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# Part 2 Module 4 Categorical Syllogisms and Diagramming

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PART 2 MODULE 4 CATEGORICAL SYLLOGISMS AND DIAGRAMMING Consider the following argument Some lawyers are judges Some judges are politicians Therefore some lawyers are politicians Although the premises and conclusion of this argument sound reasonable and although the structure of the argument looks similar to transitive reasoning this argument is invalid In order to show that the argument is invalid all we have to do is conceive of a situation in which the conclusion is false while both premises are true In order to do so it helps if we imagine a world with a small population of lawyers judges and politicians Suppose there are only two lawyers Alice and Bill and that Bill is also a judge but Alice isn t Suppose that in addition to Bill there is only one other judge Carla and Carla is also a politician but Bill isn t a politician Finally suppose there is one other politician Don who isn t a lawyer and isn t a politician In this conceivable world some lawyers are judges Bill and some judges are politicians Carla but no lawyers are politicians Since it is possible to conceive of a situation in which the conclusion is false while both premises are true this argument is invalid The previous argument is an example of a CATEGORICAL SYLLOGISM which is an argument involving two premises both of which are categorical statements Categorical statements are statements of the form all are none are or some are A categorical statement of the form all are is also called a positive universal statement A categorical statement of the form none are is also called a negative universal statement A categorical statement of the form some are or some aren t is also called an existential statement In this discussion we are primarily concerned with categorical syllogisms in which at least one premise is an existential statement because such arguments cannot be analyzed using the methods of Unit 2 Module 1 Existential statements A statement of the form Some are such as Some lawyers are judges is

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