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 aim of this chapter is to introduce the idea of an argument for a conclusion, with the central example of proofs of the existence of God as an item of independent interest. The material on argument is wrapped up in a discussion of Reason, which need not be lingered on, as the issues will return in chapter 3. If you are short of time you could cover only the sections in the absolute core, listed above. In any case, classroom time should be concentrated on working through arguments - sections 2.4 and 2.7 - picking up an intuitive picture of how one gets from premises to conclusions, and the difference between valid and invalid ways of doing so. Do not expect most students to get completely clear on this after just a week or so. You could easily spend a month drilling the concept of a deductively valid argument into them. My experience, though, is that it works better to let the concept gather slowly, leading the students on with issues that are of more intrinsic interest.
You may be giving your course so that there is an emphasis on issues about religious belief. In that case section 2.2 will be more important than the labeling above suggests, and gives a different perspective on 2.7 than the rest of the chapter.

Chapter 2 - Comments on Sections

2.1 Though most of this section is expositional prose, it ends with an activity that can be done in class. The straightforward responses to the questions are that Miriam is appealing to the authority of normal shared belief (common sense, culture), Luc is appealing to the authority of his guru, Leah is appealing to the authority of scientific method, and Jean is appealing to the authority of a book. Miriam, Naomi, and Judith are simply doubting what their interlocutor says, while Leah is appealing to the authority of science. It could be argued that Naomi is also appealing to an authority, that of theories about childhood development. In all the cases the second speaker has a generally skeptical attitude, but the emphasis of the section should be on authority rather than skepticism. They are related in that skepticism and authority are natural enemies. Skepticism usually draws on the authority of reason though, if only for its negative effect, thus making a link to 2.3.

2.2 (i) is relevant to (c), and also to (b). (ii) is relevant to (b). (iii) is relevant to (a). (iv) is relevant to (b) and also to (c). (v) is relevant to (a). (vi) is relevant to (b), and also to (c). (vii) is relevant to (b) and (c). In using this section begin by simply eliciting the points/attitudes connections. The temptation then is to allow a discussion to develop in the form of a debate between adherents of (a), (b), (c), which might easily become a brawl between the religious and the nonreligious. An alternative would be to divide the class into three groups on some arbitrary basis and ask the first to produce two points in support of (a), the second two points in support of (b), and the third two points in support of (c). The points could be elaborations of (i)-(vii) or novel points. Stress to them that they are functioning like philosophical lawyers: they have to find two good supports for the attitude in question even if they do not personally share that attitude. Then when each group's points have been stated and explained, there may be time to move to a third phase in which you do ask people to say which of the attitudes they share. Each person then should say - or indicate with a show of hands in a large class - which of the points that have been produced - (i)-(vii) plus the new ones just produced - is most troubling for them. That is, which point they feel most strongly challenges their attitude, so that they wish they had a good reply to it. (I always find that a thoughtful reaction is produced in students when you ask them to choose the strongest argument for a position they do not hold.)
A subtle philosophical point that may emerge from the discussion is that although there may be beliefs which we cannot or ought not to support with arguments, the identification of these beliefs and the defense of their claim to be beyond argument is itself a matter of rational dispute. We can argue about what should be subject to argument.

2.3 Students will very naturally be doubtful of the rationalist ambition of establishing substantial chunks of knowledge by reason alone. We live in an empiricist culture. So the easiest way of getting them to respect the power of reason is to stress three points. First, the negative power of counterargument: when some belief cannot be true, just thinking about it can often show that it is wrong. (See 3.3. and 3.4 for examples.) Second, mathematical proof, as showing that in some special areas at any rate we can establish conclusions just by reasoning. (Of course this can be challenged, but the claim is plausible, and challenging it leads to profitable discussion.) And while even committed believers these days tend to doubt that the existence of God can be proved, the ambition to do so does not seem ridiculous. Third, the deduction of further conclusions from information given by perception or authority, as when a detective discovers a clue and reasons to the identity of the murderer.

2.4 One difficulty in getting across the idea of a deductively valid argument comes from the fact that the standard examples are of perfect self-contained arguments in which all the premises are explicit. But nearly all the arguments that we meet in everyday life rely on numbers of implicit premises. This can give the impression that all these everyday arguments are faulty. The best strategy is to say honestly that you are studying artificially simple examples of good and bad argument, where everything is out in the open, and that in real life telling when someone is arguing well or badly is a much subtler business.

Many students find it surprisingly hard to identify the premises and the conclusions in an argumentative passage. Given a little argument laid out in "A, B, therefore C" form they can usually say whether it is convincing or not, and can usually separate judgments of the truth of the conclusion from judgments of the force of the argument without much difficulty. But if they are given a long passage like a newspaper column and asked to say what it assumes and what it concludes, they are more often baffled. My strategy - see 2.4 - is to provide short arguments, short enough that premises and conclusions can be identified by a sense of what might follow from what and by indicator words like "so" and "therefore." Then building up to seeing argumentative strategy in longer passages can happen slowly. In any case, the essential thing is that students know what the difference between premises and conclusion is, and that they see that an argument's validity is different from the truth of its conclusions, or premises, or both.

2.5 See the remarks above about the difficulty of identifying premises and conclusions. I have deliberately included arguments in which the conclusion is at the beginning rather than at the end. The arguments get progressively harder to structure and evaluate. (a)-(c) should not present much of a problem. (But (b) is an example of a good argument whose premises are not obviously true. So it forces the valid/sound distinction. (c) too: it should be an exercise in discriminating outrageous argument from outrageous premises.) (d) may be harder just because it is longer. The conclusion is signaled by "then," which is less explicit than "therefore." (f) is also potentially harder to grasp. I have deliberately used an example with terminology that may be unfamiliar to many, to stress that in assessing the validity of an argument, understanding the component propositions is less important than assessing its soundness. The conclusion is in the middle of the passage, not signaled by any indicator word. It is enough with (g) to get it laid out in standard form. The argument actually contains a fallacy, a confusion of "for each A there is a B" with "there is a B such that for each A," which I remark on at a couple of points later on in the book. But it is not important at this stage to dwell on this.

The first question, "which are more persuasive?" is deliberately naïve. In discussing different students' answers to it you should be able to bring out the difference between a valid argument - which would persuade a critical audience who accepted its premises - and a sound argument - which would lead a critical audience with true beliefs to a true conclusion.

2.6 These arguments may be valuable because they may intrigue. It isn't obvious what is wrong with them. My own diagnoses are that in the first the second premise is, surprisingly, false. Some rare things are cheap, for example, cheap horses. In the second the conclusion is actually true: Moscow is to the west of London, though you have to go a long way west to get there. And in the third we either have to reject the third premise - amend it to "the brother of a brother is a brother when he is distinct from the first brother" - or accept that every male is his own brother. But there are other diagnoses, and it is the articulating of them that is likely to be valuable.

2.7 Some of the arguments in 2.4 already contained several steps, so the basic idea here should not be too difficult. (There is a more sophisticated use of arguments within arguments, as in conditional proof, or arguments by reductio. But that is not to be brought in here.)

The overall argument is not valid because the premises could be true and the conclusion false in a situation in which some people of the same generation are conformist and some nonconformist, and the children of unions between conformists and nonconformists are a mixture of conformists and nonconformists. The argument would be valid if we added the premise "at any time everyone is either a parent or a child and either all parents are conformist or all parents are nonconformists" (and the "hardly needs stating" premise "children grow up to be parents.") Are there weaker premises which will do the job? This is not an issue to spend class time discussing!

2.8 It would help to get the class to read at least the Andrea/Brian dialogue in advance. The first of the skeleton arguments ("every event has a cause") can be found in Brian's intervention beginning "You do, you do, . . ." The second ("we only understand") can be found in Brian's following intervention, beginning "Weren't you listening?" The third and fourth (both beginning "we do not understand") can't be found in the dialogue. The fifth "the causes of any event") is found in the next of Brian's interventions, beginning "We don't know why."

When you ask which of the arguments the students find more convincing, the discussion may expand to include other reasons for believing there is a God. That is alright, as long as the discussion is about arguments for the existence of God. It should not become an argument about the existence of God in general.

It is important that people be able to judge the force of arguments to conclusions they do not accept. So the reactions of nonbelievers to the five arguments are worth eliciting. Which are more nearly convincing and why? It is worth pointing out that Andrea in the dialogue has some arguments against the existence of God, though they are less explicitly stated, for example, in her interventions beginning "You're going to be disappointed" and "I suppose I think." You might expand on these arguments - ideally draw attention to them and let the class expand on them - and then ask those in the class who believe in a God which ones more nearly challenge their faith.

The last part of this section introduces the fundamental technique of refuting an argument by presenting a counterexample. This is discussed in more detail in 5.6. I think that providing formal counterexamples to the five arguments for God would be too hard at this point. I chose the second argument for counterexampling because one of its two component arguments - from the universe having a purpose to the existence of God - is very easy to counter. The other component goes from every intelligible event having a purpose to there being a single purpose to all events. That this is fallacious may be harder to see. I'd suggest just presenting obviously invalid parallel arguments such as "every child has a mother; therefore there is a Mother of all children" or "we only understand the value of an object when we see how much work went into making it; we do understand the values of objects; therefore there is an amount of work that went into all objects." Then after the penny has dropped, people will begin finding additional premises to undermine the parallel.

The material in the last paragraph of the section is included for the sake of stimulation, and needn't be worked through in class, though it may be useful with a class which finds issues about God uninteresting.

2.9 Discussing paradoxes in class can be tricky, because there are individuals who will be very insistent that the reasoning is fallacious for some specific reason, and will take up a lot of time explaining themselves. The teacher then is in the delicate position of agreeing that the reasoning is fallacious, but insisting that the mistake is more subtle than the student thinks. It is hard for the student in this situation to see that the teacher is not arguing for the paradoxical conclusion in disagreeing with their diagnosis of the fault in the reasoning. If you are discussing this section in class rather than leaving it as stimulating reading - and I am not trying to discourage you from doing so - I would recommend forcing a class discussion of which premises in the two arguments are better candidates for being abandoned (see the list in the text) before particular dogmatic diagnoses arise. The point is then made that the paradox can be avoided by abandoning a belief, which might be less painful than it seems at first.

2.10 I am assuming that most students will have some sense of the dangers of picking up information from the internet. They will not have a specific list of worries though, and so this section may be of use as a means to practical skepticism. (I have taken some ideas from the HONcode site.) A class based on this section should begin with eliciting the kinds of false or misleading information that can result from ignoring each of the warning signs (1)-(7). A discussion of the general wariness appropriate to the internet could follow. This sets up the most important phase philosophically, a discussion of the ways in which the other sources listed may be really no more reliable than the internet.

Points I would expect to emerge, one way or another, in the course of this discussion are: textbooks rarely cite original sources or give the reader enough information to reproduce the relevant experiments; authorities often refer to one another in a circular fashion; life is too short to get evidence for everything; knowing that evidence could be found is important even when one doesn't actually check it; people can honestly and sincerely pass on information that is in fact false.

2.10 This section just rounds out the chapter and connects the issues with those that arise later. It would be good for students to read it, but it does not really need discussion.

Chapter 2 - Test

(A) In each of the following three arguments, underline the premises of the argument, and circle the conclusion:

(1) Classical musicians are more highly trained than rock musicians. In order to play classical music at a professional level you have to study an instrument for years. But some rock musicians have only a few weeks of formal training.

(2) You might think that the hot summers we have had lately are conclusive proof that the world's climate is getting warmer. But this may not in fact be the case: the climate may not be changing at all. For a sequence of hot summers can be the result of chance, like throwing a die and its coming down six four times in a row.

(3) Everything in the Bible is true. The Bible says that we should not kill. Therefore it is wrong to wage war, for any purpose, for warfare inevitably involves killing.

(B) Beside each of the following four arguments mark either V for valid or I for invalid (not valid):

All cats eat mice.
All mice can fly.
Therefore all cats can fly.

All cats eat mice.
All mice can fly.
Therefore all cats eat flying things.

Some cats eat mice.
Therefore some mice are eaten by cats.

You can fool all of the people most of the time.
You can fool most of the people all of the time.
Therefore you can fool most of the people most of the time.