This statistical regularity in moral affairs fully establishes their being under the presidency of law. Man is now seen to be an enigma only as an individual; in the mass he is a mathematical problem. It is hardly necessary to say, much less to argue, that mental action, being proved to be under law, passes at once into the category of natural things. Its old metaphysical character vanishes in a moment, and the distinction usually taken between physical and moral is annulled, as only an error in terms. This view agrees with what all observation teaches, that mental phenomena flow directly from the brain.

As a single atom man is an enigma: as a whole he is a mathematical problem. As an individual he is a free agent, as a species the offspring of necessity.

...while the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty.

While the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to. Individuals vary, but the percentages remain constant

A strange enigma is man

Man is an enigma whose knot has not ceased to occupy observers. The contradictions that he contains astonish reason and impose silence on it. So what is this inconceivable being who carries within him powers that clash and who is obliged to hate himself in order to esteem himself?

It is number which regulates everything and it is measure which establishes universal order.... A quiet peace, an inviolable order, an inflexible security amidst all change and turmoil characterize the world which mathematics discloses and whose depths it unlocks.

Man himself is an enigma in motion; his questions never stay asked; whereas the mold, the footprint, and by natural extension, the statue itself, like the vaults, the arches, the temples with which man records his own passing, remain immobile and fix a moment of man’s life, upon which one might endlessly meditate.

Man is a mystery, a mystery to the investigating mind of the researcher into nature; but more so indeed is man a mystery to himself. Yet there is a solution of this mystery — a solution which is not new, which is older than the enduring hills. (Ch 2)

Everything is governed by one law. A human being is a microcosmos, i.e. the laws prevailing in the cosmos also operate in the minutest space of the human being.

[O]nce man is declared “the measure of all things,” there is no longer a true, or a good, or a just, but only opinions of equal validity whose clash can be settled only by political or military force; and each force in turn enthrones in its hour of triumph a true, a good, and a just which will endure just as long as itself.

As mathematical and absolute certainty is seldom to be attained in human affairs, reason and public utility require that judges and all mankind in forming their opinions of the truth of facts should be regulated by the superior number of the probabilities on the one side or the other whether the amount of these probabilities be expressed in words and arguments or by figures and numbers.

Man is the matter of the cosmos, contemplating itself.

Man is the measure of all things: of things which are, that they are, and of things which are not, that they are not.