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  1. J. Azzouni (2013). That We See That Some Diagrammatic Proofs Are Perfectly Rigorous. Philosophia Mathematica 21 (3):323-338.
    Mistaken reasons for thinking diagrammatic proofs aren't rigorous are explored. The main result is that a confusion between the contents of a proof procedure (what's expressed by the referential elements in a proof procedure) and the unarticulated mathematical aspects of a proof procedure (how that proof procedure is enabled) gives the impression that diagrammatic proofs are less rigorous than language proofs. An additional (and independent) factor is treating the impossibility of naturally generalizing a diagrammatic proof procedure as an indication of (...)
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  2. Carlo Cellucci (forthcoming). Explanatory and Non-Explanatory Demonstrations. In P.-E. Bour & P. Schroeder-Heister (eds.), Proceedings of the 14th Congress of Logic, Methodology and Philosophy of Science Nancy, July 19-26, 2011. College Publications.
    This paper concerns the question whether there exists an objective distinction between explanatory and non-explanatory demonstrations. It distinguishes between a static and a dynamic approach to explanatory demonstration, it discusses the relevance of this distinction to mathematical practice, and considers the relation of mathematical explanation to mathematical understanding.
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  3. 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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  4. Mark McEvoy (2008). The Epistemological Status of Computer-Assisted Proofs. Philosophia Mathematica 16 (3):374-387.
    Several high-profile mathematical problems have been solved in recent decades by computer-assisted proofs. Some philosophers have argued that such proofs are a posteriori on the grounds that some such proofs are unsurveyable; that our warrant for accepting these proofs involves empirical claims about the reliability of computers; that there might be errors in the computer or program executing the proof; and that appeal to computer introduces into a proof an experimental element. I argue that none of these arguments withstands scrutiny, (...)
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  5. Mark McEvoy (2013). Experimental Mathematics, Computers and the a Priori. Synthese 190 (3):397-412.
    In recent decades, experimental mathematics has emerged as a new branch of mathematics. This new branch is defined less by its subject matter, and more by its use of computer assisted reasoning. Experimental mathematics uses a variety of computer assisted approaches to verify or prove mathematical hypotheses. For example, there is “number crunching” such as searching for very large Mersenne primes, and showing that the Goldbach conjecture holds for all even numbers less than 2 × 1018. There are “verifications” of (...)
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  6. E. Mendelson (2005). Selmer Bringsjord and Michael Zenzen. Superminds: People Harness Hypercomputation, and More. Studies in Cognitive Systems, Volume 29. Dordrecht: Kluwer Academic Publishers, 2003. Pp. Xxx + 339. ISBN 1-4020-1094-X. [REVIEW] Philosophia Mathematica 13 (2):228-230.
  7. Ryszard Stanisław Michalski (1977). Toward Computer-Aided Induction: A Brief Review of Currently Implemented Aqval Programs. Dept. Of Computer Science, University of Illinois at Urbana-Champaign.
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  8. Philip L. Peterson (1991). What is Empirical in Mathematics? Philosophia Mathematica (1):91-110.
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  9. George Polya (1990). Mathematics and Plausible Reasoning. Princeton University Press.
    Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.
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  10. George Pólya (1968). Mathematics and Plausible Reasoning. Princeton, N.J.,Princeton University Press.
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  11. David Sherry (2006). Mathematical Reasoning: Induction, Deduction and Beyond. Studies in History and Philosophy of Science Part A 37 (3):489-504.