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A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises ...
In logical argument and mathematical proof, the therefore sign, ∴, is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read therefore. While it is not generally used in formal writing, it is used in mathematics and shorthand.
A premise or premiss [a] is a proposition—a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion. [1] Arguments consist of a set of premises and a conclusion. An argument is meaningful for its conclusion only when all of its premises are true. If one or more premises are ...
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.
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
In this case, the conclusion contradicts the deductive logic of the preceding premises, rather than deriving from it. Therefore, the argument is logically 'invalid', even though the conclusion could be considered 'true' in general terms. The premise 'All men are immortal' would likewise be deemed false outside of the framework of classical logic.
Deductive reasoning is the psychological process of drawing deductive inferences.An inference is a set of premises together with a conclusion. This psychological process starts from the premises and reasons to a conclusion based on and supported by these premises.
The conclusion of a valid argument is not necessarily true, it depends on whether the premises are true. If the conclusion, itself, is a necessary truth, it is without regard to the premises. Some examples: All Greeks are human and all humans are mortal; therefore, all Greeks are mortal.