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A Guide to John Locke's Essay concerning Human Understanding - Demonstrable Rules

The moral rectitude of actions of a particular sort, Locke held, is wholly constituted by the demonstrable relation between our clear ideas of such actions and the equally clear conception of the moral law. Indeed, this relation is often so obvious—as, for example, in the cases of "murder" and "theft"—that the moral condemnation comes easily to be included as a part of our complex idea of the action itself. [Essay II xxviii 14-16] Because both my contemplated action and the moral rule can be abstractly conceived as mixed modes, the applicability of this rule to that action can be determined with perfect certainty. It is a further question whether or not the moral rule itself is demonstrably true.

Locke believed that it often is. To be sure, reliance upon an axiomatic deduction of morality from a fixed set of putatively indubitable first principles would be neither effective nor intellectually sound. [Essay IV xii 4-5] Nevertheless, demonstration is possible in principle wherever we have clear ideas, and Locke was careful to emphasize that indubitable knowledge of relations does not presuppose perfect clarity with respect to the relata. We might know that one automobile is faster than another, for example, even if we had little information about the mechanical differences that produce this result. Our awareness of relations commonly rises to a level of certainty greater than our knowledge of the things among which they hold. [Essay II xxv 4-8]

What counts toward demonstrability, on Locke's view, is the possibility of perceiving intermediate links between our ideas. Since the mixed modes of human action and the concepts of moral rules are both abstract ideas that serve as their own archetypes, it follows that the relations between them are fully demonstrable. [Essay IV iv 7-9] In this respect, at least, morality is on an equal footing with mathematics. Where there is no Property, there is no Injustice, is a Proposition as certain as any Demonstration in Euclid: For the Idea of Property, being a right to any thing; and the Idea to which the name Injusticeis given, being the Invasion or Violation of that right; it is evident, that these Ideas being thus established, and these Names annexed to them, I can as certainly know this Proposition to be true, as that a Triangle has three Angles equal to two right ones. Again, No Government allows absolute Liberty: The Idea of Government being the establishment of Society upon certain Rules or Laws, which require Conformity to them; and the Idea of absolute Liberty being for any one to do whatever he pleases; I am as capable of being certain of the Truth of this Proposition, as of any in Mathematicks. [Essay IV iii 18] The apparent advantage of mathematical over moral reasoning, Locke speculated, rests only on the relative ease with which we can represent mathematical relationships in perspicuous diagrams and the relative absence of partisan concerns. Were we to approach moral reasoning with the same degree of objectivity we commonly bring to mathematical thinking, he argued, we would achieve the same quality of demonstrable certainty about substantive moral truths. [Essay IV iii 19-20]