A Logical Foundation for Potentialist Set Theory PDF Download
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Author: Sharon Berry
Publisher: Cambridge University Press
ISBN: 1108998852
Category : Science
Languages : en
Pages : 250
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Book Description
In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.
Author: Sharon Berry
Publisher: Cambridge University Press
ISBN: 1108998852
Category : Science
Languages : en
Pages : 250
Get Book Here
Book Description
In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.
Author: Sharon Berry
Publisher: Cambridge University Press
ISBN: 1108834310
Category : Mathematics
Languages : en
Pages : 249
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Book Description
A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.
Author: Diego E. Machuca
Publisher: Taylor & Francis
ISBN: 1000648605
Category : Philosophy
Languages : en
Pages : 425
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Book Description
Recent years have seen an explosion of interest in evolutionary debunking arguments directed against certain types of belief, particularly moral and religious beliefs. According to those arguments, the evolutionary origins of the cognitive mechanisms that produce the targeted beliefs render these beliefs epistemically unjustified. The reason is that natural selection cares for reproduction and survival rather than truth, and false beliefs can in principle be as evolutionarily advantageous as true beliefs. The present volume brings together fourteen essays that examine evolutionary debunking arguments not only in ethics and philosophy of religion, but also in philosophy of mathematics, metaphysics, and epistemology. The essays move forward research on those arguments by shedding fresh light on old problems and proposing new lines of inquiry. The book will appeal to scholars and graduate students interested in the possible skeptical implications of evolutionary theory in any of the above domains.
Author: Mark Colyvan
Publisher: Cambridge University Press
ISBN: 0521826020
Category : Mathematics
Languages : en
Pages : 199
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Book Description
A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.
Author: Otávio Bueno
Publisher: Routledge
ISBN: 1317585283
Category : Philosophy
Languages : en
Pages : 432
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Book Description
Modality - the question of what is possible and what is necessary - is a fundamental area of philosophy and philosophical research. The Routledge Handbook of Modality is an outstanding reference source to the key topics, problems and debates in this exciting subject and is the first collection of its kind. Comprising thirty-five chapters by a team of international contributors the Handbook is divided into seven clear parts: worlds and modality essentialism, ontological dependence, and modality modal anti-realism epistemology of modality modality in science modality in logic and mathematics modality in the history of philosophy. Within these sections the central issues, debates and problems are examined, including possible worlds, essentialism, counterfactuals, ontological dependence, modal fictionalism, deflationism, the integration challenge, conceivability, a priori knowledge, laws of nature, natural kinds, and logical necessity. The Routledge Handbook of Modality is essential reading for students and researchers in epistemology, metaphysics and philosophy of language. It will also be very useful for those in related fields in philosophy such as philosophy of mathematics, logic and philosophy of science.
Author: Øystein Linnebo
Publisher: Oxford University Press
ISBN: 019255896X
Category : Philosophy
Languages : en
Pages : 232
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Book Description
Are there objects that are "thin" in the sense that not very much is required for their existence? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. Øystein Linnebo aims to do so by drawing on some Fregean ideas. First, to be an object is to be a possible referent of a singular term. Second, singular reference can be achieved by providing a criterion of identity for the would-be referent. The second idea enables a form of easy reference and thus, via the first idea, also a form of easy being. Paradox is avoided by imposing a predicativity restriction on the criteria of identity. But the abstraction based on a criterion of identity may result in an expanded domain. By iterating such expansions, a powerful account of dynamic abstraction is developed. The result is a distinctive approach to ontology. Abstract objects such as numbers and sets are demystified and allowed to exist alongside more familiar physical objects. And Linnebo also offers a novel approach to set theory which takes seriously the idea that sets are "formed" successively.
Author: Agustín Rayo
Publisher:
ISBN: 0199662622
Category : Mathematics
Languages : en
Pages : 241
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Book Description
Our conception of logical space is the set of distinctions we use to navigate the world. Agustín Rayo argues that this is shaped by acceptance or rejection of 'just is'-statements: e.g. 'to be composed of water just is to be composed of H2O'. He offers a novel conception of metaphysical possibility, and a new trivialist philosophy of mathematics.
Author: Geoffrey Hellman
Publisher: Cambridge University Press
ISBN: 110863074X
Category : Science
Languages : en
Pages : 167
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Book Description
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.
Author: Patrick Chambres
Publisher: Springer Science & Business Media
ISBN: 9781402071348
Category : Medical
Languages : en
Pages : 306
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Book Description
The object of this volume is to promote the interaction, and indeed construct a synergistic reciprocity between the functional perspective on metacognition and the analytical perspective. The authors examine the role of metacognition in activities as varied as classroom learning, piloting airplanes, and eyewitness testimony. The ideas and questions developed in the book will give a dynamic impulse to research in the field.
Author: David J. Hesselgrave
Publisher: Baker Academic
ISBN: 0801022223
Category : Juvenile Nonfiction
Languages : en
Pages : 352
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Book Description
Discusses how to plant new churches in North America and around the world by examining important sociological, anthropological, and historical perspectives. Focuses on church-planting methods, selecting target areas, using effective resources, and measuring growth. Also includes data on the sending church and the Christian mission and other related material.
