Dana Nelkin

ARGUMENTS: A GUIDE

I. Important concepts and terminology

Arguments fall into two broad categories: deductive and inductive.

Deductive Argument: A deductive argument is an argument whose conclusion is intended to follow from its premises.  In other words, a deductive argument aims to guarantee the truth of the conclusion, given the premises.

Inductive Argument: An inductive argument is an argument whose premises are intended to provide strong support for its conclusion (but not guarantee the truth of the conclusion).

In order for a deductive argument to be successful (that is, to succeed in showing its conclusion to be true), it must have true premises and it must be valid.

Valid: a valid argument is one whose conclusion follows from its premises.

Test for validity: Ask: “If the premises are true, must the conclusion be true?”  If the answer is “yes”, the argument is valid.  If the answer is “no”, the argument is not valid. 

Note: validity is a feature of the logical form of the argument.  An argument is valid when the premises bear the right logical relation to the conclusion.  Thus, validity has nothing to do with whether the premises or conclusion are in fact true.  For example, the following argument is valid:

Argument A

(1) If all UCSD classes are held in Montana, then Philosophy of Religion is held in Montana.

(2) All UCSD classes are held in Montana.

∴(3) Philosophy of Religion is held in Montanaa.

[The symbol, “ ∴ ” means “therefore”]

Argument A is a valid argument.  The reason is that the conclusion follows from the premises (even though one of the premises is not true).  The test for validity: if the premises are true, must the conclusion be true?  The answer is “yes”. 

However, this is not a successful argument.  The reason is that for an argument to be successful, it must not only be valid, but it must also have true premises.  When an argument has both of these qualities, the argument is sound.

II. Some Hints for judging the validity of arguments

Since validity is a feature of the logical form of arguments (and is dependent on the actual truth of the premises), it is sometimes helpful to substitute symbols for simple sentences that appear in arguments.  For example, the form of Argument A can be represented as follows:

Let P=all UCSD classes are held in Montana, and let Q=Philosophy of Religion is held in Montana.

(1) If P, then Q.

(2) P

∴(3) Q.

Since the form of the argument is valid, you can substitute any sentences you like for P and Q and the argument will be valid.  For example, Argument B below has the same form as Argument A.

Argument B

(1) If there is smoke, there is fire.

(2) There is smoke.

∴(3) There is fire.

Sometimes when you are trying to evaluate an argument that has difficult philosophical premises, it is helpful to set out a parallel argument of the same form with easier premises.  If the argument you construct is valid and has the same form as the philosophical one, then the philosophical one is valid, too. 

Here is another example:

Argument C

(1) If it is always wrong to steal, then it is wrong to steal to save someone’s life.

(2) It is not wrong to steal to save someone’s life.

∴(3) It is not always wrong to steal.

This argument has the following form:

(1) If P, then Q.

(2) Not-Q.

∴(3) Not-P.

If you are having difficulty judging whether Argument C is valid, try substituting other sentences for P and Q.  For example, let P=there is smoke and let Q=there is fire.

Argument D

(1) If there is smoke, then there is fire.

(2) There is not fire.

∴(3) There is not smoke. 

Argument D is valid.  Since it is of the same form as Argument C, Argument C is valid, too. [Note: C and D share the same form as James Rachels’ main argument for the conclusion that there is no morally significant difference between killing and letting die.]

III. Practice arguments

Here are some examples for you to evaluate.  Are each of the following valid or invalid?

Argument E

(1) Freud is either in the library or eating lunch.

(2) Freud is not in the library.

∴(3) Freud is eating lunch.

Argument F

(1) If Jamie went to the park, she did not study.

(2) Jamie did not study.

∴(3) Jamie went to the park.

Argument G

(1) San Diego is in California.

(2) If San Diego is in California, San Diego is in the USA.

∴(3) San Diego is in San Diego County.

IV. Important things to remember

Even if an argument is not sound, it does not mean that its conclusion is false. [Try to think of an example of an argument that is not sound, but has a true conclusion.]

Even if an argument has only true premises, it does not mean that its conclusion is necessarily true