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Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap

Michael Potter

Published in print:
2002
Published Online:
May 2007
ISBN:
9780199252619
eISBN:
9780191712647
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199252619.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This book is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. It reassesses the brilliant ... More


The Structure of Models of Peano Arithmetic

Roman Kossak and James Schmerl

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568278
eISBN:
9780191718199
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568278.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of nonstandard models of arithmetic. Major representation theorems are proved, ... More


Truthmakers

David M. Armstrong

in Sketch for a Systematic Metaphysics

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199590612
eISBN:
9780191723391
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199590612.003.0008
Subject:
Philosophy, Philosophy of Mind, Metaphysics/Epistemology

The notion of a truthmaker is introduced, and the importance of the notion for metaphysics is stressed. Russell was a pioneer. All truth is a matter of correspondence of a proposition to reality, so ... More


The Concept of an Object in Formal Ontology

E. J. Lowe

in The Four-Category Ontology: A Metaphysical Foundation for Natural Science

Published in print:
2005
Published Online:
May 2006
ISBN:
9780199254392
eISBN:
9780191603600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199254397.003.0005
Subject:
Philosophy, Metaphysics/Epistemology

The formal ontological concept of an object is explicated and contrasted with that of a property. F. P. Ramsey’s objections to this distinction are challenged. The sense in which objects possess an ... More


Ramsey's Problem and its Solution

E. J. Lowe

in The Four-Category Ontology: A Metaphysical Foundation for Natural Science

Published in print:
2005
Published Online:
May 2006
ISBN:
9780199254392
eISBN:
9780191603600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199254397.003.0007
Subject:
Philosophy, Metaphysics/Epistemology

F. P. Ramsey’s objections to the universal/particular distinction, especially as advocated by Bertrand Russell, are examined in depth and rebutted. At the same time, certain important lessons are ... More


Consumption En Route: The Second Turnpike Theorem

Michio Morishima

in Theory of Economic Growth

Published in print:
1969
Published Online:
November 2003
ISBN:
9780198281641
eISBN:
9780191596667
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198281641.003.0013
Subject:
Economics and Finance, Development, Growth, and Environmental

Chapter 10 was concerned with the Final State Turnpike Theorem on the assumptions that consumption of each good per worker is fixed throughout the planning period and that the authorities try to ... More


The Practical Turn: Pragmatism in Britain in the Long Twentieth Century

Cheryl Misak and Huw Price (eds)

Published in print:
2017
Published Online:
May 2018
ISBN:
9780197266168
eISBN:
9780191865237
Item type:
book
Publisher:
British Academy
DOI:
10.5871/bacad/9780197266168.001.0001
Subject:
Philosophy, General

The pragmatist approach to philosophical problems focuses on the role of disputed notions—for example, truth, value, causation, probability, necessity—in our practices. The insight at the heart of ... More


EPISTEMIC CAUSALITY

Jon Williamson

in Bayesian Nets and Causality: Philosophical and Computational Foundations

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198530794
eISBN:
9780191712982
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530794.003.0009
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter develops an epistemic theory of causality. The origins of such a theory may be found in the writings of Kant and Ramsey. According to the epistemic theory, we think in terms of cause and ... More


ω1-LIKE MODELS

Roman Kossak and James H. Schmerl

in The Structure of Models of Peano Arithmetic

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568278
eISBN:
9780191718199
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568278.003.0010
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter presents several constructions of ω1-like models with interesting second order properties. The list includes: recursively saturated rather classless models, rigid recursively saturated ... More


HOW TO CONTROL TYPES

Roman Kossak and James H. Schmerl

in The Structure of Models of Peano Arithmetic

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568278
eISBN:
9780191718199
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568278.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter makes use of an induced version of Ramsey's Theorem to prove several results: the Abramson-Harrington theorem on omitting large indiscernible sets and Hanf numbers for models of ... More


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