Indispensability Without Platonism

According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage

Willard Van Orman Quine's Philosophical Development in the 1930s and 1940s

As analytic philosophy is becoming increasingly aware of and interested in its own history, the study of that field is broadening to include, not just its earliest beginnings, but also the mid-twentieth century. One of the towering figures of this epoch is W.V. Quine (1908-2000), champion of naturalism in philosophy of science, pioneer of mathematical logic, trying to unite an austerely physicalist theory of the world with the truths of mathematics, psychology, and linguistics. Quine's posthumous papers, notes, and drafts revealing the development of his views in the forties have recently begun to be published, as well as careful philosophical studies of, for instance, the evolution of his key doctrine that mathematical and logical truth are continuous with, not divorced from, the truths of natural science. But one central text has remained unexplored: Quine's Portuguese-language book on logic, his 'farewell for now' to the discipline as he embarked on an assignment in the Navy in WWII. Anglophone philosophers have neglected this book because they could not read it. Jointly with colleagues, I have completed the first full English translation of this book. In this accompanying paper I draw out the main philosophical contributions Quine made in the book, placing them in their historical context and relating them to Quine's overall philosophical development during the period. Besides significant developments in the evolution of Quine's views on meaning and analyticity, I argue, this book is also driven by Quine's indebtedness to Russell and Whitehead, Tarski, and Frege, and contains crucial developments in his thinking on philosophy of logic and ontology. This includes early versions of some arguments from 'On What There Is', four-dimensionalism, and virtual set theory

Metaontology

The Ontological Question 'What exists?' dates back over two thousand five hundred years to the dawn of Western philosophy, and attempts to answer it define the province of ontology. The history of the Western philosophical tradition itself has been one of the differentiation and separation of the various sciences from the primordial stuff of ancient philosophy. Physics was first to break away from the tutelage of philosophy and established its independence in the seventeenth century. The other sciences followed suit fairly rapidly, with perhaps psychology being the last to separate. The results for modern philosophy - of this breakup of what was once a great empire over human reason - have been mixed. An inevitable result has been that questions considered in ancient times to belong to philosophy have fallen within the ambit of other disciplines. So speculations about the material composition and genesis of the universe that interested Thales, Heraclitus and Leucippus, are continued by contemporary cosmologists in well equipped research laboratories, and not by philosophers. However ontology, unlike cosmology, has not broken away from its parent discipline and the Ontological Question as to what exists is still argued by philosophers today. That ontology has failed to make the separation that cosmology has, is a reflection on the weakness of the methodology for settling ontological arguments. Unlike their great Rationalist predecessors, most modern philosophers do not believe that logic alone is sufficient to provide an answer as to what is. But neither do observation or experiment, in any direct way, seem to help us in deciding, for example, whether sets or intentions should be admitted to exist or not. In consequence, the status of ontology as an area of serious study has to depend on the devising of a methodology within which the Ontological Question can be tackled. The pursuit of such a methodology is the concern of metaontology and is also the concern of this thesis

Identity and quantification

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1985.MICROFICHE COPY AVAILABLE IN ARCHIVES AND HUMANITIESVita.Includes bibliographical references.by Ali Akhtar.Ph.D

Issues in the philosophical foundations of lexical semantics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1993.Includes bibliographical references (leaves 152-159).by Brian Edward Ulicny.Ph.D

The hour of traces: an analysis of the presuppositions, axiomatic formalization, and ontological implications of Reichenbach's frequency interpretation of probability

Thesis (M.A.)--Boston Universit

With reference to truth : studies in referential semantics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1982.MICROFICHE COPY AVAILABLE IN ARCHIVES AND HUMANITIESVita.Includes bibliographical references.by Douglas Fillmore Cannon.Ph.D

The Language Essence of Rational Cognition, with some Philosophical Consequences

This article analyses the essential role of language in rational cognition. The approach is functional -- I only look at the effects of the connection between language, reality and thinking. I begin by analysing rational cognition in everyday situations. Then I show that the whole scientific language is an extension and improvement of everyday language. The result is a uniform view of language and rational cognition which solves many epistemological and ontological problems. I use some of them -- the nature of ontology, truth, logic, thinking, scientific theories and mathematics, to demonstrate that the view of language and rational cognition developed in this article is fruitful and effective

Mathematics, time, and confirmation

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 2001.Includes bibliographical references (leaves 117-128).This dissertation discusses two issues about abstract objects: their role in scientific theories, and their relation to time. Chapter 1, "Why Apply Mathematics?" argues that scientific theories are not about the mathematics that is applied in them, and defends this thesis against the Quine-Putnam Indispensability Argument. Chapter 2, "Scientific Ontology," is a critical study of W. V. Quine's claim that metaphysics and mathematics are epistemologically on a par with natural science. It is argued that Quine's view relies on a unacceptable account of empirical confirmation. Chapter 3, "Prior and the Platonist," demonstrates the incompatibility of two popular views about time: the "Platonist" thesis that some objects exist "outside" time, and A. N. Prior's proposal for treating tense on the model of modality. Chapter 4, "What has Eternity Ever Done for You?" argues against the widely held view that abstract objects exist eternally ("outside" time), and presents a defense of the rival view that they exist sempiternally (at all times)Ulrich Meyer.Ph.D