Chapter 1: Reconstructing and analyzing arguments

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. We have already seen what that is; it is the concept of validity. In  chapter 2 we will learn some precise, formal methods of evaluating deductive  arguments. There are no such agreed upon formal methods of evaluation for  inductive arguments. This is an area of ongoing research in philosophy. In  chapter 3 we will revisit inductive arguments and consider some ways to  evaluate inductive arguments.