Chapter 2, Tutorial 1
Forms and Formal Fallacies
A fallacy is a poor argument, or type of argument, that nonetheless may appear convincing.
A formal fallacy is a fallacy because of its form. In all instances that we'll see, these will be invalid deductive arguments that may appear valid if one is not careful.
Think about these two definitions before moving on...
Because all our examples of formal fallacies are invalid deductive arguments, it is worth remembering our definition of validity:
An argument is valid just in case it is not possible that its conclusion be false while its premises are all true.
An argument is invalid if and only if it is not valid.
Our test for invalidity, then, is just to find a way in which it is possible for an argument's conclusion to be false while its premises are all true.
So, let's look at some examples of fallacies, i.e.,
invalid deductive arguments that may be misunderstood as good, valid reasoning.
The first and easiest formal fallacy we've addressed was illustrated with this example:
All bats are mammals, therefore all mammals are bats.
(Notice that there is something very wrong with this argument!)
This is an example of a fallacy for which we'll later need a name: illicit conversion. (We'll not use this terminology for awhile though. We'll talk about the logic of groups of things in chapter 6: "Catergory" logic.)
The point is that one can't just switch the two group names and expect to get back something true like the original. (It is true that all bats are mammals, but that doesn't mean that all mammals are bats!) So, anyone who would argue this way is making a mistake.
I'd never make a mistake like that!
It would be a mistake to switch in the following way:
If Shamu is a bat, then Shamu is a mammal.
So, if Shamu is a mammal, then Shamu is a bat.
(fallacy!)
This is the same sort of fallacy as illicit conversion.
Another example of a fallacy will look familiar:
There is fire only if there's oxygen. There is oxygen here in the room, so there is fire.
we can symbolize this
in the standard diagram.
Fire/oxygen argument:
F only if O
O
So, F.
Clearly, this silly thinking is invalid.
But, such problematic reasoning doesn't have to be so obviously mistaken. Here's
another bit of reasoning of the same fallacious form.
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.
or, in our standard diagram:
Sanchez/Bank argument:
S only if R
R
So, S (This has the same form and the same problem as in the Fire/Oxygen argument!)
Careful! This one is hard to get. But it's easiest to see that these two arguments are of the same form, and equally falacious, if we
symbolize their form this way:
only if 
The box and ovals are just placeholders to be filled in by some statement. BUT each oval must be filled in by one and the same statement. And, similarly for the box: if one statement goes in the first box, the same statement needs to go in the second.
Look again at our argument:
Fire/oxygen argument:
F only if O
O
So, F.If you put 'F' and 'O' in for the box and circle you get the Fire/Oxygen fallacy.
Anything that fits our pattern, anything that can consistently fill in for the box and circle...
only if
...is a fallacy.
We can see how wrong this form is by example.
The fire/oxygen example shows clearly how and why the reasoning based on this form is incorrect. The example counters the augment, shows it invalid.
When we give an example that shows that an argument is invalid, we call it a counterexample.
We've spent much time using our intuitions to begin to access arguments. But we need to analyze arguments more systematically. So, because many of our arguments have included "conditional statements", we'll begin to our analysis with them. Conditional statements, or "conditionals" for short, are stamens that one thing is true on the condition that something else is true. For example:
(1) If Paul lives in Quebec, then Paul lives in Canada.
Notice that this statement is true. Anyone from Quebec is from Canada. (Never mind that some Quebecois would prefer to have their own country!) So, we might say that on the condition that Paul lives in Quebec, he clearly lives in Canada.
But let's see another conditional, one that need not be true...
(2) If Paul lives in Canada, then he lives in Quebec.
Statement (2) means something different. You might want to say this if you know Paul well, know he's smitten with French ways and would live in Canada only if he could live in Quebec, only on the condition that he would be in the French speaking part of the nation.
So, (2) means something very different from (1). Indeed, (2) might be rephrased
in any of the following equivalent ways:
(3) Paul's living in Canada entails that he lives in Quebec.
(4) Paul lives in Canada only on the condition that he lives in Quebec.
(5) Paul lives in Canada only if he lives in Quebec.
OK, we will call anything of this problematic form "the fallacy of affirming the consequent" (or "the fallacy of AC for short"). Which of the following commits the fallacy of AC?
- Paul is from Quebec only if he's from Canada, but Paul is not from Quebec, so he's not from Canada.
- If Paul is from Quebec, then he's from Canada, but Paul is not from Canada, so clearly he's not from Quebec.
- Paul is from Quebec only if he's from Canada, and he is from Canada, so he's from Quebec.
| Hint: it must fit this form: | |