# 4 Categorical Propositions 4.4. Conversion, Obversion, and Contraposition

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• 4 Categorical Propositions4.4. Conversion, Obversion, and Contraposition

• Conversion, Obversion, and ContrapositionThese are 3 operations that can be used to change standard form statements or change a statement into standard form.

Conversion is the simplest: simply switch the subject and predicate terms.

No S are P -----conversion----> No P are S

• ConversionCompare the Venn Diagrams of each statement:

No S are PNo P are SSPPSFor E propositions, there is no change in diagram, and so no change in truth value.

• ConversionCompare the Venn Diagrams of each statement:

All S are PAll P are SPSFor A propositions, there IS a change in diagram, and so a change in truth value.

• ConversionCompare the Venn Diagrams of each statement:

Some S are PSome P are SPSFor I propositions, there is no change in diagram, and so no change in truth value.SPXX

• ConversionCompare the Venn Diagrams of each statement:

Some S are not PSome P are not SFor O propositions, there IS a change in diagram, and so a change in truth value.PSX

• ConversionSo, what do we know?

Immediate inferences (inferences with one premise and one conclusion) are valid for the converses of E and I propositions, but not for A and O propositions.

All puppies are evil.Therefore, all evil things are puppies.

Since this is conversion of an A proposition, it is an illicit inference an illicit conversion.

Some puppies are evil.Therefore, some evil things are puppies.

No problem.

• ObversionObversion (2 steps):Change the qualityReplace Predicate term with its complement

All S are P ------- obversion----->____________?No S are P -------obversion ------> _____________?Some S are P ----- obversion -----> _______________?Some S are not P ----obversion---> _____________?

• ObversionNo S are PAll S are non-PAll S are PNo S are non-PSome S are PSome S are not PSome S are not non-PSome S are non-P

• ContrapositionContraposition (2 steps):Switch Subject and Predicate termsReplace both Subject and Predicate terms with their complements

All S are P ------- contraposition----->____________?No S are P -------contraposition ------> _____________?Some S are P ----- contraposition -----> _______________?Some S are not P ----contraposition---> _____________?

• Contraposition

• Place an X in each distinct area of subject classRemove Xs based on what the proposition says using shading for universal propositions and eraser for particular onesRemove Xs based on Boolean interpretation using your eraserMethod to Drawing Venn Diagrams

• Helpful WordingAll non-P are non-SEvery single non-P is also a non-S

If there were any Xs inside the left part of the S circle, the statement would allow a non-P that was an S, which is denied in the statement. If there are any Xs, they would be outside the two circles (they dont appear because this is the Boolean interpretation)

• Helpful WordingNo non-P are non-SNot even one of the non-Ps is also a non-S(an X outside both circles says, here is a non-P that is also a non-S)

So, to prohibit allowing an X outside those circles, that area must be shaded.

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