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# Logical Forms, Counter-Examples, and Categorical Syllogisms PHIL 2441-004

CU Denver

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This 3 page Class Notes was uploaded by Cydney Tinsley on Thursday August 25, 2016. The Class Notes belongs to PHIL 2441-004 at University of Colorado Denver taught by Alexander Hughes in Fall 2016. Since its upload, it has received 4 views. For similar materials see Logic, Language and Scientific Reasoning in Philosophy at University of Colorado Denver.

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Date Created: 08/25/16

Logic, Language, and Scientific Reasoning Cydney Tinsley Day 2: Strength, Categorical Syllogisms, Counter-Examples, and Logical Form Strength, Categorical Syllogisms, Counter-Examples, and Logical Form 1. Validity is transitive. If you make one valid argument and then another in the same form, the other one will also be valid. Adding information (premises) to a valid argument will not deduct from the probability that the conclusion is true, given that the premises are true. Because of this, it’s possible to create long chains of valid arguments. a. Example: A is after B. B is after C. Therefore, A is after C. b. Example: Everything is red. ----------------------------Valid This is red. Everything is red. ---------------------------Valid Something is red. This is red. ---------------------------Valid Something is red. 2. Anything less than validity is not transitive. Adding information will drastically change the argument. Each link in the chain lowers the probability of the conclusion being true. a. Example: The coin has been flipped. ------------------------------ .75 Probability It will come up heads. It will come up heads. ------------------------------.75 Probability I will win the game. The coin has been flipped. ------------------------------.56 Probability (.75 X .75) I will win the game. 3. Categorical Syllogisms a. Categorical syllogisms involve quantifiers, mainly all, no and some. Each sentence in a categorical syllogism will have two categorical expressions, giving a total of three categorical expressions. If one valid Logic, Language, and Scientific Reasoning Cydney Tinsley Day 2: Strength, Categorical Syllogisms, Counter-Examples, and Logical Form argument follows the same logical form as another argument, that argument will be valid too. i. Logical Form is just the pattern, a fill-in-the-blanks. So long as you fill in the same information for each letter, you’ll get the pattern. 1. For example, this is a logical form: All __A__ __B__ All __dogs__ are __mammals__ All __B__ __C__ All __mammals__ are __animals__ _______________ _____________________________ All __A__ __C__ All __dogs__ are__animals__ 4. Counter Examples a. A counter example is used to ‘bust’ an argument or to show that the logical form is invalid. i. Example: All __A__ __B__ Some __B__ __C__ _________________ All __A__ __C__ To make a counter-example, it’s sometimes useful to make a drawing: B is the big circle. Both A and C are in their own little circles inside B. For this example, let A= 1-5, B= 1-10, and C= 6-10. If we follow the logical form above, this is what we get: All numbers 1-5 are in 1-10. Some numbers 1-10 are in 6-10. _________________ All numbers 1-5 are in 6-10. Obviously, 1-5 can’t be 6-10. Therefore, the argument is invalid. Your counter-example disproved it. Logic, Language, and Scientific Reasoning Cydney Tinsley Day 2: Strength, Categorical Syllogisms, Counter-Examples, and Logical Form

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