DEMONSTRATION.-MATHEMATICS. 21

ing chain, for instance, among the propositions of moral and metaphysical phenomena, is a different species of this same logic; but, number, quantity, and measure, having little to do with those sciences, mathematics must, from their very nature, be almost wholly inapplicable. An undue regard to mathematics has often been productive of very serious inconvenience, and of grievous mischief, when brought to bear upon those sciences: and, sometimes, even in physical pursuits much misconception has resulted. A mathematician can rise no higher than his data; and, eminently useful as his science is, not only in the descending scale, but in the examination of hypotheses, it is not within its compass to prove any simple physical proposition or first principle. All the mathematical proofs of the parallelogram of forces, for instance, are vicious, and merely arguments in a circle. Like all other sciences, Mathematic must depend upon

its own first principles: and its axioms are only general propositions raised upon individual, by induction. We know that things equal to the same are equal to one another. It is no innate scrap of knowledge; nor need we have recourse, with Plato, to a pre-existing state in which we learnt it. We know it only inductively from observation of the particulars, and it is absurd to suppose, that, in the demonstration of any proposition, we admit the particular by virtue of the axiom.

The origin of THE UNIVERSAL AND NEVER-FAILING EXPECTATION, that the same or similar causes will always be attended with the same or similar effects, an expectation upon which all physical science is founded, has been a subject of the ablest controversy. Hume denies it to be the result either of Experience or of Reason. It is not the result of Experience,' says he, for Experience is only of the past, and cannot pos

sibly extend to the future. If it be the result of Reasoning, produce the chain of Reasoning, which connects the two following propositions with one another; I have found that such an object has always been attended with such an effect; -(therefore) I foresee that other objects, which are in appearance similar, will be attended with similar effects. If there be any chain of reasoning between them, it is evidently not of the demonstrative kind; because the converse is equally conceivable. It is therefore of the probable or moral kind. Now all probable reasoning relates only to matter of fact or real existences. And all arguments concerning existence are founded on the relation of Cause and Effect. Our knowledge of that relation is derived entirely from Experience. And all Experimental conclusions proceed on the supposition, that the future will be conformable to the past. To endeavour therefore the proof of this last supposition by pro

bable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question.'

Such is the difficulty, respecting the very foundations of our knowledge, which is proposed by Hume. He attempts to solve it by attributing the Expectation to mere Custom or Habit, which he conceives may be ultimately referred to some instinct, or mechanical tendency. Reid, as usual, has recourse to an innate sense, instinct, or principle of our nature and Brown appears to acquiesce in the same solution.

The principles of connexion among our ideas, according to Hume, are Resemblance, Contiguity in time and place, and Cause and Effect. They have been more justly stated as Resemblance, Contiguity in time and place, under which the relation of Cause and Effect may be reduced, and Contrast. The ideas of men flow in trains of thought, connected by

some one or other of these three primary principles. Now, in the argument of Hume, a fallacy seems to lurk under the

6

proposition, that all probable or moral reasoning relates only to matter of fact, or real existence, and is therefore founded upon experience.' The first time a triangle, suppose an equilateral triangle, was presented to us, we had no conception of its properties. By attentive consideration we might demonstratively acquire the knowledge, that the sum of its angles is equal to two right angles. Now if another triangle, nearly similar, suppose an isosceles triangle, were presented to us; if we took it into consideration, I conceive, that, from our knowledge of the properties of the other, we should a priori suppose or infer, as an hypothesis, of this triangle also, that the sum of its angles was equal to two right angles and such an inference would have nothing whatever to do with Cause and Effect, and the truth, from which it is