Abstract
Recently, certain philosophers of mathematics (Fallis [1997]; Womack and Farach [1997]) have argued that there are no epistemic considerations that should stop mathematicians from using probabilistic methods to establish that mathematical propositions are true. However, mathematicians clearly should not use methods that are unreliable. Unfortunately, due to the fact that randomized algorithms are not really random in practice, there is reason to doubt their reliability. In this paper, I analyze the prospects for establishing that randomized algorithms are reliable. I end by arguing that it would be inconsistent for mathematicians to suspend judgement on the truth of mathematical propositions on the basis of worries about the reliability of randomized algorithms.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 255-271 |
| Number of pages | 17 |
| Journal | British Journal for the Philosophy of Science |
| Volume | 51 |
| Issue number | 2 |
| State | Published - Jun 2000 |
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ASJC Scopus subject areas
- History
- History and Philosophy of Science
- Philosophy
Cite this
The reliability of randomized algorithms. / Fallis, Don T.
In: British Journal for the Philosophy of Science, Vol. 51, No. 2, 06.2000, p. 255-271.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The reliability of randomized algorithms
AU - Fallis, Don T
PY - 2000/6
Y1 - 2000/6
N2 - Recently, certain philosophers of mathematics (Fallis [1997]; Womack and Farach [1997]) have argued that there are no epistemic considerations that should stop mathematicians from using probabilistic methods to establish that mathematical propositions are true. However, mathematicians clearly should not use methods that are unreliable. Unfortunately, due to the fact that randomized algorithms are not really random in practice, there is reason to doubt their reliability. In this paper, I analyze the prospects for establishing that randomized algorithms are reliable. I end by arguing that it would be inconsistent for mathematicians to suspend judgement on the truth of mathematical propositions on the basis of worries about the reliability of randomized algorithms.
AB - Recently, certain philosophers of mathematics (Fallis [1997]; Womack and Farach [1997]) have argued that there are no epistemic considerations that should stop mathematicians from using probabilistic methods to establish that mathematical propositions are true. However, mathematicians clearly should not use methods that are unreliable. Unfortunately, due to the fact that randomized algorithms are not really random in practice, there is reason to doubt their reliability. In this paper, I analyze the prospects for establishing that randomized algorithms are reliable. I end by arguing that it would be inconsistent for mathematicians to suspend judgement on the truth of mathematical propositions on the basis of worries about the reliability of randomized algorithms.
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M3 - Article
AN - SCOPUS:0039331126
VL - 51
SP - 255
EP - 271
JO - British Journal for the Philosophy of Science
JF - British Journal for the Philosophy of Science
SN - 0007-0882
IS - 2
ER -