APPENDIX 2: SOME PRECAUTIONARY MEASURES

In the course of this booklet we have seen various errors and fallacies and noticed some of the precautions we can take against committing them. In this Appendix I shall gather together some of the main strategies and also set out very briefly a few of the most frequent errors. We cannot cover all the errors, since to do so one would need to cover also the elementary forms of valid argument as well, but it might be useful to have a list of some of the common failings in argument.

In dealing with what people say there are a few questions one should always ask: What exactly is being said? Do we need to fill in any gaps before we can begin to investigate whether it is true or false? Is it true or false? If it is an argument, does it work as an argument, i.e. do its premises actually support its conclusion? Much of the preceding text is designed to get you to see how to answer such apparently simple questions. The answers to them are not always so simple, and they often lead to further questions, but I think if you approach what people say with these questions and the techniques I have offered you to help answer them, you should find yourself much better placed to sort the wheat from the chaff.

People often think they cannot follow arguments because the subject matter is too difficult or abstruse. I have tried to show you that you can do a great deal without knowing anything special about the subject matter of an argument. In fact, most of the problems that arise in argument are due, not to the subject matter, but to the very common and ordinary little words which hold arguments together. We have seen some of these words and their workings already; what I shall do now is list some of the main distinctions you need to bear in mind and some of the most common errors of reasoning you will find. Put baldly, as I shall here, they may look obviously erroneous; but decorated in the colourful robes of ordinary discourse they are remarkably easy mistakes to make, especially if one's thinking is guided as much by interest and commitment as by a calm desire for accuracy and truth.

And/Or

People do not usually mix up "John and Jane" with "John or Jane", but we have seen another context in which it is easier to confuse things to be taken together and things to be taken separately: the context of giving reasons for a conclusion. Here we distinguished between pattern (10) and pattern (12) on the grounds that in pattern (10) each reason had to be added together to support the conclusion, whereas in pattern (12) each reason separately supported the conclusion. Putting this issue in terms of "and" and "or", pattern (10) is, in effect, "p and q, therefore r" while pattern (12) is "p or q, therefore r" which is the same as "p, therefore r, and q, therefore r."

Not

One "not" in a sentence is usually no problem, but not a few people find it far from easy to decipher several negatives in a sentence. But the points I wish to stress are rather:

(i) it is not always clear exactly how much of a sentence is being negated (thus one may say "John doesn't think that Roseau is in Dominica" when one means John thinks it is not the case that Roseau is in Dominica - technically this is a matter of "scope");

(ii) people often make mistakes when "not" interacts with other logical words, e.g. "not both p and q" is not a good reason for "not p and not q" (rather it entails "either not p or not q", as is suggested by the idiomatic English "neither p nor q"), and again "neither p nor q" does not entail "not either p or q."

Another important interaction to beware of is that between "not" and "all" - "It is not the case that all swans are white" amounts to "Some swans are not white" and not to "No swans are white." In the next section we shall see how "not" interacts with "if...then..."

If

"If" is one of the most difficult words in logic. Indeed when you do formal logic you deliberately translate it into a bit of formal logic that behaves a lot more simply than the English "if". But for now, we should note firstly that "if" often carries the meaning of "only if" or even of "if and only if" (the precise way it does so is a matter of dispute that we can leave aside; only the resulting confusions are our present business). This is one reason why it is often very helpful to find statements with a quite different content but the same logical structure. To take an example from Mackie, does "you'll succeed if you try hard" mean what it says (if you try hard, you'll succeed; i.e., trying hard is sufficient in the circumstances for success), or does it mean only if you try hard, you'll succeed (which, as far as formal logic goes, can be seen as "if you succeed you (will have) tried hard"), i.e. trying hard is necessary in the circumstances for success, or perhaps both of these things? Taking quite different (and clearer) parallels might help to clarify this issue for someone making the claim.

The second thing to notice is that when "if" means just if, all the following are fallacious inferences:

(a) If p then q, q, so p.
(b) If p then q, not p, so not q.
(c) If p then q, so if q then p.
(d) If p then q, so if not p then not q.

(Compare also the answer to Exercise F (4).) Just as (a) and (b) mimic valid forms of argument, so (c) and (d) distort the valid argument: If p then q, so if not q then not p.

All/Some

The contrast between "all" and "some" may again appear too obvious when thus baldly stated, but in real arguments it is all too easy not to notice, say, that reasons that work for some Xs do not work for all. We have also seen (in Exercise F (5)) an example of a frequent usage in which we leave out any statement of all or some. We talk a lot about what men or women do without bothering to specify whether we mean all men, or almost all men, or most men, or most of the men we take some interest in, or just some men (which logic regards as satisfied by at least one man). While it is not always necessary to be pedantically exact, it is important to be on the look-out for the many fallacies which result from our laxity here.

The word "all" is intimately linked to "if...then..." (compare "All swans are white" with "If anything is a swan it is white" or, closer to formal logic, "For all x, if x is a swan then x is white") and so the fallacies we noticed above reappear in a new dress with "all". In particular, the following are fallacious:

(e) All A are B, so all B are A (compare (c)).
(f) All A are B, so all not-A are not-B (compare (d)).

A similar fallacy is:

(g) Some A are not B, so some B are not A.

As we saw above, the pair of words "necessary" and "sufficient" also ties into these notions. These words often carry additional meaning, but there are some important parallels to be noted: "Oxygen is necessary for life" goes along with "All living things are oxygen-using things" and with "If x is alive then x uses oxygen" (so briefly we could say, ignoring some important grammatical requirements: "A is necessary for B" = "All B are A" = "If B then A"). On the other hand, "40% is sufficient for passing the exam" goes along with "Everyone with 40% (and above) passes the exam" and with "If x gets at least 40% then x passes the exam" (briefly and ungrammatically: "A is sufficient for B" = "All A are B" = "If A then B"). Notice a consequence of these assimilations: if A is necessary for B, B is sufficient for A, and vice versa. As I have said, there is more to the meaning of these terms, but this equivalence often holds, even if it may sound somewhat strange. If oxygen is necessary for life, then finding something living is enough for there to be oxygen around.

There are other common patterns of argument involving "all" that are fallacious and which can be tested in the ways suggested in Section 6. Some have curious names derived from the traditional Aristotelian formal logic - the following is an example of what is sometimes called the fallacy of "undistributed middle":

(h) All A are C, all B are C, so all A are B.

Try using the methods of Section 7 on these two fallacies:

(i) All A are C, no B are A, so no B are C.
(j) All A are C, all A are B, so all C are B.

There are two other points which are worth noticing while discussing "all", though they can only be mentioned in this context. The first is an ambiguity in some uses of "all" between a collective and a distributive meaning. We might find this in talking about patterns (10) and (12) as we did above. If I say "All the premises in John's argument support his conclusion" I might mean "all the premises taken together, as a collectivity" (in which case we have pattern (10)) or I might mean "Each premise on its own supports the conclusion" (pattern (12)). A more general point related to this is the question of when we can truly ascribe to a whole properties which are truly ascribed to the components out of which that whole is made.

The second point is a special case of a very large issue, that of what is presupposed in our use of language. We could ask, "Does it follow from the fact that all bachelors are unmarried men that there is at least one unmarried man?" Or if you want a purely factual starting point: if all men have a heart does it follow that there is a least one man with a heart? I think usage varies here. For our present purposes, it is enough to note that if you think the conclusion does follow in these two examples you are presupposing there are As when you use the expression "all As..." Logic works more smoothly if we don't make that presupposition, and so modern logic would require us to insert the claim about existence as a separate premise in these two examples. Whatever logical theory you prefer, it is good to be aware of the issues to be addressed. (Note here that the circles we used in Section 7 assume that "all" presupposes existence, unlike in modern formal logic.)

Valid/Invalid Arguments

In Sections 6 and 7 we looked at what validity meant for deductive arguments. People can argue fallaciously from the fact that an argument is valid:

(k) Because the conclusion is true, some/all the premises are true.
(l) Because one or more premises are false, the conclusion is false. (Compare Exercise I.)
(m) Because the conclusion is false, all the premises are false.

Be sure that you see quite clearly why each of these reactions to the validity of an argument is mistaken. A similarly erroneous reaction to the invalidity of an argument is to argue:

(n) Because the argument is invalid, the conclusion is false.

Compare the above fallacies with those listed under "if": (k) with (a); and (l) above with (d). (m) does not have a corresponding fallacy but we can construct one: if (p and q) then r, not r, so both not p and not q: the correct conclusion for this argument is "not both p and q". (n) here does not have a corresponding fallacy with "if."

Operator Shifts

In the answer to Exercise F, #6 I introduced the notion of quantifier shifts (in that instance, moving "all" and "some" around). In logic we can regard many items as "operators", items that make new items out of old ones (new sentences out of existing sentences; sentences out of predicates; etc., etc.). The general point is that when we have more than one operator at work we have to be careful how we move them around (which, to use a term I used above, is a matter of changing their relative scope). Thus while we can validly move from "There is a boy that every girl loves" to "Every girl loves some boy" (formally, "For some x and for all y, y loves x" entails "For all y, and for some x, y loves x") we cannot go back the other way: every girl may love some boy or other but that does not mean there is one boy loved by every girl. Some of the fallacies we have looked at in preceding paragraphs are varieties of such operator shift mistakes: for example, "Not both p and q" cannot become "Both not p and not q." The idea of scope here can be roughly explained by saying that in "Not both p and q" the "not" reaches from the beginning to the end of the expression, while the "both...and..." is inside it; whereas in "Both not p and not q" the "both...and..." has major scope, covers the whole expression, and has inside it two "not's", the first of which stretches over "p", the second over "q". The importance of keeping an eye on operator shifts can be seen when it is noted that "it is necessary that", "it is possible that", "it is obligatory that", "John knows that", "it was the case that", and many other expressions and their cognates can be treated as operators.

As one example of a fallacious operator shift, think about:

(o) It is necessary that either you live to be 85 or you don't live to be 85, so either it is necessary that you live to be 85 or it is necessary that you don't.

Qualifications

In the section on Ellipsis I tried to show you how we can go wrong ignoring parts of what we are saying. What I am getting at now is that we can argue fallaciously by either dropping qualifications or inserting them; the former sort of error is certainly made easier by the phenomenon of ellipsis. Note, however, that just as with operator shifts, I am not saying it is always wrong to drop or insert qualifications, just that it is an area in which we must take care. An example of the fallacious dropping of a qualification in a context which may not be elliptical would be:

(p) It is permissible to tell a lie to avert great suffering, so it is permissible to tell a lie.

Adding qualifications can be equally bad:

(q) Some snakes are poisonous, so some Jamaican snakes are poisonous.

Dropping qualifications gives another way of viewing some of the arguments I mentioned above in which reasons that work for some are used as if they worked for all. We could say they work for all As that meet certain other criteria but these additional qualifications are forgotten in the conclusion.

Dubious Dichotomies

Before talking about fallacious moves in argument we should note that the very expression "either...or..." is a source of confusion. Whenever I have used it meant it as "either...or...or both"; but sometimes it seems it has a strong exclusive sense "either...or...but not both". However we account for this, it is important to see that what works with one interpretation may not work with the other. Thus there is a well-known pattern of valid argument: p or q, not p, so q. This works whichever way you understand "either...or..." But people often argue: p or q, p, so not q. With the sense I have been using, this is a fallacy; but if you give the "or" the stronger exclusive sense, it is a valid argument.

One mistaken tactic in argument is to present what is often called a "false dichotomy". You require a choice among alternatives that do not properly cover the field. The mistake is not in presenting the alternatives, but in not accepting answers from outside the range given. Many official forms exemplify this fault, as when you may be asked your marital status and offered only "married" or "single". There is a well-known variety of this fault referred to often by way of a notorious example: "When did you stop beating your wife?" Again, there is nothing wrong with asking such a question, but there is something wrong in refusing an answer that challenges the presupposition that you have in the past beaten your wife.

In thinking with sets of alternatives it is always useful to be aware of the extent to which the alternatives are exclusive (i.e. nothing can fit into more than one category) and exhaustive (i.e. are there possibilities that are not covered?).

Another kind of false dichotomy occurs when people refuse to acknowledge borderline cases between the ends of what is in fact a continuum. We have a use for the words "hairy" and "bald", but we need not have to answer for every person whether he or she is hairy or bald; people needn't be one or the other. A fallacy related to the same fact of a continuum is to deny there is any real difference between the extremes on the grounds that we cannot specify the border in between. These are both perverse ways of misunderstanding how this sort of language operates.

Mistakes in Argumentative Discourse

If you compare the topics I have mentioned in this Appendix with those covered in traditional texts on fallacies you might notice I have omitted so-called fallacies such as "begging the question" or argumentum ad hominem. The reason is that I have been restricting the term "fallacy" to invalid arguments which are mistakenly taken to be valid, whereas traditional use extends the term to cover other moves in argument which are plausibly regarded as faults of a kind.

In begging the question, or indulging in a circular argument, you are almost certain not to commit a fallacy in the narrow sense I am using, since what you are doing amounts to arguing: p, (q, r), therefore, p. And this is a valid argument pattern. You can't go from truth to falsehood simply by repeating yourself. But while there is not likely to be anything wrong with the logic of the argument, you should be able to see that such an argument is not likely to be achieving one of the main goals of argument, viz. giving support to its conclusion. If you want an audience to accept that "p" is true, you are not likely to get very far by using an argument which relies on already accepting that "p" is true. So, as an argumentative strategy, begging the question or arguing in a circle is in general to be deplored.

Ad hominem arguments are again matters of strategy rather than logic. As far as logic goes they can be valid or invalid; what makes them ad hominem is that their conclusions are not that a certain claim is true or false, but rather that a certain person cannot consistently make a certain claim. To take an unlikely example: if you say 2 x 6 = 13 and you accept that a x b = b x a and you have gone on to claim 6 x 2 = 12, I might argue against you, that given the first two claims you've accepted you can't hold that 6 x 2 = 12, but rather you must accept 6 x 2 = 13. This example illustrates what I think often makes people deeply suspicious of such ad hominem arguments - I say you are required to accept a conclusion which I would never dream of accepting myself. As I said before, the argument is not to the truth of its apparent conclusion (in this case, 6 x 2 = 13), but rather to a truth about what someone else should, in consistency, accept (in this case, you have to accept that 6 x 2 = 13 to be consistent). It thus turns away from the substantive issue to the person arguing about it. In some cases such a move is irrelevant, it is a way of diverting attention from the real issue; but in other cases it may be very relevant, perhaps especially in moral debate. In any case, we cannot issue a blanket condemnation of arguments ad hominen as an argumentative strategy.

There are other issues we could look at in the area of argument strategy - appeals to authority, use of emotional language, etc. - but which I shall leave aside. The basic question to be addressed is to what extent these moves actually contribute to rational support of the conclusions argued for. Transposed to an argumentative context they are simply questions of whether suggested means actually bring about the intended end. The basic distinction, however, is between the end of merely getting people to agree with you and the end of providing reasons sufficient to move an impartial rational mind.

Ambiguity and Vagueness

Arguments can fail to work because of ambiguities or vaguenesses in their constituent statements. In the text, we noted in particular the undercover changes in the meaning of terms that are often used as ways of evading falsification (in Section 10). We also saw a kind of ambiguity in many verbal nouns in Section 12, and perhaps more useful in ordinary discourse, the ways in which language can become virtually empty of meaning in Section 13. Ellipsis and also the laxity of ordinary language with respect to marking the scope of operators which we have just been looking at contribute further to our chances of going wrong in argument.

There are many other respects in which things can go wrong. There are parts of language where we have to be particularly careful - we cannot, for example, safely infer from the fact that John knows the capital of Jamaica is in Jamaica, that John knows that Kingston is in Jamaica. We are often plain careless in our assumptions: it doesn't follow that if you are unable to distinguish shade A from shade B, and shade B from shade C, you are unable to distinguish shade A from shade C, but it is easy to forget this fact. In our more philosophical moments we can easily mix up what is true because of the way we think with what is true of the world we think about and we can do this in various ways. We cannot hope to deal with all these topics. In a way, a lot of philosophizing is a matter of dealing with these kinds of likely error, and this booklet is not meant to be a quick guide to philosophy. I hope, however, that the ideas it does contain can serve as a basis for any such explorations you may be inclined to undertake.

URL http://www.uwichill.edu.bb/bnccde/epb/precautions.html

HTML prepared June 2000, last revised June 29th, 2000.

Return to list of publications.