And, in truth, there is scarcely any investigation in the whole body of a science requiring so high a degree of analysis and abstraction, as the inquiry, what the science itself is; in other words, what are the properties common to all the truths composing it, and distinguishing them from all other truths. Many persons, accordingly, who are profoundly conversant with the details of a science, would be very much at a loss to supply such a definition of the science itself as should not be liable to well-grounded logical objections. From this remark, we cannot except the authors of elementary scientific treatises. The definitions which those works furnish of the sciences, for the most part either do not fit them--some being too wide, some too narrow--or do not go deep enough into them, but define a science by its accidents, not its essentials; by some one of its properties which may, indeed, serve the purpose of a distinguishing mark, but which is of too little importance to have ever of itself led mankind to give the science a name and rank as a separate object of study. The definition of a science must, indeed, be placed among that class of truths which Dugald Stewart had in view, when he observed that the first principles of all sciences belong to the philosophy of the human mind. The observation is just; and the first principles of all sciences, including the definitions of them, have consequently participated hitherto in the vagueness and uncertainty which has pervaded that most difficult and unsettled of all branches of knowledge. If we open any book, even of mathematics or natural philosophy, it is impossible not to be struck with the mistiness of what we find represented as preliminary and fundamental notions, and the very insufficient manner in which the propositions which are palmed upon us as first principles seem to be made out, contrasted with the lucidity of the explanations and the conclusiveness of the proofs as soon as the writer enters upon the details of his subject. Whence comes this anomaly? Why is the admitted certainty of the results of those sciences in no way prejudiced by the want of solidity in their premises? How happens it that a firm superstructure has been erected upon an unstable foundation? The solution of the paradox _is_, that what are called first principles, are, in truth, _last_ principles. Instead of being the fixed point from whence the chain of proof which supports all the rest of the science hangs suspended, they are themselves the remotest link of the chain. Though presented as if all other truths were to be deduced from them, they are the truths which are last arrived at; the result of the last stage of generalization, or of the last and subtlest process of analysis, to which the particular truths of the science can be subjected; those particular truths having previously been ascertained by the evidence proper to their own nature.