The Basic Equipment
by Antony Flew
from his 1998 book How to Think Straight: An Introduction To Critical Reasoning
a revision of his earlier works Thinking about Thinking and Thinking Straight

1.1 The first thing to get straight in thinking about thinking is the difference between questions about validity and questions about truth. But in getting this straight we shall find that we are also sorting out every other really fundamental notion. For the indispensable notions are all connected. We cannot fully master any one without getting the same grasp upon the lot. Once the essential preparation is complete, we may proceed to the main business of the book. That business is to consider examples of thinking, usually of bad thinking, in order to learn how to do the job better. Here and now we have first to clean and tidy the tools.

1.2 The reason to begin precisely where we are beginning is that thinking about thinking is concerned, at least in the first instance, with the validity or invalidity of arguments, rather than with the truth or falsity of propositions. What is true, or false, is propositions. What is valid, or invalid, is arguments. These notions and these distinctions are absolutely basic. To say that an argument is true or that a proposition is valid is as uncomprehending or as inept as to say that someone got to first base in basketball or that someone made a home run in tennis.

1.3 Consider propositions. There are, of course, propositions and propositions. Both those mutually advantageous proposals which one businessman makes to another and those improper but delightful suggestions which playboys put to their intended playmates are called, quite properly, "propositions." But in this book -- perhaps regrettably -- we shall engage with propositions only in a quite different sense of the word. In this, our relevant sense, the word "proposition" is defined as, "whatever may be asserted or denied." So a proposition for us becomes whatever may be expressed by the that-clause in such sentences as, "She asserted that he had been there on Wednesday," or "He denied that he had ever met her."

1.4 In the irrelevant, proposal sense a proposition may be said to be attractive or unattractive, profitable or unprofitable, and many other things besides. What it cannot be, or be said to be, is either valid or invalid. In our different sense there are again several things which a proposition may be: demonstrated, for instance, or probable, or refuted. Nevertheless, the primary characteristic is truth or falsity. For demonstration here is nothing else but proving that the proposition is true. The proposition which is probable just is probably true. Refutation, again, is not merely saying, but showing, that the proposition is false. It is because refutation involves more than denial that hard-pressed spokespersons so often assert that they have refuted charges when in fact all that they have done is deny them, perhaps dishonestly.

1.5 Propositions in this understanding are not to be identified with arguments, although all arguments contain propositions. Piety demands that our first example be a dull hack hallowed by immemorial tradition. Its tedious, trite, and trivial character will ensure that no one is distracted from what is being illustrated by any interest in the illustration. Later I shall deploy interesting and important examples. I hope thus to escape the dangers of boring myself and everybody else, or suggesting that the subject itself is as trifling as this first illustration.

1.6 Set out carefully and piously, the traditional example runs: if All men are mortal, and if Socrates was a man, then it follows necessarily that Socrates was mortal. This example includes three constituent propositions. The first two serve as premises, the last as a conclusion. In other contexts and in other arguments what is here conclusion might serve as premise, and what are here premises might be derived as conclusions from other premises.

1.7 The italicization of the constituent propositions and the representation of the whole argument in a hypothetical (if this, then) form are both important. The first device brings out two things: first, in general, that arguments are concerned with the logical relations between propositions; and second, in particular, what proposition is being said to be necessarily connected with what two others. Later much more will be said both about logical relations and about logically necessary connections. For the moment it is sufficient, but necessary, to emphasize that these are always and only relations of, and connections between, propositions.

1.8 The second of the two devices, that of representing a whole argument in hypothetical form, makes it clear why, in order to know whether the exemplary argument in which these three propositions are here embodied is valid, we do not need to know whether any of its constituent propositions are true. We do not for this purpose need to know because in offering the argument we are not actually saying anything about the truth or falsity of these constituent propositions. It is all hypothetical. Another argument of the same form would be no less valid even if all of its three constituent propositions happened in fact to be false. This would be true of the absurd argument: If All tigers are strictly vegetarian, and if Socrates the son of Sophroniscus was a tiger, then it follows necessarily that Socrates the son of Sophroniscus was strictly vegetarian. As we shall see in chapter 2, such hypothetical deductions, albeit from much more sensible premises, may serve as the initial steps in a more complex pattern of argument. Such deductions lead us from the actual falsity of the original conclusion in a valid argument to the further conclusion that at least one of the original premises must also be false.

1.9 Although to say that the present argument is valid is thus not to say that any of the three constituent propositions are true, it does imply the truth of the complex hypothetical proposition: If All men are mortal, and if Socrates was a man, then it follows necessarily that Socrates was mortal. In asserting this truth, what is asserted is that the argument from the two constituent premise propositions to the constituent conclusion proposition is valid. The fact that you can say that the claim that this argument is valid (or invalid) is a true (or false) claim is, however, no more a justification for confounding validity with truth than the fact that you can say that the contention that a certain man is a homosexual is a true (or false) contention is a warrant for identifying homosexuality with truth.

1.10 To say that an argument is deductively valid is, by definition, to say that it would be impossible to assert its premise or premises while denying its conclusion or conclusions without thereby contradicting oneself. That is what deduction is. We have just seen that an argument may be valid, notwithstanding that both its premise or premises and its conclusion or conclusions are false. Similarly, an argument may be invalid, notwithstanding that both its premise or premises and its conclusion or conclusions are true.

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1.11 Later we shall return to the relations and lack of relations between validity and truth, and I will provide mnemonic illustrations. But the first thing now is to underline the connection between the two concepts of deductive validity and of contradiction and to explain what is so wrong about contradiction. Suppose someone were to maintain that, although Socrates was a man, Socrates was not mortal. No doubt such apparent irrationality in so simple a case is somewhat hard to imagine. Yet that difficulty should, if anything, make it easier to appreciate that if ever people were to behave in this way, then we would have to choose between two alternative conjectures. Either they are being in some way disingenuous, or else they are not fully masters of the meanings of all the words which they have uttered.

1.12 On the one hand, perhaps they have some sort of doctrinal commitment to affirm the two premises while nevertheless equally firmly denying the obvious conclusion. They may want to maintain that Socrates was a man and, as such, mortal, and yet that Socrates was a god and, as such, not mortal. Certainly there are those who hold that someone, though not Socrates (c. 470-399 B.C.E.), was at the same time both truly man and truly God. Or maybe our imaginary objectors have their reasons for wanting to say one thing in one context or to one group of people while saying something altogether inconsistent in another context or to another group of people. This temptation is familiar to us all. It is no prerogative of members of that scapegoat class, professional politicians.

1.13 On the other hand, it is also possible that our imaginary objectors are careless or confused about the crucial difference between all and some. Some men are mortal is consistent, as All men are mortal is not, with Some men are not mortal. Again, there is no call for any far-fetched supposing. We meet all too many cases of people who, having noticed that something or other is true for a few instances of such and such a sort of thing, proceed forthwith to assume, or even to assert, that the same is true of all things of that sort. We have, surely, all done it ourselves? (Such generalizations about all and every something or other are, by the way, called universal propositions.)

1.14 There may appear to be a third possibility, that an objector might be interpreting one of the key terms in one way in one of the premises and in another way in the other premise or in the conclusion. The word "Socrates," for instance, might he employed to refer to one person on one occasion and to another on the other. Again, "mortal" might be construed as meaning "liable to death," whereas "not mortal" was understood as metaphorically "immortal" -- immortal, that is, in that wholly different sense in which a great person who indisputably has died, or will sometime die, may nevertheless truly and consistently be numbered among the immortals.

1.15 This apparent third possibility is thus the possibility of equivocation. The word "equivocation" is here defined as "the employment of some word or expression in two or more different senses without distinction in the same context." If equivocators realize that they are equivocating in their employment of one of the key terms in an argument, then their performances are certainly disingenuous. If they do not realize this, then, equally certainly, they are "not fully masters of the meanings of all the words they have uttered." In the most literal sense they do not know what they are talking about.

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1.16 The basic point developed in the five previous paragraphs is extremely important. It is none the less so for having been made with a hackneyed, traditional example developed in a somewhat far-fetched way. This basic point is that the terms "valid" and "invalid," as applied to deductive arguments, and the expression "deductive argument" itself have all to be defined in terms of self-contradiction and the avoidance of self-contradiction. It is because these are thus central notions that our concern with logic inextricably involves us also in concerns with both meaning and truth. The basis of the necessary and inescapable involvement with meaning will be immediately obvious. Given that a valid deductive argument is, by definition, one in which to assert the premises while denying the conclusion is to contradict yourself, then it becomes at once clear that no one can be in a position to know whether or not any argument is valid, except insofar as he or she has mastered the meanings of all its crucial terms.

1.17 It may be more difficult to appreciate that there are necessary connections between logic and truth and why these connections make it so essential to argue validly and to avoid contradiction. For did not this chapter itself begin by insisting that "thinking about thinking is concerned, at least in the first instance, with the validity or invalidity of arguments rather than with the truth or falsity of propositions"? And have we not gone on to assert that arguments may be valid, though both their premises and their conclusions happen to be false, or invalid, though both their premises and their conclusions are in fact true?

1.18 Yes, this was said. It is all true. But it is also true that, though sound argument and a reasonable appreciation of the available evidence may happen sometimes to lead to false conclusions, no man who is indifferent to argument and to evidence can claim to be concerned for truth. Abraham Lincoln was profoundly right when he wrote, chiding the editor of a Springfield, Illinois, newspaper: "It is an established maxim and moral that he who makes an assertion without knowing whether it is true or false is guilty of falsehood, and the accidental truth of the assertion does not justify or excuse him." It is also true that to tolerate contradiction is similarly to be indifferent to truth. For people who, whether directly or by implication, knowingly both assert and deny one and the same proposition show by that behavior that they do not care whether they assert what is false and not true, or whether they deny what is true and not false.

1.19 To grasp this point is to raise a perennial personal challenge. Like all such personal challenges, it should be seen as being at least as much a challenge to me and to us as it is to you and to them. For whenever and wherever I tolerate self-contradiction, then and there I make it evident, either that I do not care at all about truth, or that at any rate I do care about something else more. It was thus precisely because to affirm the premises of a valid deductive argument while denying the conclusion is, by the definition of "valid deductive argument," to contradict yourself, that Socrates used to demand: "We must follow the argument wherever it leads."

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1.20 The same personally challenging point, that contradiction must be intolerable to anyone who really cares about truth, can, with the help of a little demonstration, be made more elaborately. Anyone inclined to bridle against such logic-chopping can without serious loss skip the next four paragraphs. The promised, or threatened, demonstration was apparently first mounted in the 1200s of our era either by Duns Scotus (c. 1266-1300) or by one of his pupils. (It is, by the way, ultimately to the uninhibited polemics of the philosophical opponents of the great Duns Scotus that we all owe our word "dunce." There must be some moral here!)

1.21 The demonstration goes like this: First, take as your personal premise a contradiction of your choice. I take for mine the conjunction of the two propositions: (1) The Declaration of Independence was made in 1776; and (2) The Declaration of Independence was not made in 1776. Now choose, equally freely, any false proposition. I choose: Elvis Presley is alive and well. Next, take one half of the initial contradiction as a separate premise. From The Declaration of Independence was made in 1776 it follows that The Declaration of Independence was made in 1776 and/or Elvis Presley is alive and well.

1.22 Thus, given that for whatever x may be, x is true, then for the same value of x and for any value of y it follows necessarily that x and/or y is true. The only, but sufficient, justification for employing the symbols x and y -- rather than the awkward verbal alternatives something, the same something, something else, and the same something else -- is that the point can thereby be made more briefly, more clearly, and more elegantly. The object is, as it always should be, to promote understanding. What needs to be understood is that so far it has been shown that, from my arbitrarily chosen contradictory premise, it follows that The Declaration of Independence was made in 1776 and/or Elvis Presley is alive and well. So far so unexceptionable, and altogether unexciting.

1.23 But now we consider the second half of the initial contradiction: The Declaration of Independence was not made in 1776. Taking this as one premise and the conclusion reached at the end of paragraph 1.21 as the other, it becomes impossible to avoid the false conclusion that Elvis Presley is alive and well. For to deny this while asserting these two premises would be to contradict oneself

1.24 We thus have an absolutely general and absolutely compulsive demonstration that from any contradiction which you like to choose, any other proposition, equally arbitrarily chosen, follows necessarily. By the same token, the negation of that other, arbitrarily chosen, proposition must also follow, equally necessarily. We can by the same method also deduce the opposite conclusion: Elvis Presley is not alive and well. Both every proposition and its negation thus follows from any contradiction. Hence, if contradiction is tolerated, then, in a very literal sense, anything goes. This situation must itself be totally intolerable to anyone who has any concern at all to know what is in fact true and to avoid either saying or implying what is in fact false. If all this seems pedantic, recall Bertrand Russell's mischievous definition of a pedant: "A person who prefers his statements to be true."

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1.25 Generally, therefore, when someone with pretensions to be a thinker either denounces the restrictions of logic or remains unmoved by charges of self-contradiction, we know what to think. Thomas Aquinas (c. 1225-1274) understood as well as any man that the saints and the prophets may speak of mysteries. Yet, having a grip on logical fundamentals, Aquinas never forgot that there can be no place for self-contradiction in any authentic quest for truth. Thus, in considering the omnipotence to be attributed to his God, he took account of what is in modem terms the distinction between logical and other senses of "impossibility." A suggestion is said to be logically impossible if that suggestion contains or implies a self-contradiction, or is perhaps otherwise incoherent and unintelligible. But a suggestion that is not in this sense logically impossible may be ruled out by the actual laws of nature and hence be factually impossible. As Aquinas put it in the Summa Theologica: "Whatever does not imply a contradiction is, consequently, among those possibilities in virtue of which God is described as omnipotent. But what does imply a contradiction is not subsumed under the divine omnipotence..." (I Q25 A3). You cannot, he might have said, transmute some incoherent mixture of words into sense merely by introducing the three-letter word "God" to be its grammatical subject.

1.26 One place where this distinction and this insight is indispensable is in the discussion of what theists call "The Problem of Evil." This is the theists' problem of trying to show that they are not contradicting themselves in maintaining both that there is, as indeed there is, much evil in the Universe and that the Universe is the work of an all-powerful, all-good God. It is not a bit of use to appeal here to what are, the Universe being as it happens to be, factual impossibilities. The only hope for the theist is to try to show that it would be logically impossible to have the actual goods without the actual evils, as it is, for instance, logically impossible to have the good of forgiveness without the evil of an injury to be forgiven. It is logically impossible because it is self-contradictory to speak of forgiving a nonexistent injury. For the theist it must be almost blasphemous to argue here, along lines I once saw indicated by one of a series of posters described as constituting The Wayside Pulpit: "If it never rained, there would be no hay to make when the sun shone."

1.27 The most fundamental kind of confusion about contradiction is an intellectual malpractice that Karl Marx (1818-1883) and Friedrich Engels (1820-1895) derived from their study of the enormously influential German philosopher G.W.F. Hegel (1770-1831). This is the malpractice of thinking of contradictions not only as occurring in discourse, but also as involved in the interactions of physical objects. Thus, in the essay On Contradiction supposedly written by Mao Tse-tung, we can read: "The supersession of the old by the new is the universal, forever inviolable law of the world.... Everything contains a contradiction between its new aspect and its old aspect, which constitutes a series of intricate struggles.... At the moment when the new aspect has won the dominant position over the old aspect, the quality of the old thing changes into the quality of the new thing. Thus the quality of a thing is mainly determined by the principal aspect of the contradiction that has won the dominant position."

1.28 A contradiction in this regrettable usage is thus not a verbal contradiction, but a conflict or a tension in or between things or people. Once these categories are properly distinguished, the apparent justification for employing the same word in two utterly different cases disappears. To the extent that this usage helps to collapse or to confound a categorical distinction, it is to be deplored. This same usage encourages talk of fruitful or even nonantagonistic contradictions, contradictions that are welcome, or at least venial. (Mao Tse-tung himself continued, speaking of the "contradiction" between town and country: "But in a socialist nation and in our revolutionary bases such an antagonistic contradiction becomes a nonantagonistic contradiction; and it will disappear when a communist society is realized....")

1.29 But talk of fruitful (if not, perhaps, of nonantagonistic) contradictions may have quite a different source. The contradictions then referred to are genuine verbal or symbolic contradictions, and the fruit offered has to be picked by laboring to remove the contradiction. The vital point for us is that this fruitfulness presupposes the removal of the contradiction. It is only insofar as contradiction is recognized to be intolerable that the labors which may provide fruit can begin.

1.30 Consider, for instance, disagreements about whether or not some country is democratically governed. Very obviously the party who asserts that it is appears to be contradicting the party who asserts that it is not. But perhaps these two disputants are employing the key word "democratic" in different senses. For one of them the criteria for a democracy may be that the rulers should have been popularly elected into office and -- much more important -- that it should be possible in due course to vote them out. For the other one the criterion may be that favored by rulers describing their fiefs as people's democracies, namely, that these rulers are working to promote the best interests of those whom they rule. One by now rather ancient, yet still remarkably clear expression of this conception of democracy was provided by Janos Kadar, addressing the Hungarian National Assembly on May 11, 1957, one year after a Soviet army of intervention had installed him into office as prime minister: "The task of the leaders is not to put into effect the wishes and will of the masses.... The task of the leaders is to accomplish the interests of the masses." This statement may profitably be compared and contrasted with that made by Abu Zuhair Yahya, prime minister of Iraq in 1968: "I came in on a tank, and only tanks will get me out" (quoted in [Coup d'Etat: A Practical Handbook, by Edward] Luttwak 1969, p. 146).

1.31 Because of the Hegelian or Hegelian-Marxist confusion involved in speaking of contradictions in things and because salutary challenges to resolve seeming but not actual contradictions may be preposterously misconstrued as reasons for rating actual contradictions as in themselves good, contradiction sometimes wins an undeservedly favorable press. Similar confusions and misunderstandings often get an understandably bad press for logic.

1.32 The first of these misunderstandings hinges on a failure to distinguish two senses of the word "logic." One is primary. It is the sense in which the word has been employed in this chapter up till now. The other is secondary and derivative. This is the sense in which it is true to say that Aristotle (384-322 B.C.E.), in the works grouped into what was later called the Organon, created "Logic" as an academic discipline. These two senses are most conveniently distinguished by printing the word with an initial capital whenever it is used in the second sense.

1.33 The general mistake here is that of expecting any study of that kind to be either necessary or sufficient to improve the practice to which it is directed. The musicologist does not through his musicology become a better executant. Nor does being a great performer immediately qualify one to be a musicologist. The particular point about "Logic" and "logic" was made in the late 1600s by John Locke (1632-1704) in his Essay concerning Human Understanding: "God has not been so sparing to men to make them barely two-legged creatures, and left it to Aristotle to make them rational; ... " (IV [xviii 4).

1.34 On the contrary: "Logic," as the theoretical study of the forms and principles of argument, could only begin among and be pursued by people possessing a good practical capacity to separate valid from invalid arguments. In fact, its first strong and extensive development was among the ancient Greeks and, in particular, among the supremely argumentative Athenians. (For a lively and instructive study of the peculiarities of these Greeks, which made possible the origination of so much that was essential to the development of our modern world, see Alan Cromer's Uncommon Sense: The Heretical Nature of Science [1993], especially chapters 4-6.) The present book, which is intended to help people to improve their thinking, is not an essay in theoretical Logic. It is instead an exercise in logical coaching. Such an exercise may be beneficial even though neither the coach nor the coached have or acquire any familiarity with the calculi of Logic. But it could not even begin, much less be beneficial, unless all concerned possessed at least some minimal competence in discerning soundness in argument. Without that you could not even understand the coaching.

1.35 The second and much more important reason why logic gets a bad press is that it is confused with various things which have nothing to do with it. Consider, for instance, the contrast and the possible conflict between two opposite approaches to politics and to society. On the one side are those who, like Plato (c. 428-c. 348 B.C.E.), want, as he put it in his dialogue The Republic, "to start with a clean canvas." A good example of this approach was provided by the Jacobins during the great French Revolution of 1789. They replaced all the previous subdivisions of France by eighty-three Departments, all roughly equal in area and each with its own administrative center. They also introduced a new calendar of twelve months with freshly minted names, and all the months were divided into three decads of ten days each. (A special arrangement was made to accommodate the surplus five days.) And so on. On the opposite side are those, like Aristotle, who prefer to start from wherever they are, seeing improvement as a matter of natural growth and development. Reformers of the first kind are likely to long for utopia and to have a penchant for wholesale operations. Reformers of the second kind do not expect anything to be perfect and believe that whatever progress can be made has to be made piecemeal. They understand, with the great German philosopher Immanuel Kant (1724-1804), that "out of the crooked timber of humanity no straight thing can ever be made."

1.36 Especially in the context of thinking about the French Revolution of 1789, the first great social revolution of the modern period, Edmund Burke (1729-1797)* is often seen as representative of the second approach. This approach is sometimes believed by English people to be characteristically English, although Burke himself was born and educated in Ireland. By contrast, the Abbé Sieyès,** who contrived to survive when so many of the other revolutionaries were killed, is seen as representative of the first approach, an approach which is in the same circles seen as characteristically French. Neither of these approaches is as such either logical or illogical, although particular spokespersons on one side or the other may well be logical or illogical. But when confronted with the argument of the Abbé Sieyès against legislative second chambers, his supporters are apt to applaud his famous apothegm as a fine specimen of Gallic logic while his opponents decry it upon exactly the same ground. What he said was: "If the second chamber agrees with the first, it is superfluous, whereas if it disagrees with it, it is obnoxious."

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* Burke was a member of the U.K. Parliament, most famous for his hostile and horrified Reflections on the Revolution in France. (He had been and remained sympathetic to the very different American Revolution.)

** The Abbé Sieyès is most famous for his answer to the question: "What did you do in the Revolution?" His reply was: I survived." But one might mention his pamphlet What Is the Third Estate? (1790).
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1.37 It is not for us here to decide whether this statement is especially Gallic. We do, however, need to notice that it certainly is not especially logical. If someone accepted the two conditional propositions so dogmatically asserted, then it would, of course, be illogical for that person to refuse to allow that any second chamber agreeing with the first must be superfluous and that any second chamber disagreeing with the first must be obnoxious. Yet there is no intellectual or other merit in simply asserting these drastic propositions. By doing so you make the totalitarian assumption, without providing any supporting evidence, that all dissent from any decision made by the first chamber must be immediately and automatically overridden. This is an assumption which no one has any business to make tacitly and without supporting argument. When such a brilliant refusal to examine the case for the opposition is presented as a model of logic, then there is every excuse to be suspicious. But it is not in this interpretation that we are laboring to make ourselves more logical.

1.38 We have shown why contradiction ought to be unacceptable and that logic is connected, albeit indirectly, with truth. It should now be less misleading to insist again upon the fundamental difference between questions about validity and questions about truth. To fix this in mind we need one or two dull, undistracting, naggingly unforgettable examples. Consider as premises the two propositions: All philosophers are lifelong bachelors and King Henry VIII of England was a philosopher. Both are false. But if they were true, then it would follow necessarily that King Henry VIII of England was a lifelong bachelor. Anyone who asserts the two false premises, yet denies the conclusion, would certainly be committing a self-contradiction. So now, since few people have less claim to have been lifelong bachelors than King Henry VIII, who was married six times, we have an example of a valid argument from false premises to a false conclusion.

1.39 Next, suppose that we substitute for the original second premise: President James Buchanan was a philosopher Then, again, both premises will be false. The conclusion will be that President James Buchanan was a lifelong bachelor. Applying the same test as before, it is obvious that this is derived by a valid deductive argument. But this time the conclusion is true. Thus, we now have an example of a valid argument from false premises to a true conclusion.

1.40 Someone says: All Christians believe in an omnipotent and personal God, and Mother Teresa believed in an omnipotent and personal God. If we assume that these two propositions are true, are we entitled, taking them as our premises, to deduce the conclusion: Mother Teresa was a Christian? No, of course we are not. Certainly the conclusion is true. Yet the argument, considered as an argument, is, equally certainly, invalid. To make it valid, the first premise would have to be changed to read not All Christians, but All and only Christians. So the example offered, without that essential amendment, constitutes an example of an invalid argument to a conclusion which happens nevertheless to be true.

1.41 Suppose that some people have difficulty in appreciating that such an argument must be invalid, as indeed many people may have since they happen to know that its conclusion is in fact true. Then the natural and appropriate response is to summon up parallels to enable those who have this difficulty to appreciate that neither this nor any other argument of the same form can possibly be sound. You might as well argue, we might say, that given that All swans are white (which they are not), and given that President William Clinton is white (which, in terms of race, he is), then it follows necessarily that President William Clinton is a swan (which will scarcely do). Or, again, you might as well argue that given that All Communists claimed to be opposed to racism and given that Dr. Martin Luther King claimed to be opposed to racism, then it follows necessarily, Dr. Martin Luther King was a Communist.

1.42 When we produce such parallels, we are trying to bring out the invalidity of all arguments of one particular form: the form, that is, and whatever it is, which is shared by both the original specimen and all the genuine parallels which could be deployed. The main practical reasons why parallels have to be summoned is that people are put off by what they know or believe about particular propositions in particular arguments. Because we know or believe that the proposed conclusion is true, we become less alert to the possible weakness of the inference by which it is supposedly derived.

1.43 If, therefore, we want to assess someone else's critical acumen, then the best way to do this is to attend to their responses to arguments apparently justifying the conclusions which are most congenial to them. And when, as we should do frequently, we try to test our own critical acuteness we ought to notice how we ourselves respond to wretched arguments which appear to justify the no doubt often very different conclusions which appeal most strongly to us.

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1.44 A measure of symbolization is by now necessary. But before proceeding to that, something needs to be said about the word "racism," which has become as much a term of abuse as "democratic" is of praise. For unless the disputants in any debate as to whether some person or policy is or is not racist agree upon at least some rough and ready working definition of the key term, then in the most literal sense they simply do not know what they are talking about. Two points may usefully be made at this stage.

1.45 First, if you want to abominate racists as wicked, then the word "racism" will have to be defined as referring to a kind of bad behavior, presumably that of advantaging or disadvantaging individuals for no other and better reason than that they are members of one racially defined set rather than another. By the Axiom for Sets, formulated by Georg Cantor (1845-1918), the sole essential feature of a set is that its members have at least one common characteristic, which may be of any kind. The reason for introducing the word "set" here is that it does not carry the unwanted implications of such alternatives as "group" or "class" or "community."

1.46 The alternative hypothetical is that if, whether explicitly or implicitly, one defines the word "racism" as involving no more than the holding and/or expressing of beliefs in the existence of differences on average across one racially defined set as opposed to another, then the definition makes racism not a kind of bad behavior but a sort of disfavored belief. The crucial distinction here is between beliefs that all members of some racially defined set possess some characteristic and beliefs that some characteristic is on average more or less commonly possessed across one racially defined set than across another.

1.47 This is important. For from propositions expressing beliefs of the latter sort nothing can be validly inferred about the possession or nonpossession of the characteristic in question by any particular individual member of the racially defined set in question. You cannot, for instance, validly infer the height of any particular individual member of some human set from a proposition stating only the average height across that set. So even if some or many propositions of this kind are found to be true, their truth could not constitute a reasonable objection to our trying to discover every individual's merits or demerits directly, and then proceeding to treat him or her accordingly. The policies for which such discoveries really might carry upsetting implications are policies to secure the representation of various racially defined subsets of a population in various areas of activity and achievement in proportion to their numbers in that entire population. (For a leading lawyer's critique of attempts to enforce such policies by law, see [Forbidden Grounds: The Case against Employment Discrimination Laws by Richard A.] Epstein 1992.)

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1.48 Returning now to the business of symbolizing, what the fallacious arguments of 1.40 and 1.41 have in common is the following form: Given that All so-and-so's are such-and-such and given that That is a such-and-such, then it follows necessarily that That is a so-and-so. It is a very short and a space-saving further step to replace "so-and-so," "such-and-such," and "That" by letters. If you are going to do this, now and or later, then it is also a good idea to introduce the further notational refinement of distinguishing the subjects (the "so-and-so's") from the characteristics attributed to these subjects (that of being "such-and-such") by employing capital letters from the Latin alphabet for the former and lower-case Greek letters to symbolize the latter. Thus: If All As are ø (pronounced phi) and if That is ø, then it follows necessarily that That is an A; which, of course, it does not.

1.49 So much for the key notion of the form of an argument. Here and elsewhere all the particular specimens of any general class may be described as the several tokens of that same single type. ("Token" and "type" are a useful pair of labels that are well worth remembering.) The particular type or form of argument of which we have just been considering some tokens is fallacious. It has an unfortunately unmemorable traditional name: The Fallacy of the Undistributed Middle.

1.50 In the heyday of Senator Joseph McCarthy and of the House Committee on Un-American Activities, some favored the nickname "The Un-American Fallacy." This was a backhanded tribute to McCarthy and those members of his committee who were inclined to deduce that a person must be a Communist from the evidence that he possessed some characteristic perhaps shared by all Communists, but certainly not peculiar to them. This particular nickname is long since obsolete. Yet we still need to consider the point suggested by the pessimistic German philosopher Arthur Schopenhauer (1788-1860), although discounting his false and nasty insinuation that every defect from logical perfection is studied and designing: "It would be a good thing if every trick could receive some short and obviously appropriate name, so that when a man used this or that particular trick, he could be at once reproached for it" ([The Art of Controversy by Arthur] Schopenhauer [translated and edited by T.B. Saunders] 1896, p. 18).

1.51 In the present context, the word "fallacy" does not refer to just any intellectual error. It is confined to one particular sort of such errors, that of mistaking an invalid argument for a valid one. This needs to be emphasized, since there is a common usage in which any misconception may be described as a fallacy. Thus, in the years immediately subsequent to the conclusion of World War II, many people in many countries were inclined to believe that any unwelcome large-scale events must be the effects of the explosion of atomic bombs. Those who held this belief to be mistaken could and did say, in accordance with this common usage, that it was a fallacy.

1.52 If it were only a matter of what is acceptable to dictionary makers as established and, hence, correct English usage, then the unbelievers could have rested their case for employing the word "fallacy," rather than the almost equally wounding "misconception," upon the undoubted propriety in these dictionary terms of the label "the Pathetic Fallacy." This label refers to the mistake of attributing to things which are not alive the feelings, dispositions, and reactions which can characterize only living things, in particular, people. But, in our stricter sense of the word "fallacy," neither this nor the putative misconception about the cause of those unwelcome large-scale events is a fallacy. The fallacy involved, if fallacy there was, must have been not the conclusion, but in the supporting argument. Having once mentioned The Pathetic Fallacy, if only incidentally, it is as well to seize the occasion to point out that the temptation to make mistakes of this kind lies in the fact that "Perhaps the simplest and most psychologically satisfying explanation of any observed phenomenon is that it happened that way because someone wanted it to happen that way" ([Knowledge and Decisions by Thomas] Sowell 1986, p. 97). But so very often in fact it did not.

1.53 In the case of the atomic bomb explosion hypothesis there very obviously was a fallacy involved, namely the fallacy of arguing that, simply because one series of events occurred after another series of events, the second series must have been caused by the first. This fallacy has been known traditionally -- retaining the Latin, which was employed for all teaching and learning in the universities of medieval Europe -- as the fallacy of arguing post hoc ergo propter hoc (after this therefore because of this). Until and unless someone is able to suggest a better English alternative, let us call it the Whatever-follows-must-be-the-consequence Fallacy.

1.54 The prime reasons for insisting upon the stricter usage of the term "fallacy" are efficiency and economy. We have in our rich language other words which can be used for just any kind of mistake or misconception. For a start there are the words "mistake" and "misconception." If we oafishly misemploy our verbal chisels as verbal screwdrivers, we thereby unfit them for the job to which they are best suited. So what do we use for a chisel when a chisel is what we need?

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1.55 Compare another topical example far removed from our immediate interests. Those who have enjoyed such classic gangster movies as The Roaring Twenties (1939) will remember that the word "hijack" was first introduced to refer to the forceful seizure of what was already stolen or in some other way contraband. There is surely nothing to be said for the current abusage, which makes "hijacking" an unappealing substitute for the good old word "piracy" -- so romantically redolent of the Caribbean in an earlier century. It thus leaves us without any handy single word to distinguish the true present-day analogue of the original Prohibition phenomenon. Is not the case of forcible seizure by one criminal firm of a consignment of illicit drugs belonging to another, equally criminal competitor such an example?

1.56 It is for similar reasons that I have been following and shall continue to follow stricter usages of many other everyday terms. Such stricter usages are required even in making and maintaining the fundamental distinction between questions about truth or falsity and questions about validity or invalidity. Nor is there any call to go slumming in order to unearth examples of what we need to avoid. In his Discourse on the Method, René Descartes (1591-1650), who is by common consent recognized to have been the Father of Modern Philosophy, formulates his proposed doubt-proof, rock-bottom certainty as an argument: "I think, therefore I am." Yet he still affirms that this argument is something that he "'clearly and distinctly conceives to be true" (Part IV). Allowance must of course be made in Descartes's case for the fact that he was writing in the early 1600s. But that is a reason why we have to do better. (By the way, the usual practice is to omit the definite article before the word "Method" in translating the title of this work from the original French. But that is wrong since Descartes clearly saw himself as developing and proclaiming the one and only correct method -- his.)

1.57 Some other illustrations of the need for care in the employment of key terms have been given already. Care is also always required about knowledge and refutation. To say that someone knows something is to say more than that he claims to know it or that he believes it most strongly. It is to say also both that it is true and that he is in a position to know that it is true. So neither the sincerity of his conviction nor the ingenuousness of his utterance guarantees that he really knew. That is why the sarcastic tone enters our voices or why we write the key word between disclaiming quotation marks -- in "sneer quotes" -- when a man who has claimed to know turns out to have been wrong: "He 'knew' which horse was going to win the Kentucky Derby, but he 'knew' wrong." Nor in pointing out the falsity of the proposition that he asserted to be true is one necessarily challenging his integrity. It is most probably not that he was lying, just that he was honestly -- and perhaps very expensively -- mistaken.

1.58 To say that spokespersons for individuals or organizations refuted charges laid against those individuals or those organizations is to say much more than that they denied these charges and apparently believed that what they were saying was the truth. Rather, it is to say that they deployed sufficient evidencing reasons for believing that the charges were in fact false. If you do not want to say as much as that, then you should take the trouble to be noncommittal. You ought in that case to say only that these spokespersons claimed to have refuted the charges in question.

1.59 The same desire to husband resources of vocabulary, to preserve vital distinctions, should make us stingy in our application of the term "prejudice." Often it is treated as roughly equivalent to "opinion" or "conviction," albeit with powerful pejorative overtones. In this all-too-common abusage I have my opinions and my convictions, but you and he merely have prejudices -- so called by me for no better reason than that they are yours or his and not mine. The word "prejudice" becomes a valuable extra item in the vocabulary of anyone striving to be more rational only when, and insofar as, it is employed scrupulously to pick out just those beliefs -- whether right or wrong -- that are either formed prior to proper consideration of the available evidence or else maintained in defiance of it.

1.60 It is obscurantist and demoralizing to apply the word "prejudice" in order to abuse other people's opinions, or even all strong convictions, simply as such. The judge who instructs the jury to consider carefully and without prejudice all and only the materials actually presented in court is not asking them to refuse to bring in a decisive verdict. Nor is there anything whatever wrong with anyone's opinions or with strong convictions, as such. What is obnoxious, and what merits all the abuse in the arsenal, is the willful maintaining of preconceptions against the weight of the evidence. But to do that is not an always incurable feature of the human condition. Nor is it the exclusive prerogative of other people.

1.61 Another occasionally useful distinction is that between the sense and the reference of some word or expression. The sense is the meaning and the reference is the object or objects to which the word or the expression refers; that is, the referent or the referents. The standard illustration for clarifying this distinction is provided by the expressions "the morning star" and "the evening star." The senses or meanings of these two expressions are obviously different. And when they were first introduced into the English language no one knew that they both have the same referent, namely the planet Venus. To emphasize this distinction between sense and reference, the useful convention is: when we are talking about the sense or meaning of some word or expression, to escort that word or that expression with quotation marks. But as long as words and expressions are being given their workaday employment of referring to referents, they remain unescorted. Another relevant convention is similarly to escort words and expressions with quotation marks when what is being talked about is neither their senses nor their referents, but the sounds made by their pronunciation, or indeed anything else but their meanings or their referents. For instance, we may in this way truly and clearly describe the words "cuckoo" and "sizzle" as onomatopoeic. We shall observe these conventions throughout this book and recommend readers always to do the same.

1.62 It is in terms of the distinction between sense and reference that we can explain the nature of what has traditionally been labeled the Masked Man Fallacy. It consists in arguing that because someone knows (or does not know) something under one description; therefore, they must know it (or therefore they cannot know it) as the same thing when it is considered under another description. So we cannot validly infer from the fact that someone was acquainted with what was called "the morning star" that they knew that it is identical with what was called "the evening star." Nor could we validly infer from the fact that someone was acquainted with a man who always wore a mask that the same person knew the identity of the man thus concerned to conceal his identity.

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