David Hume's Critique of Infinity

David Hume's Critique of Infinity

David Hume's Critique of Infinity

David Hume's Critique of Infinity

Synopsis

This new study of David Hume's philosophy of mathematics critically examines his objections to the concept of infinity. Although infinity raises some of the most challenging paradoxes for Hume's empiricism, there have been few detailed and no fully comprehensive systematic discussions of Hume's critique. In a series of eight interrelated arguments, Hume maintains that we cannot experience and therefore can have no adequate idea of infinity or of the infinite divisibility of extension. He proposes to replace the notion of infinity with an alternative phenomenalist theory of space and time as constituted by minima sensibilia or sensible extensionless indivisibles. The present work considers Hume's critique of infinity in historical context as a product of Enlightenment theory of knowledge, and assesses the prospects of his strict finitism in light of contemporary mathematics, science, and philosophy.

Excerpt

The problem of infinity is of central but often unappreciated importance in Hume’s philosophy. Although the question of whether extension is infinitely or only finitely divisible raises some of the most challenging philosophical paradoxes for Hume’s empiricism, there have been few detailed and no fully comprehensive systematic discussions of Hume’s objections to infinity. In this book, I offer a detailed exposition and critical evaluation of Hume’s refutation of infinite divisibility, placing Hume’s arguments in the historical context of Enlightenment philosophy of mathematics and metaphysics of space and time, and assessing the prospects of his strict finitism in light of contemporary mathematics, science, and philosophy.

Hume’s timeless relevance is partly a result of his preoccupation with universal philosophical themes. He is particularly concerned with the limitations of relying on sense experience for knowledge. He acknowledges the conflict between what can be known from experience and the deeply entrenched ‘rationalistic’ beliefs and conceptual commitments for which there is no adequate perceptual basis. The collision of experience and wayward philosophical enthusiasms is nowhere more poignant for Hume than in the case of infinite divisibility. Here philosophy confronts a concept that seems to be indispensable for the exact sciences, but which in obvious ways also appears to be humanly incomprehensible. Hume attacks the question from both directions. He lays siege to the concept of infinity on many fronts with many different arguments, and he outlines an experientially defensible theory of sensible extensionless indivisibles as an alternative empiricist theory for the finite divisibility of . . .

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