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would be able to make would not be sufficiently accurate to enable him to discover any of those properties which were not obvious at first sight, yet they might, and would be sufficient to suggest the idea of a perfect circle; for it would be obvious, that there was a point somewhere about the middle, which was nearly equi-distant from all parts of the outside. And if, upon this, he should define a perfect circle to be a figure bounded by a line, which he called the circumference, and which is every where equally distant from a point within it, called by him its centre, it is evident that he would now be in possession of a standard to which he might refer in any of his subsequent researches; and from this property of his ideal circle, that all his radii are exactly equal, he might proceed to deduce such other properties as he was able to discover; always comparing his conclusions with the definition, and not with such approximations to a circle as he could make, or might observe in nature. Now this is the very process which mathematicians have adopted. Their senses, in the first instance, presented a variety of figures to them for examination, most of which were rough and irregular, though some among them, upon a superficial view, had the appearance of regularity; yet even those, upon a closer examination, were found to have a great number of small inequalities. The general appearance, however, of any of the latter was, by supposing all these small inequalities removed, sufficient to suggest to the mind the idea of a perfect figure of its kind; which perfect figure would evidently exist only in the imagination-the description of this ideal figure is called a definition of it. A definition of any geometrical figure, if it be a good one, consists in the enunciation of some fundamental property of that figure, from which its other properties may be deduced, and which likewise distinguishes it from all other figures.
The definitions of the various figures being once established, the mathematician no longer has recourse to any form which actually exists in nature, but in all his investigations refers to the definition alone, that is, to the idea, existing in his own mind, from which the definition was taken. By
this means he is certain, that is, he has the evidence of consciousness that' he has a complete and correct idea of the figure whose properties he is investigating; and if he takes care to have the same evidence for each step of the reasoning which he employs, it is manifest that he will have the highest evidence of the correctness of his conclusion, which it is possible for man, constituted as he is, to have.
From the above it appears that all mathematical figures are ideal, or exist only in the imagination; hence the mathematician has a complete conception of the figure whose properties he is investigating-it is a creation of his own, and he has the evidence of consciousness that no circumstance respecting it, however trivial, can escape his notice he has likewise the same evidence for every step of his reasoning; for in every transition which he makes from one property to another, he has the immediate evidence of consciousness whether they agree or disagree, his mind taking cognizance of both at the same instant. Here, then, are the circumstances which give such peculiar force to mathematical evidence or demonstration; we know, by consciousness, that the things themselves are completely comprehended; we have the same evidence for every successive step in the demonstration, and at the conclusion we are conscious that we remember this; but even supposing there should be some part of the demonstration of which we have not a clear and distinct remembrance, we have the power of going over the whole again, and of repeating this re-examination till we are conscious that we do remember every part distinctly, till we are able to make the whole pass in rapid review before the mind. It is therefore clear that we have the evidence of memory and consciousness for the truth of the conclusion. But this is the highest kind of evidence which it is possible for man to have; it not only does, but must always, carry irresistible conviction to the mind, so long as the mind of man has existence.
4th. Of metaphysical truths. If we attentively examine the principles on which our reasoning on most subjects is founded, we cannot fail to observe that there are some of them so.
general, that they apply with the same ease and certainty to the most profound researches as to the most trivial and common-place transactions; while at the same time, their truth is so plain and so obvious, that any one who professes to call it in question, is immediately suspected of being either insincere or insane. And as those general principles are applicable to mind as well as to body or matter, they have been designated metaphysical, to distinguish them from physical truths. Of this class are the following-It is a direct contradiction to suppose that any thing, or any change, can be produced by absolute nothing. It is impossible for any thing to produce itself. If a change take place, that change must have been produced by something: and if the thing changed be really passive, the alteration or change must have been produced by something which was different from the thing itself. If a thing which now exists, once had no existence, that thing must have been produced by something else, &c. In all these, as well as several more of a similar description, as soon as the terms are understood, the mind immediately perceives that it would involve a direct contradiction to suppose any of them to be false. Thus, in the first of these, as soon as the term absolute nothing is understood to mean the negation of all attributes, properties or qualities, substratum and all, the complete absence of every thing which could possibly produce any thing else, we immediately perceive that it would be a direct contradiction to this negative idea to suppose any thing whatever to be produced. Here the idea of contradiction or impossibility conveyed by the terms is the sign, and the real impossibility which exists in the nature of things, for absolute nothing ever to produce something, is the thing signified. And it is the agreement of these, or the application of this idea of impossibility to those cases only where it really exists in nature, which constitutes the truth or correctness of the maxim or proposition. Again, if we examine what is meant by the expression, a thing produces itself, we immediately perceive that it involves within itself the contradictory idea that the thing was acting before it had existence, that is, it
both did and did not exist at the very same instant; and, consequently, to suppose it possible for any thing to produce itself, involves a direct contradiction. And should this examination be continued through the whole, it would be found that in all such propositions as the above, the evidence on which we give our assent to them, is the consciousness that the contrary supposition contains within itself a direct contradiction, and, therefore, cannot be true. Whence the evidence for their truth is equally strong as that for any mathematical truth whatever.
It appears from what has been said, that it is utterly beyond the power of the imagination itself to devise any method by which we can conceive it possible for any one of this class of maxims to be false, so long as the terms are used in the same signification. So that to enable any person even in his own mind to conceive them false, he must first attach different meanings to the terms in which they are expressed; but then it must be obvious that, although the sounds or characters used in announcing them remain the same, by changing the ideas affixed to those sounds or characters, the maxims themselves are really altered, and may, of course, be either true or false, according to the nature of the new ideas introduced. This naturally leads me to the consideration of another class of metaphysical propositions, which, although they have been and are still considered by the bulk of mankind to be equally certain as the former class, have nevertheless given rise to much controversy among metaphysicians; it will scarcely be necessary to add, that I allude to those relating to cause and effect, such as, Every effect must have a cause every cause must produce some effect equal causes must produce equal effects, &c. It may, perhaps, appear surprising to some, that any difference of opinion should ever have existed respecting the truth of these maxims; but this surprise will cease, when it is recollected that very different meanings have been attached to the word cause. It is commonly defined to be that which produces or effects any thing but this definition is evidently ambiguous; for if an agent, by an exertion of its power, produce or effect any thing, the word
the Human Mind, says" When we speak of one thing being the cause of another, all that we mean is, that the two are constantly conjoined, so that when we see the one we may expect the other." And the definitions of the other two writers are the same in substance as this.
cause may, according to this defini-
To avoid any misapprehension respecting the meaning of this definition, it will be necessary to keep in mind, that the word conjoined is used in opposition to connected. In the language of these philosophers it denotes that two events take place together, or else immediately after one another, but which are in other respects entirely loose and separate, and have no influence whatever upon one another.-That this was the meaning attached to the term by Hume, seems not to admit of a doubt, since he expressly says "All events seem entirely loose and separate. One event follows another, but we never can observe any tye between them. They seem conjoined, but never connected." And that D. Stewart uses it in the same sense, is evident from the decided manner in which he expresses his approbation of Hume's opinions on this subject. Professor Leslie's concurrence, also, is too notorious to require to be more particularly mentioned in this place.
Now I would ask any of the advocates of this definition, whether any person ever imagined that the state of the tides is the cause of the changes we observe in the moon: that summer is the cause of winter, or winter the cause of summer: that day is the cause of night, or night the cause of day: and yet it would be very easy to prove any one of these propositions to be true, if by the word cause we meant nothing more than "that the two are constantly conjoined, so that when we see the one we may expect the other." Nay, an expert metaphysician would find no difficulty in clearly proving to a Northumbrian, that the coming of wild geese is the cause of winter, and their departure the cause of summer, if this definition be correct.
The truth seems to be, that this is not the meaning of the word cause, even in physical inquiries; for we never in any instance use it till there arises in the mind a conviction that the two objects are not merely con
joined but connected; that the former object exercises some controuling influence over the latter; though we cannot by our senses perceive in what manner this influence is exerted. Who is there that does not feel with D. Stewart, that the natural bias of the mind is surely to conceive physical events as somehow linked together; and natural substances, as possessed of certain powers and virtues, which fit them to produce particular effects"? -But I for one must beg leave to dissent from this celebrated writer, when he adds, "that we have no reason to believe this to be the case, has been shewn in a very particular manner by Mr. Hume, and by other writers; and must, indeed, appear evident to every person, on a moment's reflection:" for neither Hume nor any other writer has ever yet shewn that physical events are not linked together; nor has any one of them proved that the " powers and virtues" which have been bestowed upon "material substances" are not such as to "fit them to produce particular effects." The whole that has been done by these writers amounts to no more than, first, to shew that we can have no knowledge of the properties of material substances, except through the medium of our senses: and, secondly, that our senses never give us any information respecting the connexion between physical events. -But, on the other hand, it must be observed, that in no case whatever do they afford us any evidence that there is really no connexion, no vinculum whatever. The fact is, they give us no information at all on the subject, either for or against. From which it appears that the vinculum or bond, if there be any, is something which can no more be perceived by our senses than the material substance or substratum itself: it, therefore, follows, that we can only come to the know ledge of its existence or non-existence, by examining whether the effects or phenomena observed are such as must proceed from its existence or non-existence.
Now, if we take any two physical events, which to our senses appear to be conjoined, we are absolutely certain that they must either be connected or they must not, for there is no other supposition besides these two possible. First, then, let us suppose them to be
really connected: it matters not whether this connexion proceeds from the nature bestowed upon them at the creation, which is the opinion of some, or whether it proceeds from those laws of action which the Supreme Being has imposed upon himself, so long as he shall continue the present system, which appears to be the opinion of others. For in either case, we are certain that the two objects or events, which we have supposed to be really connected, must always remain connected, so long as they retain the same nature, or the same laws are observed; that is, so long as man shall exist as he now is: and, consequently, if we perceive one of these objects or events, at any time or place, we are quite certain, if this supposition be correct, that the other inust be along with it. Let us now examine the other supposition, viz. that they are not connected.-Now, whenever there is a very great number of really unconnected objects or events, it admits of mathematical demonstration, that the chances against the junction of any two particular objects or events far exceeds the chances for it when there is only one trial: that the chances for the same two, being twice conjoined successively, is still far less : and, in short, that the chances against their being conjoined any considerable number of times successively, is so inconceivably great as to make such a continued conjunction approach as near to an absolute impossibility as any thing can be conceived to be, which is not really so. It therefore follows, that if two objects be really unconnected, we shall always, in a few trials, find them separate or unconjoined: whereas, if they be really connected, they never can be found separate.
But we know, from observation, that there are many physical events which appear always conjoined. For example, if cold, above a certain degree, be applied to pure water, the water is always frozen; if fire be applied to wax, it is always melted. Hence, if we compare these facts with the conclusions deduced from the two foregoing suppositions, the only possible ones, it necessarily follows that we cannot avoid believing that the application of cold to water, and of fire to wax, is somehow or other really
connected with the congelation of the former and the melting of the latter: and we then, and not till then, conceive that the application of cold to water, and of fire to wax, is the cause of the congelation of the one and the melting of the other.-From which, it appears, that so far is it from being true, "that we have no reason to believe" that physical events are linked together; the fact is, we have every reason to believe it, which it is possible for us to have, constituted as
Hence the word cause always implies something more than mere conjunction, even in physical inquiries; viz. our belief that there is a real connexion. So that in physics, as well as in metaphysics, the word cause is always used to denote that which really does, or is supposed to, produce the effect. It therefore follows, that all those arguments against the certainty and truth of the general maxims relating to cause and effect, drawn from this arbitrary and improper definition of the word cause, must be altogether futile and inapplicable. From what has been said on this subject, it appears that the evidence on which we give our assent to what have been very properly and emphatically called fundamental metaphysical truths, arises from, or resolves itself into, the consciousness that the supposition that any of them is false, involves in itself a contradiction.
[To be concluded in the next Number.]
Errors in the various Editions of the English Bible.
SINCE our last number appeared, (p. 161,) the Bible Society has advertised for false readings of the English Bibles put out under the Society's patronage; for the patent printers have so far condescended to this institution as to introduce its name into the titlepages of the copies purchased on its account. At the head of No. 68 of its "Monthly Extracts," is the following notice: "The Committee, anxious to render their Bibles and Testaments as correct as possible, request the favour of communications from time to time, of any errata which may have been discovered in reading. In
order to specify the edition in which such errata are found, it will be necessary to mention the place in which it was printed; the date, and the type, as described in the Society's Catalogue."
It is pleasing to see the Society awaking, though late, to its duty; and in order to assist its efforts towards an emendation of the printed copies of the English Bible, (the Stereotype copies in which errors are of most consequence as being most widely diffused and most likely to be permanent,) we subjoin another list of errata that have fallen under our observation.