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Fallacies. London: Methuen. ISBN 0-416-70070-5. Cf. on validity of syllogisms: "A simple set of rules of validity was finally produced in the later Middle Ages, based on the concept of Distribution." Łukasiewicz, Jan. [1957] 1987. Aristotle's Syllogistic from the Standpoint of Modern Formal Logic. New York: Garland Publishers. ISBN 0-8240-6924-2.
The fallacy of four terms is a syllogistic fallacy. Types of syllogism to which it applies include statistical syllogism, hypothetical syllogism, and categorical syllogism, all of which must have exactly three terms. Because it applies to the argument's form, as opposed to the argument's content, it is classified as a formal fallacy.
For example, oxygen is necessary for fire. But one cannot assume that everywhere there is oxygen, there is fire. A condition X is sufficient for Y if X, by itself, is enough to bring about Y. For example, riding the bus is a sufficient mode of transportation to get to work.
The rule states that a syllogism in which both premises are of form a or i (affirmative) cannot reach a conclusion of form e or o (negative). Exactly one of the premises must be negative to construct a valid syllogism with a negative conclusion. (A syllogism with two negative premises commits the related fallacy of exclusive premises.)
The fallacy of the undistributed middle occurs when the term that links the two premises is never distributed. In this example, distribution is marked in boldface: All Z is B; All Y is B; Therefore, all Y is Z; B is the common term between the two premises (the middle term) but is never distributed, so this syllogism is invalid.
An example of a language dependent fallacy is given as a debate as to who in humanity are learners: the wise or the ignorant. [18]: 3 A language-independent fallacy is, for example: "Coriscus is different from Socrates." "Socrates is a man." "Therefore, Coriscus is different from a man." [18]: 4
Another feature of an argument based on false premises that can bedevil critics, is that its conclusion can in fact be true. Consider the above example again. It may well be that it has recently rained and that the streets are wet. This does nothing to prove the first premise, but can make its claims more difficult to refute.
Logical form replaces any sentences or ideas with letters to remove any bias from content and allow one to evaluate the argument without any bias due to its subject matter. [1] Being a valid argument does not necessarily mean the conclusion will be true. It is valid because if the premises are true, then the conclusion has to be true.