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Added by: Clotilde Torregrossa, Contributed by: Simon Fokt
Abstract: Several accounts of representation in cognitive systems have recently been proposed. These look for a theory that will establish how a representation comes to have a certain content, and how these representations are used by cognitive systems. Covariation accounts are unsatisfactory, as they make intelligent reasoning and cognition impossible. Cummins' interpretation-based account cannot explain the distinction between cognitive and non-cognitive systems, nor how certain cognitive representations appear to have intrinsic meaning. Cognitive systems can be defined as model-constructers, or systems that use information from interpreted models as arguments in the functions they execute. An account based on this definition solves many of the problems raised by the earlier proposalsLehan, Vanessa. Reducing Stereotype Threat in First-Year Logic Classes2015, Feminist Philosophy Quarterly 1 (2):1-13.-
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Added by: Clotilde Torregrossa, Contributed by: Matthew Clemens
Abstract: In this paper I examine some research on how to diminish or eliminate stereotype threat in mathematics. Some of the successful strategies include: informing our students about stereotype threat, challenging the idea that logical intelligence is an 'innate' ability, making students In threatened groups feel welcomed, and introducing counter-stereotypical role models. The purpose of this paper is to take these strategies that have proven successful and come up with specific ways to incorporate them into introductory logic classes. For example, the possible benefit of presenting logic to our undergraduate students by concentrating on aspects of logic that do not result in a clash of schemas.Comment: A very accessible paper, requiring virtually no previous knowledge of logic or feminist philosophy. It is particularly appropriate for the "logic" session of a course on teaching philosophy. It can also be proposed as a preliminary reading for an intro to Logic course, insofar as knowledge of the interaction between stereotype threat and logic performance can have a positive effect on the performance of those potentially affected (as argued in the paper itself).
Leng, Mary. Mathematics and Reality2010, Oxford University Press, USA.-
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Added by: Jamie Collin
Publisher's Note: Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.Comment: This book presents the most developed account of mathematical fictionalism. The book, or chapters from it, would provide useful further reading in advanced undergraduate or postgraduate courses on metaphysics or philosophy of mathematics.
Leng, Mary. “Algebraic” Approaches to Mathematics2009, In Otávio Bueno & Øystein Linnebo (eds.). New Waves in Philosophy of Mathematics. Palgrave Macmillan.-
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Added by: Jamie Collin
Summary: Surveys the opposition between views of mathematics which take mathematics to represent a independent mathematical reality and views which take mathematical axioms to define or circumscribe their subject matter; and defends the latter view against influential objections.Comment: A very clear and useful survey text for advanced undergraduate or postgraduate courses on metaphysics or philosophy of mathematics.
Leng, Mary. What’s there to know?2007, In M. Leng, A. Paseau, and M. Potter (eds.), Mathematical Knowledge. OUP-
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Added by: Jamie Collin
Summary: Defends an account of mathematical knowledge in which mathematical knowledge is a kind of modal knowledge. Leng argues that nominalists should take mathematical knowledge to consist in knowledge of the consistency of mathematical axiomatic systems, and knowledge of what necessarily follows from those axioms. She defends this view against objections that modal knowledge requires knowledge of abstract objects, and argues that we should understand possibility and necessity in a primative way.Comment: This would be useful in an advanced undergraduate course on metaphysics, epistemology or philosophy of logic and mathematics. This is not an easy paper, but Leng does an excellent job of making clear some difficult ideas. The view defended is an important one in both philosophy of logic and philosophy of mathematics. Any reasonably comprehensive treatment of nominalism should include this paper.
Leng, Mary. Platonism and Anti-Platonism: Why Worry?2005, International Studies in the Philosophy of Science 19(1):65-84-
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Added by: Sara Peppe
Abstract: This paper argues that it is scientific realists who should be most concerned about the issue of Platonism and anti-Platonism in mathematics. If one is merely interested in accounting for the practice of pure mathematics, it is unlikely that a story about the ontology of mathematical theories will be essential to such an account. The question of mathematical ontology comes to the fore, however, once one considers our scientific theories. Given that those theories include amongst their laws assertions that imply the existence of mathematical objects, scientific realism, when construed as a claim about the truth or approximate truth of our scientific theories, implies mathematical Platonism. However, a standard argument for scientific realism, the 'no miracles' argument, falls short of establishing mathematical Platonism. As a result, this argument cannot establish scientific realism as it is usually defined, but only some weaker position. Scientific 'realists' should therefore either redefine their position as a claim about the existence of unobservable physical objects, or alternatively look for an argument for their position that does establish mathematical Platonism.Comment: Previous knowledge both on Platonism in philosophy of mathematics and scientific realism is needed. Essential paper for advanced courses of philosophy of science.
Leonelli, Sabina. What distinguishes data from models?2019, European Journal for Philosophy of Science 9 (2):22.-
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Added by: Sara Peppe
Abstract: I propose a framework that explicates and distinguishes the epistemic roles of data and models within empirical inquiry through consideration of their use in scientific practice. After arguing that Suppes' characterization of data models falls short in this respect, I discuss a case of data processing within exploratory research in plant phenotyping and use it to highlight the difference between practices aimed to make data usable as evidence and practices aimed to use data to represent a specific phenomenon. I then argue that whether a set of objects functions as data or models does not depend on intrinsic differences in their physical properties, level of abstraction or the degree of human intervention involved in generating them, but rather on their distinctive roles towards identifying and characterizing the targets of investigation. The paper thus proposes a characterization of data models that builds on Suppes' attention to data practices, without however needing to posit a fixed hierarchy of data and models or a highly exclusionary definition of data models as statistical constructs.Comment: This article deepens the role of model an data in the scientific investigation taking into account the scientific practice. Obviously, a general framework of the themes the author takes into account is needed.
Longino, Helen. Science as Social Knowledge: Values and Objectivity in Scientific Inquiry1990, Princeton University Press.-
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Added by: Nick Novelli
Publisher's Note: Conventional wisdom has it that the sciences, properly pursued, constitute a pure, value-free method of obtaining knowledge about the natural world. In light of the social and normative dimensions of many scientific debates, Helen Longino finds that general accounts of scientific methodology cannot support this common belief. Focusing on the notion of evidence, the author argues that a methodology powerful enough to account for theories of any scope and depth is incapable of ruling out the influence of social and cultural values in the very structuring of knowledge. The objectivity of scientific inquiry can nevertheless be maintained, she proposes, by understanding scientific inquiry as a social rather than an individual process. Seeking to open a dialogue between methodologists and social critics of the sciences, Longino develops this concept of "contextual empiricism" in an analysis of research programs that have drawn criticism from feminists. Examining theories of human evolution and of prenatal hormonal determination of "gender-role" behavior, of sex differences in cognition, and of sexual orientation, the author shows how assumptions laden with social values affect the description, presentation, and interpretation of data. In particular, Longino argues that research on the hormonal basis of "sex-differentiated behavior" involves assumptions not only about gender relations but also about human action and agency. She concludes with a discussion of the relation between science, values, and ideology, based on the work of Habermas, Foucault, Keller, and Haraway.Comment: Longino offers a way to accomodate critiques of science as being socially constructed with the claim that science is objective. This contextual empiricism is an interesting solution, and would provide a useful point of discussion in an exploration of these issues in a course that discusses scientific objectivity.
Maddy, Penelope. Naturalism in Mathematics1997, Oxford: Oxford University Press.-
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Added by: Jamie Collin
Publisher's Note: Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view - realism - is assessed and finally rejected in favour of another - naturalism - which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.Comment: Good further reading in advanced undergraduate or postgraduate courses on metaphysics, naturalism or philosophy of mathematics. Sections from the book - for instance, the chapters in Part II on indispensability considerations in scientific and mathematical practice - could be profitably read on their own. These sections may also be of interest in philosophy of science courses, as they provide a careful analysis of scientific practice (as it relates to what scientists take themselves to be ontologically committed to).
Maddy, Penelope. Three Forms of Naturalism2005, in The Oxford Handbook of Philosophy of Mathematics and Logic, (ed.) S. Shapiro. New York: Oxford University Press.-
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Added by: Jamie Collin
Summary: A clear introduction to mathematical naturalism and its Quinean roots; developing and defending Maddy's own naturalist philosophy of mathematics. Maddy claims that the Quinian ignores some nuances of scientific practice that have a bearing on what the naturalist should take to be the real scientific standards of evidence. Historical studies show that scientists sometimes do not take themselves to be committed to entities that are indispensably quantified over in their best scientific theories, hence the Quinian position that naturalism dictates that we are committed to entities that are indispensably quantified over in our best scientific theories is incorrect.Comment: Good primary reading in advanced undergraduate or postgraduate courses on metaphysics, naturalism or philosophy of mathematics. This would serve well both as a clear and fairly concise introduction to Quinean naturalism and to the indispensability argument in the philosophy of mathematics.
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Kukla, Rebecca. Cognitive models and representation
1992, British Journal for the Philosophy of Science 43 (2):219-32.
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