When we contemplate the world of Epicurus, and conceive the universe to be a fortuitous jumble of atoms, there is nothing grand in this idea. The clashing of atoms by blind chance has nothing in it fit to raise our conceptions, or to elevate the mind. But the regular structure of a vast system of beings, produced by creating power, and governed by the best laws which perfect wisdom and goodness could contrive, is a spectacle which elevates the understanding, and fills the soul with devout admiration.
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Every man feels that perception gives him an invincible belief of the existence of that which he perceives; and that this belief is not the effect of reasoning, but the immediate consequence of perception. When philosophers have wearied themselves and their readers with their speculations upon this subject, they can neither strengthen this belief, nor weaken it; nor can they shew how it is produced. It puts the philosopher and the peasant upon a level; and neither of them can give any other reason for believing his senses, than that he finds it impossible for him to do otherwise.
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We find sects and parties in most branches of science; and disputes which are carried on from age to age, without being brought to an issue. Sophistry has been more effectually excluded from mathematics and natural philosophy than from other sciences. In mathematics it had no place from the beginning; mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly, we find no parties among mathematicians, and hardly any disputes.
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It is natural to men to judge of things less known, by some similitude they observe, or think they observe, between them and things more familiar or better known. In many cases, we have no better way of judging. And, where the things compared have really a great similitude in their nature, when there is reason to think that they are subject to the same laws, there may be a considerable degree of probability in conclusions drawn from analogy.
The wisdom of God exceeds that of the wisest man, more than his wisdom exceeds that of a child. If a child were to conjecture how an army is to be formed in the day of battle--how a city is to be fortified, or a state governed--what chance has he to guess right? As little chance has the wisest man when he pretends to conjecture how the planets move in their courses, how the sea ebbs and flows, and how our minds act upon our bodies.
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[I]f a man bred to the seafaring life, and accustomed to think and talk only of matters relating to navigation, enters into discourse upon any other subject; it is well known, that the language and the notions proper to his own profession are infused into every subject, and all things are measured by the rules of navigation: and if he should take it into his head to philosophize concerning the faculties of the mind, it cannot be doubted, but he would draw his notions from the fabric of the ship, and would find in the mind, sails, masts, rudder, and compass.
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It is the invaluable merit of the great Basle mathematician Leonard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.
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In every case, we ought to act that part towards another, which we would judge to be right in him to act toward us, if we were in his circumstances and he in ours; or more generally - What we approve in others, that we ought to practise in like circumstances, what we condemn in others we ought not to do.