Reductio ad absurdum (reduction to absurdity) is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to (a) absurdity or (b) contradiction. Note that absurdities also occur in these other possibilities (i.e., infinite regress, paradox, circularities, and dilemmas).

In producing absurdities in an opponent's conclusions using their epistemic conditions of truth, we cut all ground from beneath their position. Murti, an Indian academic and philosopher, notes that 'self-contradiction is the only weapon that can convince an opponent.' However, suppose the opponent does not cease his position even after we prove that his assertions are self-contradictory. In that case, we must give up arguing with him.

In presenting a dialectical (debate) argument, you can avoid analyzing the individual arguments put forward by your opponent. Instead, you concern yourself only with the conclusions from the arguments. Focusing on these conclusions prevents you from being entangled in complicated and convoluted debates.

Another way to avoid convoluted debates stemming from conceptual arguments is to use the same tools these arguments utilize. That shows that the arguments a priori end in reductio ad absurdum. In this regard, opponents can refuse to accept arguments that are outside their concept of philosophy. Still, they are bound to take the very arguments they use themselves. Hence, we cut the ground beforehand from beneath the opponent's prior arguments. This way, we sever all avenues of escape from the arguments which would otherwise be made by offering posterior arguments. Consequently, to refute a thesis is to provide prior arguments demonstrating via reductio ad absurdum the absurdities stemming from your opponents' arguments for the conceptual necessity of some hypothesis. This way, we show that dilemmas, circularities, infinite regresses, paradoxes, and contradictions crop up as consequences of your opponent's arguments.

In this text, we are going to focus on the reduction of conclusions from the arguments. Suppose the conclusions lead to absurdity via a dialectical reductio ad absurdum method. In that case, there is no need to examine the arguments which generated them.

Reductio ad absurdum manages to build all views and propositions to meaninglessness

Nagarjuna, an Indian philosopher, examined the categories through which we understand the world via a reductio ad absurdum argumentation. His reduction showed that all beliefs or views about essences, individual identities, or essential natures reduce to absurdity. This reduction points to the sunyata [emptiness] of both the world and the absolute. The rejection of all views by the Prasangika Madhyamika Buddhists includes both the thesis and its antithesis. In other words, they would reject the view that 'thought' has no content (i.e., essence) and its antithesis, namely that 'thought' has an essence. The crux of a Prasangika Madhyamika Buddhist analysis (prasanga) – a reductio ad absurdum argument - is that their demonstrations are non-affirming negations. They negate but don't put forward any conclusion to such negation.

Since it is so complete to all views and propositions, the 'aha' realization is that Reductio ad absurdum manages to reduce Aristotelian logic to meaninglessness

The method argument in a case study using the debate is to use your opponent's epistemic criteria of truth. That is the laws of Aristotelian logic and a dialectical reductio ad absurdum argument. The schema of this argumentative pattern of rebuttal is: If P, then Q; but not-Q; therefore not-P.

Venn diagram of the tetralemma.

Suppose we symbolize 'having arisen from itself' by A and 'having arisen from others' by B.

1. A&~B
2. ~A&B
3. A&B
4. ~A&~B

These propositions represent the predicates of the reductio ad absurdum method. These 4 cases together occupy the four compartments of the Venn diagram above. Logically speaking, they exhaust all the possible modes of arising. Consequently, it is safe to say that Nagarjuna successfully enumerates all the possible causation theories in MUlamadhyamakakArikA. Such a method of enumeration is called a 'tetralemma' (catuSkoTi). When the concept of ~A&~B has no reference, the tetralemma reduces to a Trilemma. When concepts A and B are complementary, the tetralemma reduces to a Dilemma by abandoning the third and fourth lemmas.

As we discussed in the previous paragraph, there are four logical possibilities (tetralemma) as to the nature of a subject. Namely something:

1. it is
2. it is not
3. it is and is not
4. neither is nor is not

What Dean proposes is that there are four possibilities to the question of whether 'thought' has an essence:

1. 'Thought' has an essence.
2. 'Thought' has not an essence.
3. 'Thought' has an essence and has not an essence.
4. 'Thought' neither has an essence nor has not an essence.

Dean argues that this negation's main point is to send a person into a state of cognitive dissonance. That is, a state of mental turmoil where the only way out of the mental angst generated by the mental effort to solve these puzzles is through insight or vision. We might say through an 'aha' moment.

Since our culture (e.g., reasoning, philosophy, science) is based on Aristotelian logic to infer knowledge, reductio ad absurdum successfully manages to reduce all of our 'supposed' knowledge to meaninglessness

Mathematics, the pinnacle of logical thinking, also suggests that contradictions are inherent in 'thought.' In 1930 the mathematician Hilbert began a program to prove that mathematics was consistent. Unfortunately, Hilbert's program did not succeed. Following the discovery of such mathematical paradoxes as the Burli-Forti paradox, Russell's paradox, Cantor's paradox, and Skolem's paradox by the early 1930s. Therefore, discussions about how to live with contradictions in mathematics replaced the disagreements about eliminating the contradictions mentioned above. Attempts to avoid the paradoxes led to other paradoxical notions, but most mathematicians rejected these notions. Except in axiomatic theory, we can only formulate mathematics with contradictions and the loss of valuable results. Axiomatic theory can not be proven consistent with the result that paradoxes can occur at any time.

Since the mathematical way of looking at the world generates contradictory results from science. For example, the mathematical notion of the continuum and the quantum mechanical concept of quanta. A mystery arises here, which I mention later concerning instrumental results from logic and language. More specifically, that science uses mathematics with a different ontology to generate 'truths.' For example, the discoveries of quantum theory or the special theory of relativity were all made through extensive use of mathematics. More specifically, the concept of the continuum. Now, the mystery is that the mathematical way of looking at the world and the scientific way of looking at the world produced contradictory results. In this regard, the truths of mathematics and science require faith. Dean argues that this faith is the basis of our trust in logic and language.

In terms of its logic, what is held to be the most rational of the sciences is itself inconsistent, paradoxical, and irrational.

Research shows that emotions are hard to disentangle from cognition, as they might be impossible to untangle from each other

So through the Reductio ad absurdum method, our rational human cognition is reduced to meaninglessness. However, recently a growing body of research has pointed to the interdependence between cognition and emotion. Moreover, studies found that any definite statement about emotion's overall rationality or irrationality would be misleading. In this regard, we might use reductio ad absurdum to reduce cognition and emotions to meaninglessness.

Reductio ad absurdum does not claim that we as humans are unable to gain any knowledge

Instead, reductio ad absurdum claims that using Aristotelian logic to obtain knowledge in any shape currently supported by science (i.e., rational, emotional) is meaningless.

The dialectic reductio ad absurdum does not show that nothing can be known or be true. Instead, it shows the inadequacy of logic in laying the foundation for the known or the truth.

The dialectic demonstration of the meaninglessness of all views is epistemological. In other words, meaninglessness is epistemological, not ontological or metaphysical. The debate shows logically that a view reduces to absurdity, not what the view claims are wrong. To say that the claims are false, one must assume some position or view regarding what logic is and can do. For example, a position or view is an epistemic condition of truth. Still, the debate reduces this view to absurdity.

The debate can not make any ontological or metaphysical claims, as it is only an epistemological method. The discussion leaves the world unchanged and ontology as it is. Therefore, before the debate analysis - the world was the world; during the debate analysis - the world is not the world; after a debate analysis - the world is unchanged and still the same. In a metaphor, before the dialectic argument - a tree is a tree; during the dialectic argument - a tree is not a tree; after the dialectic argument - the tree is still a tree. This process is because:

1. the debate adds no extra knowledge as it is purely negative. It only affirms logically with nothing else to say because
2. it is only an epistemological method or tool

This method can say nothing ontologically or metaphysically- without some other perspective to give meaning to the reductions. The debate only says that a view is epistemologically meaningless, not that what the view puts forward as existence cannot exist. Because the positions or views of philosophers or the products of their 'thinking' use words. All of such words reduce to meaninglessness. Therefore, epistemologically all that they are doing is playing with words.

Word arguments or views reduce to meaninglessness. Therefore, you, me, Nietzsche, Camus, Sartre, and the whole of philosophy are '[...] all just pissing in the wind.', in the words of Neil Young. Dean argues that '... there is nothing that can be called - the philosophical method.' We as humans need to discover new methods of inferring knowledge if we are to obtain any knowledge at all.

We must also declare rational thinking and emotions as meaningless and put our hope onto other human percepts

Early Buddhist philosophers already criticized this approach that there is 'some' objective percept in our human minds. They formed five aggregates, of which emotions and cognition are just a tiny part (i.s., form, sensations, perceptions, mental activity or formations, consciousness). They stated that these five aggregates are interdependent and suffer from this same fallacy of meaninglessness. They claim that all five are interdependent and arise together - interdependent coarising.

Science already found evidence for some of the aggregates argued in the text to be interdependent and arising together (i.e., rational thinking and emotions). Therefore, it is just a matter of time until all five aggregates are investigated and found to be the same.

Therefore, the question arises. Where do we find an 'objective' and independent percept on which we can base our knowledge?

Criticism

We consider Nagarjuna's refuting all positions also to include denying the position of the fifth corner of tetralemma would imply. That is, to also refute itself. Note that this is precisely the argument for the criticism o Aristotelian logic and Dean's position in his work.

One such criticism of Nagarjuna's method comes from 'The Fifth Corner' by Priest. He states that the lines of Nāgārjuna's tetralemma is only logically consistent with one another if we accept the fifth corner - 'the ineffable.' According to Priest, if we don't accept 'the ineffable,' the lens of European logic can discern the problem. Priest says each of the lines in tetralemma involves reductio ad absurdum. In a similar way that he says dependent coarising does, in that everything arises from something else that originated from something else, ad infinitum. But only by adding the eclipsed fifth sentence, intentionally left out by Nagarjuna because the ultimate truth is unspoken (ineffable), does 'the whole machinery now make sense.'

1. A has the value t: A is effable, A obtains, and ¬A does not.
2. A has the value f: A is effable, ¬A obtains, and A does not.
3. A has the value b: A is effable, both A and ¬A obtain.
4. A has the value n: A is effable, neither A nor ¬A obtains.
5. A has the value e: A is ineffable (as is ¬A) (68).

Where A is a state of affairs, 'obtains' means it is true, '¬' means 'not,' t means true, f means false, b means both, n means neither, and e means none of the above.

On the other hand, Green argues that it would have been better if Priest sought this way to disprove the validity of the notion that the whole machine does not make sense. This view is precisely the argument Dean also makes.

On a side note, Priest is a specialist in logic and is well known for his defense of dialetheism, a word he coined to mean two contradictory statements that can both be true. According to a standard view in logic, outside of Asian philosophy and dating back to Aristotle, contradictories such as 'All men are mortal; some men are not mortal' cannot both be true. Priest was trained as a mathematician and became interested in Gödel's Incompleteness Theorems, which holds 'This sentence is not provable' to be true but not provable. From there, Priest considered other statements that have puzzled philosophers, such as the Liar's Paradox: 'This sentence is false.' Eventually, he came to the controversial conclusion that it's not that such paradoxes are incomplete, as Gödel suggested. Still, they achieve what they set out to do. According to Priest, these paradoxes show that certain contradictions are true, which he called dialetheism. This perspective is from which he approaches Nagarjuna's catuṣkoṭi or tetralemma. This view may immediately raise concerns for those in Buddhist Studies, as Priest is applying an incommensurable standard to Nagarjuna. More specifically, he assumes that his Nagarjuna presents a paradox comparable to the Liar's Paradox. That its alleged contradictions are valid and that through it, Nagarjuna establishes his position, which Priest calls the fifth corner of four.

Reference

Dean, C. L. (2003). The dialectic 'Reductio ad absurdum' argument: a method of philosophical argumentation or analysis demonstrating the meaninglessness of all views.

Green, R. S. (2020). The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi, 27, 2020.