Mark Colyvan
Biographic Data
| ID | 1228486 |
|---|---|
| NAME | Mark Colyvan |
| GIVEN NAMES | Mark |
| FAMILY NAME | Colyvan |
| SIGNATURE | COLYVAN M |
| AFFILIATIONS | The University of Sydney |
| ORCID | 0000-0002-9789-4527 |
| VERIFIED | Yes |
| TOTAL WORKS | 22 |
| TOTAL CITATIONS | 59 |
| AUTHOR COUNT | 22 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1998 |
| LATEST PUBLICATION YEAR | 2026 |
| H-INDEX | 4 |
Notations as Models: Music and Mathematics
In this paper we argue for a surprising similarity between the kinds of roles notation plays in music and in mathematics. We argue that in both cases the notation is doing more than merely documenting something that we have an independent grip on – either a musical performance/composition or a mathematical structure. In both instances, the notation can lead to new innovations, it can help in abstracting away from distracting details and it can fa…
Do conspiracy-theory interventions rest on a mistake
In this paper we argue that the problem of conspiracy theories circulating through specific social groups runs deeper than is appreciated. The epistemic networks involved in the propagation of conspiracy theories cannot always be deemed to be irrational, with motivated reasoning at their heart. There are, after all, rational epistemic bubbles—those that rightly ignore unreliable information sources. We provide a rational reconstruction of conspir…
Meta-uncertainty and the proof paradoxes
Various real and imagined criminal law cases rest on “naked statistical evidence”. That is, they rest more or less entirely on a probability for guilt/liability derived from a single statistical model. The intuition is that there is something missing in these cases, high as the probability for guilt/liability may be, such that the relevant standard for legal proof is not met. Here we contribute to the considerable debate about how this intuition …
The Prospects for a Monist Theory of Non-causal Explanation in Science and Mathematics
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…
Explanation impossible
Non-naturalistic moral explanation
Legal Probabilism: A Qualified Defence
Idealisations in normative models
Disagreement behind the veil of ignorance
An Introduction to the Philosophy of Mathematics
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 mathemati…
Philosophical Issues in Ecology: Recent Trends and Future Directions
Colyvan, M., S. Linquist, W. Grey, P. Griffiths, J. Odenbaugh, and H. P. Possingham. 2009. Philosophical issues in ecology: recent trends and future directions. Ecology and Society 14(2): 22. https://doi.org/10.5751/ES-03020-140222
Who’s Afraid of Inconsistent Mathematics
In formal logic, a contradiction is the signal of a defeat: but in the evolution of real knowledge it marks the first step in progress towards a victory . Alfred North Whitehead (1861–1947) Contemporary mathematical theories are generally thought to be consistent. But it hasn't always been this way; there have been times when the consistency of mathematics has been called into question. Some theories, such as naive set theory and (arguably) the e…
Mathematical recreation versus mathematical knowledge
Empiricism in the philosophy of mathematics has a chequered history. Mill de- fended a version of empiricism according to which the laws of arithmetic were highly general laws of nature. Mathematical truths such as 2+3 = 5 were thought by Mill to be empirical in that they tell us that if we were to take two logic books, say, and three ethics books, say, we’d have five philosophy books. But Mill’s somewhat naive empiricism found itself on the rece…
Legal Decisions and the Reference Class Problem
There has been a long history of discussion on the usefulness of formal methods in legal settings. Some of the recent debate has focussed on foundational issues in statistics, in particular, how the reference-class problem affects legal decisions based on certain types of statistical evidence. Here we examine aspects of this debate, stressing why the reference-class problem presents serious difficulties for the kinds of statistical inferences und…
No Expectations
Journal Article No Expectations Get access Mark Colyvan Mark Colyvan Department of Philosophy, University of Sydney, Sydney, NSW, 2006, Australia. [email protected] Search for other works by this author on: Oxford Academic Google Scholar Mind, Volume 115, Issue 459, July 2006, Pages 695–702, https://doi.org/10.1093/mind/fzl695 Published: 01 July 2006
Problems With the Argument From Fine Tuning
Ecological Orbits: How Planets Move and Populations Grow
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 the 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 cur…
The Indispensability of Mathematics
Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical entities indispensable to our best scientific theories. The indispensability argument has come under serious scrutiny in recent times, with many influential philosophers unconvinced of its cogency. This book outlines the indispensability argument in conside…
Is it a Crime to Belong to a Reference Class
The Miracle of Applied Mathematics
Conceptual Contingency and Abstract Existence
I discuss the issue of whether the existence or non-existence of mathematical entities is a contingent matter. I focus on the debate between Hartry Field and Bob Hale and Crispin Wright, and I argue that a good reason for accepting that mathematical entities contingently exist or contingently fail to exist has been overlooked by all participants in this debate. © The Editors of The Philosophical Quarterly, 2000
Is platonism a bad bet?
Is it a Crime to Belong to a Reference Class
Idealisations in normative models
Legal Probabilism: A Qualified Defence
Disagreement behind the veil of ignorance
The Miracle of Applied Mathematics
Conceptual Contingency and Abstract Existence
I discuss the issue of whether the existence or non-existence of mathematical entities is a contingent matter. I focus on the debate between Hartry Field and Bob Hale and Crispin Wright, and I argue that a good reason for accepting that mathematical entities contingently exist or contingently fail to exist has been overlooked by all participants in this debate. © The Editors of The Philosophical Quarterly, 2000
Legal Decisions and the Reference Class Problem
There has been a long history of discussion on the usefulness of formal methods in legal settings. Some of the recent debate has focussed on foundational issues in statistics, in particular, how the reference-class problem affects legal decisions based on certain types of statistical evidence. Here we examine aspects of this debate, stressing why the reference-class problem presents serious difficulties for the kinds of statistical inferences und…
Problems With the Argument From Fine Tuning
Philosophical Issues in Ecology: Recent Trends and Future Directions
Colyvan, M., S. Linquist, W. Grey, P. Griffiths, J. Odenbaugh, and H. P. Possingham. 2009. Philosophical issues in ecology: recent trends and future directions. Ecology and Society 14(2): 22. https://doi.org/10.5751/ES-03020-140222
Non-naturalistic moral explanation
Is platonism a bad bet?
Conceptual Contingency and Abstract Existence
I discuss the issue of whether the existence or non-existence of mathematical entities is a contingent matter. I focus on the debate between Hartry Field and Bob Hale and Crispin Wright, and I argue that a good reason for accepting that mathematical entities contingently exist or contingently fail to exist has been overlooked by all participants in this debate. © The Editors of The Philosophical Quarterly, 2000
The Indispensability of Mathematics
Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical entities indispensable to our best scientific theories. The indispensability argument has come under serious scrutiny in recent times, with many influential philosophers unconvinced of its cogency. This book outlines the indispensability argument in conside…
Is it a Crime to Belong to a Reference Class
The Miracle of Applied Mathematics
Ecological Orbits: How Planets Move and Populations Grow
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 the 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 cur…
Problems With the Argument From Fine Tuning
No Expectations
Journal Article No Expectations Get access Mark Colyvan Mark Colyvan Department of Philosophy, University of Sydney, Sydney, NSW, 2006, Australia. [email protected] Search for other works by this author on: Oxford Academic Google Scholar Mind, Volume 115, Issue 459, July 2006, Pages 695–702, https://doi.org/10.1093/mind/fzl695 Published: 01 July 2006
Mathematical recreation versus mathematical knowledge
Empiricism in the philosophy of mathematics has a chequered history. Mill de- fended a version of empiricism according to which the laws of arithmetic were highly general laws of nature. Mathematical truths such as 2+3 = 5 were thought by Mill to be empirical in that they tell us that if we were to take two logic books, say, and three ethics books, say, we’d have five philosophy books. But Mill’s somewhat naive empiricism found itself on the rece…
Legal Decisions and the Reference Class Problem
There has been a long history of discussion on the usefulness of formal methods in legal settings. Some of the recent debate has focussed on foundational issues in statistics, in particular, how the reference-class problem affects legal decisions based on certain types of statistical evidence. Here we examine aspects of this debate, stressing why the reference-class problem presents serious difficulties for the kinds of statistical inferences und…
Who’s Afraid of Inconsistent Mathematics
In formal logic, a contradiction is the signal of a defeat: but in the evolution of real knowledge it marks the first step in progress towards a victory . Alfred North Whitehead (1861–1947) Contemporary mathematical theories are generally thought to be consistent. But it hasn't always been this way; there have been times when the consistency of mathematics has been called into question. Some theories, such as naive set theory and (arguably) the e…
Philosophical Issues in Ecology: Recent Trends and Future Directions
Colyvan, M., S. Linquist, W. Grey, P. Griffiths, J. Odenbaugh, and H. P. Possingham. 2009. Philosophical issues in ecology: recent trends and future directions. Ecology and Society 14(2): 22. https://doi.org/10.5751/ES-03020-140222
An Introduction to the Philosophy of Mathematics
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 mathemati…
Idealisations in normative models
Disagreement behind the veil of ignorance
Legal Probabilism: A Qualified Defence
Explanation impossible
Non-naturalistic moral explanation
The Prospects for a Monist Theory of Non-causal Explanation in Science and Mathematics
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…
Meta-uncertainty and the proof paradoxes
Various real and imagined criminal law cases rest on “naked statistical evidence”. That is, they rest more or less entirely on a probability for guilt/liability derived from a single statistical model. The intuition is that there is something missing in these cases, high as the probability for guilt/liability may be, such that the relevant standard for legal proof is not met. Here we contribute to the considerable debate about how this intuition …
Do conspiracy-theory interventions rest on a mistake
In this paper we argue that the problem of conspiracy theories circulating through specific social groups runs deeper than is appreciated. The epistemic networks involved in the propagation of conspiracy theories cannot always be deemed to be irrational, with motivated reasoning at their heart. There are, after all, rational epistemic bubbles—those that rightly ignore unreliable information sources. We provide a rational reconstruction of conspir…
Notations as Models: Music and Mathematics
In this paper we argue for a surprising similarity between the kinds of roles notation plays in music and in mathematics. We argue that in both cases the notation is doing more than merely documenting something that we have an independent grip on – either a musical performance/composition or a mathematical structure. In both instances, the notation can lead to new innovations, it can help in abstracting away from distracting details and it can fa…
Philosophy (14 works) · Epistemology (13 works) · Metaphysics (9 works) · Philosophy of language (8 works) · Philosophy and History of Science (7 works) · Sociology (7 works) · Mathematics (6 works) · Philosophy and Theoretical Science (6 works) · Philosophy of science (6 works) · Computer Science (5 works)