Chapter One, Tutorial Three
Evaluating Arguments
We now have some experience with how people express their reasoning. But you will have noticed that arguments vary greatly in quality. Some of them seem quite good and convincing. Some arguments are silly and/or lack force. It's time to think about evaluating arguments.
To reiterate, we have defined an argument this way:
An argument is a collection of statements including some (the premises) that are given as reasons for another (a conclusion).
But if premises are given as reasons, then that means someone intends that they support the conclusion. An argument is successful, then, when it does support its conclusion, i.e., when it shows the conclusion is true or likely true.
In an argument, the premises are supposed or intended to support 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.
Before we develop clear definitions for evaluating formal/deductive and informal/inductive arguments, let's look to some cases that will help with intuitions. Be patient as we slowly motivate the definitions to come.
We began this chapter 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. But, 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. In this case, the conclusion is inescapable given the truth of the premises because of the form we've called DS.
DS is just process-of-elimination thinking; any argument of it's form is valid. This notion of a valid argument, then, is a part of formal, deductive logic.
But...
Other arguments are good ones but for reasons of content rather than form. So, we will need to evaluate informal, inductive thinking too.
The case about the twins is a case in point.
Sara and Beth are students in Logic 102 and are identical twins. Like many such twins, Sara and Beth share more than just physical traits: they tend to behave in similar ways, share interests down to very specific details, and are emotionally very similar. So, one can conclude with some confidence that Sara will love logic just in case Beth does.
This argument is a good one because, if the premises are true, then the conclusion is likely to be true.
This is a little different from what we said about the Chris A or B case. The conclusion is not inescapable, but only likely to be true. That is, even if the premises are true, it could still turn out that Sara and Beth just happen to be very different in their tastes for logic. But the premises make a pretty strong case for their conclusion. So, we'll call this argument strong. Strength is the measure of the quality of reasoning to an informal, inductive argument's conclusion.
Chris will get an 'A' or a 'B'.
He does not get an 'A'.
Chris will a 'B'.
Sara and Beth are students in Logic 102 and are identical twins.
Like many such twins, Sara and Beth share more than just physical traits: they tend to behave in similar ways, share interests down to very specific details, and are emotionally very similar.
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So, one can conclude with some confidence that Sara will love logic just in case Beth does.
Poor Arguments
Before giving the definitions, it's worth looking at some arguments that are not so good.
The 2003 invasion of Iraq was wrong. Bush is a draft dodger, an illegitimate president, and we should not have followed such a man into battle. (Problem: we will call the argument "weak" because the premises in and of themselves aren't sufficient to substantiate the conclusion.)
This thinking makes an unfortunate mistake: an attack on Bush 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 Bush'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. So, the content, the ideas expressed against Bush, do not themselves make a particular strategy the wrong one. The premises themselves make the conclusion neither inescapable nor likely to be true. If you want to argue that the 2003 invasion of Iraq was a terrible mistake, then you need to do more than sneer at Bush.
We don't yet have all the clear definitions, but the idea will be that this argument is informal/inductive but not strong. The problem with this argument is that the content or ideas expressed by the premises are not relevant to the conclusion.
We've just seen an example of poor inductive reasoning. But sometimes the fault of an argument will lie not 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. (Problem?)
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. (This has the same form and the same problem as the Sanchez argument!)
To conclude there will be fire in an area with oxygen is to make a mistake. Often we have oxygen but no fire: oxygen is a requirement for burning but is not sufficient in itself. One also needs fuel and a spark.
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.
You may be thinking that if she tells us she needs a raise, and doesn't
mention other needs, then she'll probably stay if she gets the raise.
The problem with this Sanchez case is a problem of poor form. Drawing the conclusion that she'll stay because the one mentioned requirement is met is ignoring the possibility of other requirements. Any reasoning of that form is incorrect (or "fallacious".)
Here's an easier example of poor form that
we've already seen:
All bats are mammals
All mammals are bats. (Problem! Improper form so "invalid" argument)
This is also a mistake of poor form. It just isn't reasonable to switch the animal category words "bats" and "mammals" after the word "All".
However, what
about this one?
Some bats are carnivores
Some carnivores are bats. (No problem, we'll call this a valid argument.)
As long as the word beginning the statements is "Some", then the switch of the animal category words makes sense, yes? Make sure you see that someone who believes the premise of this last argument can't reasonably deny the conclusion...because the two statements mean the same thing.
So, we're talking formal, deductive logic here. Keep that in mind as we give two definitions that apply only to deductive logic.
Definitions for Deductive Arguments
We need to say more about good and bad arguments. Let's begin by thinking about formal, deductive logic and define "valid" argument.
Roughly...
...a valid argument has premises that lead inescapably to the conclusion.
Chris will get an "A" or a "B" in logic class.
Chris (it turns out) does not get an "A".
So, Chris will get a "B".
Given the premises, i.e., assuming they are true, then...
...a grade of "B" is inescapable: there is no other possibility.
When deductive 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.
Sanchez stays at her banking job only if she gets a raise. As it turns out, she gets a raise. So, she'll continue at the bank.
However, Sanchez might get the raise but have other requirements that are unmet. In this sense, the conclusion is not inescapable even if the premises are true. If other things go wrong, she might quit even if she does get a raise. That is to say, the argument is not valid because it is possible that the conclusion is false even if the premises are true.
So, finally!, we can define validity
in terms of what the premises allow as possible:
An argument is valid just in case it is not possible that its conclusion be false while its premises are all true.
Think about this definition a bit and then
apply it.
None of the following three arguments is a bad one. Still, one is not valid. To finish off this page, click on the argument below which is NOT VALID:
- All gophers are mammals and every mammal is a vertebrate. Thus, each and every gopher is a vertebrate.
- All and only humans are bipeds. Thus birds (being non-human) are not bipeds.
- 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.
(Hint: Look for the argument that does not depend on form but on interpretation.)