5.1 and 5.2 Notes PDF

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5.1 and 5.2 Notes Fall 2018...

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5.1, 5.2 ● ●

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Syllogism ○ A deductive argument consisting of two premises and one conclusion Categorical syllogism ○ A syllogism consisting of three categorical propositions and containing a total of three different terms (each of which appears twice in distinct propositions) and capable of being translated into standard form ○ ex) ■ All soldiers are patriots ■ No traitors are patriots ■ Therefore, no traitors are soldiers Major term ○ The predicate of the conclusion Minor term ○ Subject of the conclusion Middler term ○ Provides the middle ground between the two premises ○ One that occurs once in each premise but does not occur in the conclusion Major premise ○ Premise that contains major term Minor premise ○ Premise that contains minor term Standard-form categorical syllogism ○ All three statements are standard form categorical propositions ○ The two occurences of each term are identical ○ Each term is used in the same sense throughout the argument ○ Major premise is listed first, minor premise second, and conclusion last Mood ○ Consists of the letter names of the propositions that make it up ○ Major (always first) = A, minor (always second) = O, conclusion (always last) = E, mood = AOE Figure ○ Determined by the location of the two occurences of the middle term in the premises ○ 4 options → look at pick, but remember outline of collared shirt mood/figure example ○ EIO-4 ○ Mood = EIO, figure = 4 ○ Some are unconditionally valid, others are conditionally valid (in the table from the book)

5.2 Venn Diagrams Rules for Boolean Standpoint ● Only do marks (shading or x) for premises NOT conclusion ● Do universal premises first, then particular premises ○ Two universal, doesnt matter which is first ● Use circles corresponding to terms in the statement ● Particular statements have two meanings ○ Some S are P means at least one S exists and that S is a P ● Shade ALL of the area in question ● The area where an X goes is always initially divided into two parts. If one of these parts has already been shaded, the X goes in the unshaded part ○ If one of the two parts is not shaded, the X goes on the line separating the two parts ● Dont ever put an X on the intersection of two lines or dangling outside diagram Doing it is pretty self explanatory, just practice it Rules for Aristotelian Standpoint ● Reduce the syllogism to its form and test it from Boolean standpoint. If the form is valid, proceed no further -- its valid from both standpoints ● If the syllogistic form is invalid from the Boolean standpoint and has universal premises and a particular conclusion then adopt the aristotelian standpoint and look to see if there is a venn circle that is completely shaded except for one area. If there is, enter a circled x in that area and retest the form ● If the syllogistic form is conditionally valid, determine if the circled x represents something that exists. If it does, the condition is fulfilled and the syllogism is valid from the aristotelian standpoint...