Morris, Rebecca Lea. Intellectual Generosity and the Reward Structure of Mathematics
2021, Synthese, 199(1): 345-367
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Added by: Fenner Stanley TanswellAbstract:
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 generous. I then argue that intellectual generosity is beneficial because it counteracts negative effects of the reward structure of mathematics that can stymie mathematical progress.Comment (from this Blueprint): In this paper, Morris looks at ascriptions of intellectual generosity in mathematics, focusing on the mathematician William Thurston. She looks at how generosity should be characterised, and argues that it is beneficial in counteract some of the negative effects of the reward structure of mathematics.
Morrison, Margaret. Fictions, representations, and reality
2009, In Mauricio Suárez (ed.), Fictions in Science: Philosophical Essays on Modeling and Idealization. Routledge.
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Added by: Jamie CollinSummary: Uses Maxwell's model of the ether as a case study in accounting for the role of fictions in science. Argues that we should understand idealisation and abstraction as being different from fiction. Fictional models for Morrison are those that are deliberately intended to be such that the relationship between their structure and the structure of the concrete systems they model is not (immediately) apparent. This is different from mere idealisation, where certain structural features are omitted to make calculations more tractable.Comment: Very useful as a primary or secondary reading in an advanced undergraduate course on philosophy of science (or perhaps on philosophy of fiction). It is philosophically sophisticated, but also treats the science in enough detail to provide students with some clear ideas about the nature of scientific representational practices themselves. Would be appropriate in sections on scientific representation or modelling.
Morrison, Margaret, Mary S. Morgan. Models as mediating instruments
1999, In M. S. Morgan and M. Morrison (eds.), Models as Mediators: Perspectives on Natural and Social Science. Cambridge University Press.
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Added by: Jamie CollinSummary: Morrison and Morgan argue for a view of models as 'mediating instruments' whose role in scientific theorising goes beyond applying theory. Models are partially independent of both theories and the world. This autonomy allows for a unified account of their role as instruments that allow for exploration of both theories and the world.Comment: Useful as a primary or secondary reading in an advanced undergraduate course on philosophy of science, particularly within a section on scientific modeling. The paper is particularly useful in teaching because it is not unduly technical.
Morrison, Margaret. Spin: All is not what it seems
2007, Studies in History and Philosophy of Science Part B 38(3): 529-55.
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Added by: Laura JimenezAbstract: Spin is typically thought to be a fundamental property of the electron and other elementary particles. Although it is defined as an internal angular momentum much of our understanding of it is bound up with the mathematics of group theory. This paper traces the development of the concept of spin paying particular attention to the way that quantum mechanics has influenced its interpretation in both theoretical and experimental contexts. The received view is that electron spin was discovered experimentally by Stern and Gerlach in 1921, 5 years prior to its theoretical formulation by Goudsmit and Uhlenbeck. However, neither Goudsmit nor Uhlenbeck, nor any others involved in the debate about spin cited the Stern-Gerlach experiment as corroborating evidence. In fact, Bohr and Pauli were emphatic that the spin of a single electron could not be measured in classical experiments. In recent years experiments designed to refute the Bohr-Pauli thesis and measure electron spin have been carried out. However, a number of ambiguities surround these results - ambiguities that relate not only to the measurements themselves but to the interpretation of the experiments. After discussing these various issues the author raises some philosophical questions about the ontological and epistemic status of spin.Comment: The goal of the paper is to uncover and isolate how spin presents problems for traditional realism and to illustrate the power that theories like quantum mechanics have for shaping both philosophical questions and answers. It is adequate for higher-level postgraduate courses in Philosophy of Science.
Morton, Jennifer. Moving Up Without Losing Your Way: The Ethical Costs of Upward Mobility
2019, Princeton University Press
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Added by: Tomasz Zyglewicz, Shannon Brick, Michael GreerPublisher’s Note:
Upward mobility through the path of higher education has been an article of faith for generations of working-class, low-income, and immigrant college students. While we know this path usually entails financial sacrifices and hard work, very little attention has been paid to the deep personal compromises such students have to make as they enter worlds vastly different from their own. Measuring the true cost of higher education for those from disadvantaged backgrounds, Moving Up without Losing Your Way looks at the ethical dilemmas of upward mobility—the broken ties with family and friends, the severed connections with former communities, and the loss of identity—faced by students as they strive to earn a successful place in society. Drawing upon philosophy, social science, personal stories, and interviews, Jennifer Morton reframes the college experience, factoring in not just educational and career opportunities but also essential relationships with family, friends, and community. Finding that student strivers tend to give up the latter for the former, negating their sense of self, Morton seeks to reverse this course. She urges educators to empower students with a new narrative of upward mobility—one that honestly situates ethical costs in historical, social, and economic contexts and that allows students to make informed decisions for themselves. A powerful work with practical implications, Moving Up without Losing Your Way paves a hopeful road so that students might achieve social mobility while retaining their best selves.Comment (from this Blueprint): In this book Jennifer Morton, a philosopher of education and political philosopher, revisits the question of upward mobility and the difficulties under-privileged college students face in completing college. She argues that they face huge, yet-unacknowledged costs: "ethical costs," that impact not just them but their wider (often-marginalized) communities. Her theses in this book therefore touch not just on the individual experiences of marginalized college kids but also on broader issues of social oppression and social change. To make her claims Morton draws on her own lived experiences as an immigrant and a philosopher teaching in a public institution. One might describe this empirical method as autoethnography, although she does not. She also draws upon interviews conducted with the population of students she's interested in, "strivers." Morton's book addresses the phenomenon of upward mobility, the ethical purposes and drawbacks of going to college, and dignifies the experiences of people from marginalized backgrounds who want to make a better life for them and their communities.
Müller-Hill, Eva. Formalizability and Knowledge Ascriptions in Mathematical Practice
2009, Philosophia Scientiæ. Travaux d'histoire et de philosophie des sciences, (13-2): 21-43
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Added by: Fenner Stanley TanswellAbstract:
We investigate the truth conditions of knowledge ascriptions for the case of mathematical knowledge. The availability of a formalizable mathematical proof appears to be a natural criterion:
(*) X knows that p is true iff X has available a formalizable proof of p.
Yet, formalizability plays no major role in actual mathematical practice. We present results of an empirical study, which suggest that certain readings of (*) are not necessarily employed by mathematicians when ascribing knowledge. Further, we argue that the concept of mathematical knowledge underlying the actual use of “to know” in mathematical practice is compatible with certain philosophical intuitions, but seems to differ from philosophical knowledge conceptions underlying (*).
Comment (from this Blueprint): Müller-Hill is interested in the question of when mathematicians have mathematical knowledge and to what extent it relies on the formalisability of proofs. In this paper, she undertakes an empirical investigation of mathematicians’ views of when mathematicians know a theorem is true. Amazingly, while they say that they believe proofs have an exact definition and that the standards of knowledge are invariant, when presented with various toy scenarios, their judgements seem to suggest systematic context-sensitivity of a number of factors.
Nagel, Jennifer. Knowledge as a mental state
2013, In: Gendler, Tamar (ed), Oxford Studies in Epistemology, Volume 4. Oxford: Oxford University Press. 275-310
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Added by: Jie GaoAbstract: In the philosophical literature on mental states, the paradigmatic examples of mental states are beliefs, desires, intentions, and phenomenal states such as being in pain. The corresponding list in the psychological literature on mental state attribution includes one further member: the state of knowledge. This article examines the reasons why developmental, comparative and social psychologists have classified knowledge as a mental state, while most recent philosophers - with the notable exception of Timothy Williamson - have not. The disagreement is traced back to a difference in how each side understands the relationship between the concepts of knowledge and belief, concepts which are understood in both disciplines to be closely linked. Psychologists and philosophers other than Williamson have generally have disagreed about which of the pair is prior and which is derivative. The rival claims of priority are examined both in the light of philosophical arguments by Williamson and others, and in the light of empirical work on mental state attribution.Comment: This is a good teaching material on knowledge first. There is a recent response to this paper written by Aidan McGlynn ("Mindreading knowledge", 2016) which can be used together in teaching in order to create a nice dynamic of debate.
Narayanan, Arvind. The Limits of the Quantitative Approach to Discrimination
2022, James Baldwin Lecture Series
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Added by: Tomasz Zyglewicz, Shannon Brick, Michael GreerIntroduction: Let’s set the stage. In 2016, ProPublica released a ground-breaking investigation called Machine Bias. You’ve probably heard of it. They examined a criminal risk prediction tool that’s used across the country. These are tools that claim to predict the likelihood that a defendant will reoffend if released, and they are used to inform bail and parole decisions.Comment (from this Blueprint): This is a written transcript of the James Baldwin lecture, delivered by the computer scientist Arvind Narayanan, at Princeton in 2022. Narayanan's prior research has examined algorithmic bias and standards of fairness with respect to algorithmic decision making. Here, he engages critically with his own discipline, suggesting that there are serious limits to the sorts of quantitative methods that computer scientists recruit to investigate the potential biases in their own tools. Narayanan acknowledges that in voicing this critique, he is echoing claims by feminist researchers from fields beyond computer science. However, his own arguments, centered as they are on the details of the quantitative methods he is at home with, home in on exactly why these prior criticisms hold up in a way that seeks to speak more persuasively to Narayanan's own peers in computer science and other quantitative fields.
Nederpelt, Rob, Fairouz Kamareddine. Logical reasoning: a first course
2004, London: King’s College Publications.
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Added by: Sophie Nagler, Contributed by: Sophie NaglerPublisher’s Note:
This book describes how logical reasoning works and puts it to the test in applications. It is self-contained and presupposes no more than elementary competence in mathematics. Comment: An introduction to sentential and first-order logic with a mixed philosophical and computational focus; rigorous presentation of the formalism interspersed with brief philosophical reflections on concepts, practical exercises, and pointers at technical 'real-world' applications.
2001, Cambridge University Press.
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Added by: Berta GrimauPublisher's Note: Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.Comment: This book can be used both in a general course on proof theory for advanced Undergraduates or for Masters students, and for specialized courses - for example, a course on natural deduction. Chapters 1-4 can be used as background reading of a general course. Chapter 1, 5 and 8 could be used in a course on natural deduction. The presentation is self-contained and the book should be readable without any previous knowledge of logic.
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