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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.
At present, syllogism is used exclusively as the method used to reach a conclusion closely resembling the "syllogisms" of traditional logic texts: two premises followed by a conclusion each of which is a categorical sentence containing all together three terms, two extremes which appear in the conclusion and one middle term which appears in ...
The central aspect of Aristotelian logic involves classifying all possible syllogisms into valid and invalid arguments according to how the propositions are formed. [112] [115] For example, the syllogism "all men are mortal; Socrates is a man; therefore Socrates is mortal" is valid. The syllogism "all cats are mortal; Socrates is mortal ...
Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound.
The statistical syllogism was used by Donald Cary Williams and David Stove in their attempt to give a logical solution to the problem of induction. They put forward the argument, which has the form of a statistical syllogism: The great majority of large samples of a population approximately match the population (in proportion)
The first type of enthymeme is a truncated syllogism, or a syllogism with an unstated premise. [6] Here is an example of an enthymeme derived from a syllogism through truncation (shortening) of the syllogism: "Socrates is mortal because he's human." The complete formal syllogism would be the classic: All humans are mortal. (major premise ...
B is the common term between the two premises (the middle term) but is never distributed, so this syllogism is invalid. B would be distributed by introducing a premise which states either All B is Z, or No B is Z. Also, a related rule of logic is that anything distributed in the conclusion must be distributed in at least one premise. All Z is B
Another form of logic puzzle, popular among puzzle enthusiasts and available in magazines dedicated to the subject, is a format in which the set-up to a scenario is given, as well as the object (for example, determine who brought what dog to a dog show, and what breed each dog was), certain clues are given ("neither Misty nor Rex is the German Shepherd"), and then the reader fills out a matrix ...