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transient hint, in another place, I have offered to my reader's consideration. 3. Of other $ 18. As to the third sort of our knowrelations, it ledge, viz. the agreement or disagreement is not easy to of any of our ideas in any other relation : say how far.
this, as it is the largest field of our knowledge, so it is hard to determine how far it may extend; because the advances that are made in this part of knowledge, depending on our sagacity in finding intermediate ideas, that may show the relations and habitudes of ideas, whose co-existence is not considered, it is a hard matter to tell when we are at an end of such discoveries; and when reason has all the helps it is capable of, for the finding of proofs, or examining the agreement or disagreement of remote ideas. They that are ignorant of algebra cannot imagine the wonders in this kind are to be done by it: and what farther improvements and helps, advantageous to other parts of knowledge, the sagacious mind of man may yet find out, it is not easy to determine. This at least I believe, that the ideas of quantity are not those alone that are capable of demonstration and knowledge; and that other, and perhaps more useful parts of contemplation, would afford us certainty, if vices, passions, and domineering interest did not oppose or menace such endeavours.
The idea of a Supreme Being, infinite Morality capable of de
in power, goodness, and wisdom, whose monstration workmanship we are, and on whom we
depend; and the idea of ourselves, as understanding rational beings, being such as are clear in us, would, I suppose, if duly
considered and pursued, afford such foundations of our duty and rules of action, as might place morality amongst the sciences capable of demonstration : wherein I doubt not but from self-evident propositions, by necessary consequences, as incontestable as those in mathematics, the measures of right and wrong might be
made out to any one that will apply himself with the same indifferency and attention to the one, as he does to the other of these sciences. The relation of other modes may certainly be perceived, as well as those of number and extension : and I cannot see why they should not also be capable of demonstration, if due methods were thought on to examine or pursue their agreement or disagreement. Where there is no property, there is no injustice, is a proposition as certain as any demonstration in Euclid : for the idea of property being a right to any thing; and the idea to which the name injustice is given, being the invasion or violation of that right; it is evident, that these ideas being thus established, and these names annexed to them, I can as certainly know this proposition to be true, as that a triangle has three angles equal to two right ones. Again, “ no government allows absolute liberty :" The idea of government being the establishment of society upon certain rules or laws which require conformity to them; and the idea of absolute liberty being for any one to do whatever he pleases; I am as capable of being certain of the truth of this proposition, as of any in the mathematics.
§ 19. That which in this respect has Two things given the advantage to the ideas of quan- have made tity, and made them thought more capa
thought in ble of certainty and demonstration, is,
capable of First, that they can be set down and represented by sensible marks, which have tion: their a greater and nearer correspondence with complexedthem than any words or sounds whatso
Diagrams drawn on paper are copies of the ideas in the mind, and not liable to the uncertainty that words carry in their signification. An angle, circle, or square, drawn in lines, lies open to the view, and cannot be mistaken: it remains unchangeable, and may at leisure be considered and examined, and the demonstration be revised, and all the parts of it may be gone over more than
want of sen
once without any danger of the least change in the ideas. This cannot be thus done in moral ideas; we have no sensible marks that resemble them, whereby we can set them down; we have nothing but words to express them by: which though, when written, they remain the same, yet the ideas they stand for may change in the same man; and it is
seldom that they are not different in different persons.
Secondly, another thing that makes the greater difficulty in ethics is, that moral ideas are commonly more complex than those of the figures ordinarily considered in mathematics. From whence these two inconveniencies follow: first, that their names are of more uncertain signification, the precise collection of simple ideas they stand for not being so easily agreed on, and so the sign that is used for them in communication always, and in thinking often, does not steadily carry with it the same idea. Upon which the same disorder, confusion, and error follow, as would if a man, going to demonstrate something of an heptagon, should, in the diagram he took to do it, leave out one of the angles, or by oversight make the figure with one angle more than the name ordinarily imported, or he intended it should, when at first he thought of his demonstration. This often happens, and is hardly avoidable in very complex moral ideas, where the same name being retained, one angle, i. e. one simple idea is left out or put in the complex one, (still called by the same name) more at one time than another. Secondly, from the complexedness of these moral ideas, there follows another inconvenience, viz. that the mind cannot easily retain those precise combinations, so exactly and perfectly as is necessary in the examination of the habitudes and correspondencies, agreements or disagreements, of several of them one with another; especially where it is to be judged of by long deductions, and the intervention of several other complex ideas, to show the agreement or disagreement of two remote ones.
The great help against this which mathematicians find in diagrams and figures, which remain unalterable in their draughts, is very apparent, and the me. mory would often have great difficulty otherwise to retain them so exactly, whilst the mind went over the parts of them step by step, to examine their several correspondencies. And though in casting up a long sum either in addition, multiplication, or division, every part be only a progression of the mind, taking a view of its own ideas, and considering their agreement or disagreement; and the resolution of the question be nothing but the result of the whole, made up of such particulars, whereof the mind has a clear perception : yet without setting down the se. veral parts by marks, whose precise significations are known, and by marks that last and remain in view when the memory had let them go, it would be almost impossible to carry so many different ideas in the mind, without confounding or letting slip some parts of the reckoning, and thereby making all our reasonings about it useless. In which case, the cyphers or marks help not the mind at all to perceive the agreement of any two or more numbers, their equalities or proportions : that the mind has only by intuition of its own ideas of the numbers themselves. But the numerical characters are helps to the memory, to record and retain the several ideas about which the demonstration is made, whereby a man may know how far his in. tuitive knowledge, in surveying several of the particulars, has proceeded; that so he may without con-.. fusion go on to what is yet unknown, and at last have in one view before him the result of all his perceptions and reasonings.
$ 20. One part of these disadvantages Remedies of in moral ideas, which has made them be thought not capable of demonstration, ficulties. may in a good measure be remedied by definitions, setting down that collection of simple ideas, which every term shall stand for, and then using the terms
steadily and constantly for that precise collection. And what methods algebra, or something of that kind, may hereafter suggest, to remove the other difficulties, it is not easy to foretel. Confident I am, that if men would in the same method, and with the same indifferency, search after moral, as they do mathematical truths, they would find them have a stronger connexion one with another, and a more necessary consequence from our clear and distinct ideas, and to come nearer perfect demonstration than is commonly imagined. But much of this is not to be expected, whilst the desire of esteem, riches, or power, makes men espouse the well-endowed opinions in fashion, and then seek arguments either to make good their beauty, or varnish over and cover their deformity: nothing being so beautiful to the eye as truth is to the mind; nothing so deformed and irreconcileable to the understanding as a lie. For though many a man can with satisfaction enough own a no very handsome wife in his bosom; yet who is bold enough openly to avow, that he has espoused a falsehood, and received into his breast so ugly a thing as a lie? Whilst the parties of men cram their tenets down all men's throats, whom they can get into their power, without permitting them to examine their truth or falsehood, and will not let truth have fair play in the world, nor men the liberty to search after it, what improvements can be expected of this kind? What greater light can be hoped for in the moral sciences ? The subject part of mankind in most places might, instead thereof, with Egyptian bondage expect Egyptian darkness, were not the candle of the Lord set up by himself in men's minds, which it is impossible for the breath or power of man wholly to extinguish.
$ 21. As to the fourth sort of our know4. Of real existence: ledge, viz. of the real actual existence of we have an things, we have an intuitive knowledge of intuitive
our own existence; and a demonstrative