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  1.  48
    Informational Equivalence but Computational Differences? Herbert Simon on Representations in Scientific Practice.David Waszek - 2024 - Minds and Machines 34 (1):93-116.
    To explain why, in scientific problem solving, a diagram can be “worth ten thousand words,” Jill Larkin and Herbert Simon (1987) relied on a computer model: two representations can be “informationally” equivalent but differ “computationally,” just as the same data can be encoded in a computer in multiple ways, more or less suited to different kinds of processing. The roots of this proposal lay in cognitive psychology, more precisely in the “imagery debate” of the 1970s on whether there are image-like (...)
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  2.  38
    Are Euclid's Diagrams Representations? On an Argument by Ken Manders.David Waszek - 2022 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics. The CSHPM 2019-2020 Volume. Birkhäuser. pp. 115-127.
    In his well-known paper on Euclid’s geometry, Ken Manders sketches an argument against conceiving the diagrams of the Elements in ‘semantic’ terms, that is, against treating them as representations—resting his case on Euclid’s striking use of ‘impossible’ diagrams in some proofs by contradiction. This paper spells out, clarifies and assesses Manders’s argument, showing that it only succeeds against a particular semantic view of diagrams and can be evaded by adopting others, but arguing that Manders nevertheless makes a compelling case that (...)
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  3. Signs as a Theme in the Philosophy of Mathematical Practice.David Waszek - 2024 - In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer.
    Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential to (...)
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  4.  35
    Calculus as method or calculus as rules? Boole and Frege on the aims of a logical calculus.Dirk Schlimm & David Waszek - 2021 - Synthese 199 (5-6):11913-11943.
    By way of a close reading of Boole and Frege’s solutions to the same logical problem, we highlight an underappreciated aspect of Boole’s work—and of its difference with Frege’s better-known approach—which we believe sheds light on the concepts of ‘calculus’ and ‘mechanization’ and on their history. Boole has a clear notion of a logical problem; for him, the whole point of a logical calculus is to enable systematic and goal-directed solution methods for such problems. Frege’s Begriffsschrift, on the other hand, (...)
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  5.  63
    Multiple readability in principle and practice: Existential Graphs and complex symbols.Dirk Schlimm & David Waszek - 2020 - Logique Et Analyse 251:231-260.
    Since Sun-Joo Shin's groundbreaking study (2002), Peirce's existential graphs have attracted much attention as a way of writing logic that seems profoundly different from our usual logical calculi. In particular, Shin argued that existential graphs enjoy a distinctive property that marks them out as "diagrammatic": they are "multiply readable," in the sense that there are several di erent, equally legitimate ways to translate one and the same graph into a standard logical language. Stenning (2000) and Bellucci and Pietarinen (2016) have (...)
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  6.  23
    Rigor and the Context-Dependence of Diagrams: The Case of Euler Diagrams.David Waszek - 2004 - In A. Blackwell, K. Marriott & A. Shimojima (eds.), Diagrammatic Representation and Inference. Springer. pp. 382-389.
    Euler famously used diagrams to illustrate syllogisms in his Lettres à une princesse d’Allemagne [1]. His diagrams are usually seen as suffering from a fatal “ambiguity problem” [11]: as soon as they involve intersecting circles, which are required for the representation of existential statements, it becomes unclear what exactly may be read off from them, and as Hammer & Shin conclusively showed, any set of reading conventions can lead to erroneous conclusions. I claim that Euler diagrams can, however, be used (...)
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  7.  32
    Are larger studies always better? Sample size and data pooling effects in research communities.David Waszek & Cyrille Imbert - unknown
    The persistent pervasiveness of inappropriately small studies in empirical fields is regu-larly deplored in scientific discussions. Consensually, taken individually, higher-powered studies are more likely to be truth-conducive. However, are they also beneficial for the wider performance of truth-seeking communities? We study the impact of sample sizes on collective exploration dynamics under ordinary conditions of resource limita-tion. We find that large collaborative studies, because they decrease diversity, can have detrimental effects in certain realistic circumstances that we characterize precisely. We show how (...)
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