An argument is a reason for believing something.
Arguments consist of two or more claims, one of which is a conclusion. The conclusion is the claim the argument purports to give a reason for believing. The other claims are the premises. The premises of an argument are offered as a reason for believing its conclusion.
Some arguments provide better reasons for believing their conclusions than others. Evaluating an argument involves two essential steps:
- Determine whether or not the premises support the conclusion if they are true.
- Determine whether or not the premises are true.
The second of these tasks may involve evaluating further arguments in support of the premises. There is an obvious question to ask regarding (1). Namely, what is it for the premises of an argument to support its conclusion? Here, I will introduce the two standards of support that have been recognized and developed by philosophers. One is the standard of deductive validity and the other is the standard of inductive strength.
Here are two equivalent definitions of deductive validity:
(D) A deductively valid argument is an argument where if its premises are true, then its conclusion must be true.
(D’) A deductively valid argument is an argument where it is not possible for all of its premises to be true and its conclusion false.
Deductive validity is the strictest standard of support we can uphold. In a deductively valid argument, the truth of the premises guarantees the truth of the conclusion. Here are a few examples of deductively valid arguments
- If Socrates is human then Socrates is mortal
- Socrates is a human.
- Therefore, Socrates is mortal
- All monkeys are primates
- All primates are mammals
- So, all monkeys are mammals
In contrast, the following argument is not valid:
- If Sue misses her plane she will be late for the conference.
- Sue is late for the conference.
- Therefore, she missed her plane.
To see why the last argument is not valid, try to think of a possible scenario that makes both of the premises true and the conclusion false. One scenario is where Sue catches her plane, but her cab from the airport gets stuck in traffic. The validity or invalidity of these arguments is fairly obvious. But the validity or invalidity of many arguments is not so easy to see. Formal logic provides us with tools for testing more difficult arguments for validity.
A deductively valid argument may or may not have true premises. A deductively valid argument only provides one with a good reason for believing its conclusion if its premises are in fact true. If a deductively valid argument has all true premises, we say that it is deductively sound. For an argument to be deductively sound is one way for it to pass both steps (1) and (2) for evaluating arguments.
The other widely recognized standard of support for the conclusion of an argument is inductive strength. We can define inductive strength as follows:
(I) An inductively strong argument is an argument where it is not probable that its conclusion is false given that its premises are true.
Notice that the criteria for inductive strength in (I) looks much like the criterion for deductive validity in (D’). The biggest difference is in the use of the word “probable” rather than “possible”. This is a big difference. Possibility is a yes-or-no-affair. It either is possible for the premises of an argument to be true and its conclusion false or it isn’t. On the other hand, probability is a matter of degree. The conclusion of an argument may be more or less probable given the truth of its premises.
Corresponding to the notion of deductive soundness, an inductive argument that is both strong and has true premises is called a cogent inductive argument. Unlike the notion of deductive soundness, it is possible for an inductively cogent argument to have true premises and a false conclusion.