ARGUMENT AND INFERENCE
We have defined an argument as a chain of (one or more) inferences from some initial premises to an overall conclusion. In the examples so far we have been mainly looking at arguments involving a single inference, with clearly defined premises and conclusion.
It is these single-inference arguments whose validity we investigate in our natural deduction systems for Statement and Predicate Logic. As we shall see, proofs of the validity of arguments can be analyzed as depending on a chain of inferences, so that the proofs themselves resemble closely the reasoning we undertake in arguments containing multiple inferences.Still, it is not so easy to apply the techniques we shall be developing in formal logic unless the arguments are given tidily and explicitly, in the form “premise, premise, premise.,. conclusion.” The actual arguments we are presented with in real life—the arguments we find in conversations, newspaper editorials, cartoons, and so forth—are usually anything but tidy. We’ve already seen something of this in having to supply them with implicit premises, and sometimes conclusions. But even when we’ve done this, it is very often the case that the reasoning in them is quite complex, and involves more than one inference. It is about such extended arguments involving multiple inferences that I want to say a little here.
What usually happens when two people argue is that person A makes an assertion, and offers some reasons in support, leaving what she judges to be too obvious (either premises or conclusion of the reasoning) unstated or implicit. Person B then asks for reasons why he should accept certain premises—this requires A to give further arguments for them; or she questions the logical reasoning itself—perhaps giving counterexamples. (An example of this would be the passage from Monty Python’s “Argument Sketch” considered in section 2 above, when we were considering enthymemes.) All of us are familiar with this kind of dialectical reasoning. Consequently when we argue, we try to anticipate such objections. We give reasons in support of some of the premises of the main argument, i.e., we give arguments within arguments.
Thus naturally occurring arguments tend to have a good deal of inferential structure. They contain not just one inference from the premises to the conclusion, but inferences from premises to intermediate conclusions, which then themselves serve as premises for the inference to the main point being argued for. With such arguments it is extremely helpful to lay out this structure explicitly using a diagram. Techniques for diagramming arguments are among the most valuable contributions of the “Informal Logic” movement, and to these we now turn.
1.3.2