Topic: Philosophy of the Formal Natural and Social Sciences
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Ambrose, Alice. Proof and the Theorem Proved
1959, Mind, 68(272): 435–445
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Added by: Viviane Fairbank
Abstract:

There is something curiously opaque about Wittgenstein's assertions concerning the connection between proof of a proposition p, sense of the sentence " p ", and understanding " p ". The difficulties inherent in his account are apparent, and he has
himself mentioned them, while leaving their resolution obscure. I shall now detail them, so that it will be clear what difficulties must be got round and what clarification is required.

Comment: This is a useful work of Wittgenstein exegesis by one of his students and collaborators, concerning his views on mathematical proof with discussion of several examples. It could be used in an intermediate/advanced course on the philosophy of mathematics or on Wittgenstein's philosophy more generally.
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Andersen, Line Edslev, Andersen, Hanne, Kragh Sørensen, Henrik. The Role of Testimony in Mathematics
2021, Synthese, 199(1): 859-870

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Added by: Fenner Stanley Tanswell
Abstract:
Mathematicians appear to have quite high standards for when they will rely on testimony. Many mathematicians require that a number of experts testify that they have checked the proof of a result p before they will rely on p in their own proofs without checking the proof of p. We examine why this is. We argue that for each expert who testifies that she has checked the proof of p and found no errors, the likelihood that the proof contains no substantial errors increases because different experts will validate the proof in different ways depending on their background knowledge and individual preferences. If this is correct, there is much to be gained for a mathematician from requiring that a number of experts have checked the proof of p before she will rely on p in her own proofs without checking the proof of p. In this way a mathematician can protect her own work and the work of others from errors. Our argument thus provides an explanation for mathematicians’ attitude towards relying on testimony.
Comment (from this Blueprint): The orthodox picture of mathematical knowledge is so individualistic that it often leaves out the mathematician themselves. In this piece, Andersen et al. look at what role testimony plays in mathematical knowledge. They thereby emphasise social features of mathematical proofs, and why this can play an important role in deciding which results to trust in the maths literature.
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Andersen, Line Edslev, Johansen, Mikkel Willum, Kragh Sørensen, Henrik. Mathematicians Writing for Mathematicians
2021, Synthese, 198(26): 6233-6250
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Added by: Fenner Stanley Tanswell
Abstract:

We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised Adam’s very detailed first draft. At the beginning of this collaboration, Adam was very knowledgeable about the subject of the paper and had good presentational skills but, as a new PhD student, did not yet have experience writing research papers for mathematicians. Thus, one main purpose of revising the paper was to make it take into account the intended audience. For this reason, the changes made to the initial draft and the authors’ purpose in making them provide a window for viewing how mathematicians write for mathematicians. We examined how their paper attracts the interest of the reader and prepares their proofs for validation by the reader. Among other findings, we found that their paper prepares the proofs for two types of validation that the reader can easily switch between.

Comment (from this Blueprint): In this paper, Andersen et al. track the genesis of a maths research paper written in collaboration between a PhD student and his supervisor. They track changes made to sequential drafts and interview the two authors about the motivations for them, and show how the edits are designed to engage the reader in a mathematical narrative on one level, and prepare the paper for different types of validation on another level.
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Anderson, Elizabeth. Knowledge, Human Interests, and Objectivity in Feminist Epistemology
1995, Philosophical Topics 23(2), pp. 27-58.
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Added by: Olivia Maegaard Nielsen
Abstract:


This paper aims to defuse the hysteria over value-laden inquiry by showing how it is based on a misapprehension of the arguments of the most careful advocates of such inquiry, an impoverished understanding of the goals of science, a mistaken model of the interaction of normative and evidential considerations in science, and a singular inattention to the empirical facts about how responsible inquirers go about their business.

Comment: This text provides useful arguments for feminist epistemologies, especially feminist empiricism, and would be recommended to add in a class on epistemology, feminist epistemology, or the philosophy of science, especially for more advanced students. The text is a reply to a debate between Helen Longino and Susan Haack, so reading the three authors together as part of a section in a seminar would be interesting and would provide some important context for understanding Anderson.
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Anderson, Elizabeth. Value in Ethics and Economics
1993, Cambridge: Harvard University Press.

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Added by: Rochelle DuFord
Summary: Elizabeth Anderson offers a new theory of value and rationality that rejects cost-benefit analysis in our social lives and in our ethical theories. This account of the plurality of values thus offers a new approach, beyond welfare economics and traditional theories of justice, for assessing the ethical limitations of the market. In this light, Anderson discusses several contemporary controversies involving the proper scope of the market, including commercial surrogate motherhood, privatization of public services, and the application of cost-benefit analysis to issues of environmental protection.
Comment: This book as a whole would be an excellent addition to an upper level course on morals and markets. The last three chapters (7-9) cover a number of applied issues in economics and ethics. Chapter 8, "Is Women's Labor a Commodity" would be an especially good addition to a course on business ethics or biomedical ethics that discusses paid surrogacy.
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Anderson, Elizabeth. Ethical Assumptions in Economic Theory: Some Lessons from the History of Credit and Bankruptcy
2004, Ethical Theory and Moral Practice 7.4, 347-360

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Added by: Björn Freter, Contributed by: Anna Alexandrova
Abstract: This paper evaluates the economic assumptions of economic theory via an examination of the capitalist transformation of creditor-debtor relations in the 18th century. This transformation enabled masses of people to obtain credit without moral opprobrium or social subordination. Classical 18th century economics had the ethical concepts to appreciate these facts. Ironically, contemporary economic theory cannot. I trace this fault to its abstract representations of freedom, efficiency, and markets. The virtues of capitalism lie in the concrete social relations and social meanings through which capital and commodities are exchanged. Contrary to laissez faire capitalism, the conditions for sustaining these concrete capitalist formations require limits on freedom of contract and the scope of private property rights.
Comment: Great for introducing the ideology of economics and the basics of welfare economics.
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Anderson, Elizabeth. Feminist Epistemology and Philosophy of Science
2015, Stanford Encyclopedia of Philosophy.

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Added by: Giada Fratantonio
Abstract: Feminist epistemology and philosophy of science studies the ways in which gender does and ought to influence our conceptions of knowledge, the knowing subject, and practices of inquiry and justification. It identifies ways in which dominant conceptions and practices of knowledge attribution, acquisition, and justification systematically disadvantage women and other subordinated groups, and strives to reform these conceptions and practices so that they serve the interests of these groups. Various practitioners of feminist epistemology and philosophy of science argue that dominant knowledge practices disadvantage women by (1) excluding them from inquiry, (2) denying them epistemic authority, (3) denigrating their 'feminine' cognitive styles and modes of knowledge, (4) producing theories of women that represent them as inferior, deviant, or significant only in the ways they serve male interests, (5) producing theories of social phenomena that render women's activities and interests, or gendered power relations, invisible, and (6) producing knowledge (science and technology) that is not useful for people in subordinate positions, or that reinforces gender and other social hierarchies. Feminist epistemologists trace these failures to flawed conceptions of knowledge, knowers, objectivity, and scientific methodology. They offer diverse accounts of how to overcome these failures. They also aim to (1) explain why the entry of women and feminist scholars into different academic disciplines, especially in biology and the social sciences, has generated new questions, theories, and methods, (2) show how gender and feminist values and perspectives have played a causal role in these transformations, (3) promote theories that aid egalitarian and liberation movements, and (4) defend these developments as cognitive, not just social, advances.
Comment: A very detailed primer on feminist epistemology and philosophy of science. Covers a wide range of topics and issues, its length is such that it would probably be best to assign specific sections that are of interest rather than reading the whole thing. Useful as a preliminary introduction to the topics covered, and also offers a good summary of objections to the views presented.
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Anderson, Elizabeth. Uses of value judgments in science: A general argument, with lessons from a case study of feminist research on divorce
2004, Hypatia 19 (1):1-24.
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Added by: Simon Fokt, Contributed by: Karoline Paier

Abstract: The underdetermination argument establishes that scientists may use political values to guide inquiry, without providing criteria for distinguishing legitimate from illegitimate guidance. This paper supplies such criteria. Analysis of the confused arguments against value-laden science reveals the fundamental criterion of illegitimate guidance: when value judgments operate to drive inquiry to a predetermined conclusion. A case study of feminist research on divorce reveals numerous legitimate ways that values can guide science without violating this standard.

Comment: Gives a very good introduction into values in science, provides a good basis for discussing values in science, including a very insightful case study. However, it can be challenging for students to grasp the structure of the argument.
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Anscombe, G. Elizabeth M.. Were you a Zygote?
1985, In Griffiths, A.P. (ed.) Philosophy and practice. Cambridge: Cambridge University Press.

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Added by: Simon Fokt
Abstract: The usual way for new cells to come into being is by division of old cells. So the zygote, which is a—new—single cell formed from two, the sperm and ovum, is an exception. Textbooks of human genetics usually say that this new cell is beginning of a new human individual. What this indicates is that they suddenly forget about identical twins.
Comment: This paper can be particularly useful in teaching in two contexts: (1) ethical issues at the beginning of life; and (2) metaphysics of personal identity.
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Antony, Louise M.. Is Psychological Individualism a Piece of Ideology?
1995, Hypatia, 10(3), pp. 157-174

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Added by: Adriana Alcaraz Sanchez and Jodie Russell
Abstract:
Antony challenges Naomi Scheman's claim that "psychological individualism", sustains the ideology of patriarchy. According to Scheman, psychological individualism fails to consider the social and relational context that influences psychological phenomena. Antony challenges Scheman's view that psychological individualism has no place within a feminist approach. According to Antony, Scheman's criticism about psychological individualism is misplaced and psychological states can be individuated while at the same time maintaining their part in a more complex system (i.e. social context).
Comment (from this Blueprint): Antony offers a juxtaposed view to that of Scheman on the role of the social in understanding the nature of mental states. Antony rejects individualism as a "piece of ideology" and Scheman's claim that a feminist standpoint in philosophy of mind cannot accept the individuation of mental states. This text should be read together with Scheman's.
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