4. Strong vs Weak Arguments

There are two importantly different ways in which an argument can satisfy the Logic Condition. One way is if the argument is VALID. Another way is if the argument is STRONG. We've talked about validity. Now let's talk about strength.

Here's an argument:

1. All humans have DNA.
2. Pat is human.
Therefore, Pat has DNA.

This is a valid argument. If the premises are true the conclusion can't possibly be false.

Now take a look at this argument:

1. 50% of humans are female.
2. Pat is human.
Therefore, Pat is female.

The percentage isn't exact, but we're not interested in whether the premises are actually true. We're interested in whether, if they were true, the conclusion would follow.

In this case the answer is clearly NO. Knowing that Pat is human doesn't give any good reason to think that he or she is female.

This is an example of an argument that does NOT satisfy the Logic Condition.

Now take a look at this argument:

1. 90% of humans are right-handed.
2. Pat is human.
Therefore, Pat is right-handed.

This argument is different. In this case the premises make it very likely — 90% likely — that the conclusion is true. They don't guarantee that Pat is right-handed, but we might still want to say that they provide good reasons to think that Pat is right-handed.

And if that's the case then we should say that this argument satisfies the Logic Condition. Because it has the property that, if all the premises are true, they give us good reason to believe the conclusion.

This difference is what the distinction between weak and strong arguments amounts to.

• The first argument is what we call a logically WEAK argument. It does not satisfy the Logic Condition and so it can't be a good argument.
• The second argument is a logically STRONG argument. It does satisfy the Logic Condition so it can be a good argument.

This is what distinguishes these arguments, but note what they have in common. They're both logically INVALID.

In a valid argument if the premises are true the conclusion can't possibly be false. Neither of these arguments guarantees certainty. They're both fallible inferences. Even if the premises are true you could still be wrong about the conclusion.

The difference is that in a STRONG argument the premises make the conclusion VERY LIKELY true. A WEAK argument doesn't even give us this.

How Strong Does the Inference Have to Be to Satisfy the Logic Condition?

Now these examples immediately raise an important question:

HOW strong does the inference have to be for the argument to satisfy the Logic Condition and qualify as a strong argument?

To put it another way, with what probability must the conclusion follow from the premises for the argument to qualify as strong?

50% is clearly too weak. 90% is clearly strong enough. But where's the cut-off, what's the threshold that the strength of the logical inference has to meet o count as satisfying the Logic Condition?

Well, it turns out that there is no principled answer to this question.

The distinction between valid and invalid arguments is a sharp one. Every argument is either valid or invalid. There are no "degrees" of validity. Validity is like pregnancy — you can't be almost pregnant or a little bit pregnant.

The distinction between strong and weak arguments, on the other hand, is a matter of degree. It does make sense to say that an argument is very strong, or moderately strong, or moderately weak or very weak.

But the threshold between weak and strong arguments isn't fixed or specified by logic. It is, in fact, a conventional choice that we make. We decide when the premises provide sufficient evidence or reason to justify accepting the conclusion. There are no formal principles of logic that make this decision for us.

This is actually a big topic. It needs a lot more space to properly discuss (it really belongs in a course on inductive and scientific reasoning).

Valid, Strong and Weak Argument Forms

There are some common argument forms that people generally recognize as valid, strong or weak that are helpful to know.

Here are some simple argument forms that are recognized as valid, strong or weak respectively.

VALID:

1. ALL A are B.
2. x is an A.
Therefore, x is a B.

An example of a valid argument of this form is

1. All actors are robots.
2. Tom is an actor.
Therefore, Tom is a robot .

STRONG:

If we change "ALL" to "MOST" we get an invalid but strong argument:

1. Most A are B.
2. x is an A.
Therefore, x is a B.

Here’s an instance of this argument form:

1. Most actors are robots.
2. Tom is an actor.
Therefore, Tom is a robot.

The conclusion doesn't follow with certainty, but we're stipulating that "most" means "enough to make it reasonable to believe the conclusion".

WEAK:

If we switch from "most" to "some" we get a weak argument form:

1. Some A are B.
2. x is an A.
Therefore, x is a B.

Here’s an instance of this argument form:

1. Some actors are robots.
2. Tom is an actor.
Therefore, Tom is a robot.

"Some actors are robots" doesn't even guarantee 50-50 odds. The way this term is commonly used in logic, "some" just means that AT LEAST ONE actor is a robot.

Summary

These definitions summarize what we've seen so far:

• VALID: If all the premises are true, the conclusion follows with certainty.
• STRONG: If all the premises are true, the conclusion follows with high probability.
• WEAK: If all the premises are true, the conclusion follows neither with certainty nor with high probability.

Validity, strength and weakness are logical properties of arguments that characterize the logical relationship between the premises and the conclusion.

Both valid and strong arguments satisfy the Logic Condition for an argument to be good. Weak arguments fail to satisfy the Logic Condition and so are automatically ruled out as bad.