Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

The relationship of part to whole is one of the most fundamental there is; this is the first and only full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. 'Parts could easily be the standard book on mereology for the next twenty (...) or thirty years.' Timothy Williamson, Grazer Philosophische Studien. (shrink)

I wish to express, first of all, my profound gratitude to Professor J. M. Bochenski, without whose assistance the present work would have not been possible. To be concise, I would like to state that his contribution to this book may be viewed at three levels: (1) that of the general spirit, (2) that of the specific ideas, theses or approaches which are expressed in its pages, (3) that of this work qua doctoral dissertation. The general spirit which has guided (...) my research coincides with that underlying Professor :Oochenski's own works, in particular his Formale Logik (Munchen 1956). Moreover, the particular occasion which suggested my investigation was a statement included in that book according to which the literature in the field still lacked a detailed work on Frege (p. 317). I wish, likewise, to express my gratitude to other professors of the University of Fribourg for their generous help. I mention especially Professors P. Wyser, M. D. Philippe, N. Luyten, and V. Kuiper. I have also benefited from Professor E. Specker's lectures at the Eidge nossische Technische Hochschule (ZUrich) and from Professor Olof Gigon's lectures at the University of Bern. From an earlier period I wish to express my gratitude to the professors of the philosophy department of the Universidad Nacional de Buenos Aires, especially the late Professor Francisco Romero. The Swiss National Library (Bern) has greatly facilitated access to bibliographical sources, and the library of the University of Munster (Westphalien) has kindly provided microfilms of Frege's Nachlap. (shrink)

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physical realist heavily bverlaid with the interpretation afforded by linguistic analysis, so he changed, too. But at the time, which was approximately during the second decade of the twentieth century, they were no doubt very close in their views. Russell acknowledged the influence of Wittgenstein in several places in the 1918 lectures on logical atomism. Wittgenstein might not have written the Tractatus had Russell not given the lectures on logical atomism, or at least had he not maintained the views there (...) expressed. Certainly it is true in a very large sense that the Tractatus may be interpreted as a commentary on the 1918 lectures of Russell. Wittgenstein certainly did not hear them but, as Russell said, the topics were discussed together; and the debt of the Tractatus to the views of the contents of the lectures is obvious. Since Wittgenstein was the pupil and Russell the teacher, we may assume, despite the mutual influence, that the greater effect was Russell's. There is no space in which to go into a thorough analysis of the predecessors of Wittgenstein and of the influences upon him. In addition, there is not sufficient data. One clue, however, we are given. One of his friends has informed us that Wittgenstein "did read and enjoy Plato" and "recognized congenial features" in his philosophical method 1, although, to be sure, Wittgenstein is not said to have been a great reader of philosophy. (shrink)

This volume is devoted to problems within analytic metaphysics. It defends an ontology and theory of categories inspired by Aristotle, but revised in such a way as to be compatible with modern science. The ontology of both natural and social reality is addressed, starting out from the view that universals exist but only in the spatiotemporal world. In attempting to bring Aristotle's ontology up-to-date, the author relies very much on the thinking of Edmund Husserl, conceiving the cement of the universe (...) as Husserlian relations of existential dependence and regarding intentionality as a non-reducible category in the ontology of mind. The work is thoroughly realistic in spirit, but large parts of it should nonetheless be of interest to conceptualists and nominalists, too. (shrink)

1. Many philosophers think that “What is identity across time?” is an important and meaningful question. I have a great deal of trouble seeing what this question might be. But, very often, if one cannot understand a philosophical question, one’s best course is to look at some alleged answers to it; sometimes these answers enable one to see what question it is that they are offered as answers to. The following passage by Michael Tooley is supposed to provide an answer (...) to the question we are trying to get at. (shrink)

Although the relationship of part to whole is one of the most fundamental there is, this is the first full-length study of this key concept. Showing that mereology, or the formal theory of part and whole, is essential to ontology, Simons surveys and critiques previous theories--especially the standard extensional view--and proposes a new account that encompasses both temporal and modal considerations. Simons's revised theory not only allows him to offer fresh solutions to long-standing problems, but also has far-reaching consequences for (...) our understanding of a host of classical philosophical concepts. (shrink)

ONTOLOGY This book is a book about the world. I am concerned with ontology, not merely with language. Many ontological treatises concentrate largely on the ...

A systematic overview of modern metaphysics, A Survey of Metaphysics covers all of the most important topics in the field. It adopts the fairly traditional conception of metaphysics as a subject that deals with the deepest questions that can be raised concerning the fundamental structure of reality as a whole. The book is divided into six main sections that address the following themes: identity and change, necessity and essence, causation, agency and events, space and time, and universals and particulars. It (...) focuses on contemporary views and issues throughout, rather than on the history of metaphysics. (shrink)

To enhance the treatment of relations in biomedical ontologies we advance a methodology for providing consistent and unambiguous formal definitions of the relational expressions used in such ontologies in a way designed to assist developers and users in avoiding errors in coding and annotation. The resulting Relation Ontology can promote interoperability of ontologies and support new types of automated reasoning about the spatial and temporal dimensions of biological and medical phenomena.

We propose a modular ontology of the dynamic features of reality. This amounts, on the one hand, to a purely spatial ontology supporting snapshot views of the world at successive instants of time and, on the other hand, to a purely spatiotemporal ontology of change and process. We argue that dynamic spatial ontology must combine these two distinct types of inventory of the entities and relationships in reality, and we provide characterizations of spatiotemporal reasoning in the light of the interconnections (...) between them. (shrink)

The present essay is devoted to the application of ontology in support of research in the natural sciences. It defends the thesis that ontologies developed for such purposes should be understood as having as their subject matter, not concepts, but rather the universals and particulars which exist in reality and are captured in scientific laws. We outline the benefits of a view along these lines by showing how it yields rigorous formal definitions of the foundational relations used in many influential (...) ontologies, illustrating our results by reference to examples drawn from the domain of the life sciences. (shrink)