Horkheimer saw mathematical formalism as itself a kind of metaphysics

Evidence

In addition to his distaste for their fetishism of facts, Horkheimer further objected to the Logical Positivists’ reliance on formal logic to the exclusion of a substantive alternative. To see logic as an analogue of mathematics, he held, was to reduce it to a series of tautologies with no real meaning in the historical world. To believe that all true knowledge aspired to the condition of scientific, mathematical conceptualization was a surrender to a metaphysics as bad as the one the positivists had set out to refute. — Martin Jay, The Dialectical Imagination, 245

Categorization

• XREF: Prefigures the later ‘positivism dispute’ with Popper and connects to Critical Theory’s ongoing refusal of scientism. — connects to: Denying metaphysics in favor of science is itself a metaphysical position — Wael Hallaq, Restating Orientalism: A Critique of…, 294; Positivist philosophy imposes an empirical a priori that cannot be transcended — Herbert Marcuse, One-Dimensional Man: Studies in the…, 671; Mathematical certainty led philosophers to suppose thought is superior to sense — Bertrand Russell, History of Western Philosophy, 203 (+1 more)

Broader Connections

• Denying metaphysics in favor of science is itself a metaphysical position #expands (0.85) — Wael Hallaq, Restating Orientalism, 294
• Positivist philosophy imposes an empirical a priori that cannot be transcended #expands (0.78) — Herbert Marcuse, One-Dimensional Man, 671
• Mathematical certainty led philosophers to suppose thought is superior to sense #expands (0.75) — Bertrand Russell, History of Western Philosophy, 203