Some context: Cassirer is discussing the ‘problem’ that emerges when we subsume all phenomenon under a logical framework. A variety of special problems arise here, but perhaps most fundamentally, the problem of the domination of our thought, perspectivity, expectation and understanding by force of an abstract system of mathematical and ‘logical’ mapping, which is disembodied and obscure to all non-specialists.

A further problem ensues, however, in that this domination forces us into an untenable relational position where meaning dissolves into structured analysis, statistics, and ‘logical’ forms which are both exotic and fictional: they correspond to nothing in our human experience or emotional relationship, and thus incline us to depart from participation into theory and speculative interpretation of results.

Further, the species of ‘signs’ thus emergent is not natural to our relationships or felt senses of being. It is, like deep space, both inhospitable and alienating.

“What the physicist seeks in phenomenon is a statement of their necessary connection. But in order to arrive at this statement, he must not only leave behind him the immediate world of sensory impressions, but must seemingly turn away from them entirely. The concepts with which he operates, the concepts of space and time, of mass and force, of material point and energy, of the atom or the ether, are free “fictions”.

Cognition devises them in order to dominate the world of sensory experience and survey it as a world ordered by law, but nothing in the sensory data themselves immediately corresponds to them, yet although there is no such correspondence— and perhaps precisely »because there is none — the conceptual world of physics is entirely self-contained.

Each particular concept, each special fiction and sign is like the articulated »word of a »language meaningful in itself and ordered according to fixed rules. In the very beginning of modern physics, in Galileo, we find the metaphor that the “book of nature” is written in mathematical language and can only be read through mathematical ciphers.

And since then, the entire development of exact natural science shows that every step forward in the formulation of its problems and concepts has gone hand in hand with the increasing refinement of its »system of signs. A clear understanding of Galileo’s mechanics became possible only when the universal logical locus of these concepts was, as it were, determined and a universally valid mathematical-logical logical sign for them was created in the algorism of the differential calculus.

And then, taking as his point of departure the problems connected with the discovery of the analysis of infinity, Leibniz was soon able to formulate the universal problem inherent in the function of symbolism, and to raise the universal “characteristic” to a truly philosophical plane. In his view, the logic of things, i.e., of the material concepts and relations on which the structure of science rests, cannot be separated from the logic of signs.

For the sign is no mere accidental cloak of the idea, but its necessary and essential organ. It serves not merely to communicate a complex and given thought-content, but is an instrument, by means of which this content develops and fully defines itself. The conceptual definition of a content goes hand in hand with its stabilization in some characteristic sign. Consequently, all truly strict and exact thought is sustained by the »symbolics and »semiotics on which it is based.

Every “law” of nature assumes for our thinking the form of a universal “formula”—and a formula can be expressed only by a combination of universal and specific signs. Without the universal signs provided by arithmetic and algebra, no special relation in physics, no special law of nature would be expressible. It is, as it were, the fundamental principle of cognition that the universal can only be perceived in the particular, while the particular can only be thought of in reference to the universal.”

— Ernst Cassirer, The Philosophy of Symbolic Forms, Presentation of the Problem, The Problem of Meaning

{I have inserted paragraph breaks inserted in this long paragraph to facilitate easier reading by modern readers}