Major figures of twentieth-century philosophy were enthralled by
the revolution in formal logic, and many of their arguments are
based on novel mathematical discoveries. Hilary Putnam claimed that
the Loewenheim-Skolem theorem refutes the existence of an
objective, observer-independent world; Bas van Fraassen claimed
that arguments against empiricism in philosophy of science are
ineffective against a semantic approach to scientific theories; W.
V. O. Quine claimed that the distinction between analytic and
synthetic truths is trivialized by the fact that any theory can be
reduced to one in which all truths are analytic. This book dissects
these and other arguments through in-depth investigation of the
mathematical facts undergirding them. It presents a systematic,
mathematically rigorous account of the key notions arising from
such debates, including theory, equivalence, translation,
reduction, and model. The result is a far-reaching
reconceptualization of the role of formal methods in answering
philosophical questions.
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