Deductive reasoning is the process of reaching a conclusion that is guaranteed to follow, if the evidence provided is true and the reasoning used to reach the conclusion is correct. The conclusion also must be based only on the evidence previously provided; it cannot contain new information about the subject matter. Deductive reasoning was first described by the ancient Greek philosophers such as Aristotle.
Deductive is a descriptor for one type of logical reasoning. In logic, there are two broad methods of reaching a conclusion. The alternative to deductive reasoning is inductive reasoning.
Both types of reasoning are routinely employed. One difference between them is that in deductive reasoning, the evidence provided must be a set about which everything is known before the conclusion can be drawn. Since it is difficult to know everything before drawing a conclusion, deductive reasoning has limited use in the real world. This is where inductive reasoning steps in. Given a set of evidence, however incomplete the knowledge is, the conclusion is likely to follow, but one gives up the guarantee that the conclusion follows. However it does provide the ability to learn new things that are not obvious from the evidence.
Many incorrectly teach that deductive reasoning goes from the general to the specific and that inductive reasoning travels in the opposite direction.
Deductive reasoning is supported by deductive logic, for example:
The ambiguity is that "formal logic" is very often used with the alternate meaning of symbolic logic as we have defined it, with informal logic meaning any logical investigation that does not involve symbolic abstraction; it is this sense of 'formal' that is parallel to the received usages coming from "formal languages" or "formal theory".
The boldest attempt to apply logic to mathematics was undoubtedly the logicism pioneered by philosopher-logicians such as Gottlob Frege and Bertrand Russell: the idea was that mathematical theories were logical tautologies, and the programme was to show this by means to a reduction of mathematics to logic.
Logic is extensively applied in the fields of artificial intelligence, and computer science, and these fields provide a rich source of problems in formal logic.
Traditionally, logic is studied as a branch of philosophy Philosophy is a discipline or field of study involving the investigation, analysis, and development of ideas at a general, abstract, or fundamental level.
Also studied in logic are the structure of fallacious arguments A logical fallacy is an error in logical argument which is independent of the truth of the premises.
Intuitionistic logic was proposed by L. Brouwer as the correct logic for reasoning about mathematics, based upon his rejection of the law of the excluded middle as part of his intuitionism.
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