Unit 4: Analyzing Inferences
In a certain way unit 4 is the culmination of developments since the beginning of the semester: in it logic is at last applied to some real-life arguments. Perhaps when you see the results, you’ll want to go back to filling out truth tables! More seriously, in this unit you will learn the last two steps of the three step process of argument analysis: (b) analyze the inferences and (c) add suppressed premises.
You will be given some real-life argumentative passages, and asked to identify which are the premises, which are the conclusions, and what is claimed to follow from what. These passages fill three out of four pages of the test, and are worth 170 out of the total of 260 points.
You should first review the premise & conclusion indicators from unit 1, since they are the key to analyzing inferences successfully. The rules on explicit indicators, sub-diagrams, and typical patterns are the crux of the issue.
The critical exercises on analysis of inferences are 4.1 and 4.2. There are additional exercises in the unit 4 test items section; see below. Those pages will show you the exact layout for the test questions.
You will be given some short arguments based on the standard forms, and asked what is the weakest claim one could add to make that argument valid. This is what we call a "suppressed premise". See exercises 4.3 and 4.4.
Adding suppressed premises is made much easier by using the "standard forms" we discovered with truth tables. Study the argument schemas and the standard forms very thoroughly: they are the key to success in this section. The table of section 4.3 works well for a surprisingly wide variety of real-life arguments.
There are two kinds of "suppressed premises" test item. One presents a very short one-level argument based on a standard form, and asks for the suppressed premise needed in that argument. See exercises 4.3, 4.4, and p. 4-22.
The other kind of suppressed premise test item: in the problems asking you to analyze some real-life argumentive passages, the very last step will be to supply a suppressed premise to one of the inferences. This is one of the hardest parts of real-life thinking, but relying on the standard forms, using the same skills as used in (2) can help you through it. See pages 4-23 through 4-27.
The two kinds of suppressed premise item are worth a total of 80 out of the 260 points for the entire test.
These are defined in section 4.3. The test will ask you to provide the technical definition for one of these terms, worth 10 points.
Finally, Urgently, and Earnestly recommended: the sections called "Test Items" and "Test answers", after the regular exercises, give you some actual test items from tests from prior years. Try all of these on your own before you take a test. They focus on identification of suppressed premises and analysis of inference. They will show you the format to expect during the test. The answers are in fact the "coding frames" used by the TA’s to grade those tests. So you also get to see the internals of how your answers will be graded.
Recommended sections from Patrick Hurley’s Concise Introduction to Logic:
This is the optional but recommended text for this course, and it has some useful exercises for this unit.
Section 1.6, Extended Arguments (p 63-68) gives a further description of how to analyze multi-level inferences. Note that the diagrams differ in minor ways from the simpler ones I describe: he allows multiple conclusions, for example, which you should avoid. You can also ignore the difference between "horizontal patterns" and "conjoint premises", and with very rare exceptions, treat every inference as the latter. I think his "horizontal pattern" is very rarely found in real arguments, since, from our point of view, it indicates multiple, independent arguments all for the same conclusion.
Despite these differences, Exercise 1.6, pp 68-74, is useful practice for our test. The items are also found on the "LogicCoach" CD Rom software that comes with the book.