Deductive vs. inductive arguments (Dr. Van Cleave)

By Matthew Van Cleave

The concepts of validity and soundness that we have introduced apply only to the class of what are called “deductive arguments”.  A deductive argument is an argument whose conclusion is supposed to follow from its premises with absolute certainty, thus leaving no possibility that the conclusion doesn’t follow from the premises.  For a deductive argument to fail to do this is for it to fail as a deductive argument.  In contrast, an inductive argument is an argument whose conclusion is supposed to follow from its premises with a high level of probability, which means that although it is possible that the conclusion doesn’t follow from its premises, it is unlikely that this is the case.  Here is an example of an inductive argument:

Notice that the conclusion, Tweets probably flies, contains the word “probably.”  This is a clear indicator that the argument is supposed to be inductive, not deductive.  Here is the argument in standard form:

Given the information provided by the premises, the conclusion does seem to be well supported.  That is, the premises do give us a strong reason for accepting the conclusion.  This is true even though we can imagine a scenario in which the premises are true and yet the conclusion is false.  For example, suppose that we added the following premise:

Were we to add that premise, the conclusion would no longer be supported by the premises, since any bird that is 6 ft tall and can run 30 mph, is not a kind of bird that can fly.  That information leads us to believe that Tweets is an ostrich or emu, which are not kinds of birds that can fly.  As this example shows, inductive arguments are defeasible arguments since by adding further information or premises to the argument, we can overturn (defeat) the verdict that the conclusion is well-supported by the premises.  Inductive arguments whose premises give us a strong, even if defeasible, reason for accepting the conclusion are called, unsurprisingly, strong inductive arguments.  In contrast, an inductive argument that does not provide a strong reason for accepting the conclusion are called weak inductive arguments. 

Whereas strong inductive arguments are defeasible, valid deductive arguments aren’t.  Suppose that instead of saying that most birds fly, premise 2 said that all birds fly. 

This is a valid argument and since it is a valid argument, there are no further premises that we could add that could overturn the argument’s validity.  (True, premise 2 is false, but as we’ve seen that is irrelevant to determining whether an argument is valid.)  Even if we were to add the premise that Tweets is 6 ft tall and can run 30 mph, it doesn’t overturn the validity of the argument.  As soon as we use the universal generalization, “all healthy, normally function birds can fly,” then when we assume that premise is true and add that Tweets is a healthy, normally functioning bird, it has to follow from those premises that Tweets can fly.  This is true even if we add that Tweets is 6 ft tall because then what we have to imagine (in applying our informal test of validity) is a world in which all birds, including those that are 6 ft tall and can run 30 mph, can fly. 

Although inductive arguments are an important class of argument that are commonly used every day in many contexts, logic texts tend not to spend as much time with them since we have no agreed upon standard of evaluating them.  In contrast, there is an agreed upon standard of evaluation of deductive arguments: the concept of validity.  In our next few units, we will explore inductive arguments and consider some ways to evaluate inductive arguments. In later units of the course, we will focus on deductive arguments and learn some precise, formal methods of evaluating deductive arguments.