# A categorical syllogism is a syllogism whose premises

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Chapter 2 / Exercise 5
College Algebra
Gustafson/Hughes
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A categorical syllogism is a syllogism whose premises and conclusion are in categorical form Three categories are mentioned and each category is mentioned in two different statements The subject term of the conclusion is called the minor term of the syllogism The predicate term of the conclusion is called the major term of the syllogism The term that does not occur in the conclusion is called the middle term of the syllogism We can test whether a categorical syllogism is deductively valid by using what are known as “the Rules of the Categorical Syllogism” If an argument that is a categorical syllogism meets all of these rules, the argument is deductively valid If it fails to meet at least one rule, the argument is invalid Some of the rules concern whether a term is distributed A term is distributed, in a categorical statement, if that statement - all S are P - the subject term, S, is distributed, and the predicate term, P, is not In an E statement - no S are P - both the subject term, S, and the predicate term, P, are distributed
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Chapter 2 / Exercise 5
College Algebra
Gustafson/Hughes
Expert Verified
In an I statement - some S are P - neither the subject term, S, nor the predicate term, P, are distributed Finally in an O statement - some S are not P - the subject term, S, is not distributed; however, the predicate term, P, is distributed The rules of the categorical syllogism are as follows For a syllogism to be valid, the middle term must be distributed in at least one premise For a syllogism to be valid, no term can be distributed in the conclusion unless that term is also distributed in at least one premise. For a syllogism to be valid, at least one premise must be affirmative. For a syllogism to be valid, if it has a negative conclusion, it must also have a negative premise. And if it has one negative premise, it must also have a negative conclusi Summary Some arguments are deductively valid simply because of the way in which the terms all, none, some, and not are used. We can test to see whether an argument is this type of deductively valid argument using categorical logic In particular, the rules of the categorical syllogism are used to test whether a categorical syllogism is deductively valid. Even though many everyday arguments are not explicitly written in this form, many are implicitly syllogistic, and one can apply the rules of categorical syllogisms once the argument has been translated into categorical form. Module 7 Some arguments are formally valid due to the logical relationships between propositions These arguments are formally valid in what is called “propositional logic” This unit: how to translate an argument in English into propositional logic and test the argument for validity using both the truth table and short truth table methods
The Basic Symbols of Propositional Logic Some arguments are deductively valid purely because of the formal relationships between the propositions that they contain Ex: 1. My son is on the phone, or my wife is on the phone