A System of Logic, Ratiocinative and Inductive · John Stuart Mill
Chapter VII.
Fallacies Of Confusion. § 1. Under this fifth and last class it is convenient to arrange all those fallacies in which the source of error is not so much a false estimate of the probative force of known evidence, as an indistinct, indefinite, and fluctuating conception of what the evidence is. At the head of these stands that multitudinous body of fallacious reasonings in which the source of error is the ambiguity of terms: when something which is true if a word be used in a particular sense, is reasoned on as if it were true in another sense. In such a case there is not a mal-estimation of evidence, because there is not properly any evidence to the point at all; there is evidence, but to a different point, which from a confused apprehension of the meaning of the terms used, is supposed to be the same. This error will naturally be oftener committed in our ratiocinations than in our direct inductions, because in the former we are deciphering our own or other people’s notes, while in the latter we have the things themselves present, either to the senses or to the memory. Except, indeed, when the induction is not from individual cases to a generality, but from generalities to a still higher generalization; in that case the fallacy of ambiguity may affect the inductive process as well as the ratiocinative. It occurs in ratiocination in two ways: when the middle term is ambiguous, or when one of the terms of the syllogism is taken in one sense in the premises, and in another sense in the conclusion.
Some good exemplifications of this fallacy are given by Archbishop Whately. “One case,” says he, “which may be regarded as coming under the head of Ambiguous Middle, is (what I believe logical writers mean by ‘_Fallacia Figuræ Dictionis_’) the fallacy built on the grammatical structure of language, from men’s usually taking for granted that _paronymous_ (or _conjugate_) words, _i.e._, those belonging to each other, as the substantive, adjective, verb, etc., of the same root, have a precisely corresponding meaning; which is by no means universally the case. Such a fallacy could not indeed be even exhibited in strict logical form, which would preclude even the attempt at it, since it has two middle terms in sound as well as sense. But nothing is more common in practice than to vary continually the terms employed, with a view to grammatical convenience; nor is there any thing unfair in such a practice, as long as the _meaning_ is preserved unaltered; _e.g._, ‘murder should be punished with death; this man is a murderer, therefore he deserves to die,’ etc. Here we proceed on the assumption (in this case just) that to commit murder, and to be a murderer—to deserve death, and to be one who ought to die, are, respectively, equivalent expressions; and it would frequently prove a heavy inconvenience to be debarred this kind of liberty; but the abuse of it gives rise to the Fallacy in question; _e.g._, _projectors_ are unfit to be trusted; this man has formed a _project_, therefore he is unfit to be trusted: here the sophist proceeds on the hypothesis that he who forms a _project_ must be a _projector_: whereas the bad sense that commonly attaches to the latter word, is not at all implied in the former.
This fallacy may often be considered as lying not in the Middle, but in one of the terms of the Conclusion; so that the conclusion drawn shall not be, in reality, at all warranted by the premises, though it will appear to be so, by means of the grammatical affinity of the words; _e.g._, to be acquainted with the guilty is a _presumption_ of guilt; this man is so acquainted, therefore we may _presume_ that he is guilty: this argument proceeds on the supposition of an exact correspondence between _presume_ and _presumption_, which, however, does not really exist; for ‘presumption’ is commonly used to express a kind of _slight suspicion_; whereas, ‘to presume’ amounts to actual belief. There are innumerable instances of a non-correspondence in paronymous words, similar to that above instanced; as between _art_ and _artful_, _design_ and _designing_, _faith_ and _faithful_, etc.; and the more slight the variation of the meaning, the more likely is the fallacy to be successful; for when the words have become so widely removed in sense as ‘pity’ and ‘pitiful,’ every one would perceive such a fallacy, nor would it be employed but in jest.(263)
“The present Fallacy is nearly allied to, or rather, perhaps, may be regarded as a branch of, that founded on _etymology_—viz., when a term is used, at one time in its customary, and at another in its etymological sense. Perhaps no example of this can be found that is more extensively and mischievously employed than in the case of the word _representative_: assuming that its right meaning must correspond exactly with the strict and original sense of the verb ‘represent,’ the sophist persuades the multitude that a member of the House of Commons is bound to be guided in all points by the opinion of his constituents; and, in short, to be merely their _spokesman_; whereas law and custom, which in this case may be considered as fixing the meaning of the term, require no such thing, but enjoin the representative to act according to the best of his _own_ judgment, and on his own responsibility.” The following are instances of great practical importance, in which arguments are habitually founded on a verbal ambiguity.
The mercantile public are frequently led into this fallacy by the phrase “scarcity of money.” In the language of commerce, “money” has two meanings: _currency_, or the circulating medium; and _capital seeking investment_, especially investment on loan. In this last sense the word is used when the “money market” is spoken of, and when the “value of money” is said to be high or low, the rate of interest being meant. The consequence of this ambiguity is, that as soon as scarcity of money in the latter of these senses begins to be felt—as soon as there is difficulty of obtaining loans, and the rate of interest is high—it is concluded that this must arise from causes acting upon the quantity of money in the other and more popular sense; that the circulating medium must have diminished in quantity, or ought to be increased. I am aware that, independently of the double meaning of the term, there are in the facts themselves some peculiarities, giving an apparent support to this error; but the ambiguity of the language stands on the very threshold of the subject, and intercepts all attempts to throw light upon it.
Another ambiguous expression which continually meets us in the political controversies of the present time, especially in those which relate to organic changes, is the phrase “influence of property”—which is sometimes used for the influence of respect for superior intelligence or gratitude for the kind offices which persons of large property have it so much in their power to bestow; at other times for the influence of fear; fear of the worst sort of power, which large property also gives to its possessor, the power of doing mischief to dependents. To confound these two, is the standing fallacy of ambiguity brought against those who seek to purify the electoral system from corruption and intimidation. Persuasive influence, acting through the conscience of the voter, and carrying his heart and mind with it, is beneficial—therefore (it is pretended) coercive influence, which compels him to forget that he is a moral agent, or to act in opposition to his moral convictions, ought not to be placed under restraint.
Another word which is often turned into an instrument of the fallacy of ambiguity, is Theory. In its most proper acceptation, theory means the completed result of philosophical induction from experience. In that sense, there are erroneous as well as true theories, for induction may be incorrectly performed, but theory of some sort is the necessary result of knowing any thing of a subject, and having put one’s knowledge into the form of general propositions for the guidance of practice. In this, the proper sense of the word, Theory is the explanation of practice. In another and a more vulgar sense, theory means any mere fiction of the imagination, endeavoring to conceive how a thing may possibly have been produced, instead of examining how it was produced. In this sense only are theory and theorists unsafe guides; but because of this, ridicule or discredit is attempted to be attached to theory in its proper sense, that is, to legitimate generalization, the end and aim of all philosophy; and a conclusion is represented as worthless, just because that has been done which, if done correctly, constitutes the highest worth that a principle for the guidance of practice can possess, namely, to comprehend in a few words the real law on which a phenomenon depends, or some property or relation which is universally true of it.
“The Church” is sometimes understood to mean the clergy alone, sometimes the whole body of believers, or at least of communicants. The declamations respecting the inviolability of church property are indebted for the greater part of their apparent force to this ambiguity. The clergy, being called the church, are supposed to be the real owners of what is called church property; whereas they are in truth only the managing members of a much larger body of proprietors, and enjoy on their own part a mere usufruct, not extending beyond a life interest. The following is a Stoical argument taken from Cicero, _De Finibus_, book the third: “Quod est bonum, omne laudabile est. Quod autem laudabile est, omne honestum est. Bonum igitur quod est, honestum est.” Here the ambiguous word is _laudabile_, which in the minor premise means any thing which mankind are accustomed, on good grounds, to admire or value; as beauty, for instance, or good fortune: but in the major, it denotes exclusively moral qualities. In much the same manner the Stoics endeavored logically to justify as philosophical truths, their figurative and rhetorical expressions of ethical sentiment: as that the virtuous man is alone free, alone beautiful, alone a king, etc. Whoever has virtue has Good (because it has been previously determined not to call any thing else good); but, again, Good necessarily includes freedom, beauty, and even kingship, all these being good things; therefore whoever has virtue has all these.
The following is an argument of Descartes to prove, in his _a priori_ manner, the being of a God. The conception, says he, of an infinite Being proves the real existence of such a being. For if there is not really any such being, _I_ must have made the conception; but if I could make it, I can also unmake it; which evidently is not true; therefore there must be, externally to myself, an archetype, from which the conception was derived. In this argument (which, it may be observed, would equally prove the real existence of ghosts and of witches) the ambiguity is in the pronoun _I_, by which, in one place, is to be understood my _will_, in another the _laws of my nature_. If the conception, existing as it does in my mind, had no original without, the conclusion would unquestionably follow that _I_ made it; that is, the laws of my nature must have somehow evolved it: but that my _will_ made it, would not follow. Now when Descartes afterward adds that I can not unmake the conception, he means that I can not get rid of it by an act of my will: which is true, but is not the proposition required. I can as much unmake this conception as I can any other: no conception which I have once had, can I ever dismiss by mere volition; but what some of the laws of my nature have produced, other laws, or those same laws in other circumstances, may, and often do, subsequently efface.
Analogous to this are some of the ambiguities in the free-will controversy; which, as they will come under special consideration in the concluding Book, I only mention _memoriæ causâ_. In that discussion, too, the word _I_ is often shifted from one meaning to another, at one time standing for my volitions, at another time for the actions which are the consequences of them, or the mental dispositions from which they proceed. The latter ambiguity is exemplified in an argument of Coleridge (in his _Aids to Reflection_), in support of the freedom of the will. It is not true, he says, that a man is governed by motives; “the man makes the motive, not the motive the man;” the proof being that “what is a strong motive to one man is no motive at all to another.” The premise is true, but only amounts to this, that different persons have different degrees of susceptibility to the same motive; as they have also to the same intoxicating liquid, which, however, does not prove that they are free to be drunk or not drunk, whatever quantity of the fluid they may drink. What is proved is, that certain mental conditions in the person himself must co-operate, in the production of the act, with the external inducement; but those mental conditions also are the effect of causes; and there is nothing in the argument to prove that they can arise without a cause—that a spontaneous determination of the will, without any cause at all, ever takes place, as the free-will doctrine supposes.
The double use, in the free-will controversy, of the word Necessity, which sometimes stands only for Certainty, at other times for Compulsion; sometimes for what _can not_ be prevented, at other times only for what we have reason to be assured _will_ not; we shall have occasion hereafter to pursue to some of its ulterior consequences. A most important ambiguity, both in common and in metaphysical language, is thus pointed out by Archbishop Whately in the Appendix to his Logic: “_Same_ (as well as _One_, _Identical_, and other words derived from them) is used frequently in a sense very different from its primary one, as applicable to a _single_ object; being employed to denote great _similarity_. When several objects are undistinguishably alike, _one single description_ will apply equally to any of them; and thence they are said to be all of _one and the same_ nature, appearance, etc. As, _e.g._, when we say ‘this house is built of the _same_ stone with such another,’ we only mean that the stones are undistinguishable in their qualities; not that the one building was pulled down, and the other constructed with the materials. Whereas _sameness_, in the primary sense, does not even necessarily imply similarity; for if we say of any man that he is greatly altered since such a time, we understand, and indeed imply by the very expression, that he is _one person_, though different in several qualities. It is worth observing also, that Same, in the secondary sense, admits, according to popular usage, of degrees: we speak of two things being _nearly_ the same, but not entirely: personal identity does not admit of degrees. Nothing, perhaps, has contributed more to the error of Realism than inattention to this ambiguity. When several persons are said to have _one and the same_ opinion, thought, or idea, many men, overlooking the true simple statement of the case, which is, that they are _all thinking alike_, look for something more abstruse and mystical, and imagine there must be some _One Thing_, in the primary sense, though not an individual which is present at once in the mind of each of these persons; and thence readily sprung Plato’s theory of Ideas, each of which was, according to him, one real, eternal object, existing entire and complete in each of the individual objects that are known by one name.”
It is, indeed, not a matter of inference, but of authentic history, that Plato’s doctrine of Ideas, and the Aristotelian doctrine (in this respect similar to the Platonic) of substantial forms and second substances, grew up in the precise way here pointed out; from the supposed necessity of finding, in things which were said to have the _same_ nature, or the _same_ qualities, something which was the _same_ in the very sense in which a man is the same as himself. All the idle speculations respecting τὸ ὄν, τὸ ἕν, τὸ ὅμοιον, and similar abstractions, so common in the ancient and in some modern schools of thought, sprang from the same source. The Aristotelian logicians saw, however, one case of the ambiguity, and provided against it with their peculiar felicity in the invention of technical language, when they distinguished things which differed both _specie_ and _numero_, from those which differed _numero tantum_, that is, which were exactly alike (in some particular respect at least) but were distinct individuals. An extension of this distinction to the two meanings of the word Same, namely, things which are the same _specie tantum_, and a thing which is the same _numero_ as well as _specie_, would have prevented the confusion which has been a source of so much darkness and such an abundance of positive error in metaphysical philosophy.
One of the most singular examples of the length to which a thinker of eminence may be led away by an ambiguity of language, is afforded by this very case. I refer to the famous argument by which Bishop Berkeley flattered himself that he had forever put an end to “skepticism, atheism, and irreligion.” It is briefly as follows: I thought of a thing yesterday; I ceased to think of it; I think of it again to-day. I had, therefore, in my mind yesterday an _idea_ of the object; I have also an idea of it to-day; this idea is evidently not another, but the very same idea. Yet an intervening time elapsed in which I had it not. Where was the idea during this interval? It must have been somewhere; it did not cease to exist; otherwise the idea I had yesterday could not be the _same_ idea; no more than the man I see alive to-day can be the same whom I saw yesterday if the man has died in the mean while. Now an idea can not be conceived to exist anywhere except in a mind; and hence there must exist a Universal Mind, in which all ideas have their permanent residence during the intervals of their conscious presence in our own minds. It is evident that Berkeley here confounded sameness _numero_ with sameness _specie_, that is, with exact resemblance, and assumed the former where there was only the latter; not perceiving that when we say we have the same thought to-day which we had yesterday, we do not mean the same individual thought, but a thought exactly similar: as we say that we have the same illness which we had last year, meaning only the same sort of illness.
In one remarkable instance the scientific world was divided into two furiously hostile parties by an ambiguity of language affecting a branch of science which, more completely than most others, enjoys the advantage of a precise and well-defined terminology. I refer to the famous dispute respecting the vis viva, the history of which is given at large in Professor Playfair’s Dissertation. The question was, whether the _force_ of a moving body was proportional (its mass being given) to its velocity simply, or to the square of its velocity: and the ambiguity was in the word Force. “One of the effects,” says Playfair, “produced by a moving body is proportional to the square of the velocity, while another is proportional to the velocity simply:” from whence clearer thinkers were subsequently led to establish a double measure of the efficiency of a moving power, one being called _vis viva_, and the other _momentum_. About the facts, both parties were from the first agreed: the only question was, with which of the two effects the term _force_ should be, or could most conveniently be, associated. But the disputants were by no means aware that this was all; they thought that force was one thing, the production of effects another; and the question, by which set of effects the force which produced both the one and the other should be measured, was supposed to be a question not of terminology, but of fact.
The ambiguity of the word Infinite is the real fallacy in the amusing logical puzzle of Achilles and the Tortoise, a puzzle which has been too hard for the ingenuity or patience of many philosophers, and which no less a thinker than Sir William Hamilton considered as insoluble; as a sound argument, though leading to a palpable falsehood. The fallacy, as Hobbes hinted, lies in the tacit assumption that whatever is infinitely divisible is infinite; but the following solution (to the invention of which I have no claim) is more precise and satisfactory. The argument is, let Achilles run ten times as fast as the tortoise, yet if the tortoise has the start, Achilles will never overtake him. For suppose them to be at first separated by an interval of a thousand feet: when Achilles has run these thousand feet, the tortoise will have got on a hundred; when Achilles has run those hundred, the tortoise will have run ten, and so on forever: therefore Achilles may run forever without overtaking the tortoise.
“Speaking morally, you are said to have a right to do a thing, if all persons are morally bound not to hinder you from doing it. But, in another sense, to have a right to do a thing is the opposite of having _no_ right to do it, _i.e._, of being under a moral obligation to forbear doing it. In this sense, to say that you have a right to do a thing, means that you may do it without any breach of duty on your part; that other persons not only ought not to hinder you, but have no cause to think worse of you for doing it. This is a perfectly distinct proposition from the preceding. The right which you have by virtue of a duty incumbent upon other persons, is obviously quite a different thing from a right consisting in the absence of any duty incumbent upon yourself. Yet the two things are perpetually confounded. Thus, a man will say he has a right to publish his opinions; which may be true in this sense, that it would be a breach of duty in any other person to interfere and prevent the publication: but he assumes thereupon that, in publishing his opinions, he himself violates no duty; which may either be true or false, depending, as it does, on his having taken due pains to satisfy himself, first, that the opinions are true, and next, that their publication in this manner, and at this particular juncture, will probably be beneficial to the interests of truth on the whole.
“The second ambiguity is that of confounding a right of any kind, with a right to enforce that right by resisting or punishing a violation of it. People will say, for example, that they have a right to good government, which is undeniably true, it being the moral duty of their governors to govern them well. But in granting this, you are supposed to have admitted their right or liberty to turn out their governors, and perhaps to punish them, for having failed in the performance of this duty; which, far from being the same thing, is by no means universally true, but depends on an immense number of varying circumstances,” requiring to be conscientiously weighed before adopting or acting on such a resolution. This last example is (like others which have been cited) a case of fallacy within fallacy; it involves not only the second of the two ambiguities pointed out, but the first likewise.
Ideas discussed in this chapter
Text from Project Gutenberg, public domain in the United States.