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Summary Probabilistic proofs involve non-deductively valid proof methodologies, which focus on establishing that conclusions have a high probability of being true. These methods often involve experimental practices (in a literal sense) and precise calculations to determine that some result is probably true.
Key works Adleman (1994), Fallis (1997), and Fallis (2002)
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  1. Kenny Easwaran (2009). Probabilistic Proofs and Transferability. Philosophia Mathematica 17 (3):341-362.
    In a series of papers, Don Fallis points out that although mathematicians are generally unwilling to accept merely probabilistic proofs, they do accept proofs that are incomplete, long and complicated, or partly carried out by computers. He argues that there are no epistemic grounds on which probabilistic proofs can be rejected while these other proofs are accepted. I defend the practice by presenting a property I call ‘transferability’, which probabilistic proofs lack and acceptable proofs have. I also consider what this (...)
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  2. D. Fallis (2000). The Reliability of Randomized Algorithms. British Journal for the Philosophy of Science 51 (2):255-271.
    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 (...)
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  3. Don Fallis (1997). The Epistemic Status of Probabilistic Proof. Journal of Philosophy 94 (4):165-186.
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  4. James Franklin (1987). Non-Deductive Logic in Mathematics. British Journal for the Philosophy of Science 38 (1):1-18.
    Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' or (...)
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  5. Jeffrey C. Jackson (2009). Randomized Arguments Are Transferable. Philosophia Mathematica 17 (3):363-368.
    Easwaran has given a definition of transferability and argued that, under this definition, randomized arguments are not transferable. I show that certain aspects of his definition are not suitable for addressing the underlying question of whether or not there is an epistemic distinction between randomized and deductive arguments. Furthermore, I demonstrate that for any suitable definition, randomized arguments are in fact transferable.
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