Mathematics, Matter and Method (Philosophical Papers, Volume 1)

The no-miracles argument holds that the predictive and technological success of mature science would be an inexplicable coincidence if its theories were not at least approximately true, so realism is the best explanation of that success. Putnam is the philosopher most closely associated with the formulation, and he develops the line of thought in essays from this period. Critics have challenged it on several fronts. Larry Laudan's pessimistic meta-induction points to successful theories that were later abandoned, and Bas van Fraassen's constructive empiricism denies that success requires truth. Both responses remain central to the scientific realism debate.

Yes. In his paper on the logic of quantum mechanics, Putnam argued that the apparent paradoxes of quantum theory can be dissolved by adopting a non-distributive logic in which the usual distributive law fails, treating the choice of logic as empirical in the way a choice of geometry is. The proposal drew sharp replies, including from Michael Dummett, who contended that revising logic changes the meaning of the connectives. Putnam himself later abandoned the position. The paper nonetheless remains a landmark case in discussions of whether logic is a priori.

The collection contains the material in which Putnam presses the idea, shared with Quine, that mathematics earns its standing through its role in our best physical theories. This links the volume to his short book Philosophy of Logic, where the argument receives a compact statement. Together the two works established indispensability as a standard route to mathematical realism. Later critics such as Hartry Field attempted to show that physics can be reformulated without quantifying over mathematical objects, which would undercut the premise that mathematics is indispensable.

The volume represents Putnam's metaphysical and scientific realism, which he later repudiated. In Realism and Reason and Reason, Truth and History he turned against metaphysical realism and developed internal realism, and still later he moved toward natural realism. Readers should therefore treat the book as a record of an earlier stage, not as his settled position. Reading it alongside the later volumes of the Philosophical Papers shows how arguments he once used in favor of realism, including the appeal to the success of science, were later reexamined.

The papers on space and geometry examine whether the geometry of physical space is a matter of convention or an empirical question, engaging Reichenbach and the conventionalist tradition associated with Poincaré. Putnam argues that physical geometry is answerable to evidence in the context of a total physical theory, which parallels his later treatment of logic. The discussion illustrates the volume's broader claim that categories once thought a priori or conventional are better understood as revisable parts of empirical theory. Readers interested in the history of this debate will find the papers a useful complement to Reichenbach's own writings.

A common misconception is that it presents a single, finished theory in the manner of a monograph. It is a gathering of papers written for different occasions and audiences, and the positions are not always mutually consistent. Another is that it represents Putnam's lasting commitments, when he revised or rejected several of them, including the quantum logic proposal and the metaphysical realism underlying the no-miracles argument. Treating it as a snapshot of a developing thinker is more accurate than treating it as his final word.