Midterm Review Chapter 5

For us, the options tonight are either to watch a movie at home or go out for dinner. We won't watch a movie at home. Thus we'll go out for dinner.

For us, the options tonight are either to watch a movie at home or go out for dinner. We won't watch a movie at home. ------------------------- Thus we'll go out for dinner. valid

Many undergraduates in the United States receive some form of financial aid. Since Jane is a college undergraduate, she has financial aid.

Many undergraduates in the United States receive some form of financial aid Since Jane is a college undergraduate ---------------------- she has financial aid invalid

Simon Peterson is a cardinal. Since no cardinals are Protestants, Peterson is not a Protestant.

Simon Peterson is a cardinal. Since no cardinals are Protestants --------------------- Peterson is not a Protestant. valid

Since this is a freshman-level course, it is an easy course, for all freshman-level courses are easy.

Since this is a freshman-level course for all freshman-level courses are easy. ------------------- it is an easy course valid

Such an argument is, by definition,

invalid: its premises do not entail its conclusion. Note that we're introducing here some different expressions that all mean the same thing. To say that an argument is valid is equivalent to saying that its premises entail its conclusion. And both of these are equivalent to saying that the argument is truth-preserving, and that its conclusion follows necessarily from its premise or premises.

No people who wear wool sweaters are cold. So Uncle Thorvald is never cold, because he always wears a wool sweater.

No people who wear wool sweaters are cold. Uncle Thorvald always wears a wool sweater. --------------------- Uncle Thorvald is never cold valid

What does it mean to say that a valid argument is 'truth-preserving'?

Only valid arguments are truth-preserving: If their premises are true, then it is not possible for their conclusion to be false.

Define validity and invalidity in terms of argument form.

Validity consists in this relationship, and nothing more. The fact that an argument might have one or more false premises is of no importance for its validity, which is entirely a matter of argument form. Invalidity is also a matter of argument form: an argument form is invalid if and only if an argument with that form could have true premises and a false conclusion. But 'could' here means 'logically possible,' which leaves open the possibility that a given invalid argument may have true premises and a true conclusion.

When is an argument invalid? When is an argument valid?

an argument form is invalid if and only if an argument with that form could have true premises and a false conclusion. In a valid argument, it makes no logical sense to accept the premises and reject the conclusion.

Contradictory statements

cannot have the same truth value: if one is true, the other must be false.

In claiming that false conclusions are 'possible,'

if there is some scenario, 'possible' in the sense that it implies no internal contradiction, in which these arguments' premises could be true and their conclusions false at once, then the arguments are invalid.

Since a valid argument's premises,

if true, determine that the conclusion is true, valid arguments can also be said to be truth-preserving.

Invalidity

is also a matter of argument form: an argument form is invalid if and only if an argument with that form could have true premises and a false conclusion.

Bart Simpson cannot run for governor of California because Bart Simpson is a cartoon character, and no cartoon characters are citizens of California. Only citizens of California are eligible to run for governor of California.

Bart Simpson cannot run for governor of California, because Bart Simpson is a cartoon character no cartoon characters are citizens of California. ------------------------ Only citizens of California are eligible to run for governor of California. valid

A deductive argument is

valid if and only if its premises necessitate or entail its conclusion, where 'entailment' is defined as in Box 1.

What is an argument form? And how does an argument differ from an argument form?

An argument form is the type of logical mold or pattern that each argument exemplifies. Often the same argument form is the underlying pattern of many actual arguments. To show the form of an argument, it is customary to replace some words in it by "place holders" or symbols such as capital letters, keeping only the words that have a logical function.

counterexample

A counterexample to prove the invalidity of a given argument is another argument exemplifying the same form but with true premises and a false conclusion.

All squares are polygons; for all squares are rectangles, and all rectangles are polygons.

All squares are polygons all squares are rectangles ---------------- all rectangles are polygons valid

Validity

An argument cannot be 'sort of valid.' It's either valid or it's not. Furthermore, there is a simple test to determine the validity of an argument. Validity is best thought of as a kind of relation between premises and conclusion in an argument, where the actual truth or falsity of the component statements is largely irrelevant. What matters is: do the premises necessitate the conclusion? If so, it's valid. If not, it's invalid.

The upshot of all this is:

In a valid argument, it makes no logical sense to accept the premises and reject the conclusion.

Validity and Argument Form

In any argument exemplifying a valid form, there is a relationship of entailment between premises and conclusion. If the argument's premises are true, its conclusion cannot be false. Validity consists in this relationship, and nothing more. The fact that an argument might have one or more false premises is of no importance for its validity, which is entirely a matter of argument form.

JJ's won't get the support of the Chamber of Commerce, for the Chamber of Commerce usually supports only local firms, and JJ's is from out of state.

JJ's won't get the support of the Chamber of Commerce for the Chamber of Commerce usually supports only local firms --------------------- and JJ's is from out of state. invalid

The Washington Redskins is a football team that has thousands of enthusiastic fans. The same is true of the Denver Broncos, the New York Jets, the Minnesota Vikings, and the Dallas Cowboys. It follows that all American professional football teams have thousands of fans.

The Washington Redskins is a football team that has thousands of enthusiastic fans The same is true of the Denver Broncos, the New York Jets, the Minnesota Vikings, and the Dallas Cowboys. -------------------------------- It follows that all American professional football teams have thousands of fans. invalid

What is entailment? How is entailment related to validity?

There is entailment in an argument if and only if the truth of the argument's premises guarantees the truth of its conclusion—in the sense that, if the premises are all true, the conclusion cannot be false. Such an argument is valid and truth-preserving.

entailment

There is entailment in an argument if and only if the truth of the argument's premises guarantees the truth of its conclusion—in the sense that, if the premises are all true, the conclusion cannot be false. Such an argument is valid and truth-preserving.