T2: 4 of 13

Part II of Tutorial Two

We now have some experience with how people express their reasoning. But you will have noticed that arguments vary greatly in quality. It's time to think about evaluating arguments.

To reiterate, the concept of an argument is as follows:

The premises are supposed to lead to the conclusion, to show it true or likely true.

To evaluate an argument, then, we need to check that its premises really do count as good evidence for its conclusion.

Begin with an example of an argument for which the premises (if true) are sufficient evidence to prove their conclusion:

Chris will get an 'A' or a 'B' in logic this term. He will not receive an 'A'. Thus he will receive a 'B'.

In a moment, when we give definitions, we will call this argument about Chris "valid". Roughly, the idea behind a valid argument is that the premises provide evidence making the conclusion inescapable.

But before giving the definition, it's worth looking at some arguments that are not so worthy.

The 1998 war in the Balkans was wrong. Clinton is a draft dodger and we should not have followed such a president into battle.

This thinking makes an unfortunate mistake: an attack on Clinton is used as a reason against a war. Although there is a connection between the advisability of a war and a president's character, an attack on Clinton's past is no substitute for reasoning about the war itself. The problem here is sometimes called an ad hominem fallacy: the reasoning is poor or fallacious because it's an irrelevant attack on a proponent of a cause rather than reasons that address the issue at hand.

Sometimes the fault of an argument will lie not so much with its content (what is said) as with its form (its structure). Consider:

Sanchez stays at her banking job only if she gets a raise. So, if she gets a raise, she'll continue at the bank.

This reasoning may at first seem OK. But it's not. To begin to see the problem, notice that the same form of reasoning is obviously wrong in a different context:

There is fire only if there's oxygen. So, if we add oxygen to an area, there will be fire.

But of course this is wrong. Often we have oxygen but no fire: oxygen is a necessary but not sufficient condition for burning.

Similarly for Sanchez: her staying on the job may require that she get a raise, but she may have other requirements as well. (Say, she's pregnant and needs special incentives to stay on the job: reduced office time, a means to work from home, child care. Additional money may be only one requirement of many.) The bottom line for the Sanchez argument, just like the fire-oxygen argument, is that the one premise is not sufficient for the conclusion.


Now, finally, we can see how to define the notion of a "valid" argument. The rough idea was that the premises lead us inescapably to the conclusion (as in the disjunctive syllogism case of Chris's grade). When such reasoning goes wrong (e.g., the case of Sanchez or in the oxygen/combustion example) we can see by example that there is a way for the premises to all be true while the conclusion is not. In this sense, the conclusion is not inescapable even if the premises are true. So, we define validity as follows:

An argument is valid just in case it is not possible that its conclusion be false while its premises are all true.

One of the following arguments is not valid (we'll say it's "invalid".) To finish off this page, click on the invalid argument below:

  1. All gophers are mammals and every mammal is a vertebrate. Thus, each and every gopher is a vertebrate.
  2. All and only humans are bipeds. Thus birds (being non-human) are not bipeds.
  3. In the animal kingdom of mammals, fish, reptiles, amphibians, and lower creatures, Humans alone can use language to address truly complex issues like mathematics or vacation planning. Thus Humans are the universe's only fully intelligent beings.