vations discovered in them.
In the 19th Century, modifications to syllogism were incorporated to deal with disjunctive ("A or B") and conditional ("if A then B") statements. Kant famously claimed that logic was the one completed science, and that Aristotelian logic more or less included everything about logic there was to know. Though there were alternative systems of logic such as Avicennian logic or Indian logic elsewhere, Kant's opinion stood unchallenged in the West until Frege invented first-order logic.
Still, it was cumbersome and very limited in its ability to reveal the logical structure of complex sentences. For example, it was unable to express the claim that the real line is a dense order. In the late 19th century, Charles Peirce's discovery of second-order logic revolutionized the field and the Aristotelian system has since been left to introductory material and historical study.
Everyday syllogistic mistakesEdit
People often make mistakes when reasoning syllogistically.
For instance, given the following parameters: some A are B, some B are C, people tend to come to a definitive conclusion that therefore some A are C. However, this does not follow. For instance, while some cats (A) are black (B), and some black things (B) are televisions (C), it is false that some cats (A) are televisions (C). This is because first, the mood of the syllogism invoked is illicit (III), and second, the supposition of the middle term is variable between that of the middle term in the major premise, and that of the middle term in the minor premise (not all "some" cats are by necessity of logic the same "some black things").
Determining the validity of a syllogism involves determining the distribution of each term in each statement, meaning whether all members of that term are accounted for.
In simple syllogistic patterns, the fallacies of invalid patterns are:
- Undistributed middle - Neither of the premises accounts for all members of the middle term, which consequently fails to link the major and minor term.
- Illicit treatment of the major term - The conclusion implicates all members of the major term; however, the major premise does not account for them all.
- Illicit treatment of the minor term - Same as above, but for the minor term and minor premise.
- Exclusive premises - Both premises are negative, meaning no link is established between the major and minor terms.
- Affirmative conclusion from a negative premise - If either premise is negative, the conclusion must also be.
- Existential fallacy - This is a more controversial one. If both premises are universal, i.e. "All" or "No" statements, they don't imply the existence of any members of the terms. In this case, the conclusion cannot be existential; i.e. beginning with "Some".
- Venn diagram
- Syllogistic fallacy
- The False Subtlety of the Four Syllogistic Figures
- Forms of syllogism:
- ↑ According to Copi, p. 127: 'The letter names are presumed to come from the Latin words "AffIrmo" and "nEgO," which mean "I affirm" and "I deny," respectively; the first capitalized letter of each word is for universal, the second for particular'
- ↑ Bacon, Francis. The Great Instauration, 1620
- ↑ Michael Friedman emphasizes this in his Kant and the Exact Sciences (1992)
- Aristotle, Prior Analytics. transl. Robin Smith (Hackett, 1989) ISBN 0-87220-064-7.
- Blackburn, Simon, 1996. "Syllogism" in the Oxford Dictionary of Philosophy. Oxford University Press. ISBN 0-19-283134-8.
- Broadie, Alexander, 1993. Introduction to Medieval Logic. Oxford University Press. ISBN 0-19-824026-0.
- Irving Copi, 1969. Introduction to Logic, 3rd ed. Macmillan Company.
- Jan Łukasiewicz, 1987 (1957). Aristotle's Syllogistic from the Standpoint of Modern Formal Logic. New York: Garland Publishers. ISBN 0824069242. OCLC 15015545.
- Abbreviatio Montana article by Prof. R. J. Kilcullen of Macquarie University on the medieval classification of syllogisms.
- The Figures of the Syllogism is a brief table listing the forms of the syllogism.
- Stanford Encyclopedia of Philosophy entry on Medieval Theories of Syll