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John Venn's First Venn Diagram

Representation of Propositions and Reasonings.3 number of possible rasultant alternatives would be very con- siderable. For instance, the proposition "All X is Y" needs both the diagrams, (x.Y) (xfor we cannot tell, from the mere verbal statement, whether there are any Y's which are not X. Similarly the proposition "Some X is not Z" needs three other diagrams, (These five relations, it may be remarked, comprise all the pos- sible ways in which two terms may stand to one another.) Hence the combination of the two given premises could not be adequately represented by less than six fi gures. lf more pre- mises, and more complicated ones (such as we shall presentl proceed to illustrate), are introduced, the consequent confusion would bo very serious. The fact is, as I have explained at length in the article above referred to, that the five distinct relations of classes to one another (viz. the inclusion of X in Y, their cocxtension, the inclusion of Y in X, their intersec- tion, and their mutual exclusion), which are thus pictured by these circular diagrams, rest upon a totally distinct view as to the import of a proposition from that which underlies the statements of common life and common logic. The latter statements naturally fall into four forms-the universal and particular, affirmative and negative; and it is quite impossible to make the five divisions of the one scheme fit in harmoni- ously with the four of the other.

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Venn Diagram Parodies - The Santa Brand

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