| The reason why I impute any defect to geometry, is, because its original and fundamental principles are derived merely from appearances; and it may perhaps be imagined, that this defect must always attend it, and keep it from ever reaching a greater exactness in the comparison of objects or ideas, than what our eye or imagination alone is able to attain. |
| I own that this defect so far attends it, as to keep it from ever aspiring to a full certainty: But since these fundamental principles depend on the easiest and least deceitful appearances, they bestow on their consequences a degree of exactness, of which these consequences are singly incapable. |
| It is impossible for the eye to determine the angles of a chiliagon to be equal to 1996 right angles, or make any conjecture, that approaches this proportion; but when it determines, that right lines cannot concur; that we cannot draw more than one right line between two given points; it's mistakes can never be of any consequence. |
| And this is the nature and use of geometry, to run us up to such appearances, as, by reason of their simplicity, cannot lead us into any considerable error. |
| I shall here take occasion to propose a second observation concerning our demonstrative reasonings, which is suggested by the same subject of the mathematics. |
| It is usual with mathematicians, to pretend, that those ideas, which are their objects, are of so refined and spiritual a nature, that they fall not under the conception of the fancy, but must be comprehended by a pure and intellectual view, of which the superior faculties of the soul are alone capable. |
| The same notion runs through most parts of philosophy, and is principally made use of to explain oar abstract ideas, and to shew how we can form an idea of a triangle, for instance, which shall neither be an isoceles nor scalenum, nor be confined to any particular length and proportion of sides. |
| It is easy to see, why philosophers are so fond of this notion of some spiritual and refined perceptions; since by that means they cover many of their absurdities, and may refuse to submit to the decisions of clear ideas, by appealing to such as are obscure and uncertain. |
| But to destroy this artifice, we need but reflect on that principle so oft insisted on, that all our ideas are copyed from our impressions. |
| For from thence we may immediately conclude, that since all impressions are clear and precise, the ideas, which are copyed from them, must be of the same nature, and can never, but from our fault, contain any thing so dark and intricate. |
| An idea is by its very nature weaker and fainter than an impression; but being in every other respect the same, cannot imply any very great mystery. |
| If its weakness render it obscure, it is our business to remedy that defect, as much as possible, by keeping the idea steady and precise; and till we have done so, it is in vain to pretend to reasoning and philosophy. |
| SECT. II. OF PROBABILITY, AND OF THE IDEA OF CAUSE AND EFFECT. |
| This is all I think necessary to observe concerning those four relations, which are the foundation of science; but as to the other three, which depend not upon the idea, and may be absent or present even while that remains the same, it will be proper to explain them more particularly. |
| These three relations are identity, the situations in time and place, and causation. |
| All kinds of reasoning consist in nothing but a comparison, and a discovery of those relations, either constant or inconstant, which two or more objects bear to each other. |
| This comparison we may make, either when both the objects are present to the senses, or when neither of them is present, or when only one. |
| When both the objects are present to the senses along with the relation, we call this perception rather than reasoning; nor is there in this case any exercise of the thought, or any action, properly speaking, but a mere passive admission of the impressions through the organs of sensation. |
| According to this way of thinking, we ought not to receive as reasoning any of the observations we may make concerning identity, and the relations of time and .place; since in none of them the mind can go beyond what is immediately present to the senses, either to discover the real existence or the relations of objects. |
| It is only causation, which produces such a connexion, as to give us assurance from the existence or action of one object, that it was followed or preceded by any other existence or action; nor can the other two relations be ever made use of in reasoning, except so far as they either affect or are affected by it. |
| There is nothing in any objects to perswade us, that they are either always remote or always contiguous; and when from experience and observation we discover, that their relation in this particular is invariable, we, always conclude there is some secret cause, which separates or unites them. |