What is the point of reductio ad absurdum in metaphysics?

Question

Philosophers often use reductio ad absurdum in metaphysics and philosophy of mind to make a point, to justify their position, or a thought experiment, or to reject a position or theory they do not like, but what is the point in all that if nature itself is absurd?

Consider this quote by Feynman from page 10 of QED: The Strange Theory of Light and Matter:

The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you accept Nature as She is — absurd.

What if a philosopher mounted a reductio ad absurdum on nature? would he be justified if his argument was sound?

Consider for example the problem of free will - one can imagine two philosophers who hold opposing views on free will, and who for many years reject each other's view using reductio ad absurdum; is that not absurd?

As an analogy, imagine two mathematicians who reject each other's coordinate systems for a sphere on account of including a singularity point, such as a north pole - let's call it the "absurdity" of a coordinate system - and they fail to realize that you cannot "explain" a sphere with a single coordinate system which is not "absurd" - you need at least two:

Singularities in familiar coordinates on the two-sphere can be eliminated by covering the sphere with two overlapping coordinate patches. (Gravitation, 1973, p. 12)

Or consider an example from philosophy of mind - Chalmers who is a property dualist employs a reductio ad absurdum in his famous fading and dancing qualia arguments to conclude that a robot may have conscious experience identical to his own (Wittgenstein would have rejected the whole thing on account of the absence of criteria of identity, but let us ignore that subtlety) - he admits that from his point of view as a steadfast dualist, his conclusion is highly counter intuitive - but robots with a dualist kind of qualia are not just counter intuitive - they seem to be absurd since their qualia are hopelessly epiphenomenal - their qualia can have no effect on the calculation mechanism, and they therefore have no way to "know" their qualia - that is, Chalmers arguably uses reductio ad absurdum to reject one absurdity for another.

It seems to me that if nature is absurd, then using reductio ad absurdum in metaphysics or philosophy of mind may be wrong and misleading - but nevertheless, philosophers continue to use it - maybe as someone who is stumbling through the dark and refuses to throw away a flashlight that ran out of batteries.

Wittgenstein says that philosophers mislead themselves into confusions by misusing language, and that philosophy should be done differently - in essence describing and surveying problems rather than trying to explain them:

we may not advance any kind of theory. There must not be anything hypothetical in our considerations. All explanation must disappear, and description alone must take its place. And this description gets its light -- that is to say, its purpose a from the philosophical problems. These are, of course, not empirical problems; but they are solved through an insight into the workings of our language, and that in such a way that these workings are recognized -- despite an urge to misunderstand them. The problems are solved, not by coming up with new discoveries, but by assembling what we have long been familiar with. Philosophy is a struggle against the bewitchment of our understanding by the resources of our language. (PI §109)

Do you know of philosophers who address this problem?

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you might also enjoy the following very funny video of Feynman explaining nature's craziness to students - https://youtu.be/eLQ2atfqk2c?t=24m2s - the lectures themselves are very interesting - after watching them two years ago I realized for the first time how holograms actually work.

Answer 1

It seems to me that Feynman's statement :

The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you accept Nature as She is — absurd.

cab be rephrased as : quantum mechanics conflicts with our common sense. But quantum mechanics is "right" (because it agrees with experiment); thus, we have to "amend" our common sense view of reality.

We can "formalize" it as a logical argument, but I'm not sure that this "reconstruction" was the intended meaning of Feynman.

Consider the argument :

1. quantum mechanics conflicts with common sense [this means - simplifying a lot - to consider common sense as a sort of theory]; we can say : QM → ¬ CS

2. qm agrees (confirmed ?) with experiment; thus it is true : QM

Thus, from 1. and 2. we have :

i) ¬ QM ∨ ¬ CS [because : QM → ¬ CS is equivalent to : ¬ QM ∨ ¬ CS]

ii) QM

By Disjunctive syllogism we can conclude with :

¬ CS

i.e. : "common sense is false"

This will not necessarily imply that nature is contradictory; at most, we can agree that our (human) "frameworks" (common sense, scientific theories), "developed" over the millenia in order to cope with reality, are contradictory.

You can see Quine's Naturalism.

Answer 2

Feynman also said:

“Physics is to mathematics what sex is to masturbation.”,

“Physics isn’t the most important thing. Love is.”

why not approach his comedy like regular comedy? ;-)

And what you've quoted from Feynman comes from a time when a lot of the paradoxes of quantum mechanics seemed far more perplexing. Quite some progress has been made to resolve them. But if everybody would have taken his quote seriously, nobody would have found the motivation to tackle the paradoxes.

Your mathematical example is not a proof by reductio ad absurdum, because it seriously lacks mathematical rigor. It's a caricature of mathematical practice. Just the feeling of absurdity is not enough, the absurdity must be on the level of an untenable conclusion. But if such rigor has been achieved, doubting a reductio ad absurdum is something only mathematical cranks do.

For example, it has been proven that squaring the circle with ruler and compass is impossible. After tons of pages of preliminaries, the reductio ad absurdum arrives at some point with a result: But what if a mathematical crank actually came up with a correct method to square the circle with ruler and compass? Then mathematics would enter an unprecedented crisis. There would be an error in a proof, which thousands of professional mathematicians didn't notice, or an inconsistency in the axioms. The crank would be right and a mathematician would not be justified to still believe that squaring the circle is impossible.

Similarly, by definition a philosphical argument whose conclusion contradicts reality cannot be sound. It just cannot, because soundness means the argument is valid and the premises are true. And since valid means that the conclusion is true if the premises are true, a sound argument must have a true conclusion.

A philosophical argument contradicting reality (i.e. untrue conclusion) must be invalid (inferences are faulty) or the premises must be wrong. But philosophy wouldn't enter a crisis because of it. It's a common occurrence to which we are very used to. And there is lack of consensus in philosophy, anyway.

It's not really that only a reductio ad absurdum in philosophy is problematic, it's that philosophy itself is problematic. Direct arguments are not better.

Mathematics has an insanely good track record. Its proofs, whether direct or by reductio ad absurdum, are generally accepted because of this.

Philosophy, on the other hand, has a bad track record. In fact, its track record is so bad, that few would dare to question empirical observations (though they obviously can be fallacious or misleading, too), just because they contradicted a philosophical argument. Of course this might perhaps change, maybe the track record of some parts of philosophy could get better.

Answer 3

What is the point of reductio ad absurdum?

In mathematics reductio ad absurdum is a sound method of proof as long as one operates on the base of 2-valued logic with the axiom "not (A and not-A)". On this base nearly all "working" mathematicians operate - notably exceptions are mathematicians in the wake of Brouwer.

What is absurd concerning the statement referring to the singular coordinates on the sphere? A sphere is a differentiable manifold and corresponding coordinate patches are free from singularities by definition. Covering the sphere by two coordinate patches - as the textbook of Wheeler et al. shows - avoids the problem of singular points.

For me a statement like "nature is absurd" is not senseful. Nature, i.e. real objects and facts, just are. Only the difference between certain propositions can be absurd. E.g., the gap between the propositions valid in every-day life and the insights of quantum electrodynamics or quantum mechanics in general. Hence, please indicate a reference to Feynman's quote to learn about the context of his statement.

Reductio ad absurdum is a problematic tool in philosophy. Because in general, the terms have no precise definition alike to the terms of a formalized science. But antinomies play a fundamental role in philosophical argumentation, see the four antinomies from Kant, Immanuel: Critique of Pure Reason. (B454ff) The characteristics of these antonomies are that philosophical argumentation supports the thesis as well as the antithesis. Resolving these antinomies is one of the main achievements of Kant's work.

Expanded as asked by @nir:

The principle of reductio ad absurdum is "A or non-A", the law of tertium non datur. Reductio ad absurdum proves "A" by refuting "non-A".

An antinomy violates "non(A and non-A)", the law of noncontradiction. An antinomy proves "A" and also "non-A".

Both laws are equivalent in propositional logic, which can be proved by inspecting their truth-tables.