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.
-
Expand entry
-
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 state2013, In: Gendler, Tamar (ed), Oxford Studies in Epistemology, Volume 4. Oxford: Oxford University Press. 275-310-
Expand entry
-
Added by: Jie Gao
Abstract: 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 Discrimination2022, James Baldwin Lecture Series-
Expand entry
-
Added by: Tomasz Zyglewicz, Shannon Brick, Michael Greer
Introduction: 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 course2004, Nederpelt, R. P. (Rob P. ) & Kamareddine, F. D. (2004) Logical reasoning: a first course. London: King’s College Publications.-
Expand entry
-
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.-
Expand entry
-
Added by: Berta Grimau
Publisher'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.Nelkin, Dana. The lottery paradox, knowledge and rationality2000, Philosophical Review: 109 (3): 373-409.-
Expand entry
-
Added by: Jie Gao
Summary: The knowledge version of the paradox arises because it appears that we know our lottery ticket (which is not relevantly different from any other) will lose, but we know that one of the tickets sold will win. The rationality version of the paradox arises because it appears that it is rational to believe of each single ticket in, say, a million-ticket lottery that it will not win, and that it is simultaneously rational to believe that one such ticket will win. It seems, then, that we are committed to attributing two rational beliefs to a single agent at a single time, beliefs that, together with a few background assumptions, are inconsistent and can be seen by the agent to be so. This has seemed to many to be a paradoxical result: an agent in possession of two rational beliefs that she sees to be inconsistent. In my paper, I offer a novel solution to the paradox in both its rationality and knowledge versions that emphasizes a special feature of the lottery case, namely, the statistical nature of the evidence available to the agent. On my view, it is neither true that one knows nor that it is rational to believe that a particular ticket will lose. While this might seem surprising at first, it has a natural explanation and lacks the serious disadvantages of competing solutions.Comment : The lottery paradox is one of the most central paradox in epistemology and philosophy of probability. Nelkin's paper is a milestone in the literature on this topic after which discussions on the lottery paradox flourish. It is thus a must-have introductory paper on the lottery paradox for teachings on paradoxes of belief, justification theory, rationality, etc.Nelson, Julie. Feminism and economics1995, Journal of Economic Perspectives, 9(2), 131-148.-
Expand entry
-
Added by: Simon Fokt, Contributed by: Patricia Rich
Introduction: An article in The Chronicle of Higher Education of June 30, 1993, reported, “Two decades after it began redefining debates” in many other disciplines, “feminist thinking seems suddenly to have arrived in economics.” Many economists, of course, did not happen to be in the station when this train arrived, belated as it might be. Many who might have heard rumor of its coming have not yet learned just what arguments are involved or what it promises for the refinement of the profession. The purpose of this essay is to provide a low-cost way of gaining some familiarity.
Comment : This text provides a good overview, as well as an argument regarding how the field of economics reflects masculine values, and how the field could be improved by removing this bias. It makes sense to read the text with students who have some familiarity with economics itself. It should be noted that the field of economics actually has changed in some of the ways the author recommends, since the time of publication, but the article is still relevant and provokes plenty of discussion.Nelson, Lynn Hankinson, Nelson, Jack. Logic from a Quinean Perspective: An Empirical Enterprise2002, In Falmagne, R.J. and Hass, M. eds. Representing Reason: Feminist Theory and Formal Logic. Rowman & Littlefield-
Expand entry
-
Added by: Franci Mangraviti
From the Introduction: "Lynn Hankinson Nelson and Jack Nelson extend the work begun in the former’s book Who Knows: From Quine to a Feminist Empiricism, by showing that a Quinean understanding of logic as an empirical field implies that logic remains open to revision in light of fundamental shifts in knowledge. Nelson and Nelson point to the revisions in scientific understandings made possible by the incorporation of women and women’s lives as emblematic of the possible ways that feminist thought can provide a deep reworking of the structures of knowledge and thus potentially of logic. Although they are cautious of any conclusions that logic must change, their work offers a theoretical ground from which the effects of feminist theorizing on logic can be usefully explored."
Comment : available in this BlueprintNersessian, Nancy. Creating Scientific Concepts2008, MIT Press.-
Expand entry
-
Added by: Laura Jimenez
Publisher's Note: How do novel scientific concepts arise? In Creating Scientific Concepts, Nancy Nersessian seeks to answer this central but virtually unasked question in the problem of conceptual change. She argues that the popular image of novel concepts and profound insight bursting forth in a blinding flash of inspiration is mistaken. Instead, novel concepts are shown to arise out of the interplay of three factors: an attempt to solve specific problems; the use of conceptual, analytical, and material resources provided by the cognitive-social-cultural context of the problem; and dynamic processes of reasoning that extend ordinary cognition. Focusing on the third factor, Nersessian draws on cognitive science research and historical accounts of scientific practices to show how scientific and ordinary cognition lie on a continuum, and how problem-solving practices in one illuminate practices in the other.Comment : Nersessian’s book has a two-fold foundation, first, the empirical analysis of two cases of scientific thinking (one from Maxwell and one from a verbal protocol of a scientist); second, philosophical and cognitive analysis of the overall picture of meaning change in science that is the result of her work. The book presents her argument via an introductory chapter, followed by five chapters that develop the argument. Chapter 4 is particularly interesting for the cognitive-scientist: in this chapter Nersessian develops her account of the basic cognitive processes that underlie model-based reasoning. The new approach to mental modeling and analogy, together with Nersessian’s cognitive-historical approach, make Creating Scientific Concepts equally valuable to cognitive science and philosophy of science. The book is accessible and well-written, and should be a relatively quick read for anyone with a previous background in the mentioned fields. It is mainly recommended for postgraduate courses.Ney, Alyssa. Reductionism2008, Internet Encyclopedia of Philosophy.-
Expand entry
-
Added by: Emily Paul
Introduction: Reductionists are those who take one theory or phenomenon to be reducible to some other theory or phenomenon. For example, a reductionist regarding mathematics might take any given mathematical theory to be reducible to logic or set theory. Or, a reductionist about biological entities like cells might take such entities to be reducible to collections of physico-chemical entities like atoms and molecules. The type of reductionism that is currently of most interest in metaphysics and philosophy of mind involves the claim that all sciences are reducible to physics. This is usually taken to entail that all phenomena (including mental phenomena like consciousness) are identical to physical phenomena. The bulk of this article will discuss this latter understanding of reductionism.Comment : An excellent overview of reductionism, its history, and different ways to interpret it. Clear and accessible, and useful for an intermediate metaphysics course - perhaps after having studied an applied case of reductionism - e.g. about modality. Then, students will be able to have this in mind when considering different senses of reduction. Could then be a useful gateway into metaphysics of mind. Alternatively, this article could be used near the start of a philosophy of mind course.Can’t find it?Contribute the texts you think should be here and we’ll add them soon!
-
-
-
This site is registered on Toolset.com as a development site. -
-
-
-
-
-