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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.
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:
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]
[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]
Irving Anellis's research shows that C.S. Peirce appears to be the earliest logician (in 1883) to devise a truth table matrix. [4]From the summary of Anellis's paper: [4] In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on "The Philosophy of Logical Atomism" truth table matrices.
A self-refuting idea or self-defeating idea is an idea or statement whose falsehood is a logical consequence of the act or situation of holding them to be true. Many ideas are called self-refuting by their detractors, and such accusations are therefore almost always controversial, with defenders stating that the idea is being misunderstood or that the argument is invalid.
In the 17th Century, Baruch Spinoza in his Ethics states that a thing is called contingent when "we do not know whether the essence does or does not involve a contradiction, or of which, knowing that it does not involve a contradiction, we are still in doubt concerning the existence, because the order of causes escape us". [22]
Being tautologous or contradictory is a formal property, whereas being a law of logic is a non-formal metalogical property (i.e. "One is one" is a tautology, whereas "No tautology is a contradiction" is not a tautology.). A tautology is in a logical form such that all substitution instances of any variables in it will cause for it to be true ...