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A syllogism takes the form (note: M – Middle, S – subject, P – predicate.): Major premise: All M are P. Minor premise: All S are M. Conclusion/Consequent: All S are P. The premises and conclusion of a syllogism can be any of four types, which are labeled by letters [14] as follows. The meaning of the letters is given by the table:
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 ...
[1] [2] abduction A form of reasoning characterized by drawing a conclusion based on the best available explanation for a set of premises. Often used in hypothesis formation. Abelian logic A type of relevance logic that rejects contraction and accepts that ((A → B) → B) → A. [3] [4] [5] absorption
The word "propositio" is from the Latin, meaning the first premise of a syllogism. Aristotle uses the word premise (protasis) as a sentence affirming or denying one thing or another (Posterior Analytics 1. 1 24a 16), so a premise is also a form of words. However, as in modern philosophical logic, it means that which is asserted by the sentence.
Statements in syllogisms can be identified as the following forms: a: All A is B. (affirmative) e: No A is B. (negative) i: Some A is B. (affirmative) o: Some A is not B. (negative) The rule states that a syllogism in which both premises are of form a or i (affirmative) cannot reach a conclusion of form e or o (negative). Exactly one of the ...
Sometimes a syllogism that is apparently fallacious because it is stated with more than three terms can be translated into an equivalent, valid three term syllogism. [2] For example: Major premise: No humans are immortal. Minor premise: All Greeks are people. Conclusion: All Greeks are mortal.
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 ...
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 ...