THE HIGHER USEFULNESS OF SCIENCE AND OTHER ESSAYS

By KAREN GARCIA

CONTENTS PART I HISTORY AND PHILOSOPHY OF MATHEMATICS AND LOGIC ON LOGICIST CONCEPTIONS OF FUNCTIONS AND CLASSES METAPHYSICAL NECESSITY IBN S¯IN¯A AND CON?ICT IN LOGIC A MINIMALIST FOUNDATION AT WORK THE MUNICIPAL BY-LAWS OF THOUGHT PART II TRUTH, CONSISTENCY AND PARADOX TRUTH AND THE LIAR NECESSARY AND SUF?CIENT CONDITIONS FOR UNDECIDABILITY OF THE GÖDEL SENTENCE AND ITS TRUTH PARACONSISTENT SET THEORY PARADOX, ZF, AND THE AXIOM OF FOUNDATION ABSOLUTENESS AND THE SKOLEM PARADOX PART III LOGIC, SET THEORY AND CATEGORY THEORY EQUALISERS OF FRAMES IN CONSTRUCTIVE SET THEORY ANALOGY AND ITS SURPRISES: AN EYEWITNESS’S RE?ECTIONS ON THE EMERGENCE OF REAL ALGEBRAIC GEOMETRY EULER’S CONTINUUM FUNCTORIALLY VINDICATED NATURAL NUMBERS AND IN?NITESIMALS LOGIC IN CATEGORY THEORY PART IV PHILOSOPHY OF SCIENCE GUNK, TOPOLOGY AND MEASURE PITHOLES IN SPACE-TIME: STRUCTURE AND ONTOLOGY OF PHYSICAL GEOMETRY A SILLY ANSWER TO A PSILLOS QUESTION THE VACUUM IN ANTIQUITY AND IN MODERN PHYSICS FALSI?ABILITY, EMPIRICAL CONTENT AND THE DUHEM-QUINE PROBLEM PART V DECISION THEORY AND EPISTEMOLOGY CAN KNOWLEDGE BE JUSTI?ED TRUE BELIEF? THE STOCHASTIC CONCEPT OF ECONOMIC EQUILIBRIUM: A RADICAL ALTERNATIVE COLLECTIVE CHOICE AS INFORMATION THEORY: TOWARDS A THEORY OF GRAVITAS SCIENTI?C KNOWLEDGE AND STRUCTURAL KNOWLEDGE PART VI AESTHETICS MUSING ON MUSIC INSCRUTABLE HARMONIES: THE CONTINUOUS AND THE DISCRETE AS RE?ECTED IN THE PLAYING OF JASCHA HEIFETZ AND GLENN GOULD