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Aristotle held that any logical argument could be reduced to two premises and a conclusion. [2] Premises are sometimes left unstated, in which case, they are called missing premises, for example: Socrates is mortal because all men are mortal. It is evident that a tacitly understood claim is that Socrates is a man. The fully expressed reasoning ...
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.
The form of a modus tollens argument is a mixed hypothetical syllogism, with two premises and a conclusion: If P, then Q. Not Q. Therefore, not P. The first premise is a conditional ("if-then") claim, such as P implies Q. The second premise is an assertion that Q, the consequent of the conditional claim, is not the case.
Logical reasoning is a form of thinking that is concerned with arriving at a conclusion in a rigorous way. [1] This happens in the form of inferences by transforming the information present in a set of premises to reach a conclusion.
For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics ), in the sense that if the premises are true (under ...
A form of deductive reasoning in Aristotelian logic consisting of three categorical propositions that involve three terms and deduce a conclusion from two premises. category In mathematics and logic, a collection of objects and morphisms between them that satisfies certain axioms, fundamental to category theory. category theory
In philosophical logic, the masked-man fallacy (also known as the intensional fallacy or epistemic fallacy) [1] is committed when one makes an illicit use of Leibniz's law in an argument. Leibniz's law states that if A and B are the same object, then A and B are indiscernible (that is, they have all the same properties).
Independent premises, where the premise can support the conclusion on its own: Although independent premises may jointly make the conclusion more convincing, this is to be distinguished from situations where a premise gives no support unless it is joined to another premise.