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Lecture 3

Lecture 3 Philosophy 110

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University of Miami
PHI 110
Robin Neiman

9/5/13 Deductive Reasoning Argument Reconstruction If it is wrong to discriminate against women on the basis of gender, then it is wrong to discriminate against men on the basis of gender. Premise: It is wrong to discriminate against women Implicit Premise: Men are equal to women Conclusion: Therefore, it is wrong to discriminate against men as well. (deductive argument) Argument Reconstruction Stealing is wrong. Using a friend's car without asking permission is taking property without permission. So, using a friend's car without asking is wrong. Premise: Stealing is wrong Premise: Using a friend's car without asking is taking property without permission. Implicit premise: Taking property without permission is stealing Conclusion: Therefore, taking a friend's car without asking is wrong. There are two questions that must be considered when we evaluate a deductive argument: 1) Does the conclusion follow from the premises? 2) Should the premises be accepted as true? Testing for validity only considers the answer to the first question How do deductive arguments work? like analyzing math problems Premise: John has 16 cows = 16 Premise: Jill sold two of John's cows: -2 Premise: Jack gave 6 cows to John: +6 Conclusion: John has 20 cows Mathematical and Logical Reasoning A: Subject Matter Independence B: Arguments contain different structural parts C: Context clues and common sense to correctly identify the structure of 'natural language' arguments. Statements or propositions In logic, information can be represented by variables In order to represent a statement with a variable, it must be a meaningful statement that is either true or false Jack has a horse (j) = good Jack has (h) = bad 1) Assign one unique letter to each meaningful statement. 2) Assign the same variable to 2 statements that 'mean' the same thing Jack has a pig (p) Jack has a mammal (m) A mammal does Jack have (m) Jack owns a mammal (?) Connectives 4 basic connectives of putting pieces of information together And (&) I have a turtle and a fish Therefore, I have a fish Validity Test I have a turtle. Therefore, I have a fish. Invalid T ------ : The truth of the premises does not imply the truth of the F conclusion Jack and Jill are going to the party. Therefore, Jack will go to the party. Valid J & I --------- : Premises imply conclusion.
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