Philosophia Mathematica (forthcoming)

Abstract
ABSTRACTA probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon external hyperreal-valued measures. We show that internal hyperfinite measures are not underdetermined. The importance of internality stems from the fact that Robinson’s transfer principle only applies to internal entities. We also evaluate the claim that transferless ordered fields may have advantages over hyperreals in probabilistic modeling. We show that probabilities developed over such fields are less expressive than hyperreal probabilities.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/nkaa033
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,410
External links

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

What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
A Subjectivist’s Guide to Objective Chance.David K. Lewis - 1980 - In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II. Berkeley: University of California Press. pp. 263-293.
Non-Standard Analysis.Abraham Robinson - 1961 - North-Holland Publishing Co..
Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.

View all 32 references / Add more references

Citations of this work BETA

Weintraub’s Response to Williamson’s Coin Flip Argument.Matthew W. Parker - 2021 - European Journal for Philosophy of Science 11 (3):1-21.

Add more citations

Similar books and articles

Infinite Lotteries, Perfectly Thin Darts and Infinitesimals.Alexander R. Pruss - 2012 - Thought: A Journal of Philosophy 1 (2):81-89.
Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.
Cardinality Arguments Against Regular Probability Measures.Thomas Hofweber - 2014 - Thought: A Journal of Philosophy 3 (2):166-175.
Infinitesimal Probabilities.Sylvia Wenmackers - 2016 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 199-265.
A Consistent Set of Infinite-Order Probabilities.David Atkinson & Jeanne Peijnenburg - 2013 - International Journal of Approximate Reasoning 54:1351-1360.

Analytics

Added to PP index
2020-09-29

Total views
9 ( #954,737 of 2,519,700 )

Recent downloads (6 months)
1 ( #406,314 of 2,519,700 )

How can I increase my downloads?

Downloads

My notes