University:
Manchester University
Course:
INTD 343 | Philosophy of Mind
Academic year:

2019
Views:

67

Pages:

12
Author:

Clint W.

Deductive Logic Overview (1) Distinguishing Deductive and Inductive Logic (2) Validity and Soundness (3) A Few Practice Deductive Arguments (4) Testing for Invalidity (5) Practice Exercises Deductive and Inductive Logic Deductive vs Inductive Deductive Reasoning • Formal (the inference can be assessed from the form alone). • When sound, the conclusion is guaranteed to be true. • The conclusion is extracted from the premises. Inductive Reasoning • Informal (the inference cannot be assessed by the form alone). • When cogent, the conclusion is only probably true. • The conclusion projects beyond the premises. Deductive Logic: Basic Terms Validity • A property of the form of the argument. • If an argument is valid, then the truth of the premises guarantees the truth of the conclusion. Soundness • A property of the entire argument. • If an argument is sound, then: (1) it is valid, and (2) all of its premises are true. Validity If an argument is valid, then the truth of the premises guarantees the truth of the conclusion. A valid argument can have: • True premises, true conclusion • False premises, true conclusion • False premises, false conclusion A valid argument can not have: • True premises, false conclusion Validity If an argument is valid, then the truth of the premises guarantees the truth of the conclusion. A valid argument can have: • True premises, true conclusion • False premises, true conclusion • False premises, false conclusion All dogs are mammals. Ed is a dog. ∴ Ed is a mammal. A valid argument can not have: • True premises, false conclusion Ed Validity If an argument is valid, then the truth of the premises guarantees the truth of the conclusion. A valid argument can have: • True premises, true conclusion • False premises, true conclusion • False premises, false conclusion All cats are dogs. Ed is a cat. ∴ Ed is a dog. A valid argument can not have: • True premises, false conclusion Ed Validity If an argument is valid, then the truth of the premises guarantees the truth of the conclusion. A valid argument can have: • True premises, true conclusion • False premises, true conclusion • False premises, false conclusion All cats are toads. Ed is a cat. ∴ Ed is a toad. A valid argument can not have: • True premises, false conclusion Ed Sample Deductive Arguments Deductive Argument #1 (1) If it’s raining, then you’ll need your umbrella. (2) It’s not raining. ∴ (3) You won’t need your umbrella. Checking for Invalidity Two Methods of Counter-example Alternate scenario Imagine some alternate scenario in which the premises of the argument will be true, but the conclusion false. Substitution (two-step) (1) (2) Determine the form of the argument. Substitute other statements, such that all the premises will be true but the conclusion false.