He imagined that materialist laws would apply to the macroscopic world, but that the micro-physical world might include a realm of indeterminism beyond the reach of the best experiments and observations.

He influenced Charles Sanders Peirce, who argued that no observational or experimental evidence would be perfect enough to "prove" that determinism was true.

Boutroux's most significant contribution was his 1874 The Contingency Of The Laws Of The Nature,, which included the idea of the emergence of different sets of laws at different levels of organization. The laws of physics could not "determine" the laws of chemistry. Laws of biology are not determinable from chemistry, laws of society are not the direct consequence of laws of biology, etc.

Boutroux gave the Gifford lectures of 1903-1905 on Science and Religion in Contemporary Philosophy, in which he applauded the internal and subjective views of William James, his radical empiricism, and his pragmatism.

It is an idea now grown familiar to scientists, that the mind takes an active part in the production of science. But, in saying this, they usually mean that the discovery of truth calls upon the mind for effort and inventiveness, for the intelligent use of all the resources at its disposal. They are not prepared to assert that science per se, science as constituted once for all, is merely a mode of human activity. Justified by facts, an hypothesis becomes law. The way in which the mind discovered this law has, hence-forward, no more than an historical interest.

For the philosophers with whom we are now dealing, on the contrary, the mind considered in its activity is not only the agent of science: it is veritably the subject and the substance thereof. This point of view is found to-day — maintained in an original manner — among the adherents of a famous philosophical school styling itself Pragmatistic.

According to the Pragmatists, not only does science assume an incessant contribution by the active mind which looks at things from its own standpoint and creates symbols adapted to its use; but she is predisposed to action, and has no other aim than to promote action. Go back to the origin of scientific concepts: always you will find that they denote methods to be followed in order to, lead up to the appearance of such or such phenomenon, in order to obtain such or such result. They are rules with regard to action, hypothetical imperatives: outside this signification, they have no real content. A proposition which does not engender practical consequences has no meaning. Two propositions which do not lead to a difference in the way of acting, present nothing but a verbal difference.

To say that the signification of scientific formulæ is purely practical, is to say that these formulæ refer, not to the past, but to the future. Science considers the past merely with a view to the future. She tells us what we must expect if we perform such or such act; what sensations will be produced within us, if, actually, we experience such or such sensation.

In this way is reached the pragmatistic idea of truth. Truth is not the agreement of our conceptions with such or such part of a whole, given to us ready-made, and answering to the name of world: it is, purely and simply, the service that a conception can render us, if we purpose such and such result. Truth stands for verifiability, and verifiability means aptness in guiding us through experience.