The

of premises which the former possesses. principles from which the mathematician reasons are not, as some seem to think, the axioms, but the definitions. (No consequence whatever can be drawn from any, or all, of Euclid's axioms, that would not be as readily admitted as the axiom itself.*) Now every definition of a figure is that of an object more or less complex in the notion we form of it; and the more complex the notion, the more numerous the truths that can be predicated of it. The truths of geometry, again, are expressive only of relation; and thus, the number of figures being infinite, the number of relations infinite, there is no bound to the number of consequences to be drawn from a number of premises without bound. In morals, on the contrary, the principal subjects about which the reasoning is employed, are but few in number, and so simple(as happiness and misery)-as not to admit of definition; the number of truths therefore involved in our notion of these subjects must be confined within very narrow limits. Add to which, the truths of morals are not generally truths expressive of relation, but of some absolute quality; and absolute qualities, unlike relations, must always be circumscribed in number.

The civil laws of any country may be considered as a body of assumptions, supplying, in morals, the place of that extensive variety of principles from which the mathematician reasons; and, accordingly, we find that trains of demonstrative reasoning may be carried on to any conceivable extent, for the establishment of a legal point, and the whole justice of a case resolved into a hypothetical proposition, where it may be as easy to see whether or not the matter at issue fulfils the condition of the hypothesis, as it is to determine whether a given angle is really a right one, or a given figure a complete square. --Suppose the question to be, whether A or B ought to possess a certain property. By law, then, A has a title, if a certain deed be valid; but this deed is valid if C had the power of executing it; but C had the power of executing it if next heir to D; but C was next heir to D, if D had no lawful children; but D had no lawful children if his marriage was invalid; but his mar

riage was invalid, if contracted before the dissolution of a former one; but the former one was undissolved, if the woman was alive at a certain date. Upon this last hypothesis, the whole case is brought to depend; and it is demonstrated, as strictly as a mathematician can demonstrate a theorem, that, if D's first wife was alive at a supposed time, A is entitled to the property in dispute.

The want of such a body of principles as I here suppose civil laws to supply, must ever prevent morals from being a demonstrative science, in any practical sense of the term. But though not, in this sense, demonstrative, though its truths, so far as they are necessary truths, are either simply intuitive or but little removed from that, they possess, on that very account, so much, if possible, greater certainty. In a great many cases, too, the question of fact which a general truth in morals is applied to determine, is as easily brought within the range of that truth, as the question of fact in mathematics is brought within the range of the demonstrated conclusions: so that, if the principle in morals does not advance to meet the practical case, there is as little need of its advancing-the practical case being already sufficiently close to it. That we ought not to inflict gratuitous pain - an intuitive truth, or only two steps of reasoning distant from one-is, to the full, as certain as the conclusion of a mathematical demonstration of any length; and the question of fact, what does pro

duce gratuitous pain, is, in general, as easily determined, as that, whether an angle of a field is a right one or not.

In both sciences, then, we have universal truths applicable to cases of fact. In the one science, those truths are the results of long processes of reasoning, specific in their nature, and almost infinite in number. In the other science, the universal truths are intuitive, (or nearly so,) general in their nature, and few in number. In both, but principally in the latter, difficulties may occur in the practical application of the general principles: but in mathematics, no more than in morals, will the certainty of the principles either prevent us from assuming wrong data, or from making an erroneous application of principles to those data. If there are disputed or erroneous moral precepts, so there have been disputed or erroneous measurements and calculations.

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PART II.

DOCTRINES OF THE SCIENCE OF MORALS.

CHAPTER I.

MORAL AXIOMS, OR FIRST PRINCIPLES OF MORAL TRUTH.

THE following propositions seem to me to possess all the characteristics that are required to constitute first principles of necessary truth. They are true: their truth admits of no proof: it is im possible to conceive that they could ever become untrue, or that the contrary of them could ever be true.

At all events, I should desire it to be considered, whether any defects that may be found in them are inherent in the principle proceeded upon, or only belong to the execution. And, even in regard to defects in execution, I should hope the extreme difficulty of the undertaking will be kept in view: a difficulty, which, even in the case of