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and rest; without which nothing farther can be conceived. These rules he explains and illustrates by many examples, especially of the mathematical kind: and then proceeds to shew the way of forming axioms from these genuine definitions; which he supposes to be the elements, or first principles of truths. And by considering these definitions, either simply, or comparatively, and in all their elementary relations, he deduces those truths from them, which he calls axioms. And thus, by considering the scientifical definitions of a strait line and a circle, or the relations arising from their generations; a large number of axioms may be deduced. For example, from considering the generation of a circle, by the revolution of a strait line about a fixed point, this axiom arises; viz. that the motion is slower towards the centre, and quicker towards the circumference. And so in other cases. After the requisite definitions are formed, and compared together, the last thing is to combine, or join them with each other, so as to constitute what the author calls theorems, or new truths. For two or more definitions, or natures, being thus joined together, there may hence arise different natures, or new possibilities, depending, upon each other: as we see in compound machines, &c. And this the author again illus
trates with a great variety of geometrical and physical examples. The whole procedure he declares to be the same that is used by the masters of algebra, for solving such problems, as at first sight might appear unsolvable, by any human genius. For a problem being proposed, the thing is represented to the eye, as if it were al- . ready known and discovered; so as clearly to shew what particulars are here joined together; whilst the natures, or definitions, thereof are either already known, or actually exhibited. Then each different nature is separately considered, and expressed by a different equation, in the most simple characters possible. And now these several equations are variously compared, or combined together, till a single equation thence arises, and includes the natures before expressed by different equations; so as clearly to demonstrate how the question proposed may receive a solution. The author afterwards shews how his method of discovering truth may be eased: and in order thereto, first removes the impediments in the way; among the chief whereof he places falshoods, prejudices, and errors; enquires into their origin; and produces instances thereof, in his three kinds of subjects, viz. imaginary, mathematical, and physical. He accounts those the most subtile and treacherous errors, when V O L. II. P .
imaginary matters are confounded with real, or physical ones; which he observes, to be done even by the most acute philosophers among the moderns, in laying down the principles of nature; and shews how various sects and prejudices have thence arisen, and spread themselves. - These false philosophies, and reigning prejudices, he apprehends may be corrected two ways; viz. first, by exactly distinguishing betwixt the operations of the understanding, and those of the imagination; and, secondly, by assisting the understanding, in the discovery of truth, with the imagination directed by a good method of investigation. And this help is afforded, (1.) by a just adapting of words to things; (2) by proper characters for different ideas; (3.) by motions, or moving engines, and contrivances, to assist the mind in its operations; and, (4.) by new experiments, which give new conceptions. And by this means he supposes the imagination may be brought to cooperate with the understanding. The second impediment, he makes to be this; that we do not duly regard, nor attentively consider, the things already known : and the third, that we too much regard the usefulness of knowledge, and discoveries; whereas, he says, we ought to content ourselves with the bare discovery of new truths: otherwise we block up the way to the most useful things of all. For a very small natural power, which in the abstract conception, appears of very little significance, may yet prove infinitely useful in its future applications; as in the case of the magnetic needle, printing, gunpowder, &c. For numberless inventions of this kind may be derived from trivial experiments. The fourth impediment, he makes to be a natural indisposition in men; whence they are not always fit to go upon the enquiry after truth: and for this indisposition he proposes several remedies. The fifth impediment, is a too long series of investigation; which he endeavours to remove by a proper distribution of the work, and establishing a proper order. And the sixth impediment, he makes to be this; that the affairs of life often prevent our enquiring after truth: which hindrance he proposes to remove, by directing us to follow our own inclination in pursuits. In the last place, he comes to deliver the method of discovering unknown truths, with respect, (1.) to ourselves,in following our own inclinations; (2.) with respect to those sciences, the knowledge whereof is the most necessary, or most pleasing; and, (3.) with respect to natural philosophy, which, when known is, accord
ing to him, the most delightful of all sciences. For by natural philosophy he understands a knowledge of the universe, demonstrated a priori, in exact mathematical order; and confirmed posteriori, by manifest experiments, sufficient to convince the imagination. Such is the general plan of the Medicina Mentis: wherein we may observe much sagacity and ingenuity: but perhaps, when closely examined, the work will appear a little too much influenced by the notion, which the author at first espoused, of fitting the direct algebraical method to universal philosophy; and that he has thus endeavoured to found an universal art of investigation upon one, which, though extremely noble and excellent, is yet limited or confined: or that, at best, his method is not sufficiently general, or fitted for universal practice; but rather formed according to the model of man, than the model of nature. It may also, till farther improved, appear to be more mental than practical; and to be better fitted for solving phaenomena in the ordinary manner, assigning probable reasons of things, and making all square with the human mind; than to discover, and such actuating causes as shall enable men to subdue and conquer nature by works: in which light, it seems to fall vastly short of the Novum Organum, or Art of Investigating Forms.