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The minds of men he says beset by a great number of idols and prejudices, which he therefore proposes to remove by the raising of axioms and notions by means of induction.
The errors of the human mind are fundamental, so that it is necessary that the instauration must be begun from the very foundation, that is, from natural history. He therefore removes the idols from the mind, points out the signs of false philosophy, and enumerates the causes of errors. And in order to prevent men from despairing, gives grounds of hope, and having cleared the mirror places it in a right position as to received things in a proper manner.
RAJINDER Nauth MITTER, Hindu College,
Third Class, First Year's Senior Scholar.
Morning Paper. Answer 1st. As a law of nature is a general proposition enunciating the order of sequence which the phenomena of the physical world observe; so a law of mind, may be defined (according to Stewart's view) to be a proposition enunciating the order of succession which the phenomena of the mental world observe. These laws express the relations between the several faculties and the several acts of the mind, as connected with one another in the order of cause and effect. Such for example are the laws respecting the association of ideas, or the law asserting the dependence of memory on that act of mind called attention, such again is the law of mind leading a man to believe in his own existence, the moment he is conscious of the existence of any of the sensations excited by external objects, and the law of mind leading a man to connect the belief of his own personal identity with all his reasoning operations.
The process by which these laws are to be ascertained is the same, according to Stewart as that by which the laws of the physical world are to be ascertained viz. by observation and experiment. A close attention to the objects of our consciousness will enable us to discover the relation that subsists between the operations of our mind and when we have sufficiently sifted the results of our observations, we shall at Last discover the laws that regulates our mental operations. The inductive method is the means which we must make use of, in our investigations of the laws whether of physics or of mind.
Answer 2nd. The following are the causes of the retardation of the progress of mental philosophy, taken notice of by Stewart. 1. A belief that the laws which regulate the operations of the human mind are beyond the reach of our faculties to discover and 2. That even were they known, they would be of no practical utility to us. 3. The lateness of the period when they first came to be successfully cultivated. 4. Inattention to the proper limits of human investigations. 5. Because analogy of the laws of matter were not used with sufficient caution so that men, engaged in the investigation of the laws of mind, often rested satisfied with their exertions, if they could find some affinity between a mental operation and the laws which regulate the phenomena of the material world.
Answer 3rd.—The word “ Reason" is used to signify that faculty of the human mind which enables us to distinguish I truth from false. hood, 2 right from wrong 3 and which enables us to adapt means for the accomplishment of an end. It was originally used to mark the distinctions whatever they be, which separated men from brutes and came afterwards to be limited by our notion of the obvious nature of these distinctions. Hume and others, include only the 1st and 3rd of these significations within the term “Reason." Intuition is that faculty of the mind which enables us to perceive the truth in matters which are self-evident but reasoning enables us to perceive the truth of propositions by drawing a chain of consequences and through the medium of other truths. Stewart is at great pains to show that there is no radical difference between these ; but he himself confesses that reasoning involves the idea of memory together with that of intuition. Here then lies the chief distinction between these, that one is a simple uncompounded faculty, the other the combination of several, at least of two. Stewart illustrates the distinction between them by saying, that our simple judgments, are like stones prepared by the chisel, on each of which we can raise ourselves as upon a pedestal to a small elevation, but reasoning is like these stones combined together to form a staircase, in the formation of which, great skill may be necessary but in ascending it nothing more is required than a repeation of the first act. He raises the whole of his theory on the confession of Locke that reasoning consists of intuition in every step; but we have seen the distinction between them.
Answer 4th.—The axioms are the elements of our reasoning in geometry or rather in mathematics in general, and a conviction of their truth is implied in every step of our procedure but they are not the fundamental principles of that science, as we can deduce no consequences from them, for let a man pore as long as he will on these he will scarce come to know by that means that the square of the hypotenuse in a rightangled triangle is equal to the sum of the squares of the two sides. To this effect Stewart quotes a passage from Locke and he himself subscribes to its truth. Definitions on the other hand are the fundamental principles of geometry, the hypothetical truths on which the whole science depends and for the inaccuracy of which no subsequent logical rigour can compensate. On what other basis, he triumphantly asks, except on that of the definitions, is the whole fabric of the geometrical science built ? The definitions of a circle, an ellipse, &c., are the only foundations on which the demonstrations of all their properties stand.
He illustrates this distinction by likening a process of reasoning to a chain supporting a weight (the conclusion, then the definitions will form the hook, or rather the beam to which the chain is fixed, the axioms will be the successive links or concatenations of this chain.
Answer 5th.—The fundamental laws of belief are those simple truths a conviction of which is involved in all our reasoning operations, they are therefore also called essential elements of human reason. When the axioms are not included within these, they are then only such laws, a conviction of which is involved in all our reasoning concerning probable or moral truths. Such for example as a belief in onr own existence, in our own identity in the independent existence of the material world, and a belief in the evidence of our own memory. Two analogies or coincidences are traceable between these and the axioms of geometry. 1. That from neither of these classes of truth can any direct inference be drawn; abstracted from other truths they are perfectly barren and useless. As no one can by simply poring on the geometrical axioms come to any conclusion, so by simply knowing the truths, I exist, I am the same man to-day that I was yesterday, &c. we can never arrive at any conclusion respecting the order of nature. 2. The second analogy is that a conviction of their truth is involved in all our reasoning processes. In all our investigations concerning physical truths, we take for granted that there is a material world, existing beyond the world of ideas within us; and that the laws of nature will remain the same for every succeeding day. As for our belief in our existence, in our continued identity, and in the evidence of our memory, they are taken for granted in all our reasonings whether relating to mathematical or physical subjects.
Answer 6th.—Abstraction is that act of the mind by which we take into our consideration some of the properties of an object, in exclusion to all the rest.
The undistinguishing nature of our first perceptions often leads us to classify under the same general terms, all things which appear to resemble each other. Thus the names of particular objects often come to be the common appellations of species, because we are generally led to apply the names of particular things to all other things which bear a certain degree of similarity to it.
To explain the nature of the aid which general terms lead to our general reasoning, we must take into our consideration the process by which we transfer our particular conclusions to general propositions. For it is an undisputed truth that in demonstrating a general proposition we first demonstrate it with respect to a particular case and then transfer the particluar conclusion to our general proposition by means of general terms; for Stewart enunciates it as a general law of logic that whatever things have the same name applied to them in consequence of their being included within the terms of the same definitions, are included within a demonstration where the terms of that definition are the data of our reasoning. From this it is evident that without general terms all our conclusions would have been limited to particular objects as we could not have transferred these particular conclusions to species and genera. Words help us to analyze our thoughts, being themselves the monuments of an analysis, and by that means, vastly help us to carry on our reasoning processes. In the explanation I before gave respecting the formation of general terms, I pointed out the loose way in which they were formed but it is necessary that they might lead to correct results in our general reasoning (as I just now showed that they are indispensibly requisite for this latier purpose) that they be founded on a process of philosophical abstraction. Therefore we must distinguish between these two different classes of general terms.
Answer 1st. The two different processes are 1 to demonstrate the proposition with regard to the individual diagram before us, in which we take into our consideration, the properties of a circle or triangle only as applied to that particular diagram 2 to transfer our particular conclusions, from the individual diagram before us to all figures comprehended under the same definitions. As the latter process is in all cases essentially the same, we by degrees drop it and then forgetting the successive steps, we imagine that the general conclusion is the result of a general demonstration. That the process here described really takes place will appear evident by considering, the steps over which a young geometer must pass to acquire a perfect knowledge of a geomatrical demonstration. The young tyro, has a tendency at first to make the figure in his own slate, an exact facsimile of what he sees in the margin of the pages of Euclid, he places the same letters respectively as they stand in the book and feels satisfied with respect to the truth of the proposition when he can completely follow the steps of Euclid. This shows that his whole attention is engaged in proving the proposition with respect to that particular diagram. He can easily understand any changes in point of size or magnitude but what difficulty does he feel when the figure is inverted or presented under any other position or aspect. The truth of our assumption appears more clearly when the novice has to study a proposition in which the same demonstration applies in the same words to different cases. Far from appreciating at first that the same proposition applies to all cases which are included within the terms of the enunciation, he repeats again and over again, the demonstration and applies it to one and then to the other figure and finds with a mingled feeling of pleasure and surprize that it applies equally to both. The analytical method of demonstration places the same remark in a stronger point of view. The proposition is demonstrated by general rules which serve in all cases and their extensive utility is only perceived by a subsequent process of the mind. For the purpose of establishing the truth of the last remark Stewart quotes Hally's account of his discovery of the formula for finding the conjugate foci in Optic lenses, in which the circumstance that the same formula applies to all sorts of lenses was discovered only by subsequent trial.
Answer 2nd. This extensive utility arises in the first place from the peculiar nature of the truths about which mathematics is conversant, on account of which peculiarity real cases will turn out approximating far more nearly to those which the definitions of the mathematician describe, than can be found in any other hypothetical science. If we can be certain with respect to this particular circle that all its radii are accurately equal to one arother, our conclusions with respect to it must be mathematically certain but this can never happen in practice. But in proportion to the accuracy of our data will be that of our conclusions and it fortunately happens that the same impertions which limit what are practically attainable in the former, also limits in the same proportion what is practically useful in the latter. The peculiarity in the mathematical science arises from the peculiarity of the objects (figure and magnitude) about which it is conversant, and the accuracy to which we are capable of arriving (in consequence of that mensurablity which is common to all of them, assisted by the wonderful delicacy and fineness which the instruments of the present age has attained) in calculating our data, has given a precision to our results in practical geometry, far beyond the ordinary demands of human life. This peculiarity, also which led Stewart to call magnitude and figure, the mathematical affections of matter, makes these properties, the attributes of space no less than of matter and therefore we can separate them in act no less than in thought and they are not liable to those accidents which vitiate our conclusions more or less in other branches of science. If we are therefore at due pains to ascertain our data our conclusions may be depended on within very narrow limits and the limits also of possible error can in every case be themselves determined. Thus in measuring the height of a mountain if our data be correct and we reason logically from them the result will be very nearly accurate. But in proving any proposition respecting the lever we must leave out in theory many considerations (as its weight) which palpably affect it in practice.
Answer 3rd.—The whole plausiblity of this opinion is derived from a play upon words; because the laws of nature and the laws which regulate the moral word, although both are called laws, are completely different in their significations. The agreement of the latter with the nature of things does not depend upon their being observed or not, but upon the reasonableness, the moral obligation of the laws; whereas the former being drawn from an observation of facts, in the general agreement consists the essence of the law. So that it can no longer continue to be a law of nature if any exception to it turned up. So that it is a mere quibble to say that the laws of the material world are better observed than those of the moral world.
Answer 4th.—The term probablity in its logical sense applies to all sorts of evidence not based upon hypothesis and definition, so that in this sense it is not opposed to what it is certain but to what admits of being demonstrated after the manner of the mathematicians. In its vulger sense it is applied only to those events which are expected with some degree of doubt and hesitancy. The probable evidence of the logician consists of a series beginning with bare possiblity and terminating in moral certainty which is the highest degree of evidence attainable in inoral subjects and to which the term probable will be applied by no one except a professed logician. Thus the rising of the sun tommorrow, the expectation of a man's death, though certain with respect to the genarality of mankind, are classified with probablities by the logician.
Answer 5th.-Stewart defines experience to be that species of evidence in which the same effect is inferred from the same cause under circumstances exactly similar; so that where there is the slightest difference with respect to these, the evidence cannot be called that of experience but of analogy. Thus in common language we are said to infer the fall of one stone from that of another or even from that of a leaden bullet by the evidence of experience which however is inaccurate. The evidence of experience therefore leads us to infer (with respect to the future) the same effect from the same cause acting under exactly similar circumstances. The evidence of analogy leads us to extend our inference from one case to others which appears to be similar to it. We are led by a natural principle to classify under the same common appellation all things which appear similar to one another and it is in this manner that what are vulgarly called general terms are formed and not by any philosophical analysis of the properties of the things which they represent, they are therefore extremely loose in their signification. But general terms formed for the purpose of assisting us in our philosophical investigations ought to be founded on an accurate analysis of the nature and properties of things and by means of a very careful abstraction. We must distinguish therefore between, notions