Reductio ad absurdum arguments are logically valid proofs in formal logic.
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Peer-reviewed literature and reference texts establish that reductio ad absurdum is a recognized, valid form of indirect proof and reasoning derived from classical logic and mathematics.
That is, 2 = n0(n0+1). Then for n=n0+1, 2 can be rewritten 2(n0+1) + 2. Since 2 = n0(n0+1), 2n0+1 + 2 = 2(n0+1) + 2n0(n0+1). So 2(n0+1) + 2n0(n0+1)= 2(n0+1)(n0 + 2), which completes the proof. Proof by contradiction
Proof by contradiction is a way of proving a mathematical theorem by showing that if the statement were false, then there would be a logical contradiction involved. That is, if one of the results of the theorem is assumed to be false, then there would be some inconsistency with the logic. When proving a theorem by way of contradiction, it is important to note that in the beginning of the proof. This is usually abbreviated BWOC. When the contradiction appears in the proof, there is usually a ⨳ symbol involved.[2]
Related pages
- Constructive proof
- Direct proof
- Mathematical logic
- Q.E.D. - Quadratic equation, which can be solved using a kind of proof called "completing the square"
- Reductio ad absurdum
References
- ↑ Bill Casselman. "One of the Oldest Extant Diagrams from Euclid". University of British Columbia. Retrieved September 26, 2008. - 1 2 "The Definitive Glossary of Higher Mathematical Jargon". Math Vault. 2019-08-01. Retrieved 2020-09-23.
The argumentative resource known as Reductio ad Absurdum (RA) is one of the characteristics means philosophy serves from to argumentative purposes. It consists in refusing a thesis by deducing an absurd implication from it. After a clarification of the logical basis of the RA and of the concept of "absurd implication," the author states there are two different types of RA, the "a priori" and the “a posteriori" types. The former consists in deriving a proposition, which contradicts a self-evident assertion. The latter consists in inferring a proposition, which contradicts an obvious empirical truth. Within the first category, most of the philosophical and mathematical RA arguments fall. In the last section of the paper the author explains why the arguments by Reductio ad Absurdum in philosophy lack the proving nature of its mathematical peers.Keywords: Philosophical argumentation, hypothetical reasoning, Reductio ad Absurdum
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