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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 .
The opposite symbol (∨) is called a vel, or sometimes a (descending) wedge. Some authors who call the descending wedge vel often call the ascending wedge ac (the corresponding Latin word for "and", also spelled "atque"), keeping their usage parallel.
[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]
The word "logic" originates from the Greek word logos, which has a variety of translations, such as reason, discourse, or language. [4] Logic is traditionally defined as the study of the laws of thought or correct reasoning, [5] and is usually understood in terms of inferences or arguments. Reasoning is the activity of drawing inferences.
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.
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition to another proposition "not ", written , , ′ [1] or ¯. [ citation needed ] It is interpreted intuitively as being true when P {\displaystyle P} is false, and false when P {\displaystyle P} is true.
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.