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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.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.
Lynch, Kate E.. Heritability and causal reasoning2017, Biology & Philosophy 32: 25–49.-
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Added by: Björn Freter, Contributed by: Hannah Rubin
Abstract: Gene–environment (G–E) covariance is the phenomenon whereby genetic differences bias variation in developmental environment, and is particularly problematic for assigning genetic and environmental causation in a heritability analysis. The interpretation of these cases has differed amongst biologists and philosophers, leading some to reject the utility of heritability estimates altogether. This paper examines the factors that influence causal reasoning when G–E covariance is present, leading to interpretive disagreement between scholars. It argues that the causal intuitions elicited are influenced by concepts of agency and blame-worthiness, and are intimately tied with the conceptual understanding of the phenotype under investigation. By considering a phenotype-specific approach, I provide an account as to why causal ascriptions can differ depending on the interpreter. Phenotypes like intelligence, which have been the primary focus of this debate, are more likely to spark disagreement for the interpretation of G–E covariance cases because the concept and ideas about its ‘normal development’ relatively ill-defined and are a subject of debate. I contend that philosophical disagreement about causal attributions in G–E covariance cases are in essence disagreements regarding how a phenotype should be defined and understood. This moves the debate from one of an ontological flavour concerning objective causal claims, to one concerning the conceptual, normative and semantic dependencies.Comment: This paper discusses difficulties for determining whether traits like intelligence are heritable, drawing on philosophical work regarding causal intuitions. It's accessible enough to use in a lower-level undergraduate course, but also generates good discussion in a graduate level course. It could be used to further a discussion about the nature of genes or in a discussion of philosophy of race/gender from a biological perspective.
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.
Maddy, Penelope. The Philosophy of Logic2012, Bulletin of Symbolic Logic 18(4): 481-504.-
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Added by: Berta Grimau, Contributed by: Matt Clemens
Abstract: This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic - what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics - Logicism, Intuitionism, Formalism, Realism - and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam are among the philosophers considered along the way.Comment: This is a survey article which considers positions within philosophy of logic analogous to the views held by the various schools of the philosophy of mathematics. The article touches briefly on many positions and authors and is thus an excellent introduction to the philosophy of logic, specially for students already familiar with the philosophy of mathematics. The text is informal and it does not involve any proofs.
Mangraviti, Franci. The Liberation Argument for Inconsistent Mathematics2023, The Australasian Journal of Logic, 20 (2): 278-317-
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Added by: Franci Mangraviti and Viviane FairbankAbstract:
Val Plumwood charged classical logic not only with the invalidity of some of its laws, but also with the support of systemic oppression through naturalization of the logical structure of dualisms. In this paper I show that the latter charge - unlike the former - can be carried over to classical mathematics, and I propose a new conception of inconsistent mathematics - queer incomaths - as a liberatory activity meant to undermine said naturalization.Comment:
available in this Blueprint
Marin, Sonia, et al.. A Pure View of Ecumenical Modalities2021, In Logic, Language, Information, and Computation. [Online]. Switzerland: Springer International Publishing AG. pp. 388–407-
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Added by: Sophie NaglerAbstract:
Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion on proof systems for combining logics. This discussion has been extended to alethic modalities using Simpson’s meta-logical characterization: necessity is independent of the viewer, while possibility can be either intuitionistic or classical. In this work, we propose a pure, label free calculus for ecumenical modalities, nEK, where exactly one logical operator figures in introduction rules and every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic EK. We prove that nEK is sound and complete w.r.t. the ecumenical birelational semantics and discuss fragments and extensions.
Comment: Suitable for a specialist class on logical pluralism (if focussed on ecumenical systems) or alethic modalities
Martin, Ursula, Pease, Alison. Mathematical Practice, Crowdsourcing, and Social Machines2013, in Intelligent Computer Mathematics. CICM 2013. Lecture Notes in Computer Sciences, Carette, J. et al. (eds.). Springer.-
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Added by: Fenner Stanley TanswellAbstract:
The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. The Study of Mathematical Practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question-answering system mathoverflow contains around 40,000 mathematical conversations, and polymath collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of “soft” aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a “social machine”, a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment (from this Blueprint): In this paper, Martin and Pease look at how mathematics happens online, emphasising how this embodies the picture of mathematics given by Polya and Lakatos, two central figures in philosophy of mathematical practice. They look at multiple venues of online mathematics, including the polymath projects of collaborative problem-solving, and mathoverflow, which is a question-and-answer forum. By looking at the discussions that take place when people are doing maths online, they argue that you can get rich new kinds of data about the processes of mathematical discovery and understanding. They discuss how online mathematics can become a “social machine”, and how this can open up new ways of doing mathematics.
Massimi, Michela. Pauli’s Exclusion Principle: The origin and validation of a scientific principle2005, Cambridge University Press.-
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Added by: Laura Jimenez
Publisher's Note: There is hardly another principle in physics with wider scope of applicability and more far-reaching consequences than Pauli's exclusion principle. This book explores the principle's origin in the atomic spectroscopy of the early 1920s, its subsequent embedding into quantum mechanics, and later experimental validation with the development of quantum chromodynamics. The reconstruction of this crucial historic episode provides an excellent foil to reconsider Kuhn's view on incommensurability. The author defends the prospective rationality of the revolutionary transition from the old to the new quantum theory around 1925 by focusing on the way Pauli's principle emerged as a phenomenological rule 'deduced' from some anomalous phenomena and theoretical assumptions of the old quantum theory. The subsequent process of validation is historically reconstructed and analysed within the framework of 'dynamic Kantianism'Comment: In principle, I would recommend the book for postgraduates specialized on the topic; although in terms of difficulty, an undergraduate wouldn't have any problem to understand it. The book is also useful for anyone interested in the development of quantum physics during the 20th century.
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Leng, Mary. What’s there to know?
2007, In M. Leng, A. Paseau, and M. Potter (eds.), Mathematical Knowledge. OUP
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.