The divagations that follow concern “metamoral” problems (the meaning of this term will be clarified) together with some “moral” indications. From a mathematical point of view, the following observations are manifest, although they are explained with more words than necessary (for the benefit of the nonmathematical reader). There are no historical or philological references: The professional historian or philosopher is in a better position to provide them than is the writer, who is a mathematician by profession, and the nonspecialist reader can find better sources by consulting any good history of philosophy. Occasional references to Pascal, Bentham, and others are rather more “historical fiction” than historical, since the author felt it was more important to indicate the sources of certain stimuli than to ascertain historical exactness in the attribution of such and such a thought to Tom or Dick or Harry.

The nonmathematical reader may wish to skip over (at least on a first reading) the mathematical parts.

As a brief clarification of the term “metamoral,” note that: I refer to all research aimed at establishing an organized system of prescriptions (i.e., a “moral theory”) as “moral research”; to all behavior aimed at influencing one's own or others' behavior, in particular moral theories, as “moral activity”; and finally to all research aimed at ascertaining possible moral theories, the conditions in which they acquire meaning, and their connections to the various cognitive situations with which they must coexist, as “metamoral research.”