David Hume's Critique of Infinity (Brill's Studies in Intellectual History)

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.--jacket. Introduction: Two-fold Task Of Hume's Critique -- Hume's Strict Finitism -- Dialectical Structure Of Hume's Critique -- Historical-philosophical Context -- Bayle's Trilemma For The Divisiblity Of Extension -- Legacy And Influence Of Berkeley On Hume's Metaphysics Of Space And Philosophy Of Mathematics -- The Inkspot Experiment -- Minima Sensibilia -- A Spot Of Ink On Paper -- Limitations Of Impressions And Ideas -- Sensible Extensionless Indivisibles As The Constituents Of Extension -- Against Mind-mediated Ideas Of Infinite Divisibility -- Simple And Complex Ideas -- Immediate And Mind-mediated Ideas Of Extension -- Locke's Category Of Negative Ideas -- Hume's Objections To The Negative Idea Of A Vacuum -- Kemp Smith's Analysis -- Frasca-spada's Hume On Infinite Divisibility And The Vacuum -- Hume On The Idea Of A Vacuum And Complex Mediated Ideas Of Infinite Divisibility -- Hume's Inkspot Argument -- Hume's Inkspot Metaphysics Of Space: Finite Divisibility Of Extension Into Sensible Extensionless Indivisibles -- Idea And Reality -- Adequate Ideas Of Finite Divisibility -- Bayle's Trilemma And The Metaphysics Of Space -- Hume's Solution To Aristotle's Contact Problem -- Empiricism And The Experience Of Spatial Extension -- Refutations Of Infinite Divisibility -- Hume's Reductio Arguments -- Incoherence Of Infinite Divisibility -- Argument From The Addition Of Infinite Parts -- Malezieu's Argument From The Unity Of Existents -- Finite Divisibility Of Time -- Conceivability Of Indivisible Mathematical Points -- The Geometry Dilemma. By Dale Jacquette. Includes Bibliographical References And Index.