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.










































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.

















































































Anything that fits our pattern, anything that can consistently fill in for the box and circle...

only if

                     a fallacy.

We can see how wrong this form is by example.






On to conditionals...




























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:

























A question for you...




































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?

  1. Paul is from Quebec only if he's from Canada, but Paul is not from Quebec, so he's not from Canada.
  2. If Paul is from Quebec, then he's from Canada, but Paul is not from Canada, so clearly he's not from Quebec.
  3. 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:

only if