Du Bois-Reymond's philosophical ideas greatly influenced Ernst Cassirer, who argued for the importance of an objective and physical determinism alongside a subjective and spiritual freedom - a dualistic philosophy, probably inspired by Immanuel Kant's phenomenal and noumenal realms.

Cassirer's arguments, in turn, were a great influence on the early quantum physicists, including even Max Born, who was reluctant to press his discovery of irreducible chance in the form of quantum events that could only be predicted statistically.

In his book Determinism and Indeterminism in Modern Physics, Cassirer says of du Bois-Reymond

In his famous speech "Über die Grenzen des Naturerkennens" (1872) Emil du Bois-Reymond lifted the Laplacean formula out of its long oblivion and placed it at the focal point of epistemological and scientific discussion...

It claimed to fix once and for all the permanent, unalterable form of all scientific knowledge. At the same time, however, it regarded this very form as an insuperable limit. For du Bois-Reymond elevated scientific knowledge far above all accidental, merely empirical bounds. Within its own sphere he endowed it with a kind of omniscience. But this exaltation is only the precursor of its fall. From the heights of the strictest, most exact knowledge it is dashed into the abyss of ignorance, an ignorance from which nothing can deliver it, for it is not temporary and relative but final and absolute. If it were possible for human understanding to raise itself to the ideal of the Laplacean spirit, the universe in every single detail past and future would be completely transparent. "For such a spirit the hairs on our head would be numbered and no sparrow would fall to the ground without his knowledge. He would be a prophet facing forward and backward for whom the universe would be a single fact, one great truth." And yet this one truth would present only a limited and partial aspect of the totality of being, of genuine "reality." For reality contains vast and important domains which must remain forever and in principle inaccessible to the kind of scientific knowledge thus described. No enhancement or intensification of this knowledge can bring us a step nearer to the inner mysteries of being. Our knowledge dissolves into nothingness as soon as we leave the world of material atoms and enter the world of the "spirit," of consciousness. Here our understanding ends; for even with perfect, "astronomically exact" knowledge of all the material systems of the universe, including the system of our brain, it would still be impossible for us to comprehend how material being can give rise to the enigmatic appearance of consciousness.

Cassirer limits understanding to make room for spiritual mysteries, and follows positivism in denying the possibility of "explanations"

Accordingly the demand for "explanation" not only cannot be fulfilled here - strictly speaking it cannot even be raised: ignorabimus is the only answer that science can give to the question of the essence and origin of consciousness.

In the last decades of the nineteenth century the problem as thus put by du Bois-Reymond exercised a strong influence both on metaphysics and on the theory of scientific principles. Of course the attempt was made to escape from the radical consequences he had drawn. There was no ready surrender to the apodictic dogmatic conclusion of du Bois-Reymond's speech. But there seemed to be no doubt that here an important and pertinent problem had been raised with which epistemology and science had to wrestle using every power at their disposal. Even the neo-Kantian movement, which began in the early seventies almost at the time of du Bois-Reymond's speech, did not at first alter the situation substantially.

Bois-Reymond's speech [was made in] the period of controversy over materialism, when philosophy was confronted with the crisis of deciding whether to accept the guidance of scientific thought, which seemed to lead inevitably to a strictly mechanistic view of nature, or to maintain and defend its own position over against the scientific view, granting to the "spiritual" a different and special status.

For Cassirer, the work of du Bois-Reymond is to defend the spiritual elements of philosophy against materialism

It was here that du Bois-Reymond's speech took place, interpretable as a resolution of doubt and a way out of the dilemma. For it appeared to do justice to both claims, to satisfy in a certain sense the demands of materialism as well as those of systems having a place for the spiritual. Materialism and mechanism could find satisfaction in du Bois-Reymond's definition of science, for in this domain their basic maxims were not only recognized but set up as the sole and exclusive standard. "For us there exists nothing but mechanical knowledge," du Bois-Reymond emphasized, "no matter how miserable a substitute it is for true knowledge, and accordingly only one true form of scientific thought, that of mathematical physics." On the other hand, however, this form was rejected in regard to intrinsically transcendental problems. The scientist has to give up once and for all the idea of investigating these problems, leaving the way open for others to attempt purely speculative solutions. Thus the radical advocates of materialism as well as its bitterest opponents could appeal with equal right to du Bois-Reymond's basic thesis: the former, because they found enunciated in it the identity of scientific with materialistic, mechanistic thought, the latter because in addition a reality was assumed which was in principle inaccessible to scientific thought and which remained as a dark and impenetrable residue.

Du Bois-Reymond was quite wrong about determinism, which was equated with necessity in the eighteenth-century debates about freedom versus necessity. He is right that those debates turned into questions of freedom versus determinism in the nineteenth century, but they both assumed there were causal chains that threatened human freedom. See chapter 18 on "Cassirer's Thesis" in Ian Hacking's The Taming of Chance for more.

Hans Driesch (in his History and Theory of Vitalism, p.170) says that duBois-Reymond gave the latest anti-materialist teleological theories the name "Neov italism."