Deduction: Validity is a matter of ARGUMENT FORM Separate out the “content” words from the “form” words Separate out the “content” words from the “form” words

If Washington was assassinated, then he’s dead. He wasn’t, so he’s not If W, then D Not W So not D If Washington was assassinated, then he’s dead. He wasn’t, so he’s not Invalid argument

If Clinton was assassinated, then he’s dead. He’s not dead, so he wasn’t assassinated. If C, then D Not D So not C If Clinton was assassinated, then he’s dead. He’s not dead, so he wasn’t assassinated. Valid argument

No campaign staffers are veterans, so some veterans are not pompous snobs, since all campaign staffers are pompous snobs. No campaign staffers are veterans All campaign staffers are pompous snobs Some veterans are not pompous snobs No campaign staffers are veterans All campaign staffers are pompous snobs Some veterans are not pompous snobs No C are V All C are P Some V are not P

No C are V All C are P Some V are not P Supply new content words preserving the form exactly, and trying to meet the definition of “invalid” An argument is invalid when it is possible for it to have a false conclusion despite having all true premises No Cats are Dogs T All Cats are Animals T Some Dogs are not Animals F All arguments with that form are invalid.

No Secretaries of State have been women since all women are Republicans and no Republicans have been Secretaries of State. All women are Republicans No Republicans have been Secretaries of State No Secretaries of State have been women All women are Republicans No Republicans have been Secretaries of State No Secretaries of State have been women All W are R No R are S No S are W

All W are R No R are S No S are W All cats are mammals No mammals are fish No fish are cats T -- T All Cats are mammals No mammals are animals No animals are cats T F -- F Sorry, this is a valid argument! The FORM is valid; the argument is unsound.

Strictly speaking: Arguments are cases or Substitution Instances of argument forms. When we say an argument is invalid, that’s shorthand for saying the argument is a substitution instance of an invalid argument form. When we say an argument is valid, that’s shorthand for saying it is a Substitution Instance of a valid argument form.

Some people who are desperate are criminals who will rob you. Some criminals are alcoholics, so some people who will rob you are alcoholics. Some people who are desperate are criminals who will rob you. Some criminals are alcoholics, so some people who will rob you are alcoholics. Some P who are D are C who will R. Some C are A, so some P who will R are A. Some Cats who are Furry are Animals who will Purr. Some Animals are Elephants Some Cats who will purr are Elephants T -- F

A counter-example preserves the FORM of an argument, and substitutes new content to show the possibility of that Form generating a False conclusion from True premises. Validity and Invalidity are matters of the FORM or structure of the argument, not matters dependent on the subject or content of the argument. It is impossible for a substitution instance of a valid argument form to begin with true premises and yield a false conclusion.

All galaxies are structures that contain black holes. All quasars are structures that contain black holes. All galaxies are quasars. All G are S All Q are S All G are Q All dogs are animals All cats are animals All cats are dogs TTFTTF

If gene splicing is successful, disease-resistant livestock will be produced. If genetics defects can be eliminated, disease-resistant livestock will be produced If gene splicing is successful, genetic defects can be eliminated. If G, then D If E, then D If G, then E If Socrates is a man, then he’s mortal. If Socrates is a goat, then he’s mortal. If Socrates is a man, then he’s a goat. TTFTTF

No C are E Some P are not C So Some E are not P No cats are dogs Some animals are not cats So Some dogs are not animals TTFTTF No creationists are evolutionists Some people who believe in the Bible are not creationists so Some evolutionists are not persons who believe in the Bible

Some politicians are people who will stop at nothing to win an election. No people who will stop at nothing to win an election are true statesmen So No politicians are true statesmen Some P are S No S are T So No P are T Some animals are mammals No mammals are fish So No animals are fish TTFTTF