Notice that I have put most of the evidence inside asterisks: suppose there is a good landing and the instructor praises it then the next one is worse. It wouldn't matter here if one regarded the evidence as asserted: when there is a good landing.... Notice that in either case, the arrow is very weak; it doesn't stand for strong reason-given support, merely as a way of picturing what is asserted on certain grounds. Defining the conclusion, "g", in the way I have (saying roughly if b then c and if e then f) allows the authors' argument to lead to "not g" as it seems to in the passage, although the real force of their argument is to reject the instructors' reasoning from evidence to causal claim rather than to reject that causal claim itself.

Let us close this section of our study by examining the exchange implicit in the following passage by Jacques Barzun, on a topic that is pertinent to our own concerns in this course:

(39) More than one school catalogue I have read begins by saying: 'At the -- School, the first of our objectives is to encourage students to think for themselves.' The redundancy gives away the pretense: encourage them, equip them, to think, and much will have been done. Whoever thinks does it by himself and for himself. But to encourage the utterance of opinion unchecked does nothing to encourage thought. Rather, it strengthens the prejudice against thought, by persuading each child that everybody is entitled to his own opinion, 'especially me to mine'. [22]

On the surface, Barzun reports what he has heard and then goes on to comment on it, but we can bring out his thought by seeing it as a dialogue: a school spokesman says "The first of our objectives is to encourage students to think for themselves" and Barzun scornfully replies, "You lie. Whoever thinks does it by himself and for himself. But you encourage the utterance of unchecked opinion, so you persuade children that everyone is entitled to their own opinion, so you strengthen the prejudice against thought." This omits Barzun's further comment that equipping people to think would be a fine thing, if done properly, and a few other smaller points; but the main thing is to see the dialogue implicit in the development of Barzun's argument.

EXERCISE D

Draw structure diagrams of the following passages, bearing in mind the possibility of implicit dialogue:

1. In Africa, even though the total number of drop-outs at the start of the school career appears to have fallen, there has in most cases been an increase in repeaters, indicating that educational prospects at the beginning of the school career have not really improved. [23] [Answer.]

2. It may be going too far to say that the unexamined life is not worth living, but if reason and wisdom have any value then such a life will be less than satisfactory. [47] [Answer.]

3. The view that romantic love is essential to marriage is too anarchic, and, like St Paul's view, though in an opposite sense, it forgets that children are what makes marriage important. But for children, there would be no need of any institution concerned with sex, but as soon as children enter in, the husband and wife, if they have any offspring, are compelled to realise that their feelings towards each other are no longer what is of most importance. [48] [Answer.]

4. Nationalism and socialism are incompatible for a number of reasons. First, the basis of all nationalist theories is that those supposed to make up a "nation" have a common interest. This is not true. All "nations" are divided into two antagonistic classes. Between these classes is an irreconcilable conflict of interest which can only be resolved by the conversion of the means of production into the common property of the whole community, by the dispossession of the owning class. Nationalism also assumes that the problems facing the non-owning class can be solved on a national scale, within the borders of a particular state. This is quite wrong. Capitalism is the cause of these problems. And since capitalism is a system existing all over the world it can only be abolished on a world scale. [24] [Answer.]

5. By far the commonest argument for discriminating against women takes the line that women are to be excluded because they are not equal to the task in question. They cannot be dockers or bus drivers because they are not strong enough,.... The usual feminist response to this line is an indignant denial of the whole thing: either the accusations are false, or if women are in some ways inferior to men it is because men have deprived women of proper education. There is of course much truth in this. However, this is one clear case in which feminists would do better to forget about factual argument for a while and concentrate on the logic. This reasoning is absolutely absurd for two reasons. In the first place, nearly all the differences claimed to exist between men and women are differences of average.... Second, even if there were cases where it looked as though all women actually might be worse at something than all men, that still would not account for a rule specifically excluding them or saying they should do better than men to be admitted, because, as Mill said, 'What women by nature cannot do, it is quite superfluous to forbid them from doing. What they can do, but not so well as the men who are their competitors, competition suffices to exclude them from...' [25] [Answer.]

6. Writers, philosophers and artists eat food that others have grown and use energy that others have worked to provide, and perhaps do not think enough about the value of what is given back. This line of thought tends to push intellectual activity low down the list of priorities, as the marginal luxury of the comfortable. But I hope that some of the considerations suggested by the thought experiments [in earlier chapters of the book] will check this tendency. These activities are not a dispensable frill, but are central to some of the values that give life a focus and a centre, once basic needs for food, shelter and health have been satisfied. Some of the values - relationships between men and women, parents and children, which can be of a quite unintellectual kind - are at least as important. But even here, relationships change with ways of thinking and seeing. So, if writers and others do interesting work, perhaps something is given back. Though this too may be self-deception. [26] [Answer.]

7. The idea that competition is vicious has been challenged by several writers. Every person, they say, is good at something, and failure in one area is counterbalanced by success in another. Thus, each person will find a context in which he/she will find self-esteem, accceptance, and a sense of achievement. This competitive pluralism must be acknowledged; no doubt it serves to ameliorate the effects of competition for personal goods. Nevertheless, the argument overlooks the differential status which is accorded to these competitive arrangements. Success in certain kinds of competition is accorded considerable social standing, giving those who do well wide acceptance and manoeuvrability, whereas those who succeed in less vaunted enterprises may find their acceptance limited to a very small group of people, who anyway wish for success in the more highly ranked enterprises. [49] [Answer.]

6. VARIETIES OF SUPPORT

So far we have looked at the overall pattern of simple arguments, and noted some of the intricacies in what an arguer is actually committed to. We have been mainly concerned with how to describe arguments. In this and the next few sections we shall turn to the kind of support premises give to conclusions, and our interest will be mainly evaluative. But first let us attempt to describe, or at least indicate, the two radically different kinds of support that I shall follow tradition in distinguishing.

Consider two pieces of reasoning. Suppose that the first time I arrived in Trinidad the first people I saw were all Indian. I might then have argued from the fact that I had seen ten people in Trinidad and that they were all Indian to the conclusion all Trinidadians are Indian. (You may think such an argument unbelievably silly, but many of my compatriots have beliefs about West Indians and Pakistanis that are no better based.) Now what kind of argument have I got here? I surely cannot rely very much on it; I really ought to be prepared to qualify or even radically alter my conclusion in the light of further evidence. (Suppose my first ten Trinidadians were all male, or over 16 years old; it would be almost impossible for the whole population to be like that.) So while we may allow that my premise gives some support to the conclusion, we must insist that it is precious little.

Suppose instead that I am assured that no Muslims eat pork wittingly and that I see a man order and eat some pork chops, I may then argue that the man is not a Muslim. What kind of argument have I now? My premises are that no Muslims wittingly eat pork, and that this man is wittingly eating pork. Given these two premises, surely I can't go wrong in claiming that this man is not a Muslim. (Of course, my premises might be mistaken; but so might my claims about my first ten Trinidadians - in looking at both specimen arguments we are not disputing the truth of their premises.) In this second type of argument, my premises give a kind of guarantee to the conclusion. The guarantee is not that my conclusion is true (we've noted already that my premises may be wrong), but rather that if my premises are true then my conclusion will be true too; I can't have true premises and a false conclusion. It is a conditional guarantee of truth. In this sort of argument, truth is transmitted, as it were, from the premises to the conclusion.

But equally important, this sort of argument transmits falsehood from the conclusion back to the premises taken together. Staying with our pork-eater, if he really is a Muslim then either he is not wittingly eating pork or it is false that no Muslims eat pork wittingly (as usually in this booklet, either/or allows both).

So, then, we have found two different sorts of support: one which is simply support and which doesn't offer any guarantees (in particular, it allows the premises to be true and the conclusion false), and one which incorporates a conditional guarantee that you can't have the premises true and the conclusion false. From here on things get a bit messy, both because we are beginning to cut below the surface of our reasoning and because, annoyingly, terminology is somewhat unsettled. But let me stipulate how I propose to talk: basically arguers put up arguments, and I shall classify arguments by the kind of support the arguer supposes them to have, (the first sort I shall call "non-deductive"; the one with the conditional guarantee, I shall call "deductive") and also, if necessary, by whether they do embody that kind of support (the ones that do I shall call "valid", the ones that do not I shall call "invalid").

My way of talking allows for four types of argument:

(a) valid deductive (e.g. No communists are Christians, so no Christians are communists);

(b) invalid deductive (e.g. All communists are atheists, so all atheists are communists);

(c) valid non-deductive (e.g. The mortality ratios for lung cancer for smokers and non-smokers are statistically significantly different, and the ratio for smokers is greater than 1, so smoking is a causal factor for getting lung cancer);

(d) invalid non-deductive (e.g. Most communists are atheists, so most atheists are communists).

Note that all non-deductive arguments are deductively invalid; some writers restrict "valid" and "invalid" to deductive arguments. Note also that some invalid arguments are often called "fallacies" (though in some cases what people call fallacies are perfectly valid arguments which the people dislike for some other reason). Note, finally, that many writers contrast deductive with inductive arguments; by "inductive" they may mean what I mean by "non-deductive" or some more restricted kind of argument (e.g. from singular premises to another singular conclusion - The first swan was white, the second swan was white,... so the next swan will be white - or from singular premises to some kinds of generalization - The first swan was white, the second was white,...so all (most) swans are white).

While dealing with my stipulation about the meaning of "valid", it is worth noting another and more general stipulation in logical analysis. Arguments can be described as valid or invalid, but that pair has no sense when applied to the statements, sentences or propositions making up an argument. Those statements etc. can be true or false, but not valid or invalid. Conversely, there is no sense in talking about arguments as true or false.

The point of this section is to distinguish deductive from non-deductive arguments. It is important to decide which sort of argument you are dealing with. The question is, in effect, whether the arguer supposes she can rely on the deductive guarantee - no possible situation in which the premises are true and the conclusion false. If she thinks she can, you have a fairly clear-cut issue as we shall see; but if she isn't relying on a deductive link, things are less clear. It would be nice if it were always obvious which kind of argument was in question, but unfortunately it isn't. There are at least two reasons for this, and they may overlap in some cases.

The first reason is that you can always convert a non-deductive argument into a valid deductive argument by adding extra premises. This, as it stands, is not much of a reason for finding the distinction hazy, but it is strengthened when you note that often a non-deductive argument can be transformed into a valid deductive one by adding obvious and plausible extra premises, such as an arguer might well leave out, as being too obvious or well-known to her audience. If I simply said to you "Ade eats pork, so she's not a Muslim" my one explicit premise only gives non-deductive support to my conclusion; but I could well be relying on an unstated premise that no Muslims eat pork, and with that my argument becomes deductively valid. So we have here the general problem of knowing how much to add to what gets explicitly stated in an argument.

The second sort of reason is that people may not be clear in their own minds what kind of argument they are using. After all, I have had to explain the distinction to you, and you may not yet grasp it properly. Let us look back at one of the examples I offered above - most communists are atheists, so most atheists are communists. I said this was a non-deductive argument, but some arguers might well treat it as deductive - they often behave as if the analogous argument with "all" replacing "most" is valid deductively, and the argument with "some" replacing "most" is valid deductively, so I agree that some people might treat it as a deductive argument. But I think that it is also possible for someone to realize that this argument is deductively invalid, but think it was a reasonable gamble, non-deductively. At this point, the first sort of problem might begin to arise since such a reasoner might not be arguing only from the premise that most communists are atheists, but also from a collection of other unstated premises about the distribution of the various religions, the strength of secularism in different parts of the world, and so on. (Analogous points could be made about the other example of an invalid argument above.) Again, while no one, I hope, would imagine that noting the race, colour, sex, or other salient characteristics of the first ten people they see in Trinidad would give them a reliable basis for generalization, many people do seem to treat the measurement of characteristics in a more scientific setting as if it were the direct establishment of a universal generalization, rather than a report of what was found for a minute sample under a certain range of conditions. You might measure the velocity of sound in a slim steel rod at a certain temperature, pressure, etc. and we might (erroneously in this case) suppose that you have established the velocity of sound in steel. When people are unclear, then if our concern is simply with describing the person's argument, we have to say they are unclear, but if our concern is with the actual issues rather than the arguer, then we have to decide how much revision of the argument we can allow, since the temptation here is to reconstruct the reasoning in the light of what we think the actual logical relations are. And as far as pursuing the issues goes, it may not be a bad thing to succumb to this temptation.

We have come several times upon the question of what unstated premises to add to an explicit argument. What should we do? There is no hard and fast answer, but there are a few points to note. The first I have just mentioned: we are usually more interested in the argument than the arguer. We have seen already that we talk a lot about what we and other people may be thinking, but our real concerns are not with the psychological histories of individuals, but with the matters they think about. So rather than try to specify the often somewhat indeterminate thoughts a person may have had, it is usually better, and easier, to specify the possibilities for the argument. And this amounts to looking for extra premises that are sufficient to make it a valid argument, and asking whether they are plausible. In some cases, such as the little argument already noted "Ade eats pork, so she's not a Muslim," this gives us a straightforward answer - the extra premise "No Muslims eat pork" is fairly widely known, is supposed to be true, and does no harm to the argument, indeed it makes it deductively valid. But in other cases, people make mistakes, and looking at the alternatives can help you to uncover them. Suppose McCarthy had argued "Ade's not a Christian, so she's a communist." Here we have a common sort of case where both obvious construals of the argument fail, but for different reasons. What would make the argument deductively valid? The premise "All non-Christians are communists." If McCarthy accepted this, he would have had a valid argument; but could even McCarthy have believed so implausible a claim? What might he have believed? A premise like "All communists are non-Christians" (in English, "No communists are Christians"). Depending on how you construe this, it may or may not be true, but at least it is plausible in our context. But it doesn't entail the needed "All non-Christians are communists." So we seem to have presented McCarthy with an unattractive choice: either his argument is valid, but based on an obviously false premise, or it is deductively invalid. Either way, his stated premise does not support his conclusion. (I am assuming the argument is not intended to be simply non-deductive.)

The aim, in adding extra premises, is, as Scriven says, "to find something that's strong enough to patch up the holes in the argument, but not any stronger than it has to be" [27]; or to do the best you can and thereby reveal how the argument fails. Discovering such extra assumptions requires judgment and practice; as we have noted with other issues, there is no automatic way of doing it. The best thing is to try lots of examples.

EXERCISE E

Read the following arguments carefully (you may find it helpful to do a structure diagram) and then decide whether they are deductive or non-deductive, and consider whether any extra assumptions should be added:

(1) Most Swedes are Protestants; most Swedes who visit Lourdes are not Protestants; so most Swedes do not visit Lourdes. [28] [Answer.]

(2) The word education comes from the Latin 'educa-re' (to train, to bring up), which is related to another Latin word 'educe-re' (to lead forth, to draw out). To educate is therefore to bring up or train. [29] [Answer.]

(3) Since there are more people on the earth than hairs on any one person's head, I know that there must be at least two people with the same number of hairs. [30] [Answer.]

(4) The most economical and satisfactory way for members to buy vintage clarets is when they are first available. Not only are they then almost certain to be at their least expensive, but also the widest choice of the best wine is available. [31] [Answer.]

(5) In an earlier section of this book the strong association between 'broken homes' and delinquency was noted.... The main question is whether the harm comes from disruption of bonds or distortion of relationships. This may be considered by comparing homes broken by death... and homes broken by divorce or separation.... This comparison has been made in several independent studies.... In each case the delinquency rate has been about double (compared to that for boys in intact homes) for boys whose parents had divorced or separated, whereas the delinquency rate has been only slightly (and non-significantly) raised for those who lost a parent by death. This suggests that it may be the discord and disharmony preceding the break (rather than the break itself) which led to the children developing antisocial behaviour. [50] [Answer.]

(6) Monopoly, and the hideous accumulation of capital in a few hands, carry in their own enormity, the seeds of cure. Whatever presses men together, though it may generate some vices, is favourable to the diffusion of knowledge, and ultimately promotive of human liberty. [32] [Answer.]

Suggested Answers

EXERCISE C

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     *                           * )
     *  a  )                     * )
     *     ) ---> never c, but d * )
     *  b  )                     * )
     *                           * )
     ***************************** )          (a ] )
                                   ) ---> not (  ] )
                            [c  )  )          (b ] ) ---> f
                                )                  )
           ******************** )                  )
           *                  * )  
           * e ---> never c   * )    ---> not  e ] )
           *                  * ) 
           ********************