Assessing Logical Strength

Strength is a function of the gap between premises and conclusion: The larger the gap, the weaker the argument. It is always possible to narrow the gap by introducing a new premise.

A strong argument has a small gap between the stated premises and the conclusion, and the gap can be filled by a fairly innocuous premise that would be easy to defend.

A weaker argument has a larger gap, which could be filled only by a more substantial premise that would be harder to defend.

A thoroughly weak argument has a huge gap, which could be filled only by a premise that is obviously false.

So we can measure the gap, and thus determine the argument's strength, by seeing what sort of premise it would take to fill the gap.

Example:

According to de Tocqueville's argument about democracy:
The people serve on juries. Therefore, the people control the government.

To say that the people control the government is to say that they control the government's actions--that they have some influence, direct or indirect, on everything the government does. When they serve on juries, the action they control is the action of punishing criminals. So to make the above inference strong, we need the assumed premise that punishing criminals is the only action government takes, or at least the main one. This is a dubious assumption, to say the least. After all, governments wage war, impose taxes, regulate the economy, and do many other things in addition to punishing criminals.

The need to make such a dubious assumption confirms our sense that the argument from 2 to 3 is very weak indeed.

When we evaluate the argument as a whole in light of the components, there are some principles to follow.

1. When there are independent premises within a single step--that is, when two or more arrows converge on the same conclusion- -the argument is at least as strong as the strongest component.
2. When there are dependent premises, the argument is only as strong as its weakest premise.
3. When an argument has more than one step, it can be no stronger than its weakest step. A chain can be no stronger than its weakest link.

Let us examine each of these in turn.


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