This would be the same thing as if one sought to prove by reason that there is no reason.For we only say that we know something by reason, when we are conscious that we could have known it, even if it had not been given to us in experience; hence rational knowledge and knowledge a priori are one and the same.It is a clear contradiction to try to extract necessity from a principle of experience (ex pumice aquam), and to try by this to give a judgement true universality (without which there is no rational inference, not even inference from analogy, which is at least a presumed universality and objective necessity).To substitute subjective necessity, that is, custom, for objective, which exists only in a priori judgements, is to deny to reason the power of judging about the object, i.e., of knowing it, and what belongs to it.It implies, for example, that we must not say of something which often or always follows a certain antecedent state that we can conclude from this to that (for this would imply objective necessity and the notion of an a priori connexion), but only that we may expect similar cases (just as animals do), that is that we reject the notion of cause altogether as false and a mere delusion.As to attempting to remedy this want of objective and consequently universal validity by saying that we can see no ground for attributing any other sort of knowledge to other rational beings, if this reasoning were valid, our ignorance would do more for the enlargement of our knowledge than all our meditation.For, then, on this very ground that we have no knowledge of any other rational beings besides man, we should have a right to suppose them to be of the same nature as we know ourselves to be: that is, we should really know them.I omit to mention that universal assent does not prove the objective validity of a judgement (i.e., its validity as a cognition), and although this universal assent should accidentally happen, it could furnish no proof of agreement with the object; on the contrary, it is the objective validity which alone constitutes the basis of a necessary universal consent.
Hume would be quite satisfied with this system of universal empiricism, for, as is well known, he desired nothing more than that, instead of ascribing any objective meaning to the necessity in the concept of cause, a merely subjective one should be assumed, viz., custom, in order to deny that reason could judge about God, *******, and immortality; and if once his principles were granted, he was certainly well able to deduce his conclusions therefrom, with all logical coherence.But even Hume did not make his empiricism so universal as to include mathematics.He holds the principles of mathematics to be analytical; and if his were correct, they would certainly be apodeictic also: but we could not infer from this that reason has the faculty of forming apodeictic judgements in philosophy also- that is to say, those which are synthetical judgements, like the judgement of causality.But if we adopt a universal empiricism, then mathematics will be included.
Now if this science is in contradiction with a reason that admits only empirical principles, as it inevitably is in the antinomy in which mathematics prove the infinite divisibility of space, which empiricism cannot admit; then the greatest possible evidence of demonstration is in manifest contradiction with the alleged conclusions from experience, and we are driven to ask, like Cheselden's blind patient, "Which deceives me, sight or touch?" (for empiricism is based on a necessity felt, rationalism on a necessity seen).And thus universal empiricism reveals itself as absolute scepticism.It is erroneous to attribute this in such an unqualified sense to Hume,* since he left at least one certain touchstone (which can only be found in a priori principles), although experience consists not only of feelings, but also of judgements.