What Precisely Does It Mean to Say that an Argument Is Valid?

Modified slightly August 30, 2002.

Composed by Jan Garrett
The idea of deductive validity can be defined in more than one way, but they all amount to the same thing:

To say that a deductive argument is valid means (1) its conclusion (really) necessarily follows from its premises;

To say that a deductive argument is valid means (2) it is impossible for its premises all to be true while the conclusion is false.

Check your understanding (answers with some explanation below)

True or False:

A deductive argument has to be valid if:

1) the premises are said to entail the conclusion
2) the premises necessarily entail the conclusion
3) it is impossible for the premises all to be true while the conclusion is false.
4) its premises are true
5) its conclusion is false
6) all its statements are true
7) its conclusion necessarily follows from its premises
8) we can imagine its conclusion to be true
9) the argument is an example (instance) of a valid argument form

A deductive argument has to be invalid if:

10) the premises and conclusion are all false
11) the premises are false
12) its premises do not necessarily entail its conclusion
13) the premises are all true but the conclusion is false
14) it is possible for the premises all to be true while the conclusion is false
15) at least one premise is false
16) we can tell a consistent story that makes the premises true and the conclusion false
17) we can clearly conceive a situation that makes the premises true and the conclusion false
18) the argument is an example (instance) of an invalid argument form

Answers:

Validity

1) false; even invalid arguments make the claim that their premises entail their conclusion.

2) true

3) true; this is essentially the definition of deductive validity.

4) false; all that is required is that if the premises were true, then the conclusion would have to be true.

5) false; a valid argument can have a false conclusion, but that is never sufficient to determine its validity.

6) false; the premises of a valid argument can in fact all be false; the conclusion of a valid argument can be false; the only thing required is that if the premises were true, the conclusion could not be false.

7) true; not just is said to necessarily follow . . . but really necessarily follows . . .

8) false; the possible or conceivable truth of a conclusion is no guarantee of the deductive validity of an argument; validity has to do with the relationship between premises and conclusion.

9) true; but this is useful only if you know which argument forms or argument patterns are valid ones. (In a full logic course you would learn how to determine which argument forms are valid forms.)

Invalidity

10) false; it is possible for a valid argument to have all its statements false.

11) false; it is possible for a valid argument to have false premises

12) true; but it is not enough if somebody alleges that the premises do not entail the conclusion; it must be true that the premises do not entail the conclusion. Note that we are talking about deductive entailment, or necessary entailment, not inductive or probable entailment.

13) true; the fact that the premises are all true while the conclusion is false shows that it is indeed possible for the premises all to be true while the conclusion is false. This (beginning with "it is indeed possible") is the defining characteristic of invalid arguments.

14) true; this is probably the most precise way of stating the idea of deductive invalidity

15) false; the premises of a valid argument may also be false

16) true; if we can do this, then it is possible for the premises all to be true while the conclusion is false.

17) true; same reason as in #16

18) true (this must be qualified; see note below); but to use this you must know which argument forms are invalid. (In a full logic course you would learn how to determine which argument forms are valid forms.)


Regarding question 18 I received (8-27-02) the following interesting critical note from Bryan O'Neal (bryan.oneal@moody.edu):

I wanted to thank you for your web posting on valid arguments (www.wku.edu/~garreje/validarg.htm); I think it is a helpful summary for my students. However, you may want to reconsider question 18. Being an instance of an invalid form is not a sufficient condition for being an invalid argument - for example, the classic
All men are mortal.
Socrates is a man.
Socrates is mortal.
is an instance of (the obviously invalid)
A
B
C
as well as an instance of a valid argument form. [That is,
all A are B
a is an A
a is a B.

--J.G.]

Furthermore, the following argument is valid, even though it affirms the consequent, by virtue of having a necessarily true conclusion:

If 2 + 2 = 4, then today is Tuesday.
Today is Tuesday.
2 + 2 = 4
Bryan and his bright students are correct.