MS 842 (1908) - A Neglected Argument - Early Drafts

G77

of the Ss, 25 instances will be sufficient. But if we require two figures to be correct so that .005 is the largest error we shall not mind, we must

G77

of the Ss, 25 instances will suffice. If, however, we require two figures to be exact, so that .005 is the largest error we shall not mind, ten thousand instances must be collected.

G77

incompossible such predicates are "également possibles c'est-a-dire tells que nous soyons également indécis sur leur existance." But suppose I privately set down on paper the latitude and longitude of two points on the earth's surface and calculate the angular distance between them. It may range anywhere from 0° to 180°. How are you, without knowing anything at all about what points I have selected to subdivide 180° into small parts concerning which you are également indécis? Will you assume all angular distances to be equally likely, or will [you] assume that all equal circular areas of the earth are equally likely positions, in which case a distance between them of about 90° is

G81

if I were to grant that, as a general rule, the truth of the inductive conclusion would necessarily follow if we suppose the conditions of

[various equations]

G97

certain inductive inquiries that would otherwise be requisite. But they leave other inductions (such as that which led Mendeléef to enunciate his periodic law,) quite untouched, not explaining them in any sense.

The true guarantee of the validity of induction is that it is a method of reaching conclusions which, if it be persisted in long enough, will assuredly correct any error concerning future experience into which it may temporarily lead us. This it will do not by virtue of any deductive necessity (since it never uses all the facts of experience even of the past,) but because it is manifestly adequate, with the aid of retroduction and of deductions from retroductive suggestions, to discovering any regularity there may be among experiences, while