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Advanced Math: The Hypothetical Conception

José Ferreirós

in Mathematical Knowledge and the Interplay of Practices

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167510
eISBN:
9781400874002
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167510.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter proposes the idea that advanced mathematics is based on hypotheses—that far from being a priori, it is based on hypothetical assumptions. The concept of quasi-empiricism is often linked ... More


Objectivity in Mathematical Knowledge

José Ferreirós

in Mathematical Knowledge and the Interplay of Practices

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167510
eISBN:
9781400874002
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167510.003.0009
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter proposes an idea for reconciling the hypothetical conception of mathematics with the traditional idea of the objectivity of mathematical knowledge. The basic notion is that, because new ... More


The Logic of Principia Mathematica

Peter Hylton

in Russell, Idealism, and the Emergence of Analytic Philosophy

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240181
eISBN:
9780191597763
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824018X.003.0010
Subject:
Philosophy, History of Philosophy

Here the concern is with the logic underlying Whitehead and Russell's Principia Mathematica and with the relation of that logic to Russell's underlying metaphysics. The author emphasizes the fact ... More


Axioms

Penelope Maddy

in Realism in Mathematics

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

Pursues the theoretical level of the two‐tiered epistemology of set theoretic realism, the level at which more abstract axioms can be justified by their consequences at more intuitive levels. I ... More


Word Order in Theory and Change

D. Gary Miller

in Language Change and Linguistic Theory, Volume II: Morphological, Syntactic, and Typological Change

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199583430
eISBN:
9780191595288
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199583430.003.0003
Subject:
Linguistics, Historical Linguistics, Theoretical Linguistics

This chapter begins with hypotheses about linearization and proceeds to examples of word‐order change. The theoretical portion focuses on the main formal theories, the most interesting of which ... More


Introduction

Larry S. Temkin

in Rethinking the Good: Moral Ideals and the Nature of Practical Reasoning

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199759446
eISBN:
9780199932214
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199759446.003.0001
Subject:
Philosophy, General, Moral Philosophy

This introductory chapter first sets out the purpose of the book, which is to illuminate some of the key assumptions to which many are firmly committed regarding the nature of the good, moral ideals, ... More


Juggling to Preserve Transitivity

Larry S. Temkin

in Rethinking the Good: Moral Ideals and the Nature of Practical Reasoning

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199759446
eISBN:
9780199932214
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199759446.003.0013
Subject:
Philosophy, General, Moral Philosophy

Numerous arguments have been presented illustrating that a number of beliefs that people hold about ideals and the nature of the good are incompatible. Among these beliefs are various Axioms of ... More


Second methodology of mathematics

Penelope Maddy

in Second Philosophy: A Naturalistic Method

Published in print:
2007
Published Online:
January 2009
ISBN:
9780199273669
eISBN:
9780191706264
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199273669.003.0025
Subject:
Philosophy, Logic/Philosophy of Mathematics

Given that natural science no longer dictates the course of mathematical development and that no curtailment of the free flowering of pure mathematics seems prudent, what are the appropriate methods ... More


Linearization

Juan Uriagereka

in Spell‐Out and the Minimalist Program

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199593521
eISBN:
9780191731402
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199593521.003.0002
Subject:
Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics, Syntax and Morphology

How are complex thoughts translated into simple signals? The human motor system makes our inner information public, and our sensory mechanisms reconstruct it back into an intelligible format. Such a ... More


Naturalism in Mathematics

Penelope Maddy

Published in print:
2000
Published Online:
November 2003
ISBN:
9780198250753
eISBN:
9780191597961
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198250754.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

It is well known that certain natural statements of set theory, like Cantor's continuum hypothesis (CH), cannot be proved or disproved on the basis of the standard axioms (Zermelo–Fraenkel with ... More


Difficult Atheism

Christopher Watkin

in Difficult Atheism: Post-Theological Thinking in Alain Badiou, Jean-Luc Nancy and Quentin Meillassoux

Published in print:
2011
Published Online:
September 2012
ISBN:
9780748640577
eISBN:
9780748671793
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748640577.003.0004
Subject:
Philosophy, Philosophy of Religion

This chapter continues the evaluative comparison of Badiou’s and Nancy’s approach to doing justice to the death of God by comparing the key moment in their respective accounts, namely axiomatisation ... More


General Conclusion: How to Follow an ‘Atheism’ That Never Was

Christopher Watkin

in Difficult Atheism: Post-Theological Thinking in Alain Badiou, Jean-Luc Nancy and Quentin Meillassoux

Published in print:
2011
Published Online:
September 2012
ISBN:
9780748640577
eISBN:
9780748671793
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748640577.003.0008
Subject:
Philosophy, Philosophy of Religion

The concluding chapter argues that the differences identified between the three post-theological positions represented by Badiou, Nancy and Meillassoux take us to the heart of what is at stake in the ... More


The typology of noun phrase structure

John A. Hawkins

in Cross-Linguistic Variation and Efficiency

Published in print:
2014
Published Online:
April 2014
ISBN:
9780199664993
eISBN:
9780191748547
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664993.003.0006
Subject:
Linguistics, Theoretical Linguistics, Syntax and Morphology

This chapter examines variation within the noun phrase from the perspective of efficiency. Two processing axioms are proposed. The Axiom of Constructability states that there will be at least one ... More


Traversal Parameter at the PF Interface: Graph-Theoretical Linearization of Bare Phrase Structure *

Takashi Toyoshima

in Theoretical Approaches to Disharmonic Word Order

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199684359
eISBN:
9780191764967
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199684359.003.0013
Subject:
Linguistics, Theoretical Linguistics, Syntax and Morphology

For linearization of syntactic structures, Kayne’s (1994) Linear Correspondence Axiom has been widely adopted. Yet, it is not quite compatible with Chomsky’s (1995) Minimalist theory of Bare Phrase ... More


Paradoxical Lotteries

Alexander R. Pruss

in Infinity, Causation, and Paradox

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198810339
eISBN:
9780191847325
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198810339.003.0004
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

A countably infinite fair lottery has tickets numbered 1, 2, 3, …, all of them on par. Many paradoxes arise from such lotteries. For instance, if two people get tickets from such a lottery, each will ... More


The Axiom of Choice Machine

Alexander R. Pruss

in Infinity, Causation, and Paradox

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198810339
eISBN:
9780191847325
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198810339.003.0006
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

This is a mainly technical chapter concerning the causal embodiment of the Axiom of Choice from set theory. The Axiom of Choice powered a construction of an infinite fair lottery in Chapter 4 and a ... More


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