T1.3: 3 of 8

So, frequently we need to give arguments even when our evidence only makes a conclusion likely, but not inescapable. Here's another example of this "inductive" thinking:

I have surveyed hundreds of students here at ITU and found that less than 10% say they are happy with the new course fees. My sample was selected at random. So, I conclude with confidence that the vast majority of ITU students do not find the course fees acceptable.

Here, the argument's author is clearly claiming that the evidence cited makes the conclusion likely to be true but not a certainty (surveys sometimes do go badly awry, for instance when the participants have some reason to lie.) So, this argument is a clear case of an inductive argument.

To Reiterate : An argument is inductive if and only if its premises are intended to lead to its conclusion with high probability.

We do not say that an inductive argument is valid when it succeeds at supporting its premises as intended. Rather, an inductive argument who's premises do support its conclusion as intended (i.e., they make the conclusion likely) is called "inductively strong":

An argument is inductively strong if and only if its conclusion is highly probable to be true given its premises.

Inductive strength is a counterpart to validity: by definition, deductive arguments are intended to be valid, inductive arguments are intended to be inductively strong. Of course, people often give arguments falling short of what was intended. That's why we have logic classes! But the point is that the concepts of validity and of inductive strength play similar roles for deductive and inductive arguments respectively: such arguments support their conclusions as intended.

Finally, we need to define a counterpart to "sound" for inductive arguments. Remember, that an argument is sound if and only if it's both valid and has all and only true premises. For an inductive argument, just substitute "inductively strong" for "valid" to get the notion of cogency:

An argument is cogent if and only if it is both inductively strong and all its premises are true.

Why do we study deductive logic rather than inductive logic? Doesn't it seem that most arguments are inductive anyway? These are good questions and their answers are not easy to give completely in just a few sentences. But to begin:

  1. We are interested in studying logical possibility and meaning. This is a core of logic. It's deductive logic.
  2. Even within the more common inductive thinking, deductive argumentation is often an important part. (For example, if I try to convince you that deductive logic is important — that's this page! — I'll be arguing inductively. But in so doing, I'll sometimes utilize steps that are themselves deductive. For example, 1 applies the definition of "deductive logic".)
  3. Deductive logic, unlike inductive thinking, is formalizable. This allows us to treat deductive logic in a simpler, more systematic way.