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Syllogistic fallacies – logical fallacies that occur in syllogisms. Affirmative conclusion from a negative premise (illicit negative) – a categorical syllogism has a positive conclusion, but at least one negative premise. [11] Fallacy of exclusive premises – a categorical syllogism that is invalid because both of its premises are negative ...
Example (invalid aae form): Premise: All colonels are officers. Premise: All officers are soldiers. Conclusion: Therefore, no colonels are soldiers. The aao-4 form is perhaps more subtle as it follows many of the rules governing valid syllogisms, except it reaches a negative conclusion from affirmative premises. Invalid aao-4 form: All A is B.
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 ...
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. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
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.
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.
Humbug! The skeptic's field guide to spotting fallacies in thinking – textbook on fallacies. scribd.com; List of fallacies with clear examples, infidels.org; Interactive Syllogistic Machine A web based syllogistic machine for exploring fallacies, figures, and modes of syllogisms. Logical Fallacies and the Art of Debate, csun.edu
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