Arguments

Argument Set of statements/sentences/propositions, some of which are offered as evidence for others. Conclusion: what the argument tries to prove or establish. Premises: propositions used as evidence for the conclusion. generally, well-accepted starting points Evidence: considerations that make a belief more likely to be true.

Socrates is a man. All men are mortal. Therefore, Socrates is mortal.

Deductive argument: intended to render the conclusion certain. truth of the premises would guarantee the truth of the conclusion Inductive argument: intended to render the conclusion probable. possible, even if extremely unlikely for premises to be true and conclusion false

More About Deduction

Good arguments True conclusions (important conclusions?) True premises Strong conditional support probability that conclusion is true if the premises are true

All members of species x have lungs. y is a member of species x. Therefore, y has lungs. y has lungs. Therefore, y is a member of species x.

valid invalid All members of species x have lungs. y is a member of species x. Therefore, y has lungs. y has lungs. Therefore, y is a member of species x. valid invalid

Validity A valid argument is one in which: it is logically impossible for the premises to be true and the conclusion false, together. there are no background assumptions that would make the premises consistent with a false conclusion. even an omnipotent being couldn’t make the premises true and conclusion false.

Validity Is about conditional support. don’t worry about whether the premises are actually true Holds in any context. suspend all your background knowledge about the world, except what’s needed to understand the premises and conclusion

An invalid argument is one that isn’t valid A sound argument: a valid argument with true premises follows that it must have a true conclusion

A valid argument can have: A false premise A false conclusion All false premises and a true conclusion The same sentence as one of its premises and as its conclusion Anything except: all true premises and a false conclusion

Logical terms Validity of an argument often hinges on special, logical terms: “all,” “some,” “and,” “if…then…,” “not,” etc.

valid (P1) All cetaceans are heterotrophs. (P2) Mauyak is a cetacean. (C) Mauyak is a heterotroph. Can’t place Mauyak in the Cetacean circle without putting her in the Heterotroph circle Heterotrophs Cetaceans Mauyak valid

invalid (P1) All cetaceans are heterotrophs. (P2) Mauyak is a heterotroph. (C) Mauyak is a cetacean. Can place Mauyak in the Heterotroph circle without putting her in the Cetacean circle Heterotrophs Cetaceans Mauyak Mauyak invalid

All instances of the form (P1) All Cs are Hs. (P2) m is a C. (C) m is an H. will have to be valid.

Belief Bias

Anything with a motor needs oil. Cars need oil. Therefore, cars have motors. Opprobines need oil. Therefore, opprobines have motors. invalid Arguments whose conclusions you already believe are more likely to seem valid. invalid

Why Demand Validity?

Enthymemes Incompletely stated arguments If we insist on validity, we ensure that all the reasons are made fully explicit.

(P1) The fastest jet from Los Angeles to San Francisco takes 1 hour and 15 minutes. (C) There’s no way to travel from LA to San Francisco in less than 1 hour. (P2) There is no faster way to travel from LA to San Francisco than by jet. presupposes which is currently true, but might not always be Insisting on validity forces us to make our presuppositions explicit.