Aristotelian syllogisms, known in Arabic as “qiyas al-mantiq,” are a fundamental aspect of logical reasoning developed by the ancient Greek philosopher Aristotle. A syllogism is a form of deductive reasoning consisting of two premises followed by a conclusion. The premises and conclusion are propositions, which assert or deny something about a subject.
A typical Aristotelian syllogism consists of:
- Two Premises:
- Major Premise: A general statement or principle.
- Minor Premise: A specific statement related to the major premise.
- Conclusion: A deduction derived from the two premises.
For example:
- Major Premise: All men are mortal.
- Minor Premise: Socrates is a man.
- Conclusion: Therefore, Socrates is mortal.
Aristotle identified different types of syllogisms based on the arrangement of the terms:
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Categorical Syllogisms: Involve statements that affirm or deny that “all” or “some” of the subject is in the predicate category.
- A universal affirmative (All S are P)
- A universal negative (No S are P)
- A particular affirmative (Some S are P)
- A particular negative (Some S are not P)
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Conditional Syllogisms: Involve “if-then” statements.
- Example: If A is true, then B is true.
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Disjunctive Syllogisms: Involve “either-or” statements.
- Example: Either A or B is true.
Several rules must be adhered to for a syllogism to be valid:
- Both premises must be true for the conclusion to be true.
- The middle term must be distributed at least once.
- The conclusion follows the weaker premise (if one premise is negative, the conclusion must be negative).