arguments

Arguments: 

Arguments S&V Chapter 6

Concepts: 

Concepts Argument Premise Conclusion: how to identify Deductive and Inductive arguments: how they differ Validity Soundness Logical form Logical and non-logical expressions Substitution instance: how to identify Method of counterexample

Argument: 

Argument A group of statements, one or more of which (the premises) are claimed to provide evidential reasons to believe one of the others (the conclusion) Factual claim: premises are asserted, i.e. put forth as true (at least “for the sake of the argument”) Inferential claim: premises provide evidential reasons to believe the conclusion.

Example of an argument: 

Example of an argument All men are mortal. Socrates is a man. [therefore] Socrates is mortal. 1 and 2 are premises; 3 is the conclusion.

Not everything is an argument: 

Not everything is an argument “A string of statements asserting or clarifying…views does not an argument make” Not an argument: I hate Bush. Every time I see his face I want to step on it. (assertion) Not an argument: I can’t stand Hillary. She’s such a Woman of the ‘80s--you can imagine her in a power-suit with shoulder-pads out to there and a scarf tied in a bow as a pretend necktie. (clarification)

Symptoms of an argument: 

Symptoms of an argument Premise indicators Since Because … Conclusion indicators Therefore So It follows that …

An argument is as an argument does!: 

An argument is as an argument does! An argument makes an inferential claim “The easiest way to identify an argument is to find the conclusion Ask: “What claim is the writer or speaker trying to get me to accept?”

Example of an argument: 

Example of an argument Poverty offers numerous benefits to the nonpoor. Antipoverty programs provide jobs for middle-class professionals in social work, penology, and public health. Such workers’ future advancement is tied to the continued growth of bureaucracies dependent on the existence of poverty. (J. John Palen, Social Problems)

Conclusion: 

Conclusion Poverty offers numerous benefits to the nonpoor. Antipoverty programs provide jobs for middle-class professionals in social work, penology, and public health. Such workers’ future advancement is tied to the continued growth of bureaucracies dependent on the existence of poverty. (J. John Palen, Social Problems)

Conclusion is what the arguer wants to prove: 

Conclusion is what the arguer wants to prove The conclusion is typically less obvious, more controversial than premises Premises are what we assume the hearer already believes

Deductive and Inductive Arguments: 

Deductive and Inductive Arguments Difference in inferential claim Deductive: premises are supposed to force (necessitate, guarantee) the conclusion Inductive: premises are just supposed to make conclusion probable NOTE: deductiveness and inductiveness are a matter of what is supposed to happen--not all arguments do what they’re supposed to do!

Example: An inductive argument: 

Example: An inductive argument Premise: 32% of all Nielson households watch The Simpsons. Conclusion: 32% (+/- 2%) of all American households watch The Simpsons This is a good inductive argument because the sample is large and fair The premise can’t force the conclusion because there’s more information in the conclusion!

Inductive Generalization: 

Inductive Generalization All Households Nielson Households

Inductive Arguments: 

Inductive Arguments There’s supposed to be information in the conclusion that’s not in the premises So even in a good inductive argument the premises don’t necessitate the conclusion I.e. it is logically possible for the premises to be true and the conclusion false Even though that’s improbable

Deductive Arguments: 

Deductive Arguments Premises are supposed to necessitate the conclusion Valid if this really happens: the premises really do necessitate the conclusion Validity is “internal” to the argument: it concerns the connection between premises and conclusion whether they’re true or not.

Validity: 

Validity The premises necessitate (force, guarantee) the conclusion It is not logically possible for the premises to be true and the conclusion false (“There is no possible world at which the premises are true and the conclusion is false”) It is truth-preserving: IF the premises are true then the conclusion must be true There is no information in the conclusion that’s not in the premises (“The conclusion is ‘contained’ in the premises”) It is not possible to represent the premises without representing the conclusion

A valid argument: 

A valid argument All men are mortal. Socrates is a man. [therefore] Socrates is mortal.

All men are mortal: 

All men are mortal men mortals

Socrates is a man: 

Socrates is a man men

Socrates is mortal: 

Socrates is mortal mortals men

Stupid arguments can be valid: 

Stupid arguments can be valid All Greeks are mathematicians Obama is a Greek [Therefore] Obama is a mathematician

Soundness: 

Soundness Validity + all true premises So sound arguments have true conclusions also The Obama argument is valid but not sound!

Validity is a matter of form: 

Validity is a matter of form All men are mortal Socrates is a man Socrates is mortal All Greeks are mathematicians Obama is a Greek Obama is a mathematician All S are P X is an S X is a P Both arguments are substitution instances of this form

Validity and Truth Value: 

Validity and Truth Value Valid True premises/true conclusion (sound) False premises/false conclusion False premises/true conclusion Invalid True premises/true conclusion False premises/false conclusion False premises/true conclusion True premises/false conclusion

Logical form: 

Logical form Logical expressions: all, no, some, are, not, and, or, if-then, if and only if . . . Non-logical expressions: “content” words, e.g. men, mortal, mathematician, Greek, Socrates, Obama . . .

Same logical form: 

Same logical form Same logical expressions Same pattern of same non-logical expressions

Same logical form: 

Same logical form All dogs are mammals All mammals are vertebrates All dogs are vertebrates All ants are insects All insects are arthropods All ants are arthropods

Different logical form: 

Different logical form All dogs are mammals All mammals are vertebrates All dogs are vertebrates All cats are vertebrates All mammals are vertebrates All cats are mammals

Validity is a matter of form: 

Validity is a matter of form If two arguments are of the same form then they’re either both valid or both invalid Is this true? No. But we will define “validity” as “formal validity” to make it true.

Valid but not formally valid: 

Valid but not formally valid George is a bachelor Therefore, George is not married

Why not formally valid?: 

Why not formally valid? George is a bachelor George is not married Ducati is a dog Ducati is not warm-blooded The argument at left is valid but its validity doesn’t come from its form. We resolve to ignore such arguments! We stipulate that from now on “valid” means “formally valid”!

Given our definition of validity…: 

Given our definition of validity… Arguments of the same form are the same as regards validity/invalidity So, if one argument of a given form is invalid, so are all other arguments of the same form If an argument has all true premises and a false conclusion then it must be invalid

The Method of Counterexample: 

The Method of Counterexample To test an argument for validity, we try to find another argument of the same form that has all true premises and a false conclusion. If we can find such an argument then, given our definition of validity, the original argument is shown to be invalid If we can’t, it shows nothing

Counterexample: 

Counterexample Argument C is a counterexample to Argument A iff A and C are substitution instances of the same logical form, and C has all true premises and a false conclusion If an argument has a counterexample then it is invalid!

Example: 

Example All dogs are vertebrates All mammals are vertebrates All dogs are mammals All x > 2 are x > 1 All x > 10 are x > 1 All x > 2 are x > 10 These arguments are of the same form so must be the same as regards validity/invalidity. The argument at the right must be invalid because it has all true premises and a false conclusion so the argument at the left must be invalid also. The argument at the right is a “counterexample” to the argument at the left.

So, what do I have to know for the quiz?: 

So, what do I have to know for the quiz? How to recognize arguments that are substitution instances of the same logical form How to determine when one argument is a counterexample to another What this shows about validity What we mean by soundness