# Venn Diagrams and Syllogisms

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This Demonstration lets you verify 24 valid syllogisms using Venn diagrams with only one element in the domain. The domain only needs two elements, denoted by "+" and "×", to show that a syllogistic form is not valid.

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Contributed by: Izidor Hafner (August 2016)

using code written by Marc Brodie

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

A monadic formula of first-order logic is one for which all nonlogical symbols are one-place predicates.

Theorem. If is a monadic sentence that is satisfiable, then is true in some interpretation whose domain contains at most members, where is the number of one-place predicate letters and is the number of variables in .

Therefore there is an effective procedure for deciding whether or not a monadic sentence is valid [1, p. 250].

Syllogistic forms are monadic sentences if considered as sentences of the form with predicate letters , , and .

References

[1] G. S. Boolos and R. C. Jeffrey, *Computability and Logic*, Cambridge, UK: Cambridge University Press, 1974.

[2] L. Carroll, *Symbolic Logic and The Game of Logic*, New York: Dover Publications, 1958.

[3] I. M. Copi and C. Cohen, *Introduction to Logic*, 9th ed., New York: Macmillan Publishers, 1994 pp. 214–218.

[4] J. M. BocheÅ„ski, *A History of Formal Logic*, 2nd ed. (I. Thomas, trans. and ed.), New York: Chelsea Publishing Company, 1970 p. 235.

[5] Wikipedia. "Syllogism." (Aug 3, 2016) en.wikipedia.org/wiki/Syllogism.

[6] Wikipedia. "Venn Diagram." (Aug 3, 2016) en.wikipedia.org/wiki/Venn_diagram.

[7] J. Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings," *Philosophical Magazine Series 5*, 10(59), 1880 pp. 1–18. doi:10.1080/14786448008626877.

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