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In the theory of logic, and Indian texts discussing it, the term also refers to an argument consisting of an enthymeme or sometimes for any syllogism. [1] In philosophical context, Nyaya encompasses propriety, logic and method.
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:
The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks. The Ancient Greeks such as Aristotle identified four primary distinct types of categorical proposition and gave them standard forms (now often called A, E, I, and O).
The development of Indian logic dates back to the Chandahsutra of Pingala and anviksiki of Medhatithi Gautama (c. 6th century BCE); the Sanskrit grammar rules of Pāṇini (c. 5th century BCE); the Vaisheshika school's analysis of atomism (c. 6th century BCE to 2nd century BCE); the analysis of inference by Gotama (c. 6th century BC to 2nd century CE), founder of the Nyaya school of Hindu ...
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 ...
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.
Fearful U.S. government workers wrestled ahead of a Thursday deadline with whether to accept a "buyout offer" from the Trump administration, which has warned that those who don't take it could be ...
In everyday reasoning, the fallacy of four terms occurs most frequently by equivocation: using the same word or phrase but with a different meaning each time, creating a fourth term even though only three distinct words are used. The resulting argument sounds like the (valid) first example above, but is in fact structured like the invalid ...