# Popular Science Monthly/Volume 9/June 1876/Science and the Logicians

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* SCIENCE AND THE LOGICIANS.
By DAVID BOYD, A. M.
UNDER the above heading may be comprehended the most of what we are desirous of saying in review of the article entitled "Science and Religion," by Dr. Charles F. Deems, in The Popular Science Monthly for February.
We first run counter to the author upon the definition of science taken from Sir William Hamilton's "Logic." Says he: "We can all afford to agree upon the definition rendered by the only man who has been found in twenty-two centuries to add anything important to the imperial science of logic. Sir William Hamilton defines science as a complement of cognitions having in point of form the character of logical perfection, in point of matter the character of real truth."
In the first place, Hamilton is not the only man since Aristotle that has been found to add anything important to logic. There has been a whole department, and by far the most valuable department of that science, brought into existence during the last three hundred years. We have reference to inductive logic, or scientific method. Hamilton had nothing to do with the creation of this department. His additions are wholly confined to the barren field of formal logic. The other department is the result of the joint labors of Bacon, Galileo, Newton, Herschel (John), Mill, Bain, and Jevons.
Hamilton's additions to formal logic consist chiefly in what is known as the quantification of the predicate, and the moods and figures consequent upon this. There is much difference of opinion as to the value of these additions. Mill and Bain affirm that by the quantification of the predicate no new or distinct meaning is conveyed, ​nor is there even a more intelligent rendering of an old meaning. In our own opinion the distinction between the comprehension and the extension of propositions is important; but it is paraded with too much ostentation, and treated with too much prolixity. Hamilton's great virtue is his clearness of statement and exhaustiveness of treatment. His method is admirable. Sometimes, however, there is too much display of his own erudition.
But even in the domain of formal logic Hamilton is not the only one that has within the present century made important additions. Prominent among these is De Morgan. Especially valuable are his discussions upon the different values of the logical copula. Prof. Boole has also made important additions to the syllogism, and has most ably supported the theory of the common ground occupied by logic and the mathematics. Prof. Bain also, in pure logic, has made a most important generalization. Hamilton's three laws of thought, namely, identity, non-contradiction, and excluded middle, he has reduced to the single law or canon of consistency.
So much for the assertion that Hamilton was the only man in twenty-two centuries to make any important additions to the imperial science of logic. Like enough the doctor would exclude scientific method from the imperial science. Perhaps he regards formal logic alone fit to wear the purple. But even here we see that there can be no such claim set up. If, however, he could claim this distinction, it would afford no reason for receiving his definition of science without question. That should stand or fall wholly upon its own merits. The greatest of men are not without personal biases. It is well known that Hamilton had a metaphysical bias. In his work on metaphysics the first three lectures are occupied in attempting to prove the superiority of mental science over natural science. He quotes with much approval this ancient declaration, "On earth there is nothing great but man, in man there is nothing great but mind." This being his known bias, before examining the definition, an investigator of Nature, a believer in scientific method, might have thought that it was by no means certain that he "could afford" to take it simply on his authority. However, when we come to the definition itself, the matter of it is well enough. But we have the temerity to suggest that its form might be improved without changing the substance. It is too pedantic and prolix. It is not in a shape easily to be remembered. We would render it thus: Science is real knowledge logically classified. But, as Bain remarks, positive definition is not thorough enough. As he says in his second canon on definition, it is needful to assemble for comparison the particulars of the contrasting or opposed notion. We can never know distinctly what a notion is until we contrast it with its opposite. Knowing is discriminating. What is not science? What is the other notion that lies side by side with it—in contrast, but contained under the same genus? Now, if we ​define science simply as knowledge or "complement of cognitions," it is contrasted with feeling or emotion. Its correlatives are productions designed to please, such as poetry, painting, or the fine arts generally.
If religion be regarded as proceeding wholly from the emotional nature, it may be contrasted with science and classed among aesthetic conceptions. But narrowing the definition further by qualifying knowledge by the terms "logically classified," we then have science as contrasted with or opposed to particular knowledge, or knowledge imperfectly classified. Qualifying further by placing the word real before knowledge, we have it contrasted with error or not genuine knowledge. By reading Hamilton, it will be seen that error is his antithesis to his real truth in the definition. But hypotheses are not error, since they are not held as truth. The distinguishing character of error is that, while false in fact, is is supposed to be true completely. Hypotheses are neither genuine truth nor errors, so long as they are held merely as such. They lie upon the border-lands of truth and error, and Hamilton's definition cannot banish them completely from the domain of science. They are properly allowed to hover around its borders. But we totally disagree with Dr. Deems as to the value of these "guesses" at truth. Says he, "A professor of religion has just as much right to guess as a professor of science, and the latter no more right than the former, though he may have more skill." Now, as to the right, there can be no dispute, but, as to the value of the guesses, this better skill makes all the difference in the world. Prof. Huxley is right in his estimate of guesses. Says he, "Do not allow yourself to be misled by the common notion that an hypothesis is untrustworthy because it is an hypothesis. What more have we to guide us in nine-tenths of the most important affairs of daily life than hypotheses, and often very ill-based ones? So then in science, where the evidence of an hypothesis is subjected to the most rigid examination, we may rightly pursue the same course. You may have hypotheses and hypotheses. A man may say, if he like, that the moon is made of preen cheese; that is an hypothesis. But another man, who has devoted a great deal of time and attention to the subject, and availed himself of the most powerful telescopes, and the results of the observations of others, declares that it is probably composed of materials very similar to those of which the earth is made up; and this also is an hypothesis." You perceive that it makes a good deal of difference both as to who guesses and as to what is guessed. Indeed, so many scientific hypotheses have been verified in the face of the opposing theological hypotheses, that there begins to be a strong presumption in their favor before verification. Nor is it strange that we should be led to regard them as highly probable. The investigator of Nature, familiar with her processes and her laws, founds these guesses upon broad and deep analogies.
​But we have only to follow the reverend doctor a few pages, until we find that hypotheses, so far from being extra-scientific, wholly make up our science. He mounts Hamilton's definition for the purpose of trampling upon scientific hypotheses. But, in his zeal for narrowing the sphere of science, he arrives at the remarkable conclusion that "all science is purely a classification of probabilities." He has at length kicked the definition completely from under him, and remounted a platform entirely composed of hypotheses. He, however, is careful not to say, "It is certain that there are no certainties." Still he leaves us wholly in the dark as to where may be found those "very few certainties" which it appears to him God has seen fit to show us, "more for the purpose of furnishing the idea than for any practical purpose." The God of the modern divine has still about him a touch of the jealousy of the Zeus of Æschylus. He would have chained to the rocks the modern seeker after hidden knowledge, the invader of his own domain of certainties.
We say that we are left completely in the dark as to where are to be found those few certainties which God has seen fit to show us as specimens. We are assured that they are not to be found in science. This is only classified probabilities. The "imperial science of logic" has been demolished with the rest. We wonder whether it is because science embraces only real truth that it is uncertain or probable, or is it owing to its methodical logical arrangement that it has acquired this character? He should remember that most people have faculties called memories, that last them through several pages of reading, and that there is a chance for mediate or remote contradictions to be detected.
Again, in his zeal to prove that all science and religion stand upon the common basis of faith, he overleaps himself, and gives us as the results of his logic, "Ex nihilo geometria fit." So I suppose we may be allowed to say likewise, "Ex nihilo religio fit." Is that what he started out to prove? No, it was only this very sensible proposition, that "we can acquire no knowledge by our logical understanding without faith in the laws of mental operations." This simply amounts to saying that we cannot consistently believe in the products of thinking except we believe in faculties of thinking. We suppose that no one doubts that. But believing that by no means involves the. assumption that science or knowledge rests upon the same basis as religious faith. It is a very different thing to believe in our own experiences, feelings, sensations, observations, comparisons, memories, representations, etc., and to believe in certain fundamental religious dogmas, as, for example, "God is an infinite person." God is three infinite persons. The second of these three infinite persons, which all make one infinite person, is now sitting in heaven upon a throne on the right hand of the first infinite person, neither of which has any parts, but all three make one indivisible unity. Most men will ​continue to think that the above propositions differ very much from the two fundamental axioms of mathematics, "Equals added to equals and the sums are equal; and two things each equal to a third are equal each to each." In denying these, we must deny the laws of thought, the powers of the mind in distinguishing a thing from what it is not, or from that which it stands in contrast with, or in opposition to. All the other axioms of geometry, as Bain has shown, are either verbal propositions or can be derived from these, since subtraction is implicated in addition, multiplication derived from addition, and division implicated in multiplication.
The absurd conclusion at which the doctor arrives, namely, "Ex nihilo geometria fit," ought to show him that to begin with a metaphysical point was hardly the proper way to build up the science of geometry. Of course, it being nothing, the geometry that he constructed out of it, no matter how many intermediate propositions intervened, must be nothing. Suppose we try the analytic method of arriving at definitions. But first we are compelled to controvert the assertion that it is necessary to believe the three following propositions, or there can be no geometry, namely, that "space is infinite in extent, that it is infinitely divisible, and that it is infinitely continuous."
Now, I deny that geometry has anything to do with infinity; indeed, the doctor, before he gets through, says even more than this. "Science," says he, "has the finite for its domain, religion the infinite." What we have to do with in geometry is simply the relations of the attributes or propria of definite extension. But as definite extension has for its correlative indefinite extension, we need to understand it in a sort of general way. Experience furnishes us with the mutually-implicated notions of the contained and the containing, the bounded and the bounding. We cannot separate them completely in thought. The assertion of the one implicates the other. What lies without any extension is space—indefinite space. Simply that it is outside of our particular part of space is all that we have to do with it: whether it is infinite or not is none of the business of the geometrician. Indefinite extension, or the notion of space in general, is very different from the notion, if there be such a one, the words infinite space would connote. Indefinite space is comprehensible in the only sense that it needs to be comprehended, namely, as the correlative of extension or definite space.
This brings us to the genesis of the definitions of geometry. Experience makes us at first acquainted with extended bodies. This acquaintance goes no further than a knowledge of their attributes, or propria. All these properties come into the mind as a confused aggregate; it is not clearly perceived as a whole made up of distinct parts. The relation of part to part is perceived only in a vague and general manner. The work of the geometrician is to analyze these ​parts, and to establish their exact relations. He compares, adds, subtracts, multiplies, divides. In order to communicate his knowledge of the relation of parts, he must use words; these words he must define, if their meaning is not obvious to the one instructed. But if the property is of a primary nature, and given in the experience of every one, there is no need of definition, and indeed no rational definition can be given. This is true alike of the notions, extension, surface, line, and point. Each of these is as much a datum of simple experience as the notion of white or blue; and it is just as absurd to attempt to define the one class of concepts as the other. They may be, however, brought out a little more closely by contrasting the correlatives in the manner that we have attempted with extension and indefinite space. Thus surface may be contrasted with the solid volume, or definite space, of which it forms the boundary; line with surface, of which it in turn is the boundary; and, lastly, point with line, of which it is the termination or the where of separation. It is not true that the existence of forms depends upon the motions of points. Forms are given in experience through sensation. A point is the ultimate step in the analysis of boundaries. It is sheer nonsense to attempt to construct lines out of points, surfaces out of lines, and volumes out of surfaces. All that it is necessary to say further upon this subject is, that the differentiæ of the higher mathematics are not nothings, but quantities the least conceivable. The least conceivable portion of a line is not a point; the least conceivable portion of a surface is not a line; the least conceivable portion of a volume is not a surface, for the simple reason that no portion of a thing can be its boundary.
Now, in conclusion, we say that geometry rests upon no affirmations in respect to the infinite, but, on the contrary, it is wholly occupied about the relations of the finite in space. We have the assurance from the doctor that the finite is the sphere of every science, while the sphere of religion is the infinite. This certainly would cast theology out of the sphere of science, for the doctor has laid down as one of its fundamental concepts, "God is an infinite person." Sir William Hamilton's definition, in its very first clause, also excludes theology from science, if we take himself as authority for the meaning of the term cognition. Every cognition is simply a perception of relation. The infinite and absolute—equal God—are not thinkable. Hence theology can have no "complement of cognition" out of which to classify a science.
In another place we find that the cry of conflict has its origin in confounding theology with religion. "Theology is not religion any more than psychology is human life, or zoölogy animal life, or botany plant-life. Theology is objective, religion is subjective. Theology is the scientific classification of what is known of God; religion is a loving obedience to God's commandments. Every religious man ​must have a theology, but it does not follow that every theologian must have a religion. There may be a conflict between theology and some other sciences, and religious men may deplore it," etc. Now, in our opinion, if every religious man must have a theology, and if his theology be in conflict with science, he must either be in conflict in opinion with that science or abandon his theology. But the truth is, that the real, actual conflict arises from the religious element. The conflict of opinion is in the theology of a man; the conflict, as it appears upon the stage of the world's history in acts and deeds, has sprung from the religious nature, even as defined by Dr. Deems. A man may hold what theological views you please and make no disturbance in the world, provided he does not think much about his duty in obeying the commands, word, or will of God, all of which are a part of his theology. For instance, one of the commands of God, as contained in his word, and to which he should render a "loving obedience," is "Suffer not a witch to live." Now, a man may believe in that command simply as a dogma, but, being indifferent in the matter of rendering a loving obedience, he will not let it influence his conduct, and so will make no effort to hunt up and have witches burnt. If, on the contrary, he has a loving obedience to God's word, he will trample upon every kindly feeling and instinct of his nature rather than not have the command carried out.
Accordingly, we find that it has been the pious, the sincere, the believers in duty, those wishing to render a loving obedience to God's word, or what they thought was his word, who have in every age been the persecutors. But you say that they were acting under a delusion. They mistook what was the word of God. But how are they to know what is his word, if direct commands like the foregoing are not his? Besides, if there was a mistake, it was in their theology, and not in their religion; that only impelling them to lovingly obey God's commands as they knew them. Religion is but an impulse, a blind instinct. It knows nothing about weighing and comparing opinions. Theology furnishes it with these. If these are bad, its conduct will be bad; if good, the conduct will be good. All it knows is blind obedience—zeal to do the will of God as it knows it; and the pretended science, which alone can give it guidance, is a science of the Unknowable, the Infinite, the Absolute.
We will close with a quotation from Lecky's "History of Rationalism," in reference to Luther: "He was subject to many strange hallucinations and vibrations of judgment, which he invariably attributed to the direct agency of Satan. Satan became, in consequence, the dominating conception of his life. In every critical event, in every mental perturbation, he recognized satanic power. Fools, deformed persons, the blind and the dumb, were possessed by devils. Physicians, indeed, attempted to explain these infirmities by natural causes; but those physicians were ignorant men—they did not know all the ​power of Satan. Every form of disease might be produced by Satan or his agents, the witches; and none of the infirmities to which Luther was liable were natural; but his earache was peculiarly diabolical. Hail, thunder, and plagues, are all the direct consequence of the intervention of spirits. Many of those persons who were supposed to have committed suicide had in reality been seized by the devil and strangled by him, as the traveler is strangled by the robber. The devil could transport men through the air. He could beget children; and Luther himself had come in contact with one of them. An intense love of children was one of the most amiable characteristics of the great Reformer; but on this occasion he most earnestly recommended the reputed relatives to throw the child into the river, in order to free their house from the presence of the devil. As a natural consequence of these modes of thought, witchcraft did not present the slightest improbability to his mind. In strict accordance with the spirit of his age, he continually asserted the existence and frequency of the crime, and emphatically proclaimed the duty of burning witches."
We see what a loving obedience to the word of God led Luther to recommend. That this spirit has died out, is wholly due to the advancement of science and rationalism, and not to any change in the religious spirit per se, or to any different interpretation of the Bible. The witchcraft is there, as it was in the days of Luther, and the injunction not to suffer witches to live is there, and neither has been explained any better than it was in the middle ages. But the researches of the investigators of Nature have gradually driven these notions out of the minds of men, and stamped them with the opprobrium of absurdities.
Greeley, Colorado, February 14, 1876.