Know the Truth: A Critique on the Hamiltonian Theory of Limitation. Jesse Henry Jones
are at the foundation of the abstract sciences, having for their subject, quantity. In the second division are those which pertain to mere being and its relations. Upon these rest all sciences pertaining to actual being and its relations. The third division comprises those which pertain to beauty. These are at the foundation of æsthetical science. In the fourth division are those which pertain to morals and religion. Of these the pervading element is the sense of obligation or duty. Of this the idea necessarily arises in connection with the choice by a rational being of a supreme end, and with the performance of actions supposed to bear upon that."—Moral Science, p. 161.
First.—Mathematical ideas and axioms.
Take, for instance, the multiplication table. Can any one, except a Limitist, be induced to believe that it was originally constructed; that a will put it together, and might take it apart? Seven times seven now make forty-nine. Will any one say that it might have been made to make forty-seven; or that at some future time such may be the case? Or again, take the axiom "Things which are equal to the same thing are equal to one another." Will some one say, that the intellectual beings in the universe might, with equal propriety, have been so constructed as to affirm that, in some instances, things which are equal to the same thing are unequal to one another? Or consider the properties of a triangle. Will our limitist teachers instruct us that these properties are a matter of indifference; that for aught we know, the triangle might have been made to have three right angles? Yet again. Examine the syllogism. Was its law constructed?
All M is X;
All Z is M;
All Z is X.
Will any one say that perhaps, we don't know but it might have been so made, as to appear to us that the conclusion was Some Z is not X? Or will the Limitists run into that miserable petty subterfuge of an assertion, "All this seems to us as it is, and we cannot see how it could be different; but then, our minds are so feeble, they are confined in such narrow limits, that it would be the height of presumption to assert positively with regard to stronger minds, and those of wider scope? Perhaps they see things differently." Perhaps they do; but if they do, their minds or ours falsify! The question is one of veracity, nothing more. Throughout all the range of mathematics, the positive and unqualified affirmation of the mind is that its intuitions are absolute and universal; that they are a priori laws conditional of all intellect; that of the Deity just as much as that of man. Feebleness and want of scope have nothing to do with mind in its affirmation, "Seven times seven must make forty-nine; and cannot by any possibility of effort make any other product;" and every intellect, if it sees at all, must see it so. And so on through the catalogue. From this, it follows in this instance, that human knowledge is exhaustive, and so is exactly similar, and equal to the Deity's knowledge.
Second. Those ideas and beliefs which pertain to mere being and its relations.
Take, for instance, the axiom, A material body cannot exist in the Universe without standing in some relation to all the other material bodies in that Universe. Either this is absolutely true, or it is not. If it is so true, then every intellectual being to whom it presents itself as object at all, must see it as every other does. One may see more relations than another; but the axiom in its intrinsic nature must be seen alike by all. If it is not absolutely true, then the converse, or any partially contradictory proposition, may be true. For example. A material body may exist in the Universe, and stand in no relation to some of the other material bodies in that Universe. But, few men will hesitate to say, that this is not only utterly unthinkable, but that it could only become thinkable by a denial and destruction of the laws of thought; or, in other words, by the stultification of the mind.
Take another instance, arising from the fact of parentage and offspring, in the sentient beings of the world. A pair, no matter to what class they belong, by the fact of becoming parents, establish a new relation for themselves; and, "after their kind," they are under bonds to their young. And, to a greater or less extent, their young have a claim upon them. As we ascend in the scale of being, the duty imposed is greater, and the claim of the offspring stronger. Whether it be the fierce eagle, or the timid dove, or the chirping sparrow; whether it be the prowling lion, or the distrustful deer, or the cowering hare; or whether it be the races of man who are examined, the relations established by parentage are everywhere recognized. Now, will one say that all this might be changed for aught we know; that, what we call law, is only a judgment of mankind; and so that this relation did not exist at first, but was the product of growth? And will one further say that there is no necessity or universality in this relation; but that the races might, for aught we know, have just as well been established with a parentage which involved no relation at all; that the fabled indifference of the ostrich, intensified a hundredfold, might have been the law of sentient being? Yet such results logically flow from the principles of the Limitists. Precisely the same line of argument might be pursued respecting the laws of human society. But it is not needed here. It is evident now, that what gives validity to judgments is the fact that they accord with an a priori principle in the mind.
Third. The ideas and beliefs which pertain to beauty. A science of beauty has not yet been sufficiently developed to permit of so extensive an illustration of this class as the others. Yet enough is established for our purpose. Let us consider beauty as in proportioned form. It is said that certain Greek mathematicians, subsequently to the Christian era, studied out a mathematical formula for the human body, and constructed a statue according to it; and that both were pronounced at the time perfect. Both statue and formula are now lost. Be the story true, or a legend, there is valid ground for the assertion, that the mind instinctively assumes, in all its criticisms, the axiom, There is a perfect ideal by which as standard, all art must be judged. The very fact that the mind, though acknowledging the imperfection of its own ideal, unconsciously asserts, that somewhere, in some mind, there is an ideal, in which a perfect hand joins a perfect arm, and a perfect foot a perfect leg, and these a perfect trunk; and a perfect neck supports a perfect head, adorned by perfect features, and thus there is a perfect ideal, is decisive that such an ideal exists. And this conclusion is true, because God who made us, and constructed the ground from whence this instinctive affirmation springs, is true.
Take another instance. Few men, who have studied Gothic spires, have failed to observe that the height of some, in proportion to their base, is too great, and that of others, too small. The mind irresistibly affirms, that between these opposite imperfections, there is a golden mean, at which the proportion shall be perfect. When the formula of this proportion shall be studied out, any workman, who is skilled with tools, can construct a perfect spire. The law once discovered and promulgated, becomes common knowledge. Mechanical skill will be all that can differentiate one workman from another. The fact that the law has not been discovered yet, throws no discredit upon the positive affirmation of the mind, that there must be such a law; any more than the fact of Newton's ignorance of the law of gravitation, when he saw the apple fall, discredited his instinctive affirmation, upon seeing that phenomenon, there is a law in accordance with which it fell.
Now how comes the mind instinctively and positively to make these assertions. If they were judgments, the mind would only speak of probabilities; but here, it qualifies the assertion with necessity. Men, however positive in their temperament, do not say, "I know it will rain to-morrow," but only, "In all probability it will." Not so here. Here the mind refuses to express itself doubtfully. Its utterance is the extreme of positiveness. It says must. And if its affirmation is not true, then there is no reason why those works of art which are held in highest esteem, should be adjudged better than the efforts of the tyro, except the whim of the individual, or the arbitrary determination of their admirers.
Fourth. The ideas and beliefs which pertain to morals and religion.
We now enter a sphere of which no understanding could by any possibility ever guess, much less investigate. Here no sense could ever penetrate; there is no object for it to perceive. Here all judgments are impertinent; for in this sphere are only laws, and duties, and obligations. An understanding cannot "conceive" of a moral law, because such a law is inconceivable; and it cannot perceive one, because it has no eye. If it were competent to explain every phenomenon in the other classes, it would be utterly impotent to explain a single phenomenon