Study guides
The Self-Paced Logic Project

To give a sense of the content of the course as taught in 2002, here are the study guides for all six units.

Unit 1: Starting an Argument

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!

  1. Technical definitions. (3 questions, 20% of the final grade.) Three questions will ask you to provide technical definitions for some of the key concepts of logic. These questions will be presented exactly as in Exercise 1.1. The definitions will be drawn from the following list:

    true statement
    deductively valid
    inductively strong
    valid logical form

    Most of these notions are explained in sections 1.2 and 1.3. Your definition is correct if and only if it is logically equivalent to the correct definition. Try exercise 1.1 to get a sense of what this means. At this stage (before you learn how to test for "logical equivalence") it might be simplest to memorize the technical definitions.
  2. Understanding the technical definitions. (11 questions, 10 of which are true/false, 26.6% of final grade.) The trickiest of the new notions are:

    relation of support
    logical form

    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.
  3. "Premise indicators" and "conclusion indicators". (2 questions, 6.6% of the final grade). You’ll be asked to list two or three of each kind of indicator. See section 1.1, exercise 1.2. Knowing these will be critical for later work!
  4. Identifying arguments. (5 questions, 46.6% of final grade). You will be given five passages, some of which are arguments, and some of which are not. The arguments contain explicit indicators that they are arguments: a "premise indicator" or a "conclusion indicator". You will be asked whether or not the passage is an argument. If it is an argument, you will be asked to underline the inference indicators and then identify the premises and conclusion by putting the argument in "standard form". This exercise depends on knowing the premise indicators and conclusion indicators. Try exercises 1.3, 1.4, 1.8.

Unit 2: Testing Validity

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!

  1. Logical forms and substitution instances. (8 questions, 10.9% of final grade). Learn how to abbreviate distinct independent clauses of a sentence with distinct sentence-letters. Learn why one needs to do this. See section 2.1. You will be given a sentence and asked whether it is or isn't a substitution instance of 5 different logical forms. If it matches a form, you are asked to produce a symbolization key showing how the sentence can be mapped onto that form. Then you will be given a different sentence and asked to produce three different logical forms of which it is a substitution instance. (Hint: p always works.) Try exercises 2.1, 2.2, 2.3, 2.19.
  2. Construct a truth table and use it to assess validity. (1 question, 13% of final grade.) Learn the standard truth table for each connective. Pay particular attention to the conditional, since it is the source of most of the trouble. (See §2.2, 2.4). Then learn how to construct a truth table for a complicated sentence with nested clauses (§2.3). To do well in the test you will need to be able to evaluate a truth function such as (p -> ~(q v ~s)) without having to think about it too long. You will be given a truth table to complete, and then asked to use it to assess whether a one-premise argument is or is not valid. Try exercises 2.4-2.10. 2.4 and 2.9 in particular have various one-premise arguments whose format matches the question on the test.
  3. Symbolizing Sentences. (15 questions, 32.6% of final grade). Fundamentals of symbolizing conjunctions, disjunctions, negations, conditionals, and biconditionals. Sections 2.2, 2.4. Learn how to symbolize simple English sentences of all these types. You will be given 15 sentences in English, and asked to symbolize them, using a key that is provided. Try exercises 2.11-2.16. See also the "Test items" section, which follows all the regular exercises.
  4. Symbolize an Argument and Test it for Validity. (2 distinct arguments, one per page, each with a truth table to complete; 43.5% of final grade). The goal of the test. Each argument is in ordinary English, with two to four premises and a conclusion (indicated last, with a "hence"). You are asked to symbolize each sentence in the argument, and then construct a truth table to test whether or not the argument is deductively valid. (The three truth tables are worth 26% of the final grade; the roughly 11 symbolizations in the arguments are worth 24%, and the three verdicts 6.5%.)

    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!


Unit 3: Clarifying Meaning

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).

  1. Identify some "fallacies of clarity". (7 questions, 30% of final grade). Some persuasive but invalid arguments rely upon a shift in meaning of a key term, so that two distinct premises can appear to be one. Learning how to recognize and identify these is the first skill listed above. Seven short arguments in ordinary English will be given, and you will be asked to identify which of the fallacies of clarity each passage most clearly commits. For each passage you need only identify one fallacy; and the fallacy you name should be one for which there is clearly sufficient evidence in the passage itself to convict the author of committing it.

    The four fallacies of clarity are described in section 3.3. The critical exercises for this skill are 3.7 and 3.8. It will be helpful to look at the beginning of section 6.1, on fallacies in general, before trying these.
  2. Technical Definitions. (2 questions, 21% of final grade). Talking about the meaning of words is a finicky business. As you might imagine, one must be very careful about the meanings of the words one uses when one talks about the meanings of words. You will be asked to provide the technical definitions for two of the notions out of the following list:

    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.
  3. Principles of adequate definitions. (8 true/false questions, 17% of final grade). These will be true-false questions on the principles of adequate definitions, described mostly in section 3.4. Some will require you to tell whether or not some condition S is a necessary (or sufficient) condition for some condition P. Try the examples given in exercises 3.1 - 3.6.
  4. Criticizing inadequate definitions. (2 definitions, 2 questions about each; 32% of final grade). Demonstrating that a definition is too broad, and demonstrating that a definition is too narrow. You will be given two definitions for ordinary English terms. If the definition is too broad (fails to provide a correct sufficient condition for the definiendum), you should be able to provide an example to show that it is too broad (fails to provide a correct sufficient condition).

    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.

Unit 3 Study Guide Addendum

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.

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.

First study the sections of the chapter in order. Here's how the test is organized:

  1. Technical definitions. (1 question, 3.8% of final grade). You will be asked to provide the technical definition for one notion out of the following list:

    suppressed premise
    weak statement / weak argument
    principle of charity
    straw man

    These are defined in section 4.3. They need to be understood before you embark on the business of adding suppressed premises.
  2. Adding suppressed premises. (7 questions, 21.5% of final grade). You will be given seven short arguments based on the standard forms (modus ponens, modus tollens, etc), and asked what is the weakest claim one could add to make that argument valid. This is what we call a "suppressed premise".

    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.
  3. Analyzing real-life arguments. (3 arguments, each on a full page, with 5 questions about each one; 74.7% of final grade.) You will be given some real-life argumentative passages, and asked to complete a full analysis of each argument. What makes this a little tricky is that these passages typically contain multi-level inferences. Here's what a "full analysis" includes:

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!

Unit 4 Study guide addendum

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.

Unit 5: Thinking Statistically

The tests for Unit 5 will consist of two kinds of questions:

  1. Characteristics of Statistical Fallacies. (5 multiple choice questions; 29.4% of final grade).

    These are multiple choice questions of the variety "circle all that apply", and each gives 5 choices, so you could also think of these as 30 true/false questions. Sometimes you might have to circle every answer following the question; sometimes you will circle none. The material for them is drawn entirely from the descriptions of the fallacies found in the Philosophy and Logic textbook. Pay particular attention to (a) understanding the following technical concepts:
  2. strong inductive argument
    sample / population
    random sample / biased sample
    measurement / reliable measurement
    mean / median / mode
    skewed distribution
    probable error

    I won’t ask you for the definitions of any of these terms, but you should definitely understand what they mean. Be sure you understand the notions of sampling, of measurement, and of probable error.

    In addition, the multiple choice questions will focus on: (b) the necessary and sufficient conditions for committing a particular kind of fallacy; and (c) the distinctions between different kinds of fallacies. As examples of (b), you might be asked about the problems of using a biased sample, or why the mean is the wrong kind of average to use in a skewed distribution. As an example of (c), you almost certainly will be asked about the distinction between "ignoring dispersion" and "ignoring probable error". Study the descriptions of the different fallacies very carefully: all the answers are found in them!

    Darrell Huff’s book is quite good at providing vivid examples that make the technical notions easier to understand. In my textbook I cite page numbers of various examples found in Huff. They are very much worth looking up!

    There aren’t any exact duplicates of the multiple choice questions from the test in the textbook, but try exercises 5.1 - 5.4 on the fundamental notions of sampling.

  3. Identifying Statistical Fallacies. (20 questions, 70.6% of final grade). You are given twenty brief argumentative passages, for which you must name the statistical fallacy that the passage most clearly commits.

    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).

Unit 5 Study Guide Addendun

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.

Unit 6: Detecting Fallacies

The tests for Unit 6 will consist of two kinds of questions, just as in unit 5:

  1. Characteristics of Fallacies. (6 multiple choice questions, 29.4% of final grade).

    As in unit 5, these are multiple choice questions of the variety "circle all that apply". Sometimes you might have to circle every answer following the question; sometimes you will circle none. The material for them is drawn entirely from the descriptions of the fallacies found in the Philosophy and Logic textbook. Pay particular attention to (a) the necessary and sufficient conditions for committing a particular kind of fallacy; and (b) the descriptions of the distinctions between different kinds of fallacies. Study those passages very carefully: all the answers are found in them!

    Important Note: These multiple choice questions will include questions on the characterizations of the fallacies of clarity (first covered in unit 3), so review those too. This section will also include some questions about the "strawman" fallacy. The book (on p. 6-5) says that "strawman" examples will not be included among the argumentative passages for which you must name the fallacy. While it is still true that you won’t have to identify any strawman fallacies (in part 2 of the test), there will be some multiple choice questions about them, so read the description carefully.

    Again there aren’t any exact duplicates of the multiple choice questions from the test in the book, but the questions are drawn very closely from the descriptions of the fallacies in the textbook. As an example of (a) you might be asked what conditions are necessary or sufficient to show that an argument equivocates, why begging the question is a fallacy, or what one must do to commit a strawman. As examples of (b), you might be asked about the distinction between equivocation and slippery slope, about the difference between ad hominems and valid attacks on the testimony of a witness, or the distinction between fallacious appeals to authority and legitimate ones.
  2. Identifying standard forms and fallacies. (20 questions, 70.6% of final grade). You are given 20 brief argumentative passages. Some of these are not fallacies but are valid standard form arguments. You must name either the argument form or the fallacy that the passage most clearly commits.

The fallacies will include:
I. Formal fallacies
II. Informal fallacies
A. Fallacies of clarity
B. Begging the Question
C. Fallacies of relevance

We have already done I and II.A, in units 1 and 3. These will be briefly reviewed, mostly to introduce the technical definition of a fallacy; and then we focus on II B and C. Statistical fallacies will not be included in this unit.

Just as in unit 5, if the passage is fallacious you must name a fallacy for which there is sufficient evidence to convict the author, not merely one whose absence is not precluded by the text. See the "important note about these problems" in §6.5. The specimens we examine do not need to prove their innocence; you must prove their guilt.

Study the descriptions of the various kinds of fallacies carefully. The summary decision tree in section 6.5 should be helpful. It includes all the names of fallacies you need to know for this section. (As explained above, "strawman" will not be found in part 2 of this test, though it will be mentioned in part 1.)

On fallacies of clarity you might want to review exercises 3.6, 3.7, and 3.8. The critical exercises for formal and informal fallacies are 6.1 and 6.5 through 6.9. The latter are all actually items from old tests or quizzes I wrote, so you can see what kind of question I ask. Other exercises give specific practice on some of the more difficult fallacies. For example, ad hominem (6.2), argumentum ad verecundiam (6.3), and circular reasoning (6.4). The answers to these should also be helpful in studying for part 1.

Identifying fallacies is much harder than it looks; you will need to practice as much as you can. You may use Latin names or not, as you wish. The names "argumentum ad verecundiam" and "appeal to authority" are equally acceptable.

Unit 6 Study Guide Addendum

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.