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The first original Arabic writings on logic were produced by al-Kindi (Alkindus) (805–873), who produced a summary on earlier logic up to his time. The first writings on logic with non-Aristotelian elements was produced by al-Farabi (Alfarabi) (873–950), who discussed the topics of future contingents, the number and relation of the categories, the relation between logic and grammar, and ...
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.
An epicheireme (/ ɛ p i ˈ k aɪ r i m / e-pee-KEYE-reem) [a] is a compound syllogism in which at least one of the premises is stated along with a justification for itself. [1] [2] Epicheirema are abridged polysyllogisms. [3] Like the enthymeme, epicheirema are often used in everyday speech. [citation needed]
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.
In syllogistic logic, there are 256 possible ways to construct categorical syllogisms using the A, E, I, and O statement forms in the square of opposition. Of the 256, only 24 are valid forms. Of the 24 valid forms, 15 are unconditionally valid, and 9 are conditionally valid.
A polysyllogism is a complex argument (also known as chain arguments of which there are four kinds: polysyllogisms, sorites, epicheirema, and dilemmas) [1] that strings together any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on.
However, if the latter two statements were switched, the syllogism would be valid: All students carry backpacks. My grandfather is a student. Therefore, my grandfather carries a backpack. In this case, the middle term is the class of students, and the first use clearly refers to 'all students'.
But it can be rewritten as a standard form AAA-1 syllogism by first substituting the synonymous term "humans" for "people" and then by reducing the complementary term "immortal" in the first premise using the immediate inference known as obversion (that is, the statement "No humans are immortal." is equivalent to the statement "All humans are ...