Philosophy 105
Fall 2005
Lecture Notes - Chapter 4

I. Argument Strength - Basic Ideas

Argument evaluation includes two main parts: examination of the connection between premises and conclusion, and evaluation of the premises themselves. The former is entirely internal to the argument - you don't bring in background knowledge. Three possible outcomes: valid, cogent, ill-formed. If an argument is ill-formed, it should be rejected (or revised). If it is well-formed, then evaluation continues.

There are two main terms that apply to arguments as result of the status of their premises: soundness and strength. These are analogues of truth and justification. Soundness is the evaluative term that is applied and discussed in most courses and books. But we will largely ignore it, and focus on strength instead. There are two reasons for this: i) for our purposes, the more important evaluation of an argument is whether it is strong rather than whether it is sound.

I’ll explain this below. ii) it will be easiest for us if we keep the method as similar as possible for valid arguments and for cogent arguments. While deductive soundness is easy to understand and work with, there is no clear analogue of soundness for cogent arguments. But there is an analogue in the case of strength. Thus, we’ll discuss strength almost exclusively.

II. Deductive Strength

See definition in text. Some simple examples:

Argument 1
1. All politicians are over 5’5” tall.
2. Bush is a politician.
3. Bush is over 5’5” tall.

This is valid, but weak. We know that (1) is false, so the argument is weak even if its conclusion is true. It is weak for all of us because we are all justified in rejecting (1). [It’s also an unsound argument.]

For an example of a strong argument, see Argument 4.2 in text. [It is also sound.] "Soundness" is the standard concept used in logic. A deductively sound argument is valid and has true premises.

To see why we’ll focus on strength, consider the arguments that follow:

Argument 2
1. Either the total number of voters in the next presidential election will be even or it will be odd.
2. The number will not be even.
3. The number will be odd.

Argument 3
1. Either the total number of voters in the next presidential election will be even or it will be odd.
2. The number will not be odd.
3. The number will be even.

Both are valid. One is sound. The fundamental idea of a good argument - the sort of argument we should evaluate favorably - is one that makes belief in its conclusion reasonable. But neither of these 2 arguments does that, even though one in fact is sound. They are not strong, because we are not justified in believing (2) of either argument. So, this is one case in which strength and soundness diverge. For our purposes, the judgment about strength is the important one.

A second kind of case in which strength and soundness may diverge has to do with arguments like those discussed on p. 99 of the text. These are sometimes called "circular arguments." They are valid. And they may be sound. But, typically at least, they have an unjustified premise and are weak.

It’s important to remember that for an argument to be strong it has to be reasonable to believe the conjunction of all the premises of an argument. See Argument 4.5 to understand why. It is valid. As we've set it up, each premise is reasonable. But it is not a good argument. This is because what's required is that it is reasonable to believe the conjunction of all the premises. And there are some odd cases, such as this one, where each premise looks ok but their conjunction is not reasonable. So, this condition must be included in the official interpretation of the definition of strength.

III. Inductive Strength

A. Basic Idea

Consider:

Argument 4
1. Most UR people (students, faculty, staff) are over 5 feet tall.
2. The next person to enter this room will be a UR person.
3. The next person to enter this room will be over 5 feet tall.

This is cogent, and, apparently, strong. It is a good argument and it is reasonable for you to accept its conclusion.
One point to note is simple and perfectly analogous to what we just saw with deductive strength. The relevant fact about the premises is that they are justified. Consider the following argument.

Argument 5
1. Most correct callers of a coin toss are pleased.
2. Jones will be a correct caller of a coin toss.
3. Jones will be pleased.

(Assume that you know that (1) is true and that Jones has just called a coin toss - he said “heads”.) You can't reasonably say that this argument has a false premise- that would commit you to the falsity of (2). But, as of now, it isn't a strong argument - you aren’t justified in believing its conclusion on the basis of the argument. Thus, it’s a weak argument. This is because you aren't justified in accepting (2). This is just like what we saw before in the case of deductive arguments. (Thinking about an argument that says that most incorrect callers are displeased and Jones will be incorrect can make this example exactly parallel to the one about Args 2 and 3.)

B. Why Inductive Strength is More Complicated Than Deductive Strength

Before we can conclude that an argument is inductively strong, we have to think about some other things than its form and the merits of its premises. Induction is more complex than deduction in this respect. Consider this argument:

Argument 6
1. Most UR classes do not meet in Morey.
2. PHL 105 is a UR class.
3. PHL 105 does not meet in Morey.

This is cogent, both premises are true and justified. And the conjunction issue isn't relevant either. But this isn’t a good argument - you aren’t now justified in believing its conclusion. So, if all that were required for inductive strength were cogency plus justified premises, then this arg. would pass the test. But we know that something has gone wrong here. And the problem has to do *not* with the structure or with the premises themselves. All of that is fine. The problem is that we have background evidence that is relevant here and counts against the conclusion. We will say that arguments like this one are "defeated". See the definition on p. 104.

Thus, to be strong a cogent argument must have justified premises and not be defeated. There's no counterpart to defeat in the case of valid arguments. There, any counter evidence must in some way call into question one or more of the premises, or their conjunction.

IV. Determining How Strong an Argument Is

For valid arguments, the strength of the argument (for a person) is proportional to how well justified the person is in believing the conjunction of its premises.

For cogent arguments, the strength of the argument (for a person) is determined by a combination of three factors:

1) How cogent the argument is;
2) How well justified the person is in believing the conjunction of its premises.
3) The extent to which the person's background evidence undermines the argument.

(1) and (2) increase strength, while (3) decreases it. It is very hard to give mathematical precision to these matters, but we can at least give approximate measures.

Review flow chart on p. 110.