## Modes of induction as distinguishing the modes of natural science

(A note on John of St. Thomas. Curs. Phil 1. p. 200)

Knowledge is from sense and so from induction. Either the term of the induction can be reached by a single instance, or many are required. But just as many is indefinite the sufficiency of the manifestation is indefinite. The first sort of induction is the most common kind, used in metaphysics, mathematics, logic, grammar, etc.

(Note – this does not remove the need to pick the best instance that suffices. If one proved Euclid’s interior angle proof with a right triangle, and the right triangle as the opposite angle, we could easily think that the proof rested on the equality of right angles.)

But the study of nature, as a rule, involves the second kind of induction, and so as a rule the term of the induction is always indefinite. New refuting evidence is always a possibility. Though this is true as a rule, it is not true without exception. That motion is continuous, or that a principle is ordered to a term, or that motion actualizes some potential are not the sort of inductions that become more manifested by multiplication of experiences. Any particular instance of experience suffices to manifest them, which is to say that the sort ofÂ  multiplication that is required is not of the same sort as the multiplication that, say, moves experience from “a theory” to “a law”.

1. #### thenyssan said,

July 17, 2011 at 4:11 am

Forgive the extremely dense question, but…what sort of multiplication is required then? I suddenly don’t understand induction.

2. #### Brandon said,

July 17, 2011 at 9:08 am

I don’t know if this is precisely what James has in mind, but every induction presupposes a prior division. (This is why medieval logicians talk so much about division and definition: roughly, division is to induction as definition is to demonstration.) So the multiplication has to do with the kind of division proposed. In the way we often think about induction, the division is to singulars; because these are indefinitely many, taking them into account in induction always leaves open the possibility of refutation. But other kinds of division are possible, one in which the division is to form or nature or universal, as we find it in things. You don’t have to investigate every right triangle on a flat surface to see that the Pythagorean theorem is true; generally seeing it in one, one already see how it would be multiplied, how it would apply to every other singular instance.

Poincare somewhere talks about how the induction used in mathematics differs from that used by physicists in that the induction used by mathematicians is infinite in a way the induction of the physicists cannot be; it seems to be a similar point, looked at from a different direction.

3. #### James Chastek said,

July 17, 2011 at 10:08 am

The text I’m working from in JoST is this:

All our speculative knowledge depends on induction as it depends on sense and experience, so if the universal propositions of a science are not abstracted and common in such a way that any individual can manifest the truth of them, but rather depends on the enumeration and experience of many things (as in natural science) they are not certain as the more abstract and common sciences are – sc. metaphysics and mathematics – the principles of which have total certitude in a single individual: as “anything either exists or does not”.

Omnis nostro speculatio dependet ab inductione sicut dependet a sensu et experientia; unde si propositionones universales alicuius scientiae non sunt ita abstractae et communes quod ex quocumque individuo manifestari possit ipsarum veritas, sed a plurimum numeratione et experientia pendeat sicut scientiae naturales, non sunt ita certae sicut aliae scientiae abstratiores et communiores, ut metaphs. et mathemat. quorum principia in uno individuo habent totam certitudinem ut: quodlibet est vel non est.

JoST isn’t denying any sort of need to multiply out experience here, but there is a need to multiply out experience in natural science (and moral and political science too, FWIW) that is not necessary in mathematics or metaphysics. Oddly enough, this doesn’t make nat. Sci harder to learn than metaphysics, and so there is some sort of broader experience that is necessary for metaph, even though the nature of the induction is more immediate in it and less dependent on experience.