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Rebecca Lea Morris [7]Rebecca Morris [5]Rebecca H. Morris [1]
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Rebecca Morris
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  1.  96
    Philosophy of mathematical practice: A primer for mathematics educators.Yacin Hamami & Rebecca Morris - 2020 - ZDM Mathematics Education 52:1113–1126.
    In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice . In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the (...)
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  2.  95
    Plans and planning in mathematical proofs.Yacin Hamami & Rebecca Lea Morris - 2020 - Review of Symbolic Logic 14 (4):1030-1065.
    In practice, mathematical proofs are most often the result of careful planning by the agents who produced them. As a consequence, each mathematical proof inherits a plan in virtue of the way it is produced, a plan which underlies its “architecture” or “unity”. This paper provides an account of plans and planning in the context of mathematical proofs. The approach adopted here consists in looking for these notions not in mathematical proofs themselves, but in the agents who produced them. The (...)
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  3.  67
    Motivated proofs: What they are, why they matter and how to write them.Rebecca Lea Morris - 2020 - Review of Symbolic Logic 13 (1):23-46.
    Mathematicians judge proofs to possess, or lack, a variety of different qualities, including, for example, explanatory power, depth, purity, beauty and fit. Philosophers of mathematical practice have begun to investigate the nature of such qualities. However, mathematicians frequently draw attention to another desirable proof quality: being motivated. Intuitively, motivated proofs contain no "puzzling" steps, but they have received little further analysis. In this paper, I begin a philosophical investigation into motivated proofs. I suggest that a proof is motivated if and (...)
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  4.  45
    Character and object.Rebecca Morris & Jeremy Avigad - 2016 - Review of Symbolic Logic 9 (3):480-510.
    In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. Modern presentations of the proof are explicitly higher-order, in that they involve quantifying over and summing over Dirichlet characters, which are certain types of functions. The notion of a character is only implicit in Dirichlet’s original proof, and the subsequent history shows a very gradual transition to the modern mode of presentation. In this essay, we (...)
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  5.  84
    Dedekind’s structuralism: creating concepts and deriving theorems.Wilfried Sieg & Rebecca Morris - 2018 - In Erich Reck (ed.), Logic, Philosophy of Mathematics, and their History: Essays in Honor W.W. Tait. College Publications.
    Dedekind’s structuralism is a crucial source for the structuralism of mathematical practice—with its focus on abstract concepts like groups and fields. It plays an equally central role for the structuralism of philosophical analysis—with its focus on particular mathematical objects like natural and real numbers. Tensions between these structuralisms are palpable in Dedekind’s work, but are resolved in his essay Was sind und was sollen die Zahlen? In a radical shift, Dedekind extends his mathematical approach to “the” natural numbers. He creates (...)
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  6. Opinion: Reproducibility failures are essential to scientific inquiry.A. David Redish, Erich Kummerfeld, Rebecca Morris & Alan Love - 2018 - Proceedings of the National Academy of Sciences 115 (20):5042-5046.
    Current fears of a “reproducibility crisis” have led researchers, sources of scientific funding, and the public to question both the efficacy and trustworthiness of science. Suggested policy changes have been focused on statistical problems, such as p-hacking, and issues of experimental design and execution. However, “reproducibility” is a broad concept that includes a number of issues. Furthermore, reproducibility failures occur even in fields such as mathematics or computer science that do not have statistical problems or issues with experimental design. Most (...)
     
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  7.  69
    Do mathematical explanations have instrumental value?Rebecca Lea Morris - 2019 - Synthese (2):1-20.
    Scientific explanations are widely recognized to have instrumental value by helping scientists make predictions and control their environment. In this paper I raise, and provide a first analysis of, the question whether explanatory proofs in mathematics have analogous instrumental value. I first identify an important goal in mathematical practice: reusing resources from existing proofs to solve new problems. I then consider the more specific question: do explanatory proofs have instrumental value by promoting reuse of the resources they contain? In general, (...)
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  8.  22
    Rationality in Mathematical Proofs.Yacin Hamami & Rebecca Lea Morris - 2023 - Australasian Journal of Philosophy 101 (4):793-808.
    Mathematical proofs are not sequences of arbitrary deductive steps—each deductive step is, to some extent, rational. This paper aims to identify and characterize the particular form of rationality at play in mathematical proofs. The approach adopted consists in viewing mathematical proofs as reports of proof activities—that is, sequences of deductive inferences—and in characterizing the rationality of the former in terms of that of the latter. It is argued that proof activities are governed by specific norms of rational planning agency, and (...)
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  9.  48
    The concept of “character” in Dirichlet’s theorem on primes in an arithmetic progression.Jeremy Avigad & Rebecca Morris - 2014 - Archive for History of Exact Sciences 68 (3):265-326.
    In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses ofDirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method.
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  10.  47
    Intellectual generosity and the reward structure of mathematics.Rebecca Lea Morris - 2020 - Synthese (1-2):1-23.
    Prominent mathematician William Thurston was praised by other mathematicians for his intellectual generosity. But what does it mean to say Thurston was intellectually generous? And is being intellectually generous beneficial? To answer these questions I turn to virtue epistemology and, in particular, Roberts and Wood's (2007) analysis of intellectual generosity. By appealing to Thurston's own writings and interviewing mathematicians who knew and worked with him, I argue that Roberts and Wood's analysis nicely captures the sense in which he was intellectually (...)
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  11.  32
    Understanding in mathematics: The case of mathematical proofs.Yacin Hamami & Rebecca Lea Morris - forthcoming - Noûs.
    Although understanding is the object of a growing literature in epistemology and the philosophy of science, only few studies have concerned understanding in mathematics. This essay offers an account of a fundamental form of mathematical understanding: proof understanding. The account builds on a simple idea, namely that understanding a proof amounts to rationally reconstructing its underlying plan. This characterization is fleshed out by specifying the relevant notion of plan and the associated process of rational reconstruction, building in part on Bratman's (...)
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  12.  32
    Increasing Specialization: Why We Need to Make Mathematics More Accessible.Rebecca Lea Morris - 2020 - Social Epistemology 35 (1):37-47.
    Mathematics is becoming increasingly specialized, divided into a vast and growing number of subfields. While this division of cognitive labor has important benefits, it also has a significant drawb...
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  13.  4
    Early life exposure to air pollution impacts neuronal and glial cell function leading to impaired neurodevelopment.Rebecca H. Morris, Serena J. Counsell, Imelda M. McGonnell & Claire Thornton - 2021 - Bioessays 43 (9):2000288.
    The World Health Organisation recently listed air pollution as the most significant threat to human health. Air pollution comprises particulate matter (PM), metals, black carbon and gases such as ozone (O3), nitrogen dioxide (NO2) and carbon monoxide (CO). In addition to respiratory and cardiovascular disease, PM exposure is linked with increased risk of neurodegeneration as well as neurodevelopmental impairments. Critically, studies suggest that PM crosses the placenta, making direct in utero exposure a reality. Rodent models reveal that neuroinflammation, neurotransmitter imbalance (...)
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