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is of substances in their properties, those interactions by which they define each other; its absolute knowledge is one of forms, of regulative principles, which neither matter nor mind can escape. This fundamental difference between intuitive and sensational knowledge, no analysis has been able to break down or obscure. Truths of the higher mathematics rise quite above experience, and come at once with irresistible authority to it. It is strange that Hamilton should give us a direct knowledge of matter, and yet regard all knowledge as relative.

This assertion, that all our knowledge is relative, has gained great currency; yet we can look on it only as one of those false deductions which have followed the empirical philosophy, and are fitted to sustain it. If all our knowledge comes from experience, it is all tainted by the quality of the senses, and hence is all relative to their forms and powers of discrimination. Pure knowing, pure in its object, and pure in its subjective process, becomes impossible. Yet direct insight into abstract relations is evidently of this character, and evinces its nature by the uniformity and force of the conclusions incident to it. Empirical philosophy has no way of explaining axiomatic truth and demonstrative reasoning. The reference of the necessity of these convictions to inheritance is most lame. They pertain to abstract truths often very unfamiliar, and take effect at once in connection with quite novel statements. Matters of experience under the daily observation of many generations as the rising of the sun, the blackness of crows, the whiteness of swans, carry with them by inheritance or otherwise no such necessity. That the truth of mathematics can be no other than they are, is a conviction that the mind takes with it to the study of nature, not one that it derives from nature. Of all branches of knowledge mathematics may advance most rapidly, and divorce itself