Diversity Reading List

Abstract: In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973). We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical practices in both sociological and epistemological terms.

Abstract: Philosophers of experiment have acknowledged that experiments are often more than mere hypothesis-tests, once thought to be an experiment's exclusive calling. Drawing on examples from contemporary biology, I make an additional amendment to our understanding of experiment by examining the way that `wide' instrumentation can, for reasons of efficiency, lead scientists away from traditional hypothesis-directed methods of experimentation and towards exploratory methods.

Publisher’s Note:

The ancient Maya, through their shamans, kings, warriors, and scribes, created a legacy of power and enduring beauty. The landmark publication of A Forest of Kings presented the first accessible, dramatic history of this great civilization, written by experts in the translation of glyphs. Now, in Maya Cosmos, Freidel, Schele, and Parker examine Maya mythology and religion, unraveling the question of how these extraordinary people, five million strong, have managed to preserve their most sacred beliefs into modern times. In Maya Cosmos, the authors draw upon translations of sacred texts and histories spanning thousands of years to tell us a story of the Maya, not in our words but in theirs.

Publisher'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.

Abstract: 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.

Publisher'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 probability

Introduction: 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.

Abstract: I argue that cultural practices that harm animals are not morally defensible: Tradition cannot justify cruelty. My conclusion applies to all such practices, including ones that are long-standing, firmly entrenched, or held sacred by their practitioners. Following Mary Midgley, I argue that cultural practices are open to moral scrutiny, even from outsiders. Because animals have moral status, they may not be harmed without good reason. I argue that the importance of religious or cultural rituals to adherents does not count as a sufficiently good reason to harm or kill animals, since rituals are inherently symbolic, and cultures are able to adapt and change, making adherence to cruel traditions unnecessary.

Abstract: Animal ethics committees (AECs) appeal to utilitarian principles in their justification of animal experiments. Although AECs do not grant rights to animals, they do accept that animals have moral standing and should not be unnecessarily harmed. Although many appeal to utilitarian arguments in the justification of animal experiments, I argue that AECs routinely fall short of the requirements needed for such justification in a variety of ways. I argue that taking the moral status of animals seriously—even if this falls short of granting rights to animals—should lead to a thorough revision or complete elimination of many of the current practices in animal experimentation.

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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.

Abstract: 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.

Abstract: Contemplating imaginary scenarios that evoke certain sorts of quasi?sensory intuitions may bring us to new beliefs about contingent features of the natural world. These beliefs may be produced quasi?observationally; the presence of a mental image may play a crucial cognitive role in the formation of the belief in question. And this albeit fallible quasi?observational belief?forming mechanism may, in certain contexts, be sufficiently reliable to count as a source of justification. This sheds light on the central puzzle surrounding scientific thought experiment, which is how contemplation of an imaginary scenario can lead to new knowledge about contingent features of the natural world.

Abstract: The everyday concept of a social group is approached by examining the concept of going for a walk together, an example of doing something together, or 'shared action'. Two analyses requiring shared personal goals are rejected, since they fail to explain how people walking together have obligations and rights to appropriate behaviour, and corresponding rights of rebuke. An alternative account is proposed: those who walk together must constitute the 'plural subject' of a goal (roughly, their walking alongside each other). The nature of plural subjecthood, the thesis that social groups are plural subjects, and the relation of these ideas to Rousseau's and Hobbes's, are briefly explored.

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The paper discusses two problems with Graham Priest's version of dialetheism: the thesis that one cannot be rationally obliged to both accept and reject something, and the use of a Contraction-less conditional in dealing with Curry paradoxes. Some solutions are suggested.

Abstract: This paper argues that there are powerful similarities between cognitive development in children and scientific theory change. These similarities are best explained by postulating an underlying abstract set of rules and representations that underwrite both types of cognitive abilities. In fact, science may be successful largely because it exploits powerful and flexible cognitive devices that were designed by evolution to facilitate learning in young children. Both science and cognitive development involve abstract, coherent systems of entities and rules, theories. In both cases, theories provide predictions, explanations, and interpretations. In both, theories change in characteristic ways in response to counterevidence. These ideas are illustrated by an account of children's developing understanding of the mind.