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  2. Contradiction - Wikipedia

    en.wikipedia.org/wiki/Contradiction

    This contradiction, as opposed to metaphysical thinking, is not an objectively impossible thing, because these contradicting forces exist in objective reality, not cancelling each other out, but actually defining each other's existence. According to Marxist theory, such a contradiction can be found, for example, in the fact that:

  3. Proof by contradiction - Wikipedia

    en.wikipedia.org/wiki/Proof_by_contradiction

    In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally ...

  4. Reductio ad absurdum - Wikipedia

    en.wikipedia.org/wiki/Reductio_ad_absurdum

    Reductio ad absurdum, painting by John Pettie exhibited at the Royal Academy in 1884. In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical arguments, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.

  5. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    Sometimes used for “relation”, also used for denoting various ad hoc relations (for example, for denoting “witnessing” in the context of Rosser's trick). The fish hook is also used as strict implication by C.I.Lewis p {\displaystyle p} ⥽ q ≡ ( p → q ) {\displaystyle q\equiv \Box (p\rightarrow q)} .

  6. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done in practice.

  7. Paradox - Wikipedia

    en.wikipedia.org/wiki/Paradox

    When this recursion creates a metaphysical impossibility through contradiction, the regress or circularity is vicious. Again, the liar paradox is an instructive example: "This statement is false"—if the statement is true, then the statement is false, thereby making the statement true, thereby making the statement false, and so on. [15] [18]

  8. Contraposition - Wikipedia

    en.wikipedia.org/wiki/Contraposition

    However, indirect methods such as proof by contradiction can also be used with contraposition, as, for example, in the proof of the irrationality of the square root of 2. By the definition of a rational number , the statement can be made that " If 2 {\displaystyle {\sqrt {2}}} is rational, then it can be expressed as an irreducible fraction ".

  9. Glossary of mathematical jargon - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    For example, if the variance of a random variable is said to be finite, this implies it is a non-negative real number, possibly zero. In some contexts though, for example in "a small but finite amplitude", zero and infinitesimals are meant to be excluded.