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It is a proposition that is unconditionally false (i.e., a self-contradictory proposition). [2][3]This can be generalized to a collection of propositions, which is then said to "contain" a contradiction. History. [edit] By creation of a paradox, Plato's Euthydemusdialogue demonstrates the need for the notion of contradiction.
TRIZ flowchart Contradictions matrix 40 principles of TRIZ. One tool which evolved as an extension of TRIZ was a contradiction matrix. [14] The ideal final result (IFR) is the ultimate solution of a problem when the desired result is achieved by itself.
40 principles of TRIZ method rendered schematically, stacked vertically in four-column, within single A3 paper sheet. The 40 Principles of invention are a suite of ideas that purport to aid in solving hard technical problems. The principles are based on TRIZ, a theory about problem solving. They are used together with Contradiction Matrices.
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions " p is the case " and " p is not the case " are mutually exclusive.
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. [ 1 ][ 2 ] It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. [ 3 ][ 4 ] A paradox usually involves ...
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901. [1][2] Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. [3]
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad impossibile.
Contradiction is the basis of life and drives it forward. No one phenomenon can exist without its contradictory opposite, such as victory and defeat. [7] "Unity of opposites" allows for a balance of contradiction. A most basic example of the cycle of contradiction is life and death.