English
But for my own part I must confess a suspicion, that what is often called intui- tion, is, in £Etct, only a rapid inference ; and I have not argued as if the law, by which our mind tries appearances, would have been apprehended as it is in the present life by the mind itself^ if it had not been first educated for the scene with which it is here conversant through those very perceptions which furnish it with &ct8 to reason upon, though certainly not with the power which reasons. But even the act of comparison, without which the mind could not classify things, putting like to like, and setting inconsistencies asunder, alone implies a faculty quite distinct from any bodily organ. If indeed any one likes to say that it involves mental intuition, I will not object to it. Only it is sofficient for me to observe, that the necessary order in which perceptions must be noted and brought to account, so as to monld their results into truth, is not itself a product of sensation; bat is either some instinct which may be educed from the mind, or rather perhaps a portion of that higher order, which the mind observes to embrace both itself, and all things whatsoever with which it comes in contact, and which it naturally conceives to imply a Thought, not to say at present a Thinker, presiding over the course of the world. You will perhai)s catch my meaning more clearly, if you remark the different use made of the same appearances by a man in his sound senses, and a madman. There is such a thing as madness, and the sensations of persons suffering firom it are often very acute. Yet they, seeing the same things as other men, draw most absurd and distorted inferences, for want of that controlling faculty which compares and arranges according to the law apprehended by the mind Without then venturing to say that ideas are innate, or even inherent, in the mind, I certainly ascribe to any reasoning man a kind of knowledge, or at least an internal law and a 8—2 116 TRUTH OF NUMBERS. method of dealing with knowledge, distinct from that of the senses, and I conceive your objection extends only so far as to indicate a part of the instrumentality, just as one may point to a mason^s scaffolding or his bricks ; but you no more negative the existence of something higher, than in the other case one could argue that a builder had no power of contriving and measuring. " If now you ask for specimens of the kind of knowledge referred to, I fully believe that clear instances of it may be found in the general rules of right and wrong, and in all the broad principles connected with the conscience and the affections of man ; yet many persons will conceive there to be more evi- dent signs of it in the positive sciences which regard number, quantity, and space. You will tell me, as before, that arithmetic depends upon counting. But you may detach any sort of num- bers you please from all sorts of visible objects ; and you can deal with them as pure abstractions of the mind. Now it is only when thus abstracted, or set apart from sensation, that numbers acquire that certainty which all the world ascribes to them. People may differ by scores in counting a flock of sheep, and by much more in numbering cowries or sand ; but remove your figures out of the range of sensible objects into the intellec- tual region of pure knowledge, and immediately you have the means of arriving at results, which our clever friend Saddnanda would not hesitate to adopt, and which persons differing from him widely in other things, and in countries far apart, still would never venture to impugn. There is then such a thing as truth, and it can be most irrefragably aflSirmed of things most within the range of the mind. K I had studied the measure- ment of space as thoroughly as some neighbours of mine in Britain, I could multiply a number of apposite principles, such, however, as Saddnanda will be good enough readily to recollect for me ; for example, that any two sides in any triangle must exceed the third, though we may not have measured with our fingers the particular triangle spoken of; or again, that some kinds of figures, and some numbers, are commensurate ; while MATHEMATICS. 117 others (setting aside the unit) are not so ; or again, that parallel lines will never meet, which we foresee, though we cannot test it to infinity; or that the whole is more than its part, or that the equal of one of two equals must be equal to the other. For these very simple instances will perhaps serve my argument as well as more abstruse ones. Now all these, and a thousand other such things, are truths intellectual, rather than sensible, though the senses may help in leading us up to them. We are also more certainly persuaded of them, in proportion as the pure intellect has more to do with them. When such things are taken hold of by men of deep thought and patient calculation, they grow up into vast sciences, such as are utterly remote from the ordinary perceptions of mankind, and yet such as are quite indisputably certain, even while they startle us most. You know that the mathematicians and astronomers of India were not uncelebrated in former times. It is related of Bh^cara, who is believed to have lived six hundred years ago, that he gave clear solutions of some problems in algebra, which were not known in Europe until four hundred years after his time ; and the same priority is claimed for him as regards a certain method of calculating ; and yet as soon as the result and the method of Bhdscara are known in Europe, the truth of the one, and the merit of the other, are immediately recognised ; for it does not depend on local diflferences, or on any choice of our own, whether we shall acknowledge such truths, or deny them ; because they are evident. You can therefore appreciate the kind of intel- lectual certainty of which I am speaking. " Then again it may be worth noticing, that such general truths as are apprehended by the intellect in science, may also be applied to all manner of useful contrivances in the external world. All the practical arts and manufactures flourish most wherever science is cultivated by their .side. Whether men make fire and water their servants, compelling them either to draw their chariots, like horses, or to put in motion all kinds of machineiyy so as both to lessen human toil and increase the 118 TRUTH PROCREATIVE. oomforts of life, or whether they extract from the earth minerals and medicines such as ruder ages never dreamt of, you have the kitellectual process of knowing in every case supposed as a preliminary. By such means the face of countries has been changed, and nations have attained power or civilisation. Whereas other nations, among whom intellectual knowledge kmguishes, either gradually lose whatever useful inventions their fSathers may have possessed, and fall back into the state of savages, or at least they are outstripped in the race of greatness by more intellectual nations. "Here then I doubt whether to argue, or only to prepare you for my arguing hereafter, that general principles, or truths of the most intellectual kind, may be observed by us as clearly involved in the very fabric of the world. You see, already, to how great a conclusion this idea points the way. I am not in this place employing the old argument from design, in the sense cf adaptation of means to ends, though probably we shall see hereafter that it is a thoroughly sound one. Only, as you have attempted to explain that away, and the refinements of our S&ikhyast friend on the subject of Pracriti, as well as his obser- vation of irregularities in the world, will render him unwilling to admit it, so I here suggest to you a distinct idea. The argument from design will apply to such a thing as a watch, or whatever is made with art, by hand. It holds good for the world therefore, so far as any one can reduce the world within that description of things. But now, suppose an artist could throw down the materials of a watch apparently at random, yet really in such definite proportions that they should unite and begin to proclaim the time, the process would be still more wonderful.