"But, one will say, if raw experience can not legitimatize reasoning by recurrence, is it so of experiment aided by induction? We see successively that a theorem is true of the number 1, of the number 2, of the number 3 and so on; the law is evident, we say, and it has the same warranty as every physical law based on observations, whose number is very great but limited. But there is an essential difference. Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us. Mathematical induction, that is, demonstration by recurrence, on the contrary, imposes itself necessarily, because it is only the affirmation of a property of the mind itself."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Academics from FrancePhilosophers from FranceMathematicians from FrancePhysicists from FranceEngineers from France
Original Language: English
Available Languages (1)
Sources
Ch. I. (1905) Tr. George Bruce Halstead
https://en.wikiquote.org/wiki/Henri_Poincar%C3%A9
Revision History
No revisions have been submitted for this quote.
Categories
Henri Poincaré
90 quotes on TrueQuotesView all quotes by Henri Poincaré →
Related Quotes
"We do not have and cannot have any means of discovering whether or not we are carried along in a uniform motion of tr…"
"Tout le monde y croit cependant, me disait un jour M. Lippmann, car les expérimentateurs s'imaginent que c'est un thé…"
"Le savant digne de ce nom, le géomètre surtout, éprouve en face de son œuvre la même impression que l'artiste ; sa jo…"
"La tâche de l'éducateur est de faire repasser l'esprit de l'enfant par où a passé celui de ses pères, en passant rapi…"
"C'est même des hypothèses simples qu'il faut le plus se défier, parce que ce sont celles qui ont le plus de chances d…"
"Que l'on cherche à se représenter la figure formée par ces deux courbes et leurs intersections en nombre infini dont …"
"Comme nous ne pouvons pas donner de l'énergie une définition générale, le principe de la conservation de l'énergie si…"
"What is objective must be common to many minds and consequently transmissible from one to the other, and as this tran…"
"There is no science apart from the general. It may even be said that the very object of the exact sciences is to spar…"
"La pensée ne doit jamais se soumettre, ni à un dogme, ni à un parti, ni à une passion, ni à un intérêt, ni à une idée…"