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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:
Panini, revered Sanskrit grammarian, derives the "Nyaya" from the root "i" which conveys the same meaning as "gam" – to go. "Nyaya" signifying logic is there etymologically identical with "nigama" the conclusion of a syllogism. [17]
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 ...
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.
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 ...
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]
For example the assertibles in the premises can be more complex, and the following syllogism is a valid example of the second indemonstrable (modus tollens): [31] if both p and q, then r; not r; therefore not: both p and q. Similarly one can incorporate negation into these arguments. [31]
Depending on the position of the middle term, Aristotle divides the syllogism into three kinds: syllogism in the first, second, and third figure. [14] If the Middle Term is subject of one premise and predicate of the other, the premises are in the First Figure. If the Middle Term is predicate of both premises, the premises are in the Second Figure.