Teacher's Guide - Class Planning Guide

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The Contract
Part 1 - [1] [2] [3] [4] [5] [6] | Part 2 - [7] [8] [9] [10] [11] | Part 3 - [12[13] [14] [15]

The pedagogical strategy of the chapter is to contrast induction and deduction by explaining both at the same time with similar techniques. The analogs for induction of Venn diagrams, used in section 5.7, are thus essential. (And though 5.6 is not listed as part of the absolute core, it would not fit the pedagogical strategy to skip it.) In fact, there is much less of this chapter that can be omitted than most. You can't expect a very brief exposition of deductive logic like this one to generate a real facility with even elementary logic, so the discussion of syllogisms is meant to motivate the complex of ideas of validity/counterexample/Venn diagram. Another way of putting it: a traditional logic course first gives you a lot of practice with patterns of valid argument and then progresses to precise meta-concepts of validity and invalidity. My strategy is to use examples of valid and invalid argument to motivate rough concepts of validity and invalidity. Judgments about particular arguments can then be left to the student's common sense. I am sure this is better for beginning students, and prevents the philosophically central ideas from getting lost in logical details.

I would recommend not trying to get through this chapter in a week of a normal class schedule. Two weeks makes more sense.

Chapter 5 - Comments on Sections

5.1 This expositional section sets the theme of the chapter as induction - so deduction will later emerge as a contrast to it, but not until 5.4.

5.2 It is important to work through this, to make sure the students have understood the kinds of reasoning that count as simple induction. In MORTALITY the conclusions that follow straightforwardly by simple induction are (ii), (iii), (iv). Conclusions (i) and (v) can be supported by inductive arguments whose data includes the data here, but simple induction, as defined, won't get them from this data alone. The contrast between (iii) and (iv) may raise worrying issues that are dealt with in 5.12. A series of further questions leads on to questions that hint at a conclusion students may draw for themselves, that you have to know more than that a conclusion is got by simple induction to know whether you should believe it. MICROBIOLOGY is not very difficult or puzzling, but it does take a bit of figuring out.

5.3 This is another purely expositional section, introducing the idea that reasoning it is perfectly reasonable to follow can still sometimes lead to false conclusions, thus setting the stage for 5.7. It is worth pointing out that this undercuts a key rationalist assumption. You could ask students to read both 5.1 and 5.3 before a class in which you work through 5.2

5.4 Now deduction enters. Syllogisms are here because they're easy, and because they link to Venn diagrams, making the idea of validity and the relation to induction clearer. Students could read through the section in advance of a class in which you work through the activity at the end. (I think the answers are evident. The last example is interesting because it is not just a quibble that the "nearly" stops it being a syllogism in Barbara. Choose the right cases - and a threshold for "nearly" such as 80% - and you can easily show that it is not valid; the premises can be true and the conclusion false. This is worth pointing out. Ask them about "most.") I suspect that most classes will not take a whole class session to get through 5.4, so you could have the class read 5.3 and 5.5 in advance, and then work through 5.4 and the activity at the end of 5.5 in class.

5.5 (See the remark just above about combining the activity at the end of this and 5.4.) The students are not expected to grasp even the beginnings of the symbolism of propositional or relational logic here; the point is just to see that valid arguments come in families. The point that when the premises are false the conclusion of a valid argument can be either true or false tends to be surprising, so it is worth dwelling on it. (I think it's the idea that you can start with falsehood and by good reasoning get to truth that is disconcerting. Your destination does not validate your starting point.) In the activity at the end (7) and (4) can begin a TTT pattern, (2) and (1) can begin an FTF pattern, and (7) and (5) can begin a TFT pattern. (There are other solutions too.)

5.6 Though this section takes only three pages the central ideas, of validity and counterexample, can be hard to grasp. So it is worth spending a whole class just on this, working through the examples (a)-(d) slowly. (The examples are chosen to stress again the point that validity of argument and truth of conclusion are independent questions.) You could add (i) and (ii) from 5.5 if you wanted more examples, or make up your own.

5.7 The careful discussion of deductive validity is meant to allow a non-paradoxical statement of the important fact about induction: it is often reasonable but it is not deductively valid. No need to go through extravagant Humean ideas about induction not being rational in order to get the point across. (The Humean points are worth making, as this section does, but only once the distinctions are in place.) The diagrams should combine in a simple way with the diagrams of the previous sections: inductive reasoning looks like a partially unrolled Venn diagram, valid in the exposed bit but with possible counterexamples hiding in the unrolled bit. 5.9 rehearses this connection.

5.8 This section gives some cultural background to "the problem of induction." One subtle aim of the section is to forestall the impression that beginning philosophy students sometimes get, that inductive reasoning always gives true conclusions, but there is a lurking skeptical doubt that someday it may fail. It fails routinely, and we have to live with that fact.

5.9 This is a pretty straightforward activity, rehearsing 5.7 and 5.8. It could lead to a discussion of the areas in which we expect inductive reasoning to be more and less reliable. These expectations are in part based on inductive reasoning: does this invalidate them? (No, but the class may take some convincing on this point.)

5.10 The point is to show how resistible the arguments from the fallibility of induction to skepticism are. At the same time these arguments are important and should be discussed. After getting the content of this section clear, three general positions can be contrasted. The first is "Hume's problem is a nightmare that we cannot dispel but can usually ignore"; the second is "Hume's problem is a healthy limit on the claims of science"; and the third is "Hume's problem is a manageable question of which patterns of inference will succeed how often under what conditions." Force the students to choose which one they are more attracted to, and talk it out. (One technique "Morton is maneuvering us toward the third conclusion: how can we resist him?")

5.11 A topic that would not be closely related to induction were it not for Hume. If the class is reading Hume, this section may be needed to separate issues about cause from issues about induction.

5.12 An easy approach to grue (see Box 10) but still potentially confusing, and to be avoided if the class's grasp of the issues is delicate. It is also useful if they are having no problems and need stimulation. If you want to take these issues further 10.10 rehearses them.

Chapter 5 - Test

(1) Which of the following are syllogisms in Barbara?

(a) All trees are made of wood.
Anything made of wood burns.
Therefore anything that burns is a tree.

(b) All cats chase mice.
All mice have tails.
Therefore all cats have tails.

(c) All cats are animals.
All cats are mammals.
Therefore all mammals are animals.

(2) Draw a Venn diagram showing that each of the following is invalid:

(a) All dogs bark.
Therefore everything that barks is a dog.

(b) All mice are cute.
All cute things are pink.
Therefore all pink things are mice.

(3) Which of the following are arguments by simple induction?

(a) It was warm in Key West last January; it was warm in Key West the previous January; I have never heard of January in Key West that was not warm. Therefore it is always warm in Key West in January.

(b) Three years ago on the hottest day in Edinburgh it was 25 degrees centigrade; two years ago the hottest day was 28 degrees; last year it was 30 degrees. Therefore in a year or two it will be 32 degrees on the hottest day in Edinburgh.

(c) All the samples of neolite in my laboratory dissolve in sulphuric acid. All the samples of neolite in other laboratories dissolve in sulphuric acid. There are no samples of neolite outside laboratories. Therefore neolite dissolves in sulphuric acid.

(4) Which of (a), (b), (c) in (3) is more convincing as evidence for its conclusion?
[Write on the space below. Give a brief reason.]