Sidgwick gives various tests for highest certainty. When he applies these tests to commonsense morality, he finds nothing of highest certainty. In contrast, when he applies these tests to his own axioms, he finds these axioms to have highest certainty. The axioms culminate in

Benevolence: “Each one is morally bound to regard the good of any other individual as much as his own, except in so far as he judges it to be less, when impartially viewed, or less certainly knowable or attainable by him.”

The axioms face challenges from two sides.

First, one test requires that a claim not be denied by someone of whom one has no more reason to suspect of error than oneself. For Sidgwick, then, the egoist must not deny the axioms. But it would seem that an egoist would reject benevolence.

Second, Sidgwick thinks he must show that the commonsense moralist agrees to the axioms. Benevolence seems to say that the only reason for departing from being bound to treat others like oneself is that more good would be produced. But the commonsense moralist will not agree that this is the only reason.

In reply to the threat of an egoist's disagreement, this essay argues that many of the axioms should be read as having as their antecedent “from the point of view of the universe.” The essay replies to the objection that this makes these axioms analytic.

In reply to the threat of a commonsense moralist's disagreement, this essay argues that each axiom states, in effect, a prima facie duty. The argument against the commonsense moralist concerns not benevolence but whether there are further duties that pass the tests. The essay raises the worry that here Sidgwick is unfair since sometimes he criticizes all-things-considered versions of commonsense duties; such criticisms would count against benevolence as well.

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