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Negation (the logical complement), () " It is not the case that if it is raining then I wear my coat. ", or equivalently, " Sometimes, when it is raining, I don't wear my coat . " If the negation is true, then the original proposition (and by extension the contrapositive) is false.
A statement is logically true if, and only if its opposite is logically false. The opposite statements must contradict one another. In this way all logical connectives can be expressed in terms of preserving logical truth. The logical form of a sentence is determined by its semantic or syntactic structure and by the placement of logical constants.
[88] (opposite of appeal to tradition) Appeal to poverty (argumentum ad Lazarum) – supporting a conclusion because the arguer is poor (or refuting because the arguer is wealthy). (Opposite of appeal to wealth.) [89] Appeal to tradition (argumentum ad antiquitatem) – a conclusion supported solely because it has long been held to be true. [90]
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 argument, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
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 "the house is white" and "the house is not white" are mutually exclusive.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
Moravec's paradox: Logical thought is hard for humans and easy for computers, but picking a screw from a box of screws is an unsolved problem. Movement paradox: In transformational linguistics, there are pairs of sentences in which the sentence without movement is ungrammatical while the sentence with movement is not.
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 ...