« PreviousContinue »
arisen if we had confined ourselves to the isolated fact respecting the nature of each book. Looking at them one by one, our thoughts are directed merely to the character of each and to the individual facts narrated in it. Looking at them together, we begin to think that our friend must either have been travelling in Japan or China, or that he is intending to go there, or that he must have friends in one or the other of those countries, or that he is proposing to write an article on the subject, or that for some reason or other he must have a special interest in China and in Japan.
Or, to take a historical instance: We are studying Roman history, and as we read the history of the early emperors we are disgusted at the low standard of morality prevalent among them, the cruelty, the ambition, the lust that attach to their names. We find Julius Cæsar engrossed by an insensate and unscrupulous ambition; Augustus, a man of pleasure; while the rest were among the vilest of manhood. This leads us to reflect, and the result of our reflection is to observe that when the empire had passed out of the hands of the Cæsars there was decided improvement. We also notice that the first two emperors were superior to the four who succeeded them, and we embody our reflection in an inductive syllogism:
Julius Cæsar, Augustus, Tiberius, Caligula, Domitian, Nero, were men whose lives were marked by selfishness and crime;
All the Cæsars who ruled the Roman Empire were Julius Cæsar, Augustus, Tiberius, Caligula, Domitian, Nero:
Therefore all the Cæsars who ruled the Roman Empire were men whose lives were marked by selfishness and crime.
The conclusion of this syllogism naturally leads us to ask whether there must not be some influence tending to deteriorate the character in the position of emperor of Rome, and further, whether that influence is a universal one, or is limited to this family, whose members appear to have been specially affected by it. This gives occasion to an interesting train of thought, which would never have been suggested had we not mentally gone through our process of complete induction.
The weak point of a complete induction is that in so many cases we are not perfectly sure that it is complete. We fancy that we have not overlooked any one of the particulars, whence we argue to the universal law, while all the time there is one that for some reason has escaped our notice, and perhaps this very one is fatal to the universality of our law. In the case of the Roman emperors it is always possible that there might have intervened between the reign of one emperor and the next recorded a short space of time during which there reigned some emperor whom historians never knew of, or for some reason or other passed over in silence. We may practically feel certain that this is not the case, but we never can have that perfect certainty that leaves no room for any possible doubt. Or, to take a more practical case. Let us suppose chemists arguing a century ago about the then known metals:
Iron, copper, silver, gold, lead, zinc, tin, mercury, antimony, bismuth, nickel, platinum and aluminium are all heavier than water;
Iron, copper, silver, gold, lead, etc., are all the metals;
Here would be a complete induction of the metals then known, but nevertheless the conclusion would be false. Since that time potassium, sodium, and lithium have been pronounced to be metals, and all these are lighter than water.
Of course there are some cases where an enumeration is perfectly secure of completeness, e g., if we argue that January, February, etc., have all twenty-eight days or more, we cannot be wrong in concluding that all the months of the year have twenty-eight days or more. From the fact that Sunday, Monday, Tuesday, etc., are named after some heathen deity, we conclude that all the days of the week derive their names from heathen deities. But this is merely accidental and comparatively rare.
2. We now come to incomplete or material induction.
Incomplete induction is recognized by Aristotle, though he does not say very much respecting it. It comes under his definition of induction as “a process from particulars to universals,” and the instance he gives is an instance of material and complete induction.
Pilots, charioteers, etc., who know their business are most skilful. Therefore, generally, all who know their business are most skilful.
Further, he describes it as more persuasive and clearer, and more capable of being arrived at by perception and within the reach of the masses, while the syllogism is more forcible and clearer as an answer to gainsayers.
Here it is evident that he is speaking of an argument from a limited number of instances to the whole class. He describes the object of induction as being to persuade rather than to convince ; as being clearer in the eyes of ordinary men, inasmuch as it appeals to their sensible experience; as more within their reach, since it is an argument that all can appreciate; whereas the argument that starts from first principles implies a grasp of such principles, and this is comparatively rare among the mass of men. Yet it has not the compelling force of deductive reasoning inasmuch as it can always be evaded; it is not in itself so clear as the syllogism; it does not hit home with the same irresistible force as the argument that makes its unbroken way from the first principles that none can deny to the conclusion which we seek to establish. All this is exactly applicable to material induction, and would have little or no force if he were speaking of formal or complete induction. The example, moreover, that he gives is so incomplete as scarcely to deserve the name of induction at all. He merely takes two instances of the arts, and from them at once draws the conclusion that in all the arts science and success are inseparable. Possibly he chooses this extreme instance to show how very imperfect an induction may be sufficient to establish a general law where that law has the constant and universal testimony of mankind in its favor; and that men need only to be reminded of the law by the instances adduced rather than to be taught any fresh truth from an examination of the invariable coexistence of the two objects of thought which the instances exhibited as invariably united.
But Aristotle's brief reference to induction is a remarkable contrast to the elaborate treatment of it by modern writers on logic. St. Thomas, and the scholastic logicians generally, are equally concise in their discussion of it. Even the Catholic logicians of the present day pass it over in a few paragraphs or a few pages, which are devoted in part to an attack on Baconian induction and to an assertion that induction has no force unless it can be reduced to syllogistic form. Sir W. Hamilton, Mansel, and the Scottish school of philosophers are at one with the schoolmen and modern Catholic writers in their jealousy of the intrusion of induction, and, though they do not agree with them in advocating the necessity of reducing it to the form of the syllogism, yet they would assign to it a very subordinate place in a treatise on logic. It is the modern school of experimentalists, of whom John Stuart Mill is the illustrious leader, who put forward induction as “the main question of the science of logic, the question that includes all others." This suggests to us these questions:
1. How far does material induction come into logic at all ?
2. Is it true that all induction must be capable of being reduced to a syllogistic form in order to be valid ?
3. Is the neglect of induction by modern Catholic writers to be praised or blamed ?
We are speaking here of material or incomplete induction, and unless we warn our readers to the contrary, we shall continue to use it in this sense to the end of our present chapter.
Induction, says Cardinal Zigliara, has no force whatever apart from the syllogism. Incomplete induction, says Tongiorgi, is not a form of argument different from the syllogism. Induction, says Mendive (Logica, p. 224), is a true form of reasoning, and it pertains to the essence of reasoning that it should be a true syllogism. Induction, says Liberatore (Logic, p. 90), does not differ in its essence, but only in the form it takes, from the syllogism. Yet we have seen that when reduced to syllogistic form it breaks the rules of the syllogism and uses the copula in an altogether different meaning. How, then, are we to solve the difficulty? As usual, we have to examine carefully into our use of terms. Syllogism is an ambiguous term. There is the deductive syllogism, with its figures and moods, such as we have described them above, and which is subject to and based upon the dictum de omni et nullo. Whatever may be affirmed or denied of a universal subject, may be affirmed or denied of each and all the individuals that are included under that subject. In this sense induction is outside the syllogism, and any attempt to reduce it to syllogistic form at once exhibits a violation of syllogistic laws. But besides the deductive syllogism the word syllogism is used in a wider sense for any process of reasoning based on a more general principle, viz., wherever two objects of thought are identical with a third, they are also identical with each other. This principle includes not only the deductive syllogism, but the inductive syllogism also.
Induction, therefore, comes into logic as reducible to syllogistic form, but not to the form of the deductive syllogism. This is true of both complete and incomplete induction when we argue :
James I. and II., Charles I. and II. were headstrong monarchs;
James I. and II., Charles I and II. were all the monarchs of the Stuart dynasty;
Therefore all the monarchs of the Stuart dynasty were headstrong
We violate one of the rules of the third figure by our universal conclusion. We use the copula, not for the necessary coexistence of two objects of thought, since it is conceivable that a future Stuart might arise and falsify our minor, but for the fact which is true in the concrete. Our argument, moreover, refuses to obey the authority of the dictum de omni et nullo, and is therefore no true form of the inductive syllogism.
But our argument is a perfectly valid syllogism in that it is in accordance with the principles of identity we have just given; it is in accordance with the laws of thought and is perfectly logical. But is this true of incomplete induction ? For instance: We argue from the fact that we have observed on a number of separate days to all possible days in the year. We have noticed that all the days when there has been a gradual fall in the barometer have been followed by rain, and we state the result of our observation in the following premisses :
January 18, March 4, April 7, October 19, were succeeded by rainy weather;
January 18, March 4, April 7, October 19, were days on which there was a fall of the barometer;
Therefore all the days on which there is a fall of the barometer are days followed by rainy weather.
In order that the conclusion may hold good in strict logic, we must be able to assert that January 18, March 4, April 7, October 19, are all the days when there was a fall in the barometer, and this is obviously ridiculous. But may we not put our minor in another form, and say:
What is true of January 18, March 4, April 7, October 19, is true of all days when the barometer falls;
Rain near at hand is true of January 18, March 4, April 7, October 19, therefore, rain near at hand is true of all the days on which the barometer falls. Everything, therefore, depends on the representative character of January 18, March 4, April 7, October 19. If they have nothing in common save this one feature of the fall of the barometer which can be connected with the coming change in the weather, then no one can deny that there must be some sort of connection between a fall in the barometer and rainy weather near at hand, which will justify us in predicting of days on which the barometer falls that they will be succeeded by rain.
But before we enter on an investigation of this point, there is a previous question. Does it concern us as logicians to investigate it at all? Is it within our scope to examine into the various instances in order to sift their value as evidence ? Has not the logician to assume his principles as true, supposing always that they contain nothing which violates the laws of the human mind and of right reason, or is he to employ the various methods of observation and experiment by which the truth of all a posteriori and synthetical propositions have to be tested? If these lie outside the province of logic, the moderns are not only one-sided and unfair in giving so large a space to induction, but are all wrong in their very conception of the task they have to perform.
This question can only be satisfactorily answered by reminding the reader of the distinction between formal and material (or applied) logic. Formal logic simply takes its premisses for granted as long as they do not sin against any law of thought or contradict any proposition of the truth of which we are absolutely certain. Applied logic steps outside this comparatively narrow field, and asks what the terms are which regulate our admission into the mind of any proposition as a part of our mental furniture. Formal logic, therefore, has nothing to do with the conditions under which we can arrive at universal propositions other than those to which we are compelled by the nature of the mind itself. It has nothing to do with those propositions which we are led to regard as true by reason of what we witness in the external world, and which depend upon laws learned by observation and not rooted in as a priori conditions of thought. It has nothing to do with arriving at those a posteriori truths.