realism mathematics and modality

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Realism Mathematics And Modality

Author : Hartry H. Field
ISBN : 0631180877
Genre : Science
File Size : 61. 81 MB
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An Historical Introduction To The Philosophy Of Mathematics A Reader

Author : Russell Marcus
ISBN : 9781472529480
Genre : Philosophy
File Size : 53. 31 MB
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A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.

Science Without Numbers

Author : Hartry Field
ISBN : 9780191083778
Genre : Philosophy
File Size : 38. 50 MB
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Science Without Numbers caused a stir in philosophy on its original publication in 1980, with its bold nominalist approach to the ontology of mathematics and science. Hartry Field argues that we can explain the utility of mathematics without assuming it true. Part of the argument is that good mathematics has a special feature ("conservativeness") that allows it to be applied to "nominalistic" claims (roughly, those neutral to the existence of mathematical entities) in a way that generates nominalistic consequences more easily without generating any new ones. Field goes on to argue that we can axiomatize physical theories using nominalistic claims only, and that in fact this has advantages over the usual axiomatizations that are independent of nominalism. There has been much debate about the book since it first appeared. It is now reissued in a revised contains a substantial new preface giving the author's current views on the original book and the issues that were raised in the subsequent discussion of it.

Truth And The Absence Of Fact

Author : Hartry Field
ISBN : 9780199241712
Genre : Philosophy
File Size : 24. 68 MB
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Hartry Field presents a selection of thirteen essays on a set of related topics at the foundations of philosophy; one essay is previously unpublished, and eight are accompanied by substantial new postscripts.Five of the essays are primarily about truth, meaning, and propositional attitudes, five are primarily about semantic indeterminacy and other kinds of 'factual defectiveness' in our discourse, and three are primarily about issues concerning objectivity, especially in mathematics and in epistemology. The essays on truth, meaning, and the attitudes show a development from a form of correspondence theory of truth and meaning to a more deflationist perspective.The next set of papers argue that a place must be made in semantics for the idea that there are questions about which there is no fact of the matter, and address the difficulties involved in making sense of this, both within a correspondence theory of truth and meaning, and within a deflationary theory. Two papers argue that there are questions in mathematics about which there is no fact of the mattter, and draw out implications of this for the nature of mathematics. And the final paper arguesfor a view of epistemology in which it is not a purely fact-stating enterprise.This influential work by a key figure in contemporary philosophy will reward the attention of any philosopher interested in language, epistemology, or mathematics.

The Worlds Of Possibility

Author : Charles S. Chihara
ISBN : 0199246556
Genre : Philosophy
File Size : 69. 22 MB
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Charles Chihara gives a thorough critical exposition of modal realism, the philosophical doctrine that there exist many possible worlds of which the actual world -- the universe in which we live -- is just one. The striking success of possible-worlds semantics in modal logic has made this ontological doctrine attractive. Modal realists maintain that philosophers must accept the existence of possible worlds if they wish to have the benefit of using possible-worlds semantics to assess modalarguments and explain modal principles. Chihara challenges this claim, and argues instead for modality without worlds; he offers a new account of the role of interpretations or structures of the formal languages of logic.

Mathematical Thought And Its Objects

Author : Charles Parsons
ISBN : 1139467271
Genre : Science
File Size : 59. 21 MB
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Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.

A Critical Introduction To The Metaphysics Of Modality

Author : Andrea Borghini
ISBN : 9781472521941
Genre : Philosophy
File Size : 81. 72 MB
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A Critical Introduction to the Metaphysics of Modality examines the eight main contemporary theories of possibility behind a central metaphysical topic. Covering modal skepticism, modal expressivism, modalism, modal realism, ersatzism, modal fictionalism, modal agnosticism, and the new modal actualism, this comprehensive introduction to modality places contemporary debates in an historical context. Beginning with a historical overview, Andrea Borghini discusses Parmenides and Zeno; looks at how central Medieval authors such as Aquinas, and Buridan prepared the ground for the Early Modern radical views of Leibniz, Spinoza, and Hume and discusses advancements in semantics in the later-half of the twentieth century a resulted in the rise of modal metaphysics, the branch characterizing the past few decades of philosophical reflection. Framing the debate according to three main perspectives - logical, epistemic, metaphysical- Borghini provides the basic concepts and terms required to discuss modality. With suggestions of further reading and end-of-chapter study questions, A Critical Introduction to the Metaphysics of Modality is an up-to-date resource for students working in contemporary metaphysics seeking a better understanding of this crucial topic.

Modality

Author : Bob Hale
ISBN : 9780199565818
Genre : Philosophy
File Size : 31. 98 MB
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Modality brings together contributions from both well-established leaders in the field and up-and-coming philosophers. Between them, the papers address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal logic and its relations to necessary existence and to counterfactual reasoning, and other issues central to thecurrently highly active debate among philosophers in this area. The general introduction locates the individual contributions both in the specific context of the research project for which they were produced, and in the wider context of the contemporary discussion of the metaphysics and epistemology of modality.

Meaning And Method

Author : George Boolos
ISBN : 0521360838
Genre : Philosophy
File Size : 81. 78 MB
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This volume is a report on the state of philosophy in a number of significant areas.

Actuality Possibility And Worlds

Author : Alexander R. Pruss
ISBN : 9781441120625
Genre : Religion
File Size : 83. 43 MB
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Actuality, Possibility and Worlds is an exploration of the Aristotelian account that sees possibilities as grounded in causal powers. On his way to that account, Pruss surveys a number of historical approaches and argues that logicist approaches to possibility are implausible.The notion of possible worlds appears to be useful for many purposes, such as the analysis of counterfactuals or elucidating the nature of propositions and properties. This usefulness of possible worlds makes for a second general question: Are there any possible worlds and, if so, what are they? Are they concrete universes as David Lewis thinks, Platonic abstracta as per Robert M. Adams and Alvin Plantinga, or maybe linguistic or mathematical constructs such as Heller thinks? Or is perhaps Leibniz right in thinking that possibilia are not on par with actualities and that abstracta can only exist in a mind, so that possible worlds are ideas in the mind of God?

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