AN

INTRODUCTION

ΤΟ

NATURAL PHILOSOPHY.

OF THE DEGREES OR KINDS OF KNOWLEDGE; AND THE RULES OF PHILOSOPHIZING.

THE

HE impreffions made on the organs of fenfe by external objects produce ideas in the mind. We are continually employed in amaffing a stock of general truths refpecting them, which is called knowledge.

An intelligent being, whose powers are limited, must of neceffity be unequal to the performance of many things. If any affertion be made refpecting two or more ideas, it will imply either truth or falfehood; but the cases in which we can with certainty discover the one or the other are very few, in comparison with those that are placed beyond our power of investigation. Yet, as a decifion is almost always required for the regulation of our conduct in the affairs of life, the greater part of our knowledge becomes founded on probability, instead of establishing truth. The means of acquiring knowledge may therefore be faid to be of three VOL. I.

B

kinds.

kinds. Certainties are obtained either by intuition or demonstration; probabilities are obtained by analogy.

There are fome ideas, whofe mutual relation in certain respects is fo evident, that nothing more is required to obtain the knowledge of it, than to apply them to each other. For example; if a given body be divided into parts, and the mutual relation between the whole body and one of its parts, with respect to magnitude, be demanded, the mind immediately conceives, with the clearest and most abfolute certainty, that the whole body is greater than its part. If the particular body or magnitude in contemplation be abstracted, or left out, the propofition becomes general in this form, viz. every magnitude is greater than any part of the fame. This kind of knowledge is called intuitive, and the general propofitions are termed Axioms.

When it is required to determine the mutual relation of two ideas, whofe agreement or difagreement cannot be intuitively perceived, the truth may often be obtained by the interpofition of a chain of axioms. This method of exhibiting the truth is termed demonftration, and feems to be applicable by us only to our ideas of the quantities and pofitions of magnitudes. For this reafon, it will be difficult to give an example without having recourfe to the mathematics. The following will, however, be easily understood.

Fig. 1. Let the two circles in the figure be fuppofed equal, and the circumference of each to pafs

through the center of the other. Imagine the centers to be joined by the right line A B, and the lines CA, C B, to be drawn from one of the points where the circumferences interfect each other, to the centers refpectively. Then, I fay, the lines A B, BC, CA, will be equal each to each.

The demonstration of this truth is as follows:

The word circle fignifies a plain figure, contained under one line, called the circumference, to which all right lines drawn to a certain point within the figure, called the center, are equal. As foon therefore as it is understood that the figure ACD is a circle, and that the lines A B, C B, are right lines drawn from its center to its circumference, it is acknowledged intuitively, and without further argument, that thofe lines are equal.

The fame reason in the circle ECB evinces, that the lines A B, A C, are equal.

The lines A C, CB, being thus proved to be each equal to the line AB, are likewife equal to each other. For it is an intuitive truth or axiom, that things equal to one and the fame thing are equal to each other.

The want of axioms, and the labour of demonstration, are not the only impediments to the acquifition of knowledge. Knowledge is converfant with ideas only: it can therefore be faid to poffefs reality with respect to external objects, so far only as thofe ideas may be taken or fubftituted for the things they reprefent; but it is impoffible to determine how far this may be done with ftrict propriety. In referring

from ideas to things we are liable to error, not only because the compound idea of a being confifts of an affemblage of its properties, which may be incomplete and inadequate, but likewife because those ideas may even be quite different from any thing exifting in the being itself, as may be inftanced in the ideas of colour, found, pain, &c. The great perfpicuity and certainty of mathematical knowledge arifes from the fimplicity of the notions or ideas employed, and their not depending on any external being: for, as this fcience treats only of ideas, it is of no confequence to its truths, whether the perfect figures of geometry ever had an existence; it being fufficient that their exiftence is poffible.

The greater number of our ideas being too complex and imperfect to admit of intuitive conclufions or axioms, it is evident, that in general we must be contented with lefs proof than demonstration. Instead, therefore, of endeavouring to obtain axioms by comparing ideas, we obferve events, and from the contemplation of what has happened, we form a prefumption of what will again come to pafs. Obfervation has fhewn us, that a certain event is always followed by another determinate event; we fuppofe a relation to fubfift between them; we imagine this relation to be neceffary; we diftinguish the prior event by the name of Cause, and the latter we call the Effect. This kind of knowledge, which is not founded on reafoning, but on experience alone, may be termed Analogical, and is much less perfect than what is obtained by intuition or demonstration.