Felix Kaufmann, Cassirer’s Theory of Scientific Knowledge (1949)

Felix Kaufmann’s contributed essay reconstructs Cassirer’s epistemology through its philosophical origins, its interpretation of mathematics and modern physics, and its relations to logical positivism and Dewey’s instrumentalism. Its nine sections move from Kant and Hegel through scientific concept formation, relativity, quantum theory, mathematical foundations, and perception, before assessing contemporary affinities and disagreements. Kaufmann’s central claim is that Cassirer preserves the transcendental method by distinguishing its enduring task—clarifying the conditions of objective experience—from Kant’s historically limited scientific commitments.

The opening sections situate Cassirer within the Marburg school and Hermann Cohen’s program of understanding Kant better than Kant understood himself. The “Copernican Revolution” does not replace an object-centered metaphysics with an ego-centered one. It changes the question: philosophy investigates the logical structure of experience rather than deriving knowledge from independently existing subjects and objects.

Kant's transcendental method starts from the fact of (scientific) experience and seeks to determine how this fact is possible.

Here the a priori names constitutive conditions of experience, not truths about a world beyond possible experience. Ontological claims can nevertheless retain significance when reinterpreted as regulative principles of inquiry. The unity of knowledge is a task rather than a metaphysically guaranteed possession. Hegel supplies a complementary insight: this unity becomes intelligible through the development of knowledge, whose earlier stages cannot simply be discarded.

Kaufmann then explains Cassirer’s transition from substance-concepts to function-concepts. Traditional abstraction treats concepts as collections of shared qualities, but this cannot explain either their purposive selection or their capacity to organize possible cases. Scientific concepts instead establish relations through which objects can be ordered. The transition from Aristotelian to Galilean and Newtonian physics exemplifies the replacement of hierarchies of intrinsic qualities by systems of laws. Scientific unity is consequently both systematic and historical: changing theories must remain comparable through standards that make their relative achievements intelligible.

It would indeed be impossible to demonstrate the advantage of the new system, unless there were invariant standards of comparability.

Relativity tests this account. Kaufmann concedes that Kant’s claim for the permanent physical validity of Euclidean geometry cannot survive Einstein’s general theory. Cassirer’s defense concerns the transcendental method, not that particular commitment. Geometry must be understood through its function in organizing physical knowledge, while “objectivity” itself requires philosophical clarification rather than uncritical acceptance of a physicist’s terminology. Kaufmann also ventures a stronger claim for the aprioricity of certain topological features, particularly four-dimensional space-time, presenting this as his own suggested extension.

Quantum physics similarly demands conceptual reconstruction rather than abandonment of critical philosophy. Cassirer interprets causality as a regulative commitment to continued inquiry, acknowledging that this departs from Kant’s attempted deduction. His distinction between measurement statements, laws, and principles prevents scientific knowledge from being flattened into an aggregate of observations.

Whereas facts are brought into a definite order by laws, the laws themselves are integrated into a higher unity by principles, such as the principle of the conservation of energy or the principle of least action (which is the most general of all physical principles).

Statistical mechanics already demonstrates that successful explanation need not determine every individual movement or answer every conceivable question. Quantum indeterminacy therefore does not necessarily signify skeptical defeat. The supposed demand to locate independently constituted particles absolutely loses its force when physical objects are understood as defined through the relations of a theory.

The sections on mathematics and symbolic forms generalize this account of objectification. Kaufmann endorses Cassirer’s criticisms of Russell’s reduction of number to class, Brouwer’s interpretation of mathematical time, and Hilbert’s identification of mathematical objects with visible marks. Mathematics concerns possibilities that perception cannot itself produce; experience selects among them in application. Symbols help actualize and differentiate meanings without creating them arbitrarily. Scientific symbolism belongs within a wider philosophy of cultural forms through which human beings construct an ordered world.

Perception supplies an especially important test. Color, size, and shape constancy undermine the sensationalist picture of perception as copied stimulation. Cassirer connects perceptual organization with mathematical invariance under transformations, while recognizing that perceptual tendencies are not identical with exact mathematical groups. Structural organization thus begins before scientific theorizing.

The final sections locate Cassirer between competing philosophical schools. His scientific orientation brings him close to logical positivism, but his treatment of metaphysics, rejection of physicalism, and opposition to nominalism distinguish him from it.

We might say with equal right that one of the aims of Cassirer's theory of knowledge is to disontologize philosophy without destroying it.

Dewey offers another significant affinity: both treat knowledge as the outcome of inquiry and understand coherence through methodological principles rather than mere consistency. Kaufmann sides with Cassirer on the autonomy of logic, mathematics, and meaning, but credits Dewey with a superior analysis of testing and warranted assertion. Cassirer attends chiefly to achieved theoretical organization; Dewey examines the movement from problematic situations to their resolution. This qualified comparison gives the essay its evaluative force: Cassirer’s historically informed philosophy illuminates scientific objectivity without legislating to science, yet leaves the detailed criteria of verification insufficiently developed.