Introduction to Philosophy Lecture 2 A deeper look at arguments By David Kelsey

Conclusions as premises The Margaret example (example 1), 1) Every student who made 90 percent or better on the midterms already has an A. 2) Margaret made a 94 percent on the midterms. Thus, 3) Margaret already has an A. 1) Margaret already has an A. 2) All students who have an A are excused from the final exam. Thus, 3) Margaret is excused from the final exam.

Unstated Conclusions Unstated Conclusions: Conclusions that are entailed by the words of the text. The Republicans example (example 2): 1) The political party that best reflects mainstream opinion will win the most seats in congress. 2) The republicans certainly best reflect mainstream opinion. What is the unstated conclusion?

Independent Premises Independent premises: independently support the conclusion of an argument.

The speed limit example An argument with independent premises: Speed limit example (example 3): 1) Raising the speed limit will wear out the highways faster. 2) Raising the speed limit will result in more highway deaths. Thus, 3) We should not raise the speed limit.

Dependent Premises Dependent premises: support the conclusion of an argument only with the help of some other premise. What if a dependent premise is false? Gas to waste (example 4): 1) Raising the speed limit will waste gas. 2) We don’t have any gas to waste. Thus, 3) We shouldn’t raise the speed limit.

Good arguments A good argument: The premises both support its conclusion and are reasonable Reasonable? Requisite Support?

Valid arguments Valid arguments Necessary connection between premises and conclusion The premises entail the conclusion

Valid arguments: false premises & false conclusions We can have a valid argument with a false premise and a false conclusion. George Bush example (example #5): 1) George Bush is a robot. 2) If George Bush is a robot then he isn’t the president. Thus, 3) George Bush isn’t president. And we can have a valid argument with false premises and a true conclusion: The moon is made of green cheese example (example #6): 1) The moon is made of green cheese. 2) All things made of green cheese orbit the Earth. Thus, 3) The moon orbits the Earth.

A validity metaphor Form: Valid arguments have a certain form to them The link between premises and conclusion The puzzle metaphor:

2 more Validity tricks 2 more tricks: Addition metaphor: Imagine an argument as a mathematical problem of addition. Covering up the conclusion: Cover up the conclusion and ask: what do the premises entail?

Sound Arguments A sound argument: The Giants example (example #7): 1) The Giants won the superbowl. 2) If a team loses a playoff game, then they don’t win the superbowl. Thus, 3) The Giants didn’t lose a playoff game. Dreaming example (example #8): 1) Either I am in class right now or I am dreaming it. 2) I am in class right now. Thus, 3) I am not dreaming it.

Strong Arguments A strong argument April showers example (example #9): 1) Every April we get some rain. Thus, 2) We will get some rain this April.

Strong arguments: false premises & false conclusions A strong argument with a false premise and a false conclusion: Gravity example (example #10): 1) Every time I have ever dropped anything from my hand it floats up to the sky. Thus, 2) if I drop this pencil it will float up to the sky. A strong argument with true premises and a false conclusion. Swans example (#11): 1) Every swan I have ever seen is white. Thus, 2) all swans are white. (All swans are not in fact white as there are black swans in Australia!)

Cogent arguments A cogent argument: 1. 2. The sun will rise & set tomorrow (example #12): 1) Every day of my life the sun has risen in the morning and set in the evening. Thus, 2) Tomorrow the sun will rise in the morning and set in the evening.

Deduction and Induction Deductive arguments: valid or intended to be valid. Necessary conclusions Which of our 12 examples are deductive? Inductive arguments: not valid. Strong? Likely conclusions Which of our 12 examples are inductive?

Unstated Premises again Identifying the unstated Ask: What must be assumed to make it either valid or strong? Add a general claim that connects the premises and conclusion Cheating example (#12): 1) This is the second time you caught her cheating. 2) she shouldn’t pass the class. This argument becomes valid when we add this premise: 1.5)

Determining the Unstated premise Now Ask: Is the assumption reasonable? Yes or No? Determining what must be assumed to make an argument strong

Unstated premises & Strong arguments The bloodhound example (#13): 1) Moore’s dog is a bloodhound. Thus, 2) Moore’s dog has a keen sense of smell. What do we need to add to make this argument valid? What do we need to add to make this argument strong?