Logical Probability and the Strength of Mathematical Conjectures

@article{Franklin2016LogicalPA,
  title={Logical Probability and the Strength of Mathematical Conjectures},
  author={James Franklin},
  journal={The Mathematical Intelligencer},
  year={2016},
  volume={38},
  pages={14-19}
}
  • J. Franklin
  • Published 12 April 2016
  • Philosophy
  • The Mathematical Intelligencer
Mathematicians often speak of the evidence for unproved conjectures, such as the Riemann Hypothesis. It is argued that such evidence should be seen in terms of logical probability in Keynes's sense: a strictly logical degree of partial implication. That is essentially the same as objective Bayesianism. Examples are given and explained in terms of the objective logical strength of evidence. 
4 Citations
Bayesian Perspectives on Mathematical Practice
TLDR
The (objective) Bayesian view of probability is explained, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics and how the evaluation of evidence for conjectures works in mathematical practice.
Hung Jury: The Verdict on Uncertainty
Classical probability and the statistical methods built around it, like hypothesis testing, have been shown to have many glaring weaknesses, as the work of Hung Nguyen has shown with clarity and
Bayesian Perspectives on Mathematical Practice
  • J. Franklin
  • Mathematics
    Handbook of the History and Philosophy of Mathematical Practice
  • 2021

References

SHOWING 1-10 OF 27 REFERENCES
Non-deductive Logic in Mathematics: The Probability of Conjectures
Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no
Resurrecting Logical Probability
The logical interpretation of probability, or ``objective Bayesianism''– the theory that (some) probabilitiesare strictly logical degrees of partial implication – is defended.The main argument
The objective Bayesian conceptualisation of proof and reference class problems
The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a
Probability Theory: The Logic of Science
This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. Now results are discussed, along with the application of probability theory to a wide
Philosophy and the practice of Bayesian statistics.
  • A. Gelman, C. Shalizi
  • Economics
    The British journal of mathematical and statistical psychology
  • 2013
TLDR
It is argued that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism.
Mathematics by experiment - plausible reasoning in the 21st century
TLDR
Pi and its friends, and “Normality: A stubborn question,” from Mathematics by Experiment: Plausible Reasoning in the 21st Century, A. K. Peters, Natick, MA, 2nd edition, 2008.
Is it Plausible?
We mathematicians have handy ways of discovering what stands a chance of being true. And we have a range of different modes of evidence that help us form these expectations; such as: analogies with
Mathematics And Plausible Reasoning Vol I Induction And Analogy In Mathematics
Thank you very much for downloading mathematics and plausible reasoning vol i induction and analogy in mathematics. As you may know, people have look numerous times for their favorite readings like
The case for objective Bayesian analysis
TLDR
It is suggested that the statistical community should accept formal objective Bayesian techniques with confidence, but should be more cautious about casual objectiveBayesian techniques.
...
1
2
3
...