To give a sense of the content of the course as taught in 2002, here are the study guides for all six units.
The study guides are meant to enable you to predict what the test on the unit will look like, to practice the sorts of questions that will be on it, and to know how the different parts are weighted. It gives pointers on how to study and practice for each section. If you use the study guides, you should never be surprised by what's on a test. That's our goal. In particular, there is no need to take a test on a unit just in order to see "what the test is like": the study guide tells you this. There is no need to waste test sessions!
relation of support
Understanding why validity is not the same as the truth of the conclusion is probably the hardest part of unit 1. There will ten true-false questions probing your understanding of this notion. Try exercises 1.5, 1.6, 1.7. In addition, one short answer question will ask you to explain or describe some aspect of the technical definitions listed in (1) above. If you understand those definitions this should not be hard.
Validity seems like hocus-pocus until you understand the notion of logical form and learn how to test "whether a logical form has any substitution instances in which all the premises are true but the conclusion false". By the end of this unit you will know how to do these things.
Warning: the test for Unit 2 will take considerably more time than that for Unit 1!
English variants of connectives. Learn how to recognize the folk variants for the five kinds of sentential connective. See section 2.5. Some of sentences mixed into the problems will use these variants.
It can be tricky to see the equivalences among some of these variant forms. Likewise, the "difficult combinations" (such as "not both p and not q" vs. "both not p and not q") can be hard to parse. One thing that will make both tasks easier is to understand some basic logical equivalences. See section 2.6. I strongly suggest you learn them, and test those you don’t believe with a truth table, before you get too bogged down memorizing the English variants or the "difficult combinations". Knowing the equivalences will cut down on the memory load. (Notice that symbolizations in (2) and (3) together account for more than half the final grade.)
New in this unit: actual test items. For symbolization and testing for validity, try the pages included from some actual tests used in 1998. These follow the answers to the regular exercises. The "test answers" section is the coding frame used by TA’s to grade that test, so you can see how partial credit gets assigned. What a deal!
Analysis of statements consists of techniques for analyzing and clarifying meaning. The three main skills to acquire are: learning to recognize and classify the various "fallacies of clarity" (1), and then, to avoid them, learning what a "definition" is, and how to criticize such a thing (2, 3, 4).
extension / intension / connotation
ambiguous / vague
collective v. distributive attribution (§ 3.3)
definiens / definiendum
necessary condition / sufficient condition
too broad / too narrow
The question format will be exactly as in test 1 (or exercise 1.1). See sections 3.2, 3.4, 3.5.
The definitions are of simple, ordinary terms, and so your example should be a simple one that very clearly shows that the definition is too broad. Similarly if the definition is too narrow (fails to provide a correct necessary condition), you will provide a (different) example to show it is too narrow. These two aspects require different sorts of examples, and be sure you understand what sort of example is needed for each. The questions might be phrased either in terms of too broad vs. too narrow, or in terms of sufficient condition vs. necessary condition, so be sure that you also understand the connections between those terms. See section 3.4, and practice with exercise 3.9.
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 material for this unit.
Hurley describes the Slippery Slope fallacy on p 146, and the other fallacies of clarity (Equivocation, Composition, and Division) in Section 3.4, pp. 164 ff. Because they are mixed in with a large collection of other fallacies, his exercises for 3.3 and 3.4 will probably be far too difficult at this point. (They will be useful for unit 6, where the fallacies of clarity are included again, together with a bunch of other ones.)
Chapter 2 of Hurley is very useful as a supplemental explanation of varieties of meaning and principles of definition. See sections 2.1 and 2.2 on varieties of meaning and the extension/intension distinction. Exercise 2.2, part II, p. 92, and ex. 2.3, part III, p 100, might be helpful for our part 3.
Sections 2.3 and 2.4 go into considerable detail on principles of definition; he explains purposes and techniques of definition more fully than I do. Likewise section 2.5 gives eight rules for adequate definitions, while for our purposes the only essential rule is rule 3 ("a definition should be neither too broad nor too narrow"). Exercises 2.4, part I, p 107 and 2.5, part I, p 214, provide many examples of inadequate definitions to be criticized, as in our part 4. These exercises are also both found in the "LogicCoach" software on the CD Rom that comes with the book.
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.
First study the sections of the chapter in order. Here's how the test is organized:
The trick to this sort of problem is to first figure out what standard form the passage most clearly resembles; after that it's a snap, since you can generate the suppressed premise directly from the form and the substitutions. That's why we did all that work in unit 2! 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. Then try exercises 4.3 and 4.4.
a. Underline the explicit inference indicators. (Total of 5.4% of final grade). Review these 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.
b. Bracket and number the statements in the argument. (Total of 28.8% of final grade). The only wrinkle to remember (or review from unit 2) is that each distinct claim needs a distinct number, and two claims that are synonymous get the same number.
c. Write out the "argument schema" (the (1), since (2), therefore (3) business). (Total of 5.8% of final grade.) This is new to this unit, and is explained in sections 4.1 and 4.2. It is the key to handling multi-level inferences; if you get it right, the next step is relatively easy.
d. Diagram the entire argument, including any sub-arguments. (Total of 23.1% of final grade). Here you identify the role of each statement as a premise or a conclusion, or both; identify the "main" argument of the passage, and all its "sub-arguments".
See especially section 4.2. The critical exercises are 4.1 and 4.2. There are additional exercises in the unit 4 test items section; see below.
e. In one of the inferences in the passage (which will be identified for you) the author needs a suppressed premise. What is it? (Total of 11.5% of final grade).
See section 4.3. 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 the actual test items, described next, for examples.
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 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. What a treat!
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. 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.
The tests for Unit 5 will consist of two kinds of questions:
strong inductive argument
sample / population
random sample / biased sample
measurement / reliable measurement
mean / median / mode
Some passages commit more than one error; you need identify only one. The error you cite must be an error that is definitely present in the passage; it cannot be one which is merely suggested by the text, one could be present but might not be, or one which the text merely fails to definitively rule out. (See also the "important note about these problems" at the beginning of section 5.7.) These errors have names, and you should be able to name each kind of error. It is hard to learn the names of all the fallacies. Section 5.7 gives a summary: a checklist to use to detect deviations from healthy statistical inference. But then you simply need to practice on lots of examples.
The critical exercises: 5.5 through 5.8. Exercises 5.6 through 5.8 are actual items from old tests on statistical fallacies. (Exercise 5.5 has good items too, but I have never used them in a test.)
Fallacies identified with asterisks ("converse accident", for example) are less common and more technical, and are included here for the sake of completeness and to help you understand Huff. But you will not be responsible for the ones with asterisks, and I won’t ask questions about them in tests (in either part 1 or part 2).
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 9.4, Statistical Reasoning, pp. 545-62, has a useful description of sampling, probable error (under the label "sampling error"), dispersion, types of averages, and other core concepts for part 1 of our test. Exercise 9.4, p. 563, part I is good practice for our part 2; his part III is good practice for our part 1. (Unfortunately these exercises are not on the LogicCoach CD Rom.)
Section 9.2, Causality and Mill’s Methods, p. 505, provides considerable supplementation to my description of making causal inferences. If you want to understand how to avoid the post hoc fallacy, I recommend reading this section, though our tests do not cover Mill’s methods.
The tests for Unit 6 will consist of two kinds of questions, just as in unit 5:
The fallacies will include:
I. Formal fallacies
II. Informal fallacies
A. Fallacies of clarity
B. Begging the Question
C. Fallacies of relevance
Recommended exercises 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. The exercises include true/false questions that will help with part 1 of our tests, and lots of "name that fallacy" items like those in part 2.
On Fallacies of Relevance read section 3.2 and try exercise 3.2, p 133, parts I and II, which is also on the CD-Rom. Hurley does include some fallacies for which you will not be held responsible (Accident, Ignoratio Elenchi, Red Herring), and those you should just ignore. Don’t rely on his characterizations of the fallacies; they are in places imprecise, and mine are the ones that you will be examined on.
In section 3.3, fallacies of weak induction, Hurley places Appeal to Authority, Appeal to Ignorance, and Slippery Slope, along with three other fallacies that won’t be on our tests (Converse Accident, False Cause, and Weak Analogy). If you ignore the latter, exercise 3.3, p 148, parts I-III, is quite useful (and also on the LogicCoach CD).
Section 3.4 is least useful, because it has the highest proportion of fallacies that won’t be covered on our tests. Hurley puts Begging the Question, Equivocation, Composition, and Division in this section, along with 4 others that we don’t cover. Exercise 3.4 though includes sections (I-III) that include all the different fallacies from the entire chapter, and is worth trying.
Exercise 3.5 (part I, p 187-97) is also good practice for section 2 of our test. It has sixty items illustrating fallacies found in editorials and news magazines. It is also on the LogicCoach CD.
The Self-paced Logic Project homepage.
Austen Clark's homepage.
The Philosophy Department homepage.