserve bivalance, that either is(P) or not(is(P)), but not(is(P)) doesn't have to entail that is(not-P). Similarly, there is nothing strictly prohibiting it being the case that be(P) and be(not-P), if for example there were some morally intractable situation where both P and not-P were required, and so any outcome was unacceptable; it is merely necessary, to preserve bivalence, that either be(P) or not(be(P)), but not(be(P)) doesn't have to entail be(not-P).

    Fleshing out the philosophical implications of things like descriptively meaningless claims and morally intractable situations is a topic for further discussion. But in any case a logic of this form is in principle capable of discussing things that are, in a loose sense, "both true and false" or "neither true nor false", without technically violating the principle of bivalence.
    Pfhorrest
  • Wayfarer
    13.1k
    Also see Graham Priest on Nagarjuna (Aeon Magazine).
  • Gregory
    3.7k
    If P is 70% true and 30% false, the laws of Aristotle are violated. I think this is what Hegel was after
  • TheMadFool
    10.8k
    for example P were some kind of descriptively meaningless statementPfhorrest

    This is interesting. Suppose there's a proposition P. According to Nagarjuna's tetralemma, there are 4 possibilities:

    1. P
    2. Not P
    3. P And Not P
    4. Not (P Or Not P)

    If you deny all 4 possibilities it means two things: 1. You're suspending judgement as regards P's truth/falsehood Or 2. P is meaningless (it has no truth value)

    In other words, to suspend judgement on the truth value of a proposition P = declaring proposition P meaningless.
  • TheMadFool
    10.8k
    eternalismWayfarer

    A conversation I had with a Buddhist:

    Q. Does the self exist?
    A. No!
    Q. Nihilism?
    A. No!

    Q. Does the self not exist?
    A. No!
    Q. Eternalism?
    A. No!

    As you can see, Buddhism is in the habit of negating all claims, much in the same way I suggested we do to qualify as a true skeptic.
  • TheMadFool
    10.8k
    Pyrrho doubted that he doubtedGregory

    That's mind-blowing. Any references that I can use?
  • Wayfarer
    13.1k
    A conversation I had with a BuddhistTheMadFool

    I did one of the 10-day Vipassana courses some time back.

    Rule no 1: no conversation.

    For very small windows of opporunity, you were allowed to talk to the supervising teacher about questions, doubts, discomfort (of which there was plenty) but never about 'philosophy'.
  • TheMadFool
    10.8k
    I did one of the 10-day Vipassana courses some time back.

    Rule no 1: no conversation.

    For very small windows of opporunity, you were allowed to talk to the supervising teacher about questions, doubts, discomfort (of which there was plenty) but never about 'philosophy'.
    Wayfarer

    :up: Meditation does wonders for the mind and body or so I hear. BTW thanks for the links
  • Gregory
    3.7k


    I got that information from the skepticism section on historyofphilosophy.net
  • TheMadFool
    10.8k
    I got that information from the skepticism section on historyofphilosophy.netGregory

    A gazillion thanks. :up:
  • TheMadFool
    10.8k
    Let's review the whole thing for clarity:

    The tetralemma as it stands:
    Only one but necessarily one of the following obtains for any given proposition P:

    1. P: I affirm P
    2. Not P: I Deny P
    3. P And Not P: I Affirm and I Deny P
    4. Not (P or Not P): Neither I Affirm P nor I Deny P [suggests that there's a third possibility]

    If, some say say Pyrrhonism does this, we reject all 4 possibilities the following happens:

    5. Not P: I Deny that I Affirm P
    6. Not Not P: I Deny that I Deny P
    7. Not (P And Not P): I Deny that (I Affirm P and I Deny P)
    8. Not Not (P or Not P): I Deny that I Neither Affirm P nor I Deny P [denies a third possibility]

    If Nagarjuna's "Not" is the standard negation we see in logic then, it leads to:

    9. Not P
    10. P
    11. P or Not P
    12. P or Not P

    Since the original tetralemma is a disjunction: 1 Or 2 Or 3 Or 4, it follows that denying the tetralemma yields:

    13. (P or Not P) Or (P or Not P) Or (P or Not P)

    The statement 13 simplifies to: P or Not. However, the tetralemma denies this: 4. Not (P or Not P) and that means there's a third possibility, neither P nor not P, and that possibility is: we don't know anything about P's truth value, something that's dear to a true skeptic's heart.

    Does this make sense?
  • TheMadFool
    10.8k
    It was never put in those dry scholastic terms in the early Buddhist texts.Wayfarer

    An old thread I know but I think there's something interesting going on.

    Given any proposition p, there are 4 possible states it can be in, yes p, no p, yes p and no p, snd neither yes p nor no p.
    1. p (yes p)
    2. ~p (no p)
    3. p &~p (yes p & no p)
    4. ~(p v ~p) (neither yes p nor no p)

    Nagarjuna calls them the 4 extremes. He negates them all

    1. p: not p
    2. not p: not not p
    3. (p & ~p): not (p & not p)
    4. ~(p v ~p): not ~(p v ~p)
  • Banno
    13.5k
    An excellent example of Wittgensteinian Silentism.

    It only goes amiss when "developed into the principle that..."
  • Wayfarer
    13.1k
    From Wiki entry on the Buddhist ‘doctrine of two truths’:

    By and large, Kaccayana, this world is supported by a polarity, that of existence and non-existence. But when one sees the origination of the world as it actually is with right discernment, "non-existence" with reference to the world does not occur to one. When one sees the cessation of the world as it actually is with right discernment, "existence" with reference to the world does not occur to one.Wikipedia entry ‘Two Truths’

    The philosophical point is that ‘things’ don’t possess intrinsic reality or independent existence, because they arise due to a combination of circumstances. But they are not simply non-existent (‘like the horns of a rabbit’ in one of the traditional if whimsical metaphors). Their reality is conditional.

    I think - and I don’t know if I could back this up with any references - that there is actually some convergence with Parmenides on this point - where Parmenides says that ‘that which truly is, cannot not be, and that which is not, cannot come to be.’ Can you see the conceptual similarity?

    So the ‘polarity of existence and non-existence’ might be interpreted as follows - that ‘the world’ (i.e. most people) instinctively think that things either exist or don’t exist. But the nature of existence is that things don’t fall into either category - they’re not truly existent or totally real, in that if they were, they would be eternal, but not non-existent either.

    Another key term in Nāgārjuna is svabhava meaning ‘self-originated’ or ‘self-born’. This is usually expressed in negative terms by saying that no individual particular possesses svabhava. I think in later traditions such as the Buddha-nature teachings, Buddha nature is understood to exemplify what is self-born. But that is a rather technical subject.
  • Wayfarer
    13.1k
    it has to be understood what is being negated though. After all, Wittgenstein himself lectured and wrote, if he’d simply remained silent all his life, then we’d know nothing about him.
  • Banno
    13.5k
    The message shown by the Blessed One was clear. However the articulation of it, as given in the OP, is nonsense, as @Pfhorrest shows.
  • 180 Proof
    5k
    Given any proposition p, there are 4 possible states it can be in, yes p, no p, yes p and no p, snd neither yes p nor no p.
    1. p (yes p)
    2. ~p (no p)
    3. p &~p (yes p & no p)
    4. ~(p v ~p) (neither yes p nor no p)

    Nagarjuna calls them the 4 extremes. He negates them all

    1. p: not p
    2. not p: not not p
    3. (p & ~p): not (p & not p)
    4. ~(p v ~p): not ~(p v ~p)
    TheMadFool
    Yeah but, however 'judgment p' is sliced & diced, in principle, sufficient grounds are required to warrant any assent, doubt or dissent; otherwise, in practice, all propositional stances are just arbitrary (idle). This critical insight is usually / traditionally missed in discussions of Pyrrho (and, given his Indian influences, I assume 'sufficient grounds' is also a feature of Nagarjuna's tetralemma ... though I've not studied him or his "school" anywhere near enough to be confident about that). See Peirce (re: fallibility), Dewey (re: inquiry) & Witty (re: doubt) for further developments of 'non-relativist' 'non-antirealist' 'non-nihilistic' 'woo woo-free' skepticism.
  • Banno
    13.5k
    I wouldn't mind seeing something a bit more concrete than this obviously self-refuting edict.

    Have you a proper citation?
  • Wayfarer
    13.1k
    There’s a pretty good Wiki article here https://en.m.wikipedia.org/wiki/Similarities_between_Pyrrhonism_and_Buddhism

    Even proposes that the influence was from the Greek to the Indian sources, rather than vice versa, as is commonly assumed.

    There’s also a connection with scepticism and Husserl’s epoche, suspension of judgement concerning what is not evident. But it’s important to note this is not propositional but dispositional, i.e. concerned with fostering awareness of bodily and mental states, not with the judgement of abstract propositions.
  • TheMadFool
    10.8k
    Thanks for replying and I just want to pick your brain on what I think is a link, tenuous though it may be between Nagarjuna's approach and the Zen notion of Mu (Not)

    My understanding of Nagarjuna's tetralemma is sketchy at best but if it is what I think it is then, Nagarjuna (saint, scholar, philosopher) aims to create a state of mind very similar to the Zen Mu.

    An excerpt from the Wikipedia page on what Mu is:

    Some English translation equivalents of wú or mu 無 are:

    "no", "not", "nothing", or "without"

    nothing, not, nothingness, un-,

    is not, has not, not any

    Pure human awareness, prior to experience or knowledge. This meaning is used especially by the Chan school

    A negative.

    Caused to be nonexistent

    Impossible; lacking reason or cause

    Nonexistence; nonbeing; not having; a lack of, without

    The 'original nonbeing' from which being is produced in the Tao Te Ching.
    — Wikipedia

    That out of the way, take a look at what Nagarjuna says:

    For any given proposition p, there are only four possible truth states that can be viz.

    1. p (p is true)

    2. Not p (p is not true)

    3. p & not p (p is true and not p is true)

    4. Neither p nor not p (not p is true and not not p is true)

    Nagarjuna, if I read him correctly, wants us to refuse or deny all 4 possibilities. Let's take a proposition that you seem to be familiar with viz. the buddha exists after death. The conversation that takes place, as recorded in buddhiat texts I suppose, goes something like this:

    Assuming E = the buddha exists after death.

    1. E. No!
    2. Not E. No!
    3. E and not E. No!
    4. Neither E nor not E. No!

    In my humble opinion, this actually amounts to,

    1. Refusing to assign a truth value to E

    or

    2. Proposing a "third alternative" to the usual habit of thinking about propositions in a binary way: affirm or deny a proposition, nothing else is possible.

    Since our minds seem to deal only with propositions that have truth values, Nagarjuna's tetralemma by divorcing truth states (true/false) from propositions sentences maybe,

    1. suggesting that we look at sentences (utterances, written) not just as true/false/affirmation/denial but as something more than that if that even makes sense.

    2. proposing a third alternative to handling sentences i.e. there's one more, as of yet undiscovered (I'm not sure about this), way of comprehrnding sentences in addition to the two we're familiar with which are affirming and denying them.

    3. attempting to deliberately, for reasons unknown to me, drive a wedge between thoughts and mind. From the little that I know, the mind seems capable only of tackling sentences that can be affirmed or denied or only those whose truth values can be ascertained or, more to the point, assigned in ways that are unproblematic.

    Of course, there's fuzzy logic, paraconsistent logic, dialetheism, and other more exotic varieties of logic out there. Perhaps Nagarjuna's work anticipated these modern developments. I'm not certain.

    Nevertheless, denying every possibility for a proposition as Nagarjuna does manage, in an in-your-face kinda fashion, to make sentences, in a sense, unthinkable. This seems to square with the Zen practice of emptying one's mind of, well, thoughts otherwise known as Mu.

    Mind you, this is only a hunch, a tentative hypothesis about the link between Nagarjuna's tetralemma and Zen Mu and other ideas.
  • baker
    2.1k
    The way I see it, the point is to understand why a particular question is a wrong question. There are several reasons why a question can be a wrong question. A quick way to ascertain that is to look at one's intentions for asking it.

    Ven. Sāriputta said: “All those who ask questions of another do so from any one of five motivations. Which five?

    “One asks a question of another through stupidity & bewilderment. One asks a question of another through evil desires & overwhelmed with greed. One asks a question of another through contempt. One asks a question of another when desiring knowledge. Or one asks a question with this thought,1 ‘If, when asked, he answers correctly, well & good. If not, then I will answer correctly (for him).’


    https://www.dhammatalks.org/suttas/AN/AN5_165.html

    In the mind of an ordinary person, the five motivations, or at least the first four, tend to be intertwined, which results in confusion. Hence the importance of purification practices, thorough which one's motivations become streamlined.
  • baker
    2.1k
    Assuming E = the buddha exists after death.

    1. E. No!
    2. Not E. No!
    3. E and not E. No!
    4. Neither E nor not E. No!
    TheMadFool

    A buddha is impossible to define comprehensively (it is said that it takes a buddha to know one). Hence it is impossible to make definitive claims as to what a buddha is or isn't.
  • Gregory
    3.7k
    I wouldn't mind seeing something a bit more concrete than this obviously self-refuting edict.

    Have you a proper citation?
    Banno

    https://historyofphilosophy.net/sextus

    https://historyofphilosophy.net/pyrrho

    https://historyofphilosophy.net/skeptics-academy

    Those are the interesting videos I first heard of it in (not a perfect citation, sorry), but I've seen writers on this forum say that they doubt that they doubt. It's an attempt to break out of logic and find intuition. On a logic grid it's contradictory, but seen through a different way it might make sense. Intuition and logic are both important. "Intelligence is recognitive: it cognises an intuition, but only because that intuition is already its own." Hegel

    The Skeptics of Greece may have been using this kind of logic as a koan
  • Banno
    13.5k
    I've seen writers on this forum say that they doubt that they doubt.Gregory

    ...and your opinion of this view?
  • god must be atheist
    3.3k
    Also see Graham Priest on Nagarjuna (Aeon Magazine).Wayfarer

    Also see Covid Shaman on "Ganja to Marijuana" (Ibid, The Atlantic, Nov 14-65, vol 23, issue 22.).
  • Gregory
    3.7k
    ...and your opinion of this view?Banno

    I don't think doubting that you are doubting is healthy. People try lots of techniques to free their mind but I doubted that I doubted one time earlier this year behind a restaurant and logic seemed to slip away and spirituality didn't enter my brain so I don't have a high opinion of doubts anymore. Keeping a balance between faith and reason can be a problem sometimes but doubting as hard as Descartes leads to some ridiculous arguments
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