If the thought and understanding were alone capable of fixing the boundaries of right and wrong, the character of virtuous and vicious either must lie in some relations of objects, or must be a matter of fact, which is discovered by our reasoning.  This consequence is evident.  As the operations of human understanding divide themselves into two kinds, the comparing of ideas, and the inferring of matter of fact; were virtue discovered by the understanding; it must be an object of one of these operations, nor is there any third operation of the understanding. which can discover it.  There has been an opinion very industriously propagated by certain philosophers, that morality is susceptible of demonstration; and though no one has ever been able to advance a single step in those demonstrations; yet it is taken for granted, that this science may be brought to an equal certainty with geometry or algebra.  Upon this supposition. vice and virtue must consist in some relations; since it is allowed on all hands, that no matter of fact is capable of being demonstrated.  Let us, therefore, begin with examining this hypothesis, and endeavour, if possible, to fix those moral qualities, which have been so long the objects of our fruitless researches.  Point out distinctly the relations, which constitute morality or obligation, that we may know wherein they consist, and after what manner we must judge of them.

If you assert, that vice and virtue consist in relations susceptible of certainty and demonstration, you must confine yourself to those four relations, which alone admit of that degree of evidence; and in that case you run into absurdities, from which you will never be able to extricate yourself.  For as you make the very essence of morality to lie in the relations, and as there is no one of these relations but what is applicable, not only to an irrational, but also to an inanimate object; it follows, that even such objects must be susceptible of merit or demerit.  Resemblance, contrariety, degrees in quality, and proportions in quantity and number; all these relations belong as properly to matter, as to our actions, passions, and volitions.  It is unquestionable, therefore, that morality lies not in any of these relations, nor the sense of it in their discovery.

[Footnote 13.  As a proof, how confused our way of thinking on this subject commonly is, we may observe, that those who assert, that morality is demonstrable, do not say, that morality lies in the relations, and that the relations are distinguishable by reason.  They only say, that reason can discover such an action, In such relations, to be virtuous, and such another vicious.  It seems they thought it sufficient, if they could bring the word, Relation, into the proposition, without troubling themselves whether it was to the purpose or not.  But here, I think, is plain argument.  Demonstrative reason discovers only relations.