Book: Mathematics, Matter and Method

Overview
Hilary Putnam gathers essays that probe the foundations and practice of philosophy through careful encounters with mathematics, physics, and language. The tone combines philosophical rigor with an attentiveness to the sciences: technical tools from logic and model theory are marshaled alongside broader metaphysical and semantic concerns. The result is a sustained attempt to reconcile the apparent objectivity of mathematical and scientific claims with the indeterminacies revealed by semantic theory.

Philosophy of Mathematics
Putnam defends the objectivity of mathematics while resisting simplistic Platonist pictures. Mathematical statements are treated as genuinely truth-apt, yet Putnam emphasizes that understanding mathematical truth requires attention to the methods and structures that give those statements their bite. He is critical of purely formalist or intuitionist accounts that strip mathematics of its explanatory role, arguing instead that mathematical practice and the role of proofs, models, and interpretation must shape philosophical accounts of mathematical ontology and truth.

Mathematics and Physics
A central preoccupation is the striking applicability of mathematics to empirical science. Putnam wrestles with why abstract structures should so effectively capture physical regularities, and he treats that problem as philosophically urgent rather than merely curious. Rather than offering a single reductive explanation, he frames the issue in terms of the interplay between theoretical virtues, model choice, and empirical success, suggesting that the success of mathematics is best understood through close attention to the ways scientific theories deploy mathematical resources.

Language, Meaning, and Model Theory
Putnam brings model-theoretic techniques to bear on problems of reference and meaning. He highlights how multiple, equally adequate semantic interpretations can be constructed for a given theory, producing a kind of indeterminacy about which ontology the theory truly commits to. This move undercuts naïve metaphysical readings that assume a one-to-one mapping from theory to world and forces a reconception of semantic and epistemic responsibility: semantics cannot be insulated from empirical and pragmatic considerations.

Methodological Commitments and Influence
The essays exemplify a methodological stance that takes scientific practice seriously without surrendering core philosophical questions to technical specialists. Putnam blends close logical scrutiny with broader metaphysical and epistemological reflection, insisting that philosophical accounts must be informed by, and responsive to, the conceptual resources developed in science and logic. The writings proved influential by showing how analytic philosophy could engage with mathematical practice, physical theory, and semantic theory in ways that reshape longstanding debates about realism, reference, and the nature of mathematical truth.