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Aristotle's theory of the syllogism: a logico-philological study of Book A of the Prior Analytics. Dordrecht: Reidel. Rescher, Nicholas. 1966. Galen and the Syllogism. University of Pittsburgh Press. ISBN 978-0822983958. Smiley, Timothy. 1973. "What is a syllogism?" Journal of Philosophical Logic 2:136–54. Smith, Robin. 1986.
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 ...
[2] In the Analytics then, Prior Analytics is the first theoretical part dealing with the science of deduction and the Posterior Analytics is the second demonstratively practical part. Prior Analytics gives an account of deductions in general narrowed down to three basic syllogisms while Posterior Analytics deals with demonstration. [3]
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.
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 ...
The dictum de omni is the highest principle of affirmative syllogisms. It says: Whatever is universally affirmed of a concept is also affirmed of everything contained under it. This is grounded on the rule of affirmative ratiocination. A concept that contains other concepts has been abstracted from them and is a predicate. Whatever belongs to ...
When the premises are not certain, such a syllogism is called dialectical, and these are dealt with in the eight books of the Topics. A syllogism which seems to be perfect both in matter and form, but which is not, is called sophistical , and these are dealt with in the book On Sophistical Refutations .
Aristotle's logical work is collected in the six texts that are collectively known as the Organon.Two of these texts in particular, namely the Prior Analytics and De Interpretatione, contain the heart of Aristotle's treatment of judgements and formal inference, and it is principally this part of Aristotle's works that is about term logic.