T2: 8 of 13

We've defined the notion of an argument's "validity" (i.e., its being valid) in terms of possibility:

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

The conclusion just couldn't possibly be false, is inescapable, given the truth of it's premises.

On the concept of possibility:

When one wishes to give a valid argument, then one is involved in what is called "Deductive Logic".

An argument is deductive if and only if its premises are intended to lead to the conclusion in a valid way.

Many of the arguments we've seen are deductive. A case in point is the example about Chris — Chris was to receive an 'A' or 'B' but as it turned out did not get an 'A'; we were forced to conclude that he received a 'B'.

But not all deductive arguments are good, valid ones. The Sanchez case is an example:

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

We've seen that this argument is not valid (remember why? if not, you might click here). But it's a deductive one if its intent is to provide valid argumentation.

Now, there is much reasoning which is not deductive. Often we try to give good reasons but do not expect that these reasons alone make the conclusion inescapable. Think about reasons to join a cause, become a vegetarian, to believe in ghosts, to show that the universe is expanding. Such evidence is typically meant to show that the conclusion is a good bet, that it is likely true. But the evidence is not meant to show the conclusion inescapable. So these sorts of reasoning are non-deductive. We will call them "inductive".

Our earlier example will do as a case of inductive thinking:

Sara and Beth are students in Logic 101 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.

An inductive argument can be defined as follows.

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

Inductive arguments can take the information in the premises and attempt to amplify it. If all goes well, the conclusion will provide new information beyond that of the premises. Predictions are usually the result of inductive thinking (I might predict tommorow's likely weather based on past experience). Another common sort of induction is reasoning from premises about happenings to a conclusion about their best explanation (I hear lots of noises through the wall and conclude that my neighbors are likely home).

Now, click on the arguments below which are most likely inductive...

  1. Life in 19th Century Europe was very difficult. A couple of reasons illustrate: disease was rampant, food was scarce in the newly industrialized regions, and the work was oppressive.
  2. The coming years will bring extremes in weather patterns. This is evidenced by the extremes of the past several years and by the indications that global warming is upon us.
  3. Up until today, I had climbed only one 5.12 rock pitch. Today I managed to do one more. Thus as of today I have climbed two 5.12s.