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Philosophy 103: Introduction to Logic
Ordinary Language Inferences

Abstract: Three ordinary language examples of using immediate inferences demonstrate the uses of standard form categorical propositions and their logical relations.

1. Irving Kristol wrote in the Wall Street Journal, "This (a study showing all the officers in a precinct in New York are honest), however, is rather like saying that the majority of New York City's police officers are honest and honorable men. Of course they are. But the statement itself implies that a not altogether insignificant minority are less than that, and the presence of such a minority is fairly taken to constitute a rather serious problem."


Kristol is using subalternation to go from an I statement to an O statement.
Statement Reason T.V.
1. Some NYC police officers are honest men. given true
2. Some NYC police officers are not honest men. subcontrariety unknown
Kristol has made a mistake in his reasoning.

2. C.S. Price in his The Improvement of Sight writes, "Any strain imposed on the mind will be reflected in the eyes, and similarly anything which rests the mind will benefit them."


Price is using contraposition and conversion of an A proposition.
Statement Reason T.V.
1. All mental strains are nonbenefits to the eyes. given true
2. All benefits to the eyes are nonmental strains. contraposition true
3. All nonmental strains are benefits to the eyes. conversion unknown
Price has made an error; the truth values of the two statements are not logically related.

3. A. Conan Doyle implies that Watson's medical practice is large. In Doyle's, "The Adventure of the Creeping Man," he writes, "Monday morning found us on our way to the famous university town--an easy effort on the part of Holmes, who had no roots to pull up, but one which involved frantic planning and hurrying on my part, as my practice was by this time not inconsiderable." Are these statements consistent?


The logical relation involved is obversion of an E proposition.
Statement Reason TV
1. No things which are my practice are inconsiderable in size. given true
2. All things which are my practice are considerable in size. obversion true
Notice that the translation, "All things which are my practice are not inconsiderable" would be mistaken. Sometimes called the "Sneaky O" proposition, statements of the form "All S is not P" usually mean in part "Some S is not P."  E.g., consider the statement, "All swans are not white." The meaning is "Some swans are not white."Return to Logic Homepage
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