Infinite Lotteries, Perfectly Thin Darts and Infinitesimals

One of the problems that Bayesian regularity, the thesis that all contingent propositions should be given probabilities strictly between zero and one, faces is the possibility of random processes that randomly and uniformly choose a number between zero and one. According to classical probability theory, the probability that such a process picks a particular number in the range is zero, but of course any number in the range can indeed be picked. There is a solution to this particular problem on the books: a measure that assigns the same infinitesimal probability to each number between zero and one. I will show that such a measure, while mathematically interesting, is pathological for use in confirmation theory, for the same reason that a measure that assigns an infinitesimal probability to each possible outcome in a countably infinite lottery is pathological. The pathology is that one can force someone to assign a probability within an infinitesimal of one to an unlikely event
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1002/tht3.13
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 16,661
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

View all 6 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles
Yaroslav Sergeyev (2010). Lagrange Lecture: Methodology of Numerical Computations with Infinities and Infinitesimals. Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.

Monthly downloads

Added to index


Total downloads

26 ( #117,489 of 1,726,249 )

Recent downloads (6 months)

4 ( #183,615 of 1,726,249 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.