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Added by: Fenner Stanley TanswellAbstract:
According to the received view, genuine mathematical justification derives from proofs. In this article, I challenge this view. First, I sketch a notion of proof that cannot be reduced to deduction from the axioms but rather is tailored to human agents. Secondly, I identify a tension between the received view and mathematical practice. In some cases, cognitively diligent, well-functioning mathematicians go wrong. In these cases, it is plausible to think that proof sets the bar for justification too high. I then propose a fallibilist account of mathematical justification. I show that the main function of mathematical justification is to guarantee that the mathematical community can correct the errors that inevitably arise from our fallible practices.Hamami, Yacin, Morris, Rebecca Lea. Philosophy of mathematical practice: a primer for mathematics educators2020, ZDM, 52(6): 1113-1126.-
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Added by: Fenner Stanley TanswellAbstract:
In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice. In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the distinction between formal and informal proofs, visualization and artefacts, mathematical explanation and understanding, value judgments, and mathematical design. We conclude with some remarks on the potential connections between the philosophy of mathematical practice and mathematics education.Comment (from this Blueprint): While this paper by Hamami & Morris is not a necessary reading, it provides a fairly broad overview of the practical turn in mathematics. Since it was aimed at mathematics educators, it is a very accessible piece, and provides useful directions to further reading beyond what is included in this blueprint.
Cheng, Eugenia. Mathematics, Morally2004, Cambridge University Society for the Philosophy of Mathematics.-
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Added by: Fenner Stanley TanswellAbstract:
A source of tension between Philosophers of Mathematics and Mathematicians is the fact that each group feels ignored by the other; daily mathematical practice seems barely affected by the questions the Philosophers are considering. In this talk I will describe an issue that does have an impact on mathematical practice, and a philosophical stance on mathematics that is detectable in the work of practising mathematicians. No doubt controversially, I will call this issue ‘morality’, but the term is not of my coining: there are mathematicians across the world who use the word ‘morally’ to great effect in private, and I propose that there should be a public theory of what they mean by this. The issue arises because proofs, despite being revered as the backbone of mathematical truth, often contribute very little to a mathematician’s understanding. ‘Moral’ considerations, however, contribute a great deal. I will first describe what these ‘moral’ considerations might be, and why mathematicians have appropriated the word ‘morality’ for this notion. However, not all mathematicians are concerned with such notions, and I will give a characterisation of ‘moralist’ mathematics and ‘moralist’ mathematicians, and discuss the development of ‘morality’ in individuals and in mathematics as a whole. Finally, I will propose a theory for standardising or universalising a system of mathematical morality, and discuss how this might help in the development of good mathematics.
Comment (from this Blueprint): Cheng is a mathematician working in Category Theory. In this article she complains about traditional philosophy of mathematics that it has no bearing on real mathematics. Instead, she proposes a system of “mathematical morality” about the normative intuitions mathematicians have about how it ought to be.
Fabre, Cécile. Cosmopolitan peace2016, Oxford University Press UK-
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Added by: Ten-Herng LaiAbstract:
This chapter explores why, from a cosmopolitan point of view, we should remember some wars, and furthermore how we should remember them. It contrasts itself with remembering war for partial and/or nationalist purposes, and also deals with the particularity problem, on why people of certain countries should remember their past wars.Comment (from this Blueprint): There are several articles on why some commemorations are unacceptable. Remembering war appropriately could shed some light on what good commemorations consist in. Moreover, this paper also discusses why some of our war remembrances are suboptimal.
Berninger, Anja. Commemorating Public Figures–In Favour of a Fictionalist Position2020, Journal of Applied Philosophy-
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Added by: Ten-Herng LaiAbstract:
In this article, I discuss the commemoration of public figures such as Nelson Mandela and Yitzhak Rabin. In many cases, our commemoration of such figures is based on the admiration we feel for them. However, closer inspection reveals that most (if not all) of those we currently honour do not qualify as fitting objects of admiration. Yet, we may still have the strong intuition that we ought to continue commemorating them in this way. I highlight two problems that arise here: the problem that the expressed admiration does not seem appropriate with respect to the object and the problem that continued commemorative practices lead to rationality issues. In response to these issues, I suggest taking a fictionalist position with respect to commemoration. This crucially involves sharply distinguishing between commemorative and other discourses, as well as understanding the objects of our commemorative practices as fictional objects.Comment (from this Blueprint): This is a persuasive article arguing for a somewhat counter-intutive conclusion. The fictionalist approach, that what we honour is not the historical figure, but some idealised version of them, seems to capture what we actually do in the real world, even if we think we are not doing this. Do compare the position on eliminativism with Frowe's paper.
Shahvisi, Arianne. Colonial monuments as slurring speech acts2021, Journal of Philosophy of Education 55(3):453-468-
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Added by: Ten-Herng LaiAbstract:
In recent years, the removal of monuments which glorify historical figures associated with racism and colonialism has become one of the most visible and contested forms of decolonisation. Yet many have objected that there is educational value in leaving such monuments standing. In this paper, I argue that public monuments can be understood as speech acts which communicate messages to those who live among them. Some of those speech acts derogate particular social groups, contributing to their marginalisation in much the way that slurs do. Comparing derogating monuments to slurs is also productive in suggesting morally appropriate responses to their harms. I explore the limits of the use-mention distinction in relation to the harmfulness of slurs and apply this to show that attempting to recontextualise harmful monuments in situ—by, for example, changing the text on an accompanying plaque in order to retain the monument for its educational value—will not solve the problem in most cases. I conclude that the removal of slurring monuments, or their relocation to museum exhibitions dedicated to presenting a more critical view of history, is a more robust and reliable way of protecting against harm, and that this consideration outweighs any purported educational value in leaving monuments in place.Comment (from this Blueprint): Speech act theory is a very good way to understand why problematic monuments are problematic. It also has some important implications concerning what we ought to do with these monuments and whether they have good educational value. Especially regarding the second thing, the analogy with slurs is an illuminating one. There are better ways to teach the objectionableness of slurs than mentioning them constantly. Similarly, there are better ways to teach historical lessons than preserving problematic monuments.
Frowe, Helen. The Duty to Remove Statues of Wrongdoers2019, Journal of Practical Ethics 7(3):1-31-
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Added by: Ten-Herng LaiAbstract:
This paper argues that public statues of persons typically express a positive evaluative attitude towards the subject. It also argues that states have duties to repudiate their own historical wrongdoing, and to condemn other people’s serious wrongdoing. Both duties are incompatible with retaining public statues of people who perpetrated serious rights violations. Hence, a person’s being a serious rights violator is a sufficient condition for a state’s having a duty to remove a public statue of that person. I argue that this applies no less in the case of the ‘morally ambiguous’ wrongdoer, who both accomplishes significant goods and perpetrates serious rights violations. The duty to remove a statue is a defeasible duty: like most duties, it can be defeated by lesser-evil considerations. If removing a statue would, for example, spark a violent riot that would risk unjust harm to lots of people, the duty to remove could be outweighed by the duty not to foreseeably cause unjust harm. This would provide a lesser-evil justification for keeping the statue. But it matters that the duty to remove is outweighed, rather than negated, by these consequences. Unlike when a duty is negated, one still owes something in cases of outweighing. And it especially matters that it is outweighed by the predicted consequences of wrongful behaviour by others.Comment (from this Blueprint): This paper highlights several important things. First, statues are blunt tools and express pro-attitudes to the persons they represent as a whole. Second, it sets out a clear standard for removal, and defends the conclusion that we should remove many or even most existing statues. Third, to the question “what if removal incites violence?” this paper provides a good answer. Fourth, a legitimate question is what we should do about statues of wrongdoers of the distant past? The discussion on this here is insightful.
Burch-Brown, Joanna. Is it Wrong to Topple Statues and Rename Schools?2017, Journal of Political Theory and Philosophy 1(1):59-88-
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Added by: Ten-Herng LaiAbstract:
In recent years, campaigns across the globe have called for the removal of objects symbolic of white supremacy. This paper examines the ethics of altering or removing such objects. Do these strategies sanitize history, destroy heritage and suppress freedom of speech? Or are they important steps towards justice? Does removing monuments and renaming schools reflect a lack of parity and unfairly erase local identities? Or can it sometimes be morally required, as an expression of respect for the memories of people who endured past injustices; a recognition of this history's ongoing legacies; and a repudiation of unjust social hierarchies?Comment (from this Blueprint): It is often thought that statues and monuments, even those of terrible people, are innocuous, that they cannot harm or affect us negatively. This paper helps to spell out the harms of preserving these commemorations. Among other important issues, this paper also engages with the “anachronism” problem, that we are judging people of the past with contemporary standards. This paper also gives a good introduction on the notion of “ideology” and its relation to objectionable commemorations.
Broadie, Sarah. Plato’s Sun-Like Good: Dialectic in the Republic2021, Cambridge University Press-
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, Contributed by: Quentin PharrPublisher’s Note:
Plato's Sun-Like Good is a revolutionary discussion of the Republic's philosopher-rulers, their dialectic, and their relation to the form of the good. With detailed arguments Sarah Broadie explains how, if we think of the form of the good as 'interrogative', we can re-conceive those central reference-points of Platonism in down-to-earth terms without loss to our sense of Plato's philosophical greatness. The book's main aims are: first, to show how for Plato the form of the good is of practical value in a way that we can understand; secondly, to make sense of the connection he draws between dialectic and the form of the good; and thirdly, to make sense of the relationship between the form of the good and other forms while respecting the contours of the sun-good analogy and remaining faithful to the text of the Republic itself.Comment: This text is an excellent companion text for reading Plato's Republic - especially Books 5 and 6. It provides clear interpretations of the various metaphors and analogies that Plato presents in those books, and it provides one of the most important new interpretations of Plato's conception of philosopher-rulers, the Form of the Good, and philosophical dialectic. This text is primarily for those students who are looking to dive into the relevant debates associated with these books in the Republic. Accordingly, it requires some understanding of some of Plato's other dialogues, as well as some understanding of philosophical and mathematical methodologies as conceived by Plato.
M. Giulia Napolitano, Reuter, Kevin. What is a Conspiracy Theory?2021, Erkenntnis-
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Added by: Sara Peppe, Contributed by: Ethan LandesAbstract:
In much of the current academic and public discussion, conspiracy theories are portrayed as a negative phenomenon, linked to misinformation, mistrust in experts and institutions, and political propaganda. Rather surprisingly, however, philosophers working on this topic have been reluctant to incorporate a negatively evaluative aspect when either analyzing or engineering the concept conspiracy theory. In this paper, we present empirical data on the nature of the concept conspiracy theory from five studies designed to test the existence, prevalence and exact form of an evaluative dimension to the ordinary concept conspiracy theory. These results reveal that, while there is a descriptive concept of conspiracy theory, the predominant use of conspiracy theory is deeply evaluative, encoding information about epistemic deficiency and often also derogatory and disparaging information. On the basis of these results, we present a new strategy for engineering conspiracy theory to promote theoretical investigations and institutional discussions of this phenomenon. We argue for engineering conspiracy theory to encode an epistemic evaluation, and to introduce a descriptive expression—such as ‘conspiratorial explanation’—to refer to the purely descriptive concept conspiracy theory.Comment: This paper empirically tests whether "conspiracy theory" is evaluative or merely means a theory that evokes a conspiracy, as previous philosophers have typically argued. Using both survey based methods and corpus linguistics, they find that the term does appear to be necessarily derogatory. The paper is very approachable and would be suitable primary/secondary reading for an undegraduate course on conspiracy theories, experimental philosophy, or conceptual engineering.
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De Toffoli, Silvia. Groundwork for a Fallibilist Account of Mathematics
2021, The Philosophical Quarterly, 71(4).
Comment (from this Blueprint): De Toffoli makes a strong case for the importance of mathematical practice in addressing important issues about mathematics. In this paper, she looks at proof and justification, with an emphasis on the fact that mathematicians are fallible. With this in mind, she argues that there are circumstances under which we can have mathematical justification, despite a possibility of being wrong. This paper touches on many cases and questions that will reappear later across the Blueprint, such as collaboration, testimony, computer proofs, and diagrams.