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# lecture 5 - Logic and Reasoning[5 PHIL 102 Sept 7*Check the...

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Logic and Reasoning [5] PHIL 102 Sept 7 *Check the Compass website frequently!* Homework barb2right not graded, no deadline barb2right some of it discussed Friday barb2right your responsibility barb2right troubles? Reach out! RECAP Chapter 1: what CT is good for? How to do it? Chapter 2: what are the obstacles to CT? How can we overcome them? Chapter 3: making sense of arguments So far… Statement (claim): An assertion that something is or is not the case. = a proposition is (expressed by) a sentence that is true or false “Washington is the capital of the USA” “Grass is blue” Not statements (claims, propositions) : “Close the door!” (order) “Ouch” (exclamation) Deductive Arguments 1. A deductive argument is intended to provide conclusive support for its conclusion. 2. A deductive argument that succeeds in providing conclusive support for its premise is said to be valid . A valid argument is such that if its premises are true, its conclusion must be true. 3. A deductively valid argument with true premises is said to be sound. Chapter 3: Making Sense of Arguments Recap: Validity Valid argument: a. the conclusion follows from the premises b. there is no way for the premises to be true and the conclusion false c. if you accept the premises (as T), you must accept the conclusion (as T) Note that there are valid arguments with - false premises and true conclusion - one false premise and false conclusion - one false premise and true conclusion (examples?) Can there be valid arguments with true premises and false conclusion? 5 Recap: Soundness S = V + TP - Sound argument = valid, and has true premises - We can be sure the conclusion is true - Rules out oddities such as Bread is a stone Stones are nourishing Therefore, bread is nourishing. 6

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Inductive Arguments 1. An inductive argument is intended to provide probable support for its conclusion. 2. An inductive argument that succeeds in providing probable support for its conclusion is said to be strong . A strong argument is such that if its premises are true, its conclusion is probably true . 3. An inductively strong argument with true premises is said to be cogent. Examples of inductive arguments Most lawyers are rich. Therefore, Jones, who is a lawyer, is likely to be rich. - Strength of support for the conclusion? So-so Examples of inductive arguments Scientific studies show that 99% of pigeons have three feet. Therefore, it’s likely that the next pigeon I see at my window will have three feet. - Strength of support for the conclusion? Very good. - But first premise false! Judging Arguments —telling (1) whether an argument is deductive or inductive and (2) whether it gives good reasons for accepting the conclusion Step 1. Find the argument’s conclusion and then its premises. Step 2. Ask: Is it the case that if the premises are true the conclusion must be true?
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