Friend, Michele. Introducing Philosophy of Mathematics
2007, Acumen; reprinted by Routledge (2014).
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Added by: Berta Grimau, Contributed by: Matt ClemensPublisher's Note: What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.Comment: This book provides an introduction to the philosophy of mathematics. No previous mathematical skills/knowledge required. Suitable for undergraduate courses on philosophy of mathematics.
Galavotti, Maria Carla. A Philosophical Introduction to Probability
2005, CSLI Publications
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Added by: Sara PeppePublisher's Note: Not limited to merely mathematics, probability has a rich and controversial philosophical aspect. 'A Philosophical Introduction to Probability' showcases lesser-known philosophical notions of probability and explores the debate over their interpretations. Galavotti traces the history of probability and its mathematical properties and then discusses various philosophical positions on probability, from the Pierre Simon de Laplace's 'classical' interpretation of probability to the logical interpretation proposed by John Maynard Keynes. This book is a valuable resource for students in philosophy and mathematics and all readers interested in notions of probabilityComment: Very good article for philosophy of science and philosophy of probability courses. It works perfectly to build basic knowledge on the theme of probability.
Galavotti, Maria Carla. The notion of subjective probability in the works of Ramsey and de Finetti
1991, Theoria 57 (3): 239-259.
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Added by: Sara PeppeIntroduction: The decade from the mid-twenties to the mid-thirties was undoubtedly the most crucial for the twentieth Century notion of subjective probability. It was in 1926 that Frank Ramsey wrote his essay 'Truth and probability', presented at the Moral Science Club in Cambridge and published posthumously in 1931. There he put forward for the first time a definition of probability as degree of belief, that had been anticipated only by E. Borel in 1924, in a review of J. M. Keynes' Treatise on Ten years after Ramsey's paper, namely in 1935, Bruno de Finetti gave a series of lectures at the Institut Poincare in Paris, published in 1937 under the title 'La prévision: ses lois logiques, ses sources subjectives'. In this paper subjective probability, defined in a way analogous to that adopted by Ramsey, was implemented with the notion of exchangeability, that de Finetti had already worked out in 1928- 1930. Exchangeability confers applicability to the notion of subjective probability, and fills the gap between frequency and probability as degree of belief. It was only when these two were tied together that subjectivism could become a full-fledged interpretation of probability and gain credibility among probabilists and statisticians. One can then say that with the publication of 'La prévision' the formation process of a subjective notion of probability was completed.Comment: This article is focused on subjective probability in the works of Ramsey and de Finetti even if the main part of the work is devoted to Ramsey. This text is crucial in order to understand the subjectivist line of thinking.
Garavaso, Pieranna. The Woman of Reason: On the Re-appropriation of Rationality and the Enjoyment of Philosophy
2015, Meta-Philosophical Reflection on Feminist Philosophies of Science, pp.185-202.
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Added by: Franci MangravitiAbstract:
This paper starts out from two feminist criticisms of classical logic, namely Andrea Nye’s general rejection of logic and Val Plumwood’s criticism of the standard notion of negation in classical logic. I then look at some of Gottlob Frege’s reflections on negation in one of his later Logical Investigations. It will appear clear that Frege’s notion of negation is not easily pegged in the general category of ‘Otherness’ that Plumwood uses to characterize negation in classical logic. In the second half of the paper, I discuss the claim that the adversarial method of argumentation in philosophy is hostile to feminist goals and perhaps responsible for the low numbers of women engaged in academic philosophy. Against this hypothesis, I claim that a more naturalistic perspective on logic can avoid essentialism and provide a feminist friendly and pluralist view of logic, human reasoning, and philosophical argumentation.
Comment: available in this Blueprint
Gardiner, Georgi, Zaharatos, Brian. The Safe, the Sensitive, and the Severely Tested: A Unified Account
2022, Synthese 200(5): 1–33
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Added by: Clotilde Torregrossa, Contributed by: Georgi GardinerAbstract:
This essay presents a unified account of safety, sensitivity, and severe testing. S’s belief is safe iff, roughly, S could not easily have falsely believed p, and S’s belief is sensitive iff were p false S would not believe p. These two conditions are typically viewed as rivals but, we argue, they instead play symbiotic roles. Safety and sensitivity are both valuable epistemic conditions, and the relevant alternatives framework provides the scaffolding for their mutually supportive roles. The relevant alternatives condition holds that a belief is warranted only if the evidence rules out relevant error possibilities. The safety condition helps categorise relevant from irrelevant possibilities. The sensitivity condition captures ‘ruling out’. Safety, sensitivity, and the relevant alternatives condition are typically presented as conditions on warranted belief or knowledge. But these properties, once generalised, help characterise other epistemic phenomena, including warranted inference, legal verdicts, scientific claims, reaching conclusions, addressing questions, warranted assertion, and the epistemic force of corroborating evidence. We introduce and explain Mayo’s severe testing account of statistical inference. A hypothesis is severely tested to the extent it passes tests that probably would have found errors, were they present. We argue Mayo’s account is fruitfully understood using the resulting relevant alternatives framework. Recasting Mayo’s condition using the conceptual framework of contemporary epistemology helps forge fruitful connections between two research areas—philosophy of statistics and the analysis of knowledge—not currently in sufficient dialogue. The resulting union benefits both research areas.Comment: This essay can be paired with Deborah Mayo, to explain her view. It can also be used at the end of a "safety versus sensitivity" modue or a module on rival theories of knowledge, to suggest how the views can be compatible. The math can be skipped over. Gardiner has a "cheat sheet" on her website for this essay.
Gardiner, Georgi. Relevance and Risk: Relevant Alternatives and the Epistemology of Risk
2021, Synthese 199: 481–511.
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Added by: Clotilde Torregrossa, Contributed by: Georgi GardinerAbstract:
The epistemology of risk examines how risks bear on epistemic properties. A common framework for examining the epistemology of risk holds that strength of evidential support is best modelled as numerical probability given the available evidence. In this essay I develop and motivate a rival ‘relevant alternatives’ framework for theorising about the epistemology of risk. I describe three loci for thinking about the epistemology of risk. The first locus concerns consequences of relying on a belief for action, where those consequences are significant if the belief is false. The second locus concerns whether beliefs themselves—regardless of action—can be risky, costly, or harmful. The third locus concerns epistemic risks we confront as social epistemic agents. I aim to motivate the relevant alternatives framework as a fruitful approach to the epistemology of risk. I first articulate a ‘relevant alternatives’ model of the relationship between stakes, evidence, and action. I then employ the relevant alternatives framework to undermine the motivation for moral encroachment. Finally, I argue the relevant alternatives framework illuminates epistemic phenomena such as gaslighting, conspiracy theories, and crying wolf, and I draw on the framework to diagnose the undue skepticism endemic to rape accusations.Comment: You can assign sections 1-6 to introduce epistemological theory, and then (the next class) teach sections 7 to 9 as social applications. This breaks the essay into two sections of equal length.
Gastelum, Melina. Intercultural education based on situated cognition practices
2024, Una educación intercultural basada en prácticas cognitivas situadas. Andamios 21(54), pp. 83-109
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Added by: Maria Jimena Clavel VazquezAbstract:
In this article we want to enrich a view of intercultural education that can use the conceptualizations of 4E cognition (enactive, embedded, embodied and extended). We follow the idea that education can be understood as a community of situated practices. We argue that the perspective of practices acquires a sense from the 4E cognition that will help to promote an educational epistemology that does not only hover over gnoseological processes but brings into play other categories of the sociocultural environment that help other types of reflections that lead towards a critical, political and ethical interculturality.Comment: available in this Blueprint
Gendler, Tamar Szabó. Alief and Belief
2008, Journal of Philosophy 105 (10): 634-663.
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Added by: Jie GaoAbstract: I introduce and argue for the importance of a cognitive state that I call alief. Paradigmatic alief can be characterized as a mental state with associatively-linked content that is representational, affective and behavioral, and that is activated - consciously or unconsciously - by features of the subject's internal or ambient environment. Alief is a more primitive state than either belief or imagination: it directly activates behavioral response patterns (as opposed to motivating in conjunction with desire or pretended desire.) I argue that alief explains a large number of otherwise perplexing phenomena and plays a far larger role in causing behavior than has typically been recognized by philosophers. I argue further that the notion can be invoked to explain both the effectiveness and the limitations of certain sorts of example-based reasoning, and that it lies at the core of habit-based views of ethics.Comment: In this influential paper, Gendler argues for the existence of an important cognitive states that she calls alief. It is a highly-relevant material for teachings on many topics, for example forms of belief, rationality and belief, varieties of irrationality, implicit bias and etc, in upper-division undergraduate courses and postgraduate courses.
Gendler, Tamar Szabó. Alief in Action (and Reaction)
2008, Mind and Language 23 (5): 552- 585
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Added by: Jie GaoAbstract: I introduce and argue for the importance of a cognitive state that I call alief. An alief is, to a reasonable approximation, an innate or habitual propensity to respond to an apparent stimulus in a particular way. Recognizing the role that alief plays in our cognitive repertoire provides a framework for understanding reactions that are governed by nonconscious or automatic mechanisms, which in turn brings into proper relief the role played by reactions that are subject to conscious regulation and deliberate control.Comment: This is an introductory paper on alief. It provides an account of alief and argues for its role in governing non-conscious or automatic actions. The paper is useful for teachings on philosophy of action, mental attitudes, moral philosophy, social psychology, etc.
Gendler, Tamar Szabó. Galileo and the Indispensability of Scientific Thought Experiment
1998, British Journal for the Philosophy of Science 49 (3):397-424.
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Added by: Andrea BlomqvistAbstract: By carefully examining one of the most famous thought experiments in the history of science - that by which Galileo is said to have refuted the Aristotelian theory that heavier bodies fall faster than lighter ones - I attempt to show that thought experiments play a distinctive role in scientific inquiry. Reasoning about particular entities within the context of an imaginary scenario can lead to rationally justified concluusions that - given the same initial information - would not be rationally justifiable on the basis of a straightforward argument.Comment: This paper would be good to put as further reading in a week focusing on thought experiments. Suitable for a third year module.
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