David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Philosophical Review 123 (1):1-41 (2014)
Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that this popular view is the result of two mistakes. The first mistake, which this essay calls the “numerical fallacy,” is to assume that a distinction that isn't represented by different numbers isn't represented at all in a mathematical representation. In this case, the essay claims that although the real numbers do not make all relevant distinctions, the full mathematical structure of a probability function does. The second mistake is that the hyperreals make too many distinctions. They have a much more complex structure than credences in ordinary propositions can have, so they make distinctions that don't exist among credences. While they might be useful for generating certain mathematical models, they will not appear in a faithful mathematical representation of credences of ordinary propositions
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Colin Howson (2013). Finite Additivity, Another Lottery Paradox and Conditionalisation. Synthese 191 (5):1-24.
Alan Hájek (2014). Unexpected Expectations. Mind 123 (490):533-567.
Daniel Jeremy Singer (2014). Sleeping Beauty Should Be Imprecise. Synthese 191 (14):3159-3172.
Justin M. Dallmann (2014). A Normatively Adequate Credal Reductivism. Synthese 191 (10):2301-2313.
Alexander R. Pruss (2014). Regular Probability Comparisons Imply the Banach–Tarski Paradox. Synthese 191 (15):3525-3540.
Similar books and articles
Nick Haverkamp & Moritz Schulz (2012). A Note on Comparative Probability. Erkenntnis 76 (3):395-402.
Kenneth L. Manders (1986). What Numbers Are Real? PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:253 - 269.
Jeremy Gwiazda (2012). On Infinite Number and Distance. Constructivist Foundations 7 (2):126-130.
Robert Sugden (2011). Explanations in Search of Observations. Biology and Philosophy 26 (5):717-736.
Eric Steinhart (2002). Why Numbers Are Sets. Synthese 133 (3):343 - 361.
Alan Hájek (2008). Arguments for–or Against–Probabilism? British Journal for the Philosophy of Science 59 (4):793 - 819.
Georges Dicker (2000). Regularity, Conditionality, and Asymmetry in Causation. The Proceedings of the Twentieth World Congress of Philosophy 7:129-138.
Véronique Izard, Pierre Pica, Elizabeth S. Spelke & Stanislas Dehaene (2008). Exact Equality and Successor Function: Two Key Concepts on the Path Towards Understanding Exact Numbers. Philosophical Psychology 21 (4):491 – 505.
Helen Beebee (2003). Seeing Causing. Proceedings of the Aristotelian Society 103 (3):257-280.
Alexandre Borovik, Renling Jin & Mikhail G. Katz (2012). An Integer Construction of Infinitesimals: Toward a Theory of Eudoxus Hyperreals. Notre Dame Journal of Formal Logic 53 (4):557-570.
Yaroslav Sergeyev (2009). Numerical Computations and Mathematical Modelling with Infinite and Infinitesimal Numbers. Journal of Applied Mathematics and Computing 29:177-195.
Added to index2011-12-13
Total downloads373 ( #4,322 of 1,792,980 )
Recent downloads (6 months)59 ( #15,811 of 1,792,980 )
How can I increase my downloads?