philosophy of mathematics structure and ontology

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Philosophy Of Mathematics

Author : Stewart Shapiro
ISBN : 9780195094527
Genre : Mathematics
File Size : 36. 83 MB
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Shapiro argues that both realist and anti-realist accounts of mathematics are problematic. To resolve this dilemma, he articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

An Introduction To The Philosophy Of Mathematics

Author : Mark Colyvan
ISBN : 9780521826020
Genre : Mathematics
File Size : 48. 42 MB
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This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.

Thinking About Mathematics

Author : Stewart Shapiro
ISBN : 0192893068
Genre : Philosophy
File Size : 85. 68 MB
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Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

Platonism And Anti Platonism In Mathematics

Author : Mark Balaguer
ISBN : 0195143981
Genre : Mathematics
File Size : 61. 22 MB
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In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He establishes that both platonism and anti-platonism are defensible views and introduces a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, proceeding to defend anti-platonism (in particular, mathematical fictionalism) against various attacks--most notably the Quine-Putnam indispensability attack.

Matter Imagination And Geometry

Author : Dmitriĭ Vladimirovich Nikulin
ISBN : 075461574X
Genre : Philosophy
File Size : 34. 6 MB
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The focus is on key thinkers Plotinus and Descartes (with the occasional appearance of Plato, Aristotle, Euclid, Proclus, Newton and others), in whom the fundamental presuppositions of ripe antiquity and of early modernity find their definite expression."--Jacket.

Mathematics As A Science Of Patterns

Author : Michael D. Resnik
ISBN : 0198236085
Genre : Mathematics
File Size : 26. 72 MB
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Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism about the metaphysics of mathematics--the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology.

Philosophy Of Mathematics

Author : David Bostock
ISBN : 9781405189927
Genre : Mathematics
File Size : 48. 8 MB
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Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era. Offers beginning readers a critical appraisal of philosophical viewpoints throughout history Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism Provides readers with a non-partisan discussion until the final chapter, which gives the author?s personal opinion on where the truth lies Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals

On The Elements Of Ontology

Author : D. W. Mertz
ISBN : 9783110454512
Genre : Philosophy
File Size : 46. 68 MB
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Elements argues for an ontology derived of ten theses detailing the natures and fundamental ontic status of attribution and structure. Attribution assayed as intension-conditioned unifying-agency yields a one-category ontology of individuated attribute instances, with instances’ unifying acts and universal intensions, and their internal and externally effected modes of composition, accounting for all unity and entities as hierarchical structures.

Writing The Book Of The World

Author : Theodore Sider
ISBN : 9780199697908
Genre : Philosophy
File Size : 37. 5 MB
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Theodore Sider presents a broad new vision of metaphysics centred on the idea of structure. To describe the world well we must use concepts that 'carve at the joints', so that conceptual structure matches reality's structure. This approach illuminates a wide range of topics, such as time, modality, ontology, and the status of metaphysics itself.

Why Is There Philosophy Of Mathematics At All

Author : Ian Hacking
ISBN : 9781107729827
Genre : Science
File Size : 88. 57 MB
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This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.

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