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  1. The Role of Notations in Mathematics.Carlo Cellucci - 2020 - Philosophia 48 (4):1397-1412.
    The terms of a mathematical problem become precise and concise if they are expressed in an appropriate notation, therefore notations are useful to mathematics. But are notations only useful, or also essential? According to prevailing view, they are not essential. Contrary to this view, this paper argues that notations are essential to mathematics, because they may play a crucial role in mathematical discovery. Specifically, since notations may consist of symbolic notations, diagrammatic notations, or a mix of symbolic and diagrammatic notations, (...)
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  • Mathematical Knowledge, the Analytic Method, and Naturalism.Fabio Sterpetti - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge: Approaches From Psychology and Cognitive Science. New York: Routledge. pp. 268-293.
    This chapter tries to answer the following question: How should we conceive of the method of mathematics, if we take a naturalist stance? The problem arises since mathematical knowledge is regarded as the paradigm of certain knowledge, because mathematics is based on the axiomatic method. Moreover, natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some authors tried to naturalize (...)
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  • Model Building and Problem Solving: A Case from Libor Market Derivatives.Giulia Miotti - 2019 - Topoi 40 (4):1-9.
    In my paper I focus on the growth of knowledge in finance from an heuristic viewpoint and I propose the analysis of two different knowledge-advancing strategies usually adopted at the frontier of knowledge, i.e. problem-solving and model-building. I show how these two strategies, even though both effective in the short-run, nonetheless provide descriptions of the target object and which are different in their descriptive and knowledge-advancing depth. In order to do so, I propose a case study borrowed from the modelling (...)
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  • Model Building and Problem Solving: A Case from Libor Market Derivatives.Giulia Miotti - 2019 - Topoi 40 (4):783-791.
    In my paper I focus on the growth of knowledge in finance from an heuristic viewpoint and I propose the analysis of two different knowledge-advancing strategies usually adopted at the frontier of knowledge, i.e. problem-solving and model-building. I show how these two strategies, even though both effective in the short-run, nonetheless provide descriptions of the target object and which are different in their descriptive and knowledge-advancing depth. In order to do so, I propose a case study borrowed from the modelling (...)
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  • Scientific Discovery Reloaded.Emiliano Ippoliti - 2020 - Topoi 39 (4):847-856.
    The way scientific discovery has been conceptualized has changed drastically in the last few decades: its relation to logic, inference, methods, and evolution has been deeply reloaded. The ‘philosophical matrix’ moulded by logical empiricism and analytical tradition has been challenged by the ‘friends of discovery’, who opened up the way to a rational investigation of discovery. This has produced not only new theories of discovery, but also new ways of practicing it in a rational and more systematic way. Ampliative rules, (...)
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