become a necessary complement of the Logic of the Understanding; and a considerable portion, if not the whole, of the Hegelian Dialectic must be incorporated with the Formal Science of Kant. To shew that such a treatment, instead of being a completion, would be a corruption of the Science,— instead of making Logic fruitful of truths, would make it prolific of chimeras,-instead of attaining knowledge, would aim at impossibilities, has been one of the main objects of the preceding inquiry.

CHAP. VI.

ON LOGICAL NECESSITY AND THE LAWS OF THOUGHT.

THE result of the two preceding chapters has been to mark off two classes of Necessary Truths, which, though dependent, as all such truths must be, upon mental laws and limitations, do not, properly speaking, exhibit the operation of Laws of Thought, nor come within the province of Logic. We have now to examine the psychological character of the laws of pure thinking, and the kind of necessity exhibited in consequence by strictly logical processes. The following passage from Mr. Mill's Logic may serve to introduce the subject.

"This maxim, (the dictum de omni et nullo,) when considered as a principle of reasoning, appears united to a system of metaphysics once indeed generally received, but which for the last two centuries has been considered as finally abandoned, though there have not been wanting, in our own day, attempts at its revival. So long as what were termed Universals were regarded as a peculiar kind of substances, having an objective existence distinct from the individual objects classed under

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them, the dictum de omni conveyed an important meaning; because it expressed the intercommunity of nature, which it was necessary upon that theory that we should suppose to exist between those general substances and the particular substances which were subordinated to them. That every thing predicable of the universal was predicable of the various individuals contained under it, was then no identical proposition, but a statement of what was conceived as a fundamental law of the universe. The assertion that the entire nature and properties of the substantia secunda formed part of the properties of each of the individual substances called by the same name; that the properties of Man, for example, were properties of all men; was a proposition of real significance when Man did not mean all men, but something inherent in men, and vastly superior to them in dignity. Now, however, when it is known that a class, an universal, a genus or species, is not an entity per se, but neither more nor less than the individual substances themselves which are placed in the class, and that there is nothing real in the matter except those objects, a common name given to them, and common attributes indicated by the name; what, I should be glad to know, do we learn by being told, that whatever can be affirmed of a class, may be affirmed of every object contained in the class? The class is nothing but the objects contained in it: and the dictum de omni

merely amounts to the identical proposition, that whatever is true of certain objects, is true of each of those objects. If all ratiocination were no more than the application of this maxim to particular cases, the syllogism would indeed be, what it has so often been declared to be, solemn trifling. The dictum de omni is on a par with another truth, which in its time was also reckoned of great importance, 'Whatever is, is;' and not to be compared in point of significance to the cognate aphorism, 'It is impossible for the same thing to be and not to be;' since this is, at the lowest, equivalent to the logical axiom that contradictory propositions cannot both be true. To give any real meaning to the dictum de omni, we must consider it not as an axiom but as a definition; we must look upon it as intended to explain, in a circuitous and paraphrastic manner, the meaning of the word class"."

I quote the above passage from a work of high and in many respects of deserved reputation, as a remarkable instance of the total misconception of the nature and purpose of Logic, arising from that erroneous view to which I have before alluded, which regards the Aristotelian and the Baconian Organon as forming portions of the same system, and as subservient to the same end, that of physical investigation or the discovery of "fundamental laws of the universe." That the deductive method

a Mill's Logic, vol. i. p. 234.

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may be advantageously applied to purposes of physical inquiry is unquestionable; and in this respect Mr. Mill has certainly not underrated its value. Any single proposition of any syllogism or chain of syllogisms may thus materially contain a fact or a law of nature: but that the fundamental principle on which all reasoning is supposed to depend can by any possibility exhibit a law of external nature and not a law of mind, is a supposition which, if tenable, would make a science of Mill Logic impossible. If the dictum de omni were, as Mr. Mill supposes, formed on the hypothesis that universals had a distinct existence in nature apart from the mind that contemplates them, Logic might be entitled to rank with Optics or Astronomy, as a science of the laws of this or that order of natural phenomena; or it might perhaps aspire to the character of a general Cosmology, including these and other physical sciences as subordinate branches; but it could not pretend to the slightest knowledge of the laws which the mind obeys in thinking; and its principles, as mere generalizations from experience, could never attain to more than a physical necessity, as the statement of certain facts in the existing constitution of the world.

A science is never ultimately benefitted by dissembling any conclusion to which its principles appear fairly to lead; still less can it gain by adulterating those principles themselves with foreign matter, borrowed from other departments, in the