Systematic Philosophy

to know what can be known

The Quality Of An Argument

We are examining arguments. We want to know how good they are. How should we proceed? One might think that the answer will differ from argument to argument, with some criteria applying to some arguments and different criteria applying to others. But that’s not true. For all finite, non-circular arguments, there is just one set of criteria to apply. This makes assessing arguments a relatively straightforward task.

Two criteria

Let’s consider just finite, non-circular arguments. The quality of this type of argument is determined by two criteria:

When assessing an argument, these are the only factors that matter. Everything else can be ignored.

How do transparent validity and quality of premises work together to determine the quality of an argument? First, for an argument to be good, it must be transparently valid. If it is not transparently valid, it is automatically a bad argument. This is not to say that transparent validity makes an argument good. By itself, it doesn’t. It is just a necessary condition, not a sufficient one.

If an argument is transparently valid, its quality is then determined by the quality of its premises. In particular, an argument is at best as good as its worst premise. If an argument has zero or one imperfect premises, then the argument is exactly as good as its worst premise. If an argument has two or more imperfect premises, then it is worse than its worst premise. How much worse? This depends on how bad the various premises are.

In this regard, an argument is like a chain. A chain is at most as strong as its weakest link. If it has just zero or one imperfect links, then the chain is exactly as strong as its weakest link. If it has two or more imperfect links, the chain is weaker than its weakest link – so long as we suppose that the links do not always fail in order of weakness. How much weaker? This depends on how weak the various links are.

At most as strong as the weakest link.

Some examples

Let’s consider a few examples.

  1. Socrates is a person.
  2. All people are mortal.
  3. Therefore, Socrates is mortal. [1,2]
  4. All mortal things have parts.
  5. Therefore, Socrates has parts. [3,4]
  6. All things that have parts are made of particles.
  7. Therefore, Socrates is made of particles. [5,6]

To assess this argument, first we consider whether it is transparently valid. In fact, it is transparently valid. So it passes the first test. Next we consider its premises. How good is each? Answering this question is difficult. In fact, answering it may require us to answer the central question of philosophical methodology. Since that is its own topic, for now we will just answer from our pre-theoretical perspective. Pre-theoretically, we might say that step 1 is extremely plausible and steps 2, 4 and 6 are very plausible. If we say these things, then we should conclude that the argument is somewhat plausible. We could not say it is very plausible, as the argument has four imperfect premises and thus is worse than its weakest premise. But pre-theoretically we would not say that it was a weak argument either. As far as things go, one extremely plausible premise and three very plausible premises is pretty good.

Next, consider this:

  1. All cats are animals.
  2. All dogs are animals.
  3. Therefore, all cats are dogs. [1,2]

As before, we begin by checking transparent validity. Is the argument transparently valid? The answer is no. This makes assessment easy: the argument is automatically bad, just like every argument that is not transparently valid. We do not even need to assess the quality of the argument’s premises.

Finally, consider this argument:

  1. All rabbits are cubes.
  2. All cubes are spatial.
  3. Therefore, all rabbits are spatial. [1,2]

Again, first we consider transparent validity. Is this argument transparently valid? The answer is yes. So we move on to the premises. How good is each? Sticking with our pre-theoretical perspective, step 1 is deeply, deeply implausible. Step 2, on the other hand, is perfect or nearly so. It follows that from our pre-theoretical perspective, this argument is at best really bad. If we judge step 2 to be perfect, then the argument has only one imperfect premise and thus is exactly as strong as its weakest premise. Which is to say, exactly really bad.

Precision in assessment

We said that the first argument above was, speaking pre-theoretically, better than weak but worse than very plausible. This might seem preposterously imprecise. In fact, the question of whether and how we can make argument assessment more precise is itself an important philosophical question.

The permissibility of abbreviation?

We said that the goodness of an argument requires that it be transparently valid. Some people will object to this, saying that it is sometimes okay to abbreviate arguments and leave out some of the more obvious steps. Of course, in almost every case abbreviating an argument will render it no longer transparently valid.

It is true that in practice it is often fine to abbreviate arguments and leave out obvious steps. However, it is also true that in practice, people very frequently abbreviate arguments and leave out crucial steps that should not have been left out. We don’t want to leave out crucial steps. We don’t want others to leave out crucial steps. People have been leaving out crucial steps for thousands of years and we’d like that to stop. That is why we require that arguments be transparently valid.

An “abbreviated” argument.

There are benefits to working with abbreviated arguments. They are easier to write down, for instance. If people would like to work with abbreviated arguments, that is fine. Our attitude is just that when it comes time to officially assess an argument, that argument should be presented in its full form. At that point, no step should be skipped.

More on the assessment of arguments

There is more to be said about how we assess arguments. First, we can explain why we assess arguments the way we do. Second, we can contrast the criteria we use with other potential criteria and explain why those other criteria are wrong. Third, above we restricted conversation to finite, non-circular arguments. How should we assess infinite arguments? How should we assess circular arguments? Follow the links to read more.

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Written by Geoff Anders

May 26, 2011 at 10:39 am

Posted in Uncategorized

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