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Mark Colyvan [103]M. Colyvan [8]
  1. The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford University Press.
    This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.
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  2. There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.
    Hartry Field has shown us a way to be nominalists: we must purge our scientific theories of quantification over abstracta and we must prove the appropriate conservativeness results. This is not a path for the faint hearted. Indeed, the substantial technical difficulties facing Field's project have led some to explore other, easier options. Recently, Jody Azzouni, Joseph Melia, and Stephen Yablo have argued that it is a mistake to read our ontological commitments simply from what the quantifiers of our best (...)
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  3. An Inferential Conception of the Application of Mathematics.Otávio Bueno & Mark Colyvan - 2011 - Noûs 45 (2):345-374.
    A number of people have recently argued for a structural approach to accounting for the applications of mathematics. Such an approach has been called "the mapping account". According to this view, the applicability of mathematics is fully accounted for by appreciating the relevant structural similarities between the empirical system under study and the mathematics used in the investigation ofthat system. This account of applications requires the truth of applied mathematical assertions, but it does not require the existence of mathematical objects. (...)
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  4. How Mathematics Can Make a Difference.Sam Baron, Mark Colyvan & David Ripley - 2017 - Philosophers' Imprint 17.
    Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.
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  5. The Explanatory Power of Phase Spaces.Aidan Lyon & Mark Colyvan - 2008 - Philosophia Mathematica 16 (2):227-243.
    David Malament argued that Hartry Field's nominalisation program is unlikely to be able to deal with non-space-time theories such as phase-space theories. We give a specific example of such a phase-space theory and argue that this presentation of the theory delivers explanations that are not available in the classical presentation of the theory. This suggests that even if phase-space theories can be nominalised, the resulting theory will not have the explanatory power of the original. Phase-space theories thus raise problems for (...)
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  6.  47
    An Introduction to the Philosophy of Mathematics.Mark Colyvan - 2012 - Cambridge University Press.
    Machine generated contents note: 1. Mathematics and its philosophy; 2. The limits of mathematics; 3. Plato's heaven; 4. Fiction, metaphor, and partial truths; 5. Mathematical explanation; 6. The applicability of mathematics; 7. Who's afraid of inconsistent mathematics?; 8. A rose by any other name; 9. Epilogue: desert island theorems.
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  7.  68
    Legal Probabilism: A Qualified Defence.Brian Hedden & Mark Colyvan - 2019 - Journal of Political Philosophy 27 (4):448-468.
    Journal of Political Philosophy, EarlyView.
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  8. Indexing and Mathematical Explanation.Alan Baker & Mark Colyvan - 2011 - Philosophia Mathematica 19 (3):323-334.
    We discuss a recent attempt by Chris Daly and Simon Langford to do away with mathematical explanations of physical phenomena. Daly and Langford suggest that mathematics merely indexes parts of the physical world, and on this understanding of the role of mathematics in science, there is no need to countenance mathematical explanation of physical facts. We argue that their strategy is at best a sketch and only looks plausible in simple cases. We also draw attention to how frequently Daly and (...)
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  9. Road Work Ahead: Heavy Machinery on the Easy Road.M. Colyvan - 2012 - Mind 121 (484):1031-1046.
    In this paper I reply to Jody Azzouni, Otávio Bueno, Mary Leng, David Liggins, and Stephen Yablo, who offer defences of so-called ‘ easy road ’ nominalist strategies in the philosophy of mathematics.
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  10.  72
    A Counterfactual Approach to Explanation in Mathematics.Sam Baron, Mark Colyvan & David Ripley - 2020 - Philosophia Mathematica 28 (1):1-34.
    ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.
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  11. Mathematics and Aesthetic Considerations in Science.Mark Colyvan - 2002 - Mind 111 (441):69-74.
  12. Disagreement Behind the Veil of Ignorance.Ryan Muldoon, Chiara Lisciandra, Mark Colyvan, Carlo Martini, Giacomo Sillari & Jan Sprenger - 2014 - Philosophical Studies 170 (3):377-394.
    In this paper we argue that there is a kind of moral disagreement that survives the Rawlsian veil of ignorance. While a veil of ignorance eliminates sources of disagreement stemming from self-interest, it does not do anything to eliminate deeper sources of disagreement. These disagreements not only persist, but transform their structure once behind the veil of ignorance. We consider formal frameworks for exploring these differences in structure between interested and disinterested disagreement, and argue that consensus models offer us a (...)
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  13. Indispensability Arguments in the Philosophy of Mathematics.Mark Colyvan - 2008 - Stanford Encyclopedia of Philosophy.
    One of the most intriguing features of mathematics is its applicability to empirical science. Every branch of science draws upon large and often diverse portions of mathematics, from the use of Hilbert spaces in quantum mechanics to the use of differential geometry in general relativity. It's not just the physical sciences that avail themselves of the services of mathematics either. Biology, for instance, makes extensive use of difference equations and statistics. The roles mathematics plays in these theories is also varied. (...)
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  14. Time Enough for Explanation.Sam Baron & Mark Colyvan - 2016 - Journal of Philosophy 113 (2):61-88.
    The present paper advances an analogy between cases of extra-mathematical explanation and cases of what might be termed ‘extra-logical explanation’: the explanation of a physical fact by a logical fact. A particular case of extra-logical explanation is identified that arises in the philosophical literature on time travel. This instance of extra-logical explanation is subsequently shown to be of a piece with cases of extra-mathematical explanation. Using this analogy, we argue extra-mathematical explanation is part of a broader class of non-causal explanation. (...)
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  15. Can the Eleatic Principle Be Justified?Mark Colyvan - 1998 - Canadian Journal of Philosophy 28 (3):313-335.
    The Eleatic Principle or causal criterion is a causal test that entities must pass in order to gain admission to some philosophers’ ontology.1 This principle justifies belief in only those entities to which causal power can be attributed, that is, to those entities which can bring about changes in the world. The idea of such a test is rather important in modern ontology, since it is neither without intuitive appeal nor without influential supporters. Its supporters have included David Armstrong (1978, (...)
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  16. Problems With the Argument From Fine Tuning.Mark Colyvan, Jay L. Garfield & Graham Priest - 2005 - Synthese 145 (3):325-338.
    The argument from fine tuning is supposed to establish the existence of God from the fact that the evolution of carbon-based life requires the laws of physics and the boundary conditions of the universe to be more or less as they are. We demonstrate that this argument fails. In particular, we focus on problems associated with the role probabilities play in the argument. We show that, even granting the fine tuning of the universe, it does not follow that the universe (...)
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  17. Modelling the Moral Dimension of Decisions.Mark Colyvan, Damian Cox & Katie Siobhan Steele - 2010 - Noûs 44 (3):503-529.
    In this paper we explore the connections between ethics and decision theory. In particular, we consider the question of whether decision theory carries with it a bias towards consequentialist ethical theories. We argue that there are plausible versions of the other ethical theories that can be accommodated by “standard” decision theory, but there are also variations of these ethical theories that are less easily accommodated. So while “standard” decision theory is not exclusively consequentialist, it is not necessarily ethically neutral. Moreover, (...)
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  18. Scientific Realism and Mathematical Nominalism: A Marriage Made in Hell.Mark Colyvan - unknown
    The Quine-Putnam Indispensability argument is the argument for treating mathematical entities on a par with other theoretical entities of our best scientific theories. This argument is usually taken to be an argument for mathematical realism. In this chapter I will argue that the proper way to understand this argument is as putting pressure on the viability of the marriage of scientific realism and mathematical nominalism. Although such a marriage is a popular option amongst philosophers of science and mathematics, in light (...)
     
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  19. Mathematical Recreation Versus Mathematical Knowledge.Mark Colyvan - 2007 - In Mary Leng, Alexander Paseau & Michael D. Potter (eds.), Mathematical Knowledge. Oxford University Press. pp. 109--122.
  20. Relative Expectation Theory.Mark Colyvan - 2008 - Journal of Philosophy 105 (1):37-44.
    Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated with the St. (...)
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  21. A Topological Sorites.Zach Weber & Mark Colyvan - 2010 - Journal of Philosophy 107 (6):311-325.
    This paper considers a generalisation of the sorites paradox, in which only topological notions are employed. We argue that by increasing the level of abstraction in this way, we see the sorites paradox in a new, more revealing light—a light that forces attention on cut-off points of vague predicates. The generalised sorites paradox presented here also gives rise to a new, more tractable definition of vagueness.
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  22. Idealisations in Normative Models.Mark Colyvan - 2013 - Synthese 190 (8):1337-1350.
    In this paper I discuss the kinds of idealisations invoked in normative theories—logic, epistemology, and decision theory. I argue that very often the so-called norms of rationality are in fact mere idealisations invoked to make life easier. As such, these idealisations are not too different from various idealisations employed in scientific modelling. Examples of the latter include: fluids are incompressible (in fluid mechanics), growth rates are constant (in population ecology), and the gravitational influence of distant bodies can be ignored (in (...)
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  23.  70
    The Prospects for a Monist Theory of Non-Causal Explanation in Science and Mathematics.Alexander Reutlinger, Mark Colyvan & Karolina Krzyżanowska - forthcoming - Erkenntnis:1-21.
    We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation (CTE) for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical explanations requires us (...)
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  24. Resolving Disagreement Through Mutual Respect.Carlo Martini, Jan Sprenger & Mark Colyvan - 2013 - Erkenntnis 78 (4):881-898.
    This paper explores the scope and limits of rational consensus through mutual respect, with the primary focus on the best known formal model of consensus: the Lehrer–Wagner model. We consider various arguments against the rationality of the Lehrer–Wagner model as a model of consensus about factual matters. We conclude that models such as this face problems in achieving rational consensus on disagreements about unknown factual matters, but that they hold considerable promise as models of how to rationally resolve non-factual disagreements.
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  25. Just What is Vagueness?Otávio Bueno & Mark Colyvan - 2012 - Ratio 25 (1):19-33.
    We argue that standard definitions of ‘vagueness’ prejudice the question of how best to deal with the phenomenon of vagueness. In particular, the usual understanding of ‘vagueness’ in terms of borderline cases, where the latter are thought of as truth-value gaps, begs the question against the subvaluational approach. According to this latter approach, borderline cases are inconsistent (i.e., glutty not gappy). We suggest that a definition of ‘vagueness’ should be general enough to accommodate any genuine contender in the debate over (...)
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  26.  42
    Making Ado Without Expectations.Mark Colyvan & Alan Hájek - 2016 - Mind 125 (499):829-857.
    This paper is a response to Paul Bartha’s ‘Making Do Without Expectations’. We provide an assessment of the strengths and limitations of two notable extensions of standard decision theory: relative expectation theory and Paul Bartha’s relative utility theory. These extensions are designed to provide intuitive answers to some well-known problems in decision theory involving gaps in expectations. We argue that both RET and RUT go some way towards providing solutions to the problems in question but neither extension solves all the (...)
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  27. Is It a Crime to Belong to a Reference Class.Mark Colyvan, Helen M. Regan & Scott Ferson - 2001 - Journal of Political Philosophy 9 (2):168–181.
    ON DECEMBER 10, 1991 Charles Shonubi, a Nigerian citizen but a resident of the USA, was arrested at John F. Kennedy International Airport for the importation of heroin into the United States.1 Shonubi's modus operandi was ``balloon swallowing.'' That is, heroin was mixed with another substance to form a paste and this paste was sealed in balloons which were then swallowed. The idea was that once the illegal substance was safely inside the USA, the smuggler would pass the balloons and (...)
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  28. The Ontological Commitments of Inconsistent Theories.Mark Colyvan - 2008 - Philosophical Studies 141 (1):115 - 123.
    In this paper I present an argument for belief in inconsistent objects. The argument relies on a particular, plausible version of scientific realism, and the fact that often our best scientific theories are inconsistent. It is not clear what to make of this argument. Is it a reductio of the version of scientific realism under consideration? If it is, what are the alternatives? Should we just accept the conclusion? I will argue (rather tentatively and suitably qualified) for a positive answer (...)
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  29. Vagueness and Truth.Mark Colyvan - unknown
    In philosophy of logic and elsewhere, it is generally thought that similar problems should be solved by similar means. This advice is sometimes elevated to the status of a principle: the principle of uniform solution. In this paper I will explore the question of what counts as a similar problem and consider reasons for subscribing to the principle of uniform solution.
     
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  30. The Miracle of Applied Mathematics.Mark Colyvan - 2001 - Synthese 127 (3):265-277.
    Mathematics has a great variety ofapplications in the physical sciences.This simple, undeniable fact, however,gives rise to an interestingphilosophical problem:why should physical scientistsfind that they are unable to evenstate their theories without theresources of abstract mathematicaltheories? Moreover, theformulation of physical theories inthe language of mathematicsoften leads to new physical predictionswhich were quite unexpected onpurely physical grounds. It is thought by somethat the puzzles the applications of mathematicspresent are artefacts of out-dated philosophical theories about thenature of mathematics. In this paper I argue (...)
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  31. Confirmation Theory and Indispensability.Mark Colyvan - 1999 - Philosophical Studies 96 (1):1-19.
    In this paper I examine Quine''s indispensability argument, with particular emphasis on what is meant by ''indispensable''. I show that confirmation theory plays a crucial role in answering this question and that once indispensability is understood in this light, Quine''s argument is seen to be a serious stumbling block for any scientific realist wishing to maintain an anti-realist position with regard to mathematical entities.
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  32. No Expectations.Mark Colyvan - 2006 - Mind 115 (459):695-702.
    The Pasadena paradox presents a serious challenge for decision theory. The paradox arises from a game that has well-defined probabilities and utilities for each outcome, yet, apparently, does not have a well-defined expectation. In this paper, I argue that this paradox highlights a limitation of standard decision theory. This limitation can be (largely) overcome by embracing dominance reasoning and, in particular, by recognising that dominance reasoning can deliver the correct results in situations where standard decision theory fails. This, in turn, (...)
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  33. Tolerating Gluts.Zach Weber, David Ripley, Graham Priest, Dominic Hyde & Mark Colyvan - 2014 - Mind 123 (491):813-828.
  34.  22
    Ecological Orbits: How Planets Move and Populations Grow.Lev Ginzburg & Mark Colyvan - unknown
    The main focus of the book is the presentation of the 'inertial' view of population growth. This view provides a rather simple model for complex population dynamics, and is achieved at the level of the single species without invoking species interactions. An important part of this account is the maternal effect. Investment of mothers in the quality of their daughters makes the rate of reproduction of the current generation depend not only on the current environment, but also on the environment (...)
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  35. Philosophical Issues in Ecology: Recent Trends and Future Directions.Mark Colyvan, William Grey, Paul E. Griffiths, Jay Odenbaugh, Stefan Linquist & Hugh P. Possingham - 2009 - Ecology and Society 14 (2).
    Philosophy of ecology has been slow to become established as an area of philosophical interest, but it is now receiving considerable attention. This area holds great promise for the advancement of both ecology and the philosophy of science. Insights from the philosophy of science can advance ecology in a number of ways. For example, philosophy can assist with the development of improved models of ecological hypothesis testing and theory choice. Philosophy can also help ecologists understand the role and limitations of (...)
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  36. Applying Inconsistent Mathematics.Mark Colyvan - unknown
    At various times, mathematicians have been forced to work with inconsistent mathematical theories. Sometimes the inconsistency of the theory in question was apparent (e.g. the early calculus), while at other times it was not (e.g. pre-paradox na¨ıve set theory). The way mathematicians confronted such difficulties is the subject of a great deal of interesting work in the history of mathematics but, apart from the crisis in set theory, there has been very little philosophical work on the topic of inconsistent mathematics. (...)
     
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  37. In Defence of Indispensability.Mark Colyvan - 1998 - Philosophia Mathematica 6 (1):39-62.
    Indispensability arguments for realism about mathematical entities have come under serious attack in recent years. To my mind the most profound attack has come from Penelope Maddy, who argues that scientific/mathematical practice doesn't support the key premise of the indispensability argument, that is, that we ought to have ontological commitment to those entities that are indispensable to our best scientific theories. In this paper I defend the Quine/Putnam indispensability argument against Maddy's objections.
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  38. Heaps of Gluts and Hyde-Ing the Sorites.JC Beall & Mark Colyvan - 2001 - Mind 110 (438):401--408.
    JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected]
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  39. (Book Review) Ontological Independence as the Mark of the Real. [REVIEW]Mark Colyvan - 2005 - Philosophia Mathematica 13 (2):216-225.
  40. Paradox Without Satisfaction.OtáVio Bueno & Mark Colyvan - 2003 - Analysis 63 (2):152–156.
    Consider the following denumerably infinite sequence of sentences: (s1) For all k > 1, sk is not true. (s2) For all k > 2, sk is not true. (s3) For all k > 3, sk is not true.
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  41. Paraconsistent Vagueness: Why Not?Dominic Hyde & Mark Colyvan - 2008 - Australasian Journal of Logic 6:107-121.
    The idea that the phenomenon of vagueness might be modelled by a paraconsistent logic has been little discussed in contemporary work on vagueness, just as the idea that paraconsistent logics might be fruitfully applied to the phenomenon of vagueness has been little discussed in contemporary work on paraconsistency. This is prima facie surprising given that the earliest formalisations of paraconsistent logics presented in Jáskowski and Halldén were presented as logics of vagueness. One possible explanation for this is that, despite initial (...)
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  42. The End of Mystery.Sam Baron & Mark Colyvan - 2019 - American Philosophical Quarterly 56 (3):247-264.
    Tim travels back in time and tries to kill his grandfather before his father was born. Tim fails. But why? Lewis's response was to cite "coincidences": Tim is the unlucky subject of gun jammings, banana peels, sudden changes of heart, and so on. A number of challenges have been raised against Lewis's response. The latest of these focuses on explanation. This paper diagnoses the source of this new disgruntlement and offers an alternative explanation for Tim's failure, one that Lewis would (...)
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  43. Mathematics: Truth and Fiction? Review of Mark Balaguer's Platonism and Anti-Platonism in Mathematics.Mark Colyvan & Edward N. Zalta - 1999 - Philosophia Mathematica 7 (3):336-349.
    Mark Balaguer’s project in this book is extremely ambitious; he sets out to defend both platonism and fictionalism about mathematical entities. Moreover, Balaguer argues that at the end of the day, platonism and fictionalism are on an equal footing. Not content to leave the matter there, however, he advances the anti-metaphysical conclusion that there is no fact of the matter about the existence of mathematical objects.1 Despite the ambitious nature of this project, for the most part Balaguer does not shortchange (...)
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  44.  39
    Logical Non-Apriorism and the Law of Non-Contradiction.Otavio Bueno & Mark Colyvan - 2004 - In Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.), The Law of Non-Contradiction : New Philosophical Essays. Oxford University Press. pp. 156--175.
    A common response to those who question the Law of Non-Contradiction is that it is impossible to debate such a fundamental law of logic. The reasons for this response vary, but what seems to underlie them is the thought that there is a minimal set of logical resources without which rational debate is impossible. This chapter argues that this response is misguided. First, it defends non-apriorism in logic: the view that logic is in the same epistemic boat as other scientific (...)
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  45.  11
    The Miracle of Applied Mathematics.Mark Colyvan - 2001 - Synthese 127 (3):265-278.
    Mathematics has a great variety ofapplications in the physical sciences.This simple, undeniable fact, however,gives rise to an interestingphilosophical problem:why should physical scientistsfind that they are unable to evenstate their theories without theresources of abstract mathematicaltheories? Moreover, theformulation of physical theories inthe language of mathematicsoften leads to new physical predictionswhich were quite unexpected onpurely physical grounds. It is thought by somethat the puzzles the applications of mathematicspresent are artefacts of out-dated philosophical theories about thenature of mathematics. In this paper I argue (...)
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  46. The Natural Environment is Valuable but Not Infinitely Valuable.Mark Colyvan, James Justus & Helen M. Regan - 2010 - Conservation Letters 3:224-228.
    It has been argued in the conservation literature that giving conservation absolute priority over competing interests would best protect the environment. Attributing infinite value to the environment or claiming it is ‘priceless’ are two ways of ensuring this priority (e.g. Hargrove 1989; Bulte and van Kooten 2000; Ackerman and Heinzerling 2002; McCauley 2006; Halsing and Moore 2008). But such proposals would paralyse conservation efforts. We describe the serious problems with these proposals and what they mean for practical applications, and we (...)
     
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  47. Is Probability the Only Coherent Approach to Uncertainty?Mark Colyvan - unknown
    In this article, I discuss an argument that purports to prove that probability theory is the only sensible means of dealing with uncertainty. I show that this argument can succeed only if some rather controversial assumptions about the nature of uncertainty are accepted. I discuss these assumptions and provide reasons for rejecting them. I also present examples of what I take to..
     
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  48. Looking for Contradictions.J. C. Beall & Mark Colyvan - 2001 - Australasian Journal of Philosophy 79 (4):564 – 569.
  49. Naturalism and the Paradox of Revisability.Mark Colyvan - 2006 - Pacific Philosophical Quarterly 87 (1):1–11.
    This paper examines the paradox of revisability. This paradox was proposed by Jerrold Katz as a problem for Quinean naturalised epistemology. Katz employs diagonalisation to demonstrate what he takes to be an inconsistency in the constitutive principles of Quine's epistemology. Specifically, the problem seems to rest with the principle of universal revisability which states that no statement is immune to revision. In this paper it is argued that although there is something odd about employing universal revisability to revise itself, there (...)
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  50. Analogical Thinking in Ecology: Looking Beyond Disciplinary Boundaries.Mark Colyvan & Lev R. Ginzburg - 2010 - The Quarterly Review of Biology 85 (2):171--182.
    ABSTRACT We consider several ways in which a good understanding of modern techniques and principles in physics can elucidate ecology, and we focus on analogical reasoning between these two branches of science. Analogical reasoning requires an understanding of both sciences and an appreciation of the similarities and points of contact between the two. In the current ecological literature on the relationship between ecology and physics, there has been some misunderstanding about the nature of modern physics and its methods. Physics is (...)
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