The four-cornered logic is often misunderstood resulting in confusion and controversy. So here I'd like to share my thoughts about it: nothing new, some of us may, esp. those who have been looking at it from the Madhyamika teachings of Nagarjuna and from a metaphysical standpoint, find it is devoid of the usual mental gymnastics and is less than esoteric. One usually finds only the teachings of Nagarjuna in any discussion that concerns tetralemma type logic. I quote here three discourses from the Pali, all three of which contain tetralemma and carry the very essence of the Buddha’s teachings.
Tetralemma (catu skoti, Sk.) is coined from the Latin words tetra (four times) and lemma(premise). It involves the enumeration of four propositions as opposed to dilemma, which has two propositions. In its most basic form it consists of an enumeration of four alternatives expressed positively as: A, not A, both A and not A, neither A nor not A. They may also be expressed negatively as minus A or negative A instead of positive A.
Suchness is suchness. There is no comparative; it is something that is beyond, so we would have to call it because it is beyond our reality, making it difficult to render an ontological characterization of it in the Western philosophical sense. If not, we could call it a different dimension in the normal sense of reality or emptiness or voidness or a medium - all of which refer to mental constructs that somehow refer to something which has a physical quantity, or magnitude, or proportion, or implies one of three Cartesian coordinates that determine a position in space, or which has none of all these. All of these are misnomers, perhaps, for want of a better word, like for instance nihil privativum. Suchness is a good attempt at describing something that cannot. It is a concept – one conceptualized - a product of the duality of mind, like emptiness as opposed to fullness.
Nihil Privatvum (nihil = nothing, privatvum = not existing) is a word for the ultimate reality, that has crept in from the Latin and originated from Greek. It is different tonihil negatum or nothing negative - to negate all exitents at the ultimate level – in Madhyamika Buddhism found by Nagarjuna and later in the Prasangika view in Tibetan Buddhism, which position however is not in disagreement with the sunyata, but a more detailed critique of the original concept of sunyata, which you will find later in my explanation of negative tetralemma.
Traditional laws of thought attributed to Aristotle and arguments against them have shaped Western philosophy over time. By strictly following these laws of thought we have sought to ground our thinking in clear and distinct ideas eliminating those ideas that are vague or contradictory. According to Classical laws of thought the four statements in tetralemma are incompatible with each other. Only one of them can be true.
In addition to the three classical laws of thought I have presented several other laws briefly, without going into too much detail. In presenting them here my intention is to contrast Western Philosophy, esp. the branch of metaphysics with tetralemma type logic used by the Buddha.
Metaphysics denotes philosophical enquiry of a non-empirical character into the nature of existence or in other words abstract theory with no basis in reality. Then there are also the laws of science that follow empirical analyses, none of which go as far as to find the concept of sunyata. This body of study is so vast that one could easily get lost in them and of one’s purpose.
Unlike the physicists today the Buddha was an empiricist. He used logic for reasoning. He concerned himself with things verifiable by observation, by perception and experience rather than theory or pure logic. And, he concerned himself with ending suffering, not finding proof to pure logic or theory, not to arrive at any Eureka moment. He did so not because he could not, as we have seen with his many responses to all those who challenged him, but just because it was an outcome of wrong reflection, a vain full exercise, that served no useful purpose. He went on to name ten useless questions (avyakatavatthuni) that do not warrant an answer as they are speculative views, and which bring suffering, serves no useful purpose (in the Aggivaccagotta Sutta) and not conducive to enlightenment.
The law of identity (A=A) –
The principle of identity tells us that A is A and B is B – in other words A is not in B and B is not in A and vice versa. Simply put a flower is a flower and the cloud is a cloud and the flower is not in the cloud nor can the cloud be in the flower.
The law of non-contradiction (A does not equal ~A) –
The law states that contradictory statements cannot both at the same time be true, e.g. the two propositions "A is B" and "A is not B" are mutually exclusive.
The laws of non-contradiction, along with its complement, the law of excluded middle (the third of the three classic laws of thought), are correlates of the law of identity (the first of the three laws). Because the law of identity partitions its logical Universe into exactly two parts: a "logical object" and everything else, it creates a dichotomy wherein the two parts are "mutually exclusive" and "jointly exhaustive". The law of non-contradiction is merely an expression of the mutually exclusive aspect of that dichotomy, and the law of excluded middle, an expression of its jointly exhaustive aspect.
The law of the excluded middle (either A or not A but not both A and ~A) - The law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is true, or its negation is. For example, if P is the proposition: Socrates is mortal. Then the law of excluded middle holds that the logical disjunction: Either Socrates is mortal, or it is not the case that Socrates is mortal, is true by virtue of its form alone. That is, the "middle" position, that Socrates is neither mortal nor not-mortal, is excluded by logic, and therefore either the first possibility (Socrates is mortal) or its negation (it is not the case that Socrates is mortal) must be true.
We are all too familiar with “To be or not to be…” the opening words of a soliloquy from Shakespeare’s Hamlet, a dilemma, used in situations in which a difficult choice has to be made between two or more alternatives, esp. ones that are equally undesirable. In logic it is an argument forcing an opponent to choose either of two unfavorable alternatives, neither of which is practically acceptable – “to be” or “not to be”.
A Syllogism is an instance of a form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises); a common or middle term is present in the two premises but not in the conclusion, which may be invalid (e.g. all dogs are animals, all animals have four legs, therefore all dogs have four legs) – in other words deductive reasoning as distinct from induction
Induction and Deduction –
Induction is an inference of a general law from particular instances. Often contrasted with deduction, the production of facts to prove a general statement – in mathematics – a means of proving a theorem by showing that if it is true of any particular case it is true of the next case in a series and then showing that it is indeed true in one particular case.
The law of sub-contrariety – The law of sub-contrariety explains a double negative that does not establish and stops short of a positive - the opposition of propositions – where both are not false but they could be true.
Parmanides Two propositions are said to be subcontraries if they cannot both be false, although they might both be true. Example: "Some philosophers are idlers.". What proposition is the same in quantity, but differs in quality? The particular negative or the O proposition does so: "Some philosophers are not idlers." This logical relation is called subcontrariety. In other words, I (idlers) and O (not idlers) are subcontraries of each other. What would happen if both the I and O statements could be false? If we were to draw a venn diagram we would find that if it were so then it would be an empty class! Or in other words both cannot be false. Now this comes very close to describing the concept of Sunyata.
The Philosophers Parmanides and Heraclitus are worthy of mention for their wisdom. They are the basis upon which Aristotlian thought is founded. They resonate of the laws of nature and of Buddhist thought. Heraclitus' work was a continuous treaties on nature according to Diogenes the 3rd Century biographer of Greek philosophers. Heraclitus after careful observation of the river became famous for his saying that no man steps on the same river twice, said to explain the ever-changing nature of the universe. But he was unable to see its sunyata nature. Parmanides was famous for his views on nature and reality and of worldly appearances based on the senses. He work is said to have influenced Plato whose student was Aristotle.
Where’s the Fire?
The Aggivacchagotta Sutta (MN72) [[[Bhikku]] Nanamoli & Bhikku Bodhi translation]) records of the Buddha’s response on being questioned extensively by a wandering acetic Vacchagotta if he held the view “After death a Tathagata exists; only this is true, anything else is wrong”. (here Tathagata refers to a being who has gone beyond, and refers to the Buddha). The dialogue runs thus (excerpt):
<poem> The Budhha in response: I do not hold the view that The Tathagata exists after death, and likewise replied to three other questions The Tathagata does not exist after death. The Tathagata both exists and does not exist after death. The Tathagata neither exists nor does not exist after death. And upon being questioned similarly if a bhikku’s mind once liberated through not clinging reappears [after death], the Buddha replied thus to a series of question: The terms reappear does not apply; If so then he does not reappear? The term does not reappear does not apply; Then he both reappears and does not reappear? The term both reappear and does not reappear does not apply; Then he neither reappears nor does not reappear? The term neither reappears or does not reappear does not apply;
As Vaccagotta was bewildered and confused the Buddha explained thus:
Vaccagotta: It burns dependent on grass and sticks.
Vaccagotta: I would.
The Buddha: When the fire were to be extinguished which direction did it go: to the east, west, north or south? Vaccagotta: That would not apply. The fire burnt in dependence of the grass and sticks and when it is used up, without fuel it is reckoned as extinguished. So the Buddha explained that likewise the Thathagata has abandoned material form and cut of all roots and is no longer subject to future arising.
What the Buddha makes clear is that existence (eternalism), non-existence (annihilationism), both, or neither, do not apply to the situation. By the Buddha saying merely that the flame is blown out he means that all roots are cut or the fires of greed, hatred, and delusion, all of which play a role in craving (which conditions repeated becoming) are cooled. Through Nirvana (blowing out, cooling), one leaves the fuel of craving behind, and thus extinguishes suffering for good.
Positive Tetralemma –
Both A and -A
Neither A nor –A
The view or belief in the self (existence) is one extreme thought and the belief in the non-self (non-existence) is another, both of which existed before the time of the Buddha, usually referred to as existentialism and nihilism, which can be helpful in explaining tertralemma.
Say I have a cloth with me and you ask me, "Is it a red cloth?" and I say no. Then you ask me "Is it some other color?" and I say no. And of course you will be confused and for good reason. But what if I was to tell you that the cloth is not a solid color, it is a checkered print? If you were incapable of conceiving of such a possibility then you would be in the same position as one grappling with existence and non-existence.
Let’s me explain this further by taking the four causal theories. The Buddha denied the four causal theories that were present in his time of Self causation, external causation, both self and external causation and arising out of a non-cause - that implied (1) existence or (2) non-existence or (3) both or (4) neither of a permanent existence of an eternal substantial self.
Explaining it through several different ways that included dialectics the Buddha propounded the theory of the middle way, that there is neither and that both the extreme views are born out of ignorance. He presented the theory of “dependant arising”. Now, if you look at both (1) and (2) propositions – both together would be a dilemma, whereas the four together are a tetralemma. The two additional propositions can be seen if we were to examine all four.
Let’s look at each implication further.
4. Anirvacaniya = neither. This is the case of illusory existence, the typical example being when one happens upon a rope and is startled perceiving it as a snake. The "snake" did not exist as a snake, but as a rope, it did exist. Hence the "snake" per se was neither existing nor not-existing
Let us take what is known as the two truths (satyadvaya) - typically designated ‘conventional’ and ‘ultimate’. A positive tetralemma can be found in an expression of the conventional validity of the two truths.
Conventional truth applies to facts about the everyday reality of things, people and events. It is designated conventional in the sense of being the product of human interests and dispositions and does not correspond to anything independently or inherently true - nothing is inherently real, i.e., nothing exists by virtue of its own independent essence, the familiar everyday world is, nonetheless, conventionally real and exists in a way which does not contradict experience.
Ultimate truth is deemed inexpressible in the sense that, in the absence of convention, there is no ascription of existence/non-existence itself. Both conventional and ultimate truth has the same consequence – nothing can be said to exist by virtue of its own essence. Thus the contradictory standpoints of (naïve or philosophical) reification and nihilism are repudiated in favour of a ‘middle way’.
The four formulations of propositions are traditionally presented in an order in which each view presents a progressively better expression of the middle way perspective whilst each is valid with qualification. A positive tetralemma can be found when one states that, e.g.:
For what reason? Because that bhikku is liberated by directly knowing this: the extent of designation and the extent of the pathway for designation, the extent of language and the extent of the pathway for language, the extent of description and the extent of the pathway for description, the extent of wisdom and the extent of the sphere of wisdom, the extent of the round and the extent to which the round turns. To say of a bhikku who is liberated by directly knowing that he holds the view ‘One does not know and one does not see’ – that would not be proper.
Not (A and -A)
Not (neither A nor -A)
The negative tetralemma is about what can't be said about Sunyata - that ultimately, nothing can be said. But however in this case the fourth lemma can be wrongfully implied to mean the independent existence of time to which sunyata can be propositionally related – which is a common mistake made by many by which some would say that the negative tetralemma is the self-destructing logic of the ultimate truth (the emptiness of emptiness), which would deny the validity of any philosophical assertion of any kind including that of the attribution of existence and non-existence to anything. However one must realize that the doctrine of two truths – the conventional truth and the ultimate truth, ipso facto a convention, falls into the realm of conventional truth and the denial is this conventional doctrine.
Another example which falls on to the class of a negative tetralemma can be found in the Kalakarama Sutta (Anguttara Nikaya (II, 24ff) - the Buddha said “…whatsoever is seen, heard, sensed, cognized, sought after and pondered over by the mind
– All that do I know – but have not taken a stand upon it
– All that I do not know – to say so would be a falsehood in me
– If I were to say I both know and know it not – that too would be a falsehood in me
– If I were to say I neither know it nor am I ignorant (nor do I not know it) - it would be a fault in me.
The negative tetralemma is about what can't be said about what is known by the mind - that ultimately, nothing can be said – the reason being that the Thatagata does not hold as true or false whatever is esteemed as truth by others – the Thatagata:
- does not conceive of an unseen, unheard, unsensed, uncongnized; he
Nagarjuna's negative tetralemmas are interesting. Nagarjuna tests the limits of expressibility, and the contradictory situation at that limit, at which when we take the ultimate perspective. In chapter 22 verse 11 of the Mulamadhyamakarika he states:
"Empty" should not be asserted.
"Non-empty" should not be asserted.
Here Nagarjuna is rejecting any theorizing either the empty, non-empty, both or neither. Neither the empty or non-empty should be reified, these are used only for purpose of communication, or expressing an experience, which being dependent has no static self-nature. The last line makes it clear that Nagarjuna is discussing what can't be said from the ultimate perspective - from a point of view transcendent of the conventional. And it turns out here that nothing can be said, even that all phenomena are empty, nor its negation. Although we can't even say that nothing can be said we say it. And we have thereby characterized the ultimate perspective, which, if we are correct in our characterization, can't be done.
All things lack fundamental natures (svabhava), and it turns out that they all have the same nature, that is, emptiness, and hence both have and lack that very nature. This is a direct consequence of the purely negative character of the property of emptiness. Nagarjuna demonstrates that the emptiness of emptiness permits the negation of the distinction between the two truths.
So simply put the theory of emptiness is a convention so the theory of emptiness must negate itself. It was never there until we created it, just like the fire in the Aggivaccagotta Sutta. There was nothing before, there is nothing after, and the expression of this nothing through conventional expression of a something must negate itself because it is a conventional expression – a product of simple dualism.
When reflecting on limits of expressibility I would like to take your mind back to a passage in the the Mahanidana sutta which I stated earlier ….. ........................that bhikku is liberated by directly knowing this: the extent of designation and the extent of the pathway for designation, the extent of language and the extent of the pathway for language, the extent of description and the extent of the pathway for description, the extent of wisdom and the extent of the sphere of wisdom, the extent of the round and the extent to which the round turns. To say of a bhikku who is liberated by directly knowing that he holds the view ‘One does not know and one does not see’ – that would not be proper…