This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) those that are more readily available for mathematico-scientific use. (shrink)

This paper is concerned with the way different axiom systems for set theory can be justified by appeal to such intuitions as limitation of size, predicativity, stratification, etc. While none of the different conceptions historically resulting from the impetus to provide a solution to the paradoxes turns out to rest on an intuition providing an unshakeable foundation,'each supplies a picture of the set-theoretic universe that is both useful and internally well motivated. The same is true of more recently proposed axiom (...) systems for non-well-founded universes, and an attempt is made to motivate such axiom systems on the basis of an old and respected ‘algebraic’ intuition. (shrink)

George Berkeley, Bishop of Cloyne, was one of the great philosophers of the early modern period. He was a brilliant critic of his predecessors, particularly Descartes, Malebranche, and Locke. He was a talented metaphysician famous for defending idealism, that is, the view that reality consists exclusively of minds and their ideas. Berkeley's system, while it strikes many as counter intuitive, is strong and flexible enough to counter most objections. His most studied works, the Treatise Concerning the Principles of Human Knowledge (...) Principles, for short) and Three Dialogues between Hylas and Philonous Dialogues), are beautifully written and dense with the sort of arguments that delight contemporary philosophers. He was also a wide ranging thinker with interests in religion (which were fundamental to his philosophical motivations), the psychology of vision, mathematics, physics, morals, economics, and medicine. Although many of Berkeley's first readers greeted him with incomprehension, he influenced both Hume and Kant, and is much read (if little followed) in our own day. (shrink)

The subject of this essay-based dissertation is Hume’s natural philosophy. The dissertation consists of four separate essays and an introduction. These essays do not only treat Hume’s views on the topic of natural philosophy, but his views are placed into a broader context of history of philosophy and science, physics in particular. The introductory section outlines the historical context, shows how the individual essays are connected, expounds what kind of research methodology has been used, and encapsulates the research contributions of (...) the essays. The first essay treats Newton’s experimentalist methodology in gravity research and its relation to Hume’s causal philosophy. It is argued that Hume does not see the relation of cause and effect as being founded on a priori reasoning, similar to the way in which Newton criticized non-empirical hypotheses about the causal properties of gravity. Contrary to Hume’s rules of causation, the universal law does not include a reference either to contiguity or succession, but Hume accepts it in interpreting the force and the law of gravity instrumentally. The second article considers Newtonian and non-Newtonian elements in Hume more broadly. He is sympathetic to many prominently Newtonian themes in natural philosophy, such as experimentalism, critique of hypotheses, inductive proof, and the critique of Leibnizian principles of sufficient reason and intelligibility. However, Hume is not a Newtonian philosopher in many respects: his conceptions regarding space and time, the vacuum, the specifics of causation, the status of mechanism, and the reality of forces differ markedly from Newton’s related conceptions. The third article focuses on Hume’s Fork and the proper epistemic status of propositions of mixed mathematics. It is shown that the epistemic status of propositions of mixed mathematics, such as those concerning laws of nature, is that of matters of fact. The reason for this is that the propositions of mixed mathematics are dependent on the Uniformity Principle. The fourth article analyzes Einstein’s acknowledgement of Hume regarding special relativity. The views of the scientist and the philosopher are juxtaposed, and it is argued that there are two common points to be found in their writings, namely an empiricist theory of ideas and concepts and a relationist ontology regarding space and time. (shrink)

To the great puzzlement of his readers, Berkeley begins by arguing that nothing exists other than minds and ideas, but concludes by claiming to have defended the existence of bodies. How can Berkeley's idealism amount to such a defense? I introduce resources from Berkeley's philosophy of language, and especially his analysis of the discourse of physics, to defend a novel answer to this question. According to Berkeley, the technical terms of physics are meaningful despite failing to designate any reality; their (...) meaningfulness derives from the useful role they play in organizing and predicting our experience. I argue that Berkeleian bodies have the same status as these theoretical entities: they are mere 'quasi-entities' introduced by our ways of speaking and thinking in order to serve our practical purposes. Berkeley nevertheless considers this to be a defense of the existence of bodies because he endorses a radically deflationary semantics for 'exists.'. (shrink)