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Although Bertrand Russell at first argued against these remarks by Wittgenstein and Poincaré, claiming that mathematical truths were not only non-tautologous but were synthetic, he later spoke in favor of them in 1918: Everything that is a proposition of logic has got to be in some sense or the other like a tautology.
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 propositions cannot both be true and false at the same time, e. g. the two propositions "the house is white" and "the house is not white" are mutually exclusive.
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:
[67] [69] An inconsistent formula is also called self-contradictory, [1] and said to be a self-contradiction, [1] or simply a contradiction, [82] [83] [84] although this latter name is sometimes reserved specifically for statements of the form (). [1]
The metaphysical distinction between necessary and contingent truths has also been related to a priori and a posteriori knowledge. A proposition that is necessarily true is one in which its negation is self-contradictory; it is true in every possible world. For example, considering the proposition "all bachelors are unmarried:" its negation (i ...
Treating logical truths, analytic truths, and necessary truths as equivalent, logical truths can be contrasted with facts (which can also be called contingent claims or synthetic claims). Contingent truths are true in this world, but could have turned out otherwise (in other words, they are false in at least one possible world).
The leader of a cultlike group connected to six killings in three states was ordered held without bail Tuesday in Maryland, where she faces trespassing and other charges. Jack LaSota, 34, and two ...
A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]