This second edition encourages the integration of technology into a pedagogically sound learning sequence for primary mathematics.

Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

The work of Robert Hooke on acoustics and music theory is a larger subject than might seem the case from studies of his career so far available. First, there are his experiments for the Royal Society which can be defined as purely acoustical, which anticipate later experiments performed by men such as J. Sauveur and E. Chladni. Second, there are passages in many of his writings which by extensive use of musical analogy attempt to account for all physical phenomena of (...) the universe, which operates on the principles of ‘harmony’ and ‘dissonance’. It is in this context that the hitherto unpublished manuscript presented at the end of this paper should be considered. This essay, which combines both the older tradition of the ‘praise of music’ and the newer consideration of the physical nature of musical sound, illustrates a particular aspect of Hooke's thought which exercised a profound influence on all his studies. (shrink)

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical (...) realism. She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics. (shrink)

Many philosophers claim to be naturalists, but there is no common understanding of what naturalism is. Maddy proposes an austere form of naturalism called 'Second Philosophy', using the persona of an idealized inquirer, and she puts this method into practice in illuminating reflections on logical truth, philosophy of mathematics, and metaphysics.

Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of (...) the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments. (shrink)

Foucault's analysis of biopolitics has been appraised by Didier Fassin as successfully recognizing an essential trait of contemporary society: the attribution of an absolute value to abstract life and the emergence of political governmentalities managing life. Yet, claims Fassin, Foucault overlooked the need for paying close analytical attention to the everyday detail of lives differentially rendered worth living. Giving a focus to anthropologist Veena Das's work on sexual violence, this paper considers the surprising use by a number of contemporary post-Foucauldian (...) theorists of the resources made available by philosopher Stanley Cavell's reading of Wittgenstein as an alternative for the analysis of everyday violence. Having discussed a further tenor of criticism of Foucault – suggestions that the articulation of biopolitics and its forms of indirect murder as a general phenomenon fail to describe the prior or framing conditions under which certain human lives are more vulnerable than others to becoming disposable life – the paper reconstructs a new lexicon of terms devised by Das which would be more adequate to such analysis. In fact, the paper argues that Foucault is just as available for such reconfiguration as other theorists to whom Das responds differently. (shrink)

Penelope Deutscher reconsiders the role of procreation in Foucault's thought, especially its proximity to risk, mortality, and death. Foucault's Futures brings together his work on sexuality and biopolitics to provide new insights into the conflicted political status of reproductive conduct and what it means for feminism and critical theory.

We adopt and extend the concept of ‘noncooperative space’ to analyze how (aspirant) black women intellectual activists attempt to sustain their efforts within settings that publicly endorse racial equality, while, in practice, the contexts remain deeply racist. Noncooperative spaces reflect institutional, organizational, and social environments portrayed by powerful white agents as conducive to anti-racism work and promoting racial equality but, indeed, constrain individuals who challenge racism. Our work, which is grounded in intersectionality, draws on an autoethnographic account of racially motivated (...) domestic violence suffered by our lead author. Our analysis suggests that (aspirant) black women intellectual activists must develop courage to sustain their ‘voice’ within noncooperative spaces. However, the three interlinked dimensions of noncooperative spaces—namely, deceiving design, hegemonic actors’ indifference to racism, and (some assimilated gatekeepers’) false equivalence—may gradually erode a black female scholar’s courage. This forces her ‘voice’ to vanish temporarily, or even permanently. Courage is thus fragile and depletable. Yet, courage can be regenerated, resulting in regaining voice. Consequently, we propose courageous collective action by white allies and black and brown individuals who voluntarily and officially cooperate within and across various spaces to achieve racial equality. (shrink)

I discuss a thesis that I call ‘The Appearance of Mind-Independence’, to the effect that, to the subject of an ordinary perceptual experience, it seems that the experience involves the awareness of a mind-independent world. Although this thesis appears to be very widely accepted, I argue that it is open to serious challenge. Whether such a challenge can be maintained is especially relevant to the assessment of any theory, such as Berkeley’s idealism, according to which the only objects of which (...) we are aware in perception are mind-dependent. But the issue is of significance for the philosophy of perception more generally. In the course of my sceptical discussion, I argue that recent work by Campbell and Cassam may be flawed by a failure to take sufficiently seriously the requirements for genuine mind-independence. (shrink)

It’s often said that set theory provides a foundation for classical mathematics because every classical mathematical object can be modeled as a set and every classical mathematical theorem can be proved from the axioms of set theory. This is obviously a remarkable mathematical fact, but it isn’t obvious what makes it ‘foundational’. This paper begins with a taxonomy of the jobs set theory does that might reasonably be regarded as foundational. It then moves on to category-theoretic and univalent foundations, exploring (...) to what extent they do these same jobs, and to what extent they might do other jobs also reasonably regarded as foundational. (shrink)

Traditional accounts of the feminist history of philosophy have viewed reason as associated with masculinity and subsequent debates have been framed by this assumption. Yet recent debates in deconstruction have shown that gender has never been a stable matter. In the history of philosophy 'female' and 'woman' are full of ambiguity. What does deconstruction have to offer feminist criticism of the history of philosophy? _Yielding Gender_ explores this question by examining three crucial areas; the issue of gender as 'troubled'; deconstruction; (...) and feminist criticism of the history of philosophy. The first part of the book discusses the work of Judith Butler, Jacques Derrida, and contemporary French feminist philosophy including key figures such as Luce Irigiray. Particular attention is given to the possibilities offered by deconstruction for understanding the history of philosophy. The second part considers and then challenges feminist interpretations of some key figures in the history of philosophy. Penelope Deutscher sketches how Rousseau, St. Augustine and Simone de Beauvoir have described gender and argues that their readings of gender are in fact empowered by gender's own contradiction and instability rather than limited by it. (shrink)

Story is central to everyday theology, translating concepts into images which reach into our deepest psyche. This is graphically illustrated in the story of the Magi which conveys in dramatic form essences of belief and understanding. St. Francis appreciated the power of drama and imagery and the Franciscans, nurtured in this tradition, carried it with them to Mexico. Of all these stories introduced after 1524, one of the most enthusiastically received by the Aztecs was the story of the feast of (...) the Epiphany. It is a testament to its popularity that we have inherited two almost contemporaneous autos, La Adoración de los Reyes and La Comedia de los Reyes. Horcasitas comments on this phenomenon: “The Feast of the... (shrink)

The human microbiome has become one of the dominant biomedical frameworks of the contemporary moment that may be understood to be post-Pasteurian. The recognitions the human microbiome opens up for thinking about the biological self and the individual have ontological and epistemological ramifications for considering what and who the human being is. As this article illustrates, the microbiopolitics of the human microbiome challenges the immunitarian Pasteurian model in which the organismic self shores itself up and defends itself against a microbial (...) non-self or other. Instead, this theory presents the human organism as comprised of multiple ecosystems and as a multitude, suggesting that the thanatopolitical attempts to wipe out microbial others (evident in the overuse and misuse of antibiotics, for example) are giving way to an affirmative microbiopolitics grounded in generative multispecies relationality. This article sets out to make the case for this affirmative microbiopolitics. (shrink)

This paper reconstructs Steel’s multiverse project in his ‘Gödel’s program’ (Steel [2014]), first by comparing it to those of Hamkins [2012] and Woodin [2011], then by detailed analysis what’s presented in Steel’s brief text. In particular, we reconstruct his notion of a ‘natural’ theory, describe his multiverse axioms and his translation function, and assess the resulting status of the Continuum Hypothesis. In the end, we reconceptualize the defect that Steel thinks CH might suffer from and isolate what it would take (...) to remove it while working within his framework. As our goal is to present as coherent and compelling a philosophical and mathematical story as we can, we allow ourselves to augment Steel’s story in places (e.g., in the treatment of Amalgamation) and to depart from it in others (e.g., the removal of ‘meaning’ from the account). The relevant mathematics is laid out in the appendices. (shrink)

What is the modal significance of sortal concepts? It is generally accepted that sortal concepts provide persistence conditions with modal implications that are de re, and not merely de dicto. I do not think that this important assumption has received the scrutiny that it deserves. In this paper, I examine the contrast between a ‘pure de dicto’ theory of the persistence conditions associated with sortal concepts and a variety of de re theories, both essentialist and non-essentialist. I conclude that although (...) there is a defensible argument against the pure de dicto theory, it has two interesting implications. First, the argument lends no support to an essentialist version of the de re theory. Secondly, it appears to support the rejection of the pure de dicto theory only by a theorist who is also a pluralist about coincidence. Hence it appears to provide no justification for the rejection of the pure de dicto theory on the part of a contingent identity theorist. (shrink)

_ Source: _Volume 8, Issue 3, pp 193 - 197 This piece gives an overview of my book, _What Do Philosophers Do? Skepticism and the Practice of Philosophy_.

My topic here is metaphilosophy, the question of how philosophy is properly done. For some years now, I've been developing a particularly austere, roughly naturalistic approach to philosophical questions that I call 'second philosophy'. It has seemed to me that one effective way to convey the spirit of second philosophy is to compare and contrast it with other more familiar methods, like transcendental or therapeutic philosophy. Here I hope to pursue this sort of engagement with two other venerable schools of (...) thought: Hume's 'science of man' and Reid's 'philosophy of common sense'. Hume presents a fitting starting point for any discussion of naturalism -- even more so when Reid is on the agenda -- so my first pass at a portrait of the second philosopher traces her relations to the 'scientist of man'. Of course, Hume's cheerfully industrious inquirer eventually lands on the barren rock of skepticism, so we'll also take a second-philosophical look at the kinds of considerations that led poor Hume to his shipwreck. This sets the stage for Reid. (shrink)

Sexual difference as a basis of equality : an introduction to Irigarayan politics -- Irigaray on language : from the speech of dementia to the problem of sexual indifference -- Rethinking the politics of recognition : the declaration of Irigarayan sexuate rights -- Irigarayan performativity : is this a question of can saying it make it so? -- Sexuate genre : ethics and politics for improper selves -- Anticipating sexual difference : mediation, love, and divinity -- Interrogating an unasked question (...) : is there sexual difference? -- The impossible friend : traversing the heterosocial, the homosocial, and the successes of failure -- Sexed discourse and the language of the philosophers : to be two -- Effacement redoubled? : between the Orient and the Occident. (shrink)

A novel treatment of an issue central to much current work in metaphysics: the distinction between the essential and accidental properties of individuals. Mackie challenges widely held views, and arrives at what she calls "minimalist essentialism," an unorthodox theory according to which ordinary individuals have relatively few interesting essential properties. Mackie's clear and accessible discussions of issues surrounding necessity and essentialism mean that the book will appeal as much to graduate students as it will to seasoned metaphysicians.

Sleep enhances integration across multiple stimuli, abstraction of general rules, insight into hidden solutions and false memory formation. Newly learned information is better assimilated if compatible with an existing cognitive framework or schema. This article proposes a mechanism by which the reactivation of newly learned memories during sleep could actively underpin both schema formation and the addition of new knowledge to existing schemata. Under this model, the overlapping replay of related memories selectively strengthens shared elements. Repeated reactivation of memories in (...) different combinations progressively builds schematic representations of the relationships between stimuli. We argue that this selective strengthening forms the basis of cognitive abstraction, and explain how it facilitates insight and false memory formation. (shrink)

First published in 1991. Routledge is an imprint of Taylor & Francis, an informa company.

Professor Deutscher studies Beauvoir's philosophy on "otherness" not just through her famous views on gender (in her celebrated 1949 work The...

This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic—what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics—Logicism, Intuitionism, Formalism, Realism—and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam (...) are among the philosophers considered along the way. (shrink)