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.

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)

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.

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)

This paper explores women's accounts of prostitution in terms of the lived experience of the body, drawing on life story narratives and arts images created by women in the sex industry. These narratives show that women's experiences of prostitution constitute a spectrum of (dis)embodiment that is inflected, not determined, by settings and contexts. Theoretical approaches to embodiment were sought that acknowledged tensions between violation and a sense of empowerment. Therefore, the ontology of selling sex, and associated experiences such as violence, (...) drug use and self-harm are explored using feminist applications of Merleau-Ponty's notion of the `habit body'. A key focus is how the body is constituted by embodied experiences of abuse (e.g. the work of Parkins and of Weiss), and how women negotiate ownership of the body within commercial sex transactions. This highlights the process of repositioning the body by selling sex, in accordance with the accumulated experiences of the habit body. Thus, to borrow from Wendy Parkins, women perceive that they are acting meaningfully through the body, even when reproducing dynamics of objectification and dissociation. (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_.

The effort to fit simple logical truths–like `if it's either red or green and it's not red, then it must be green'–into Kant's account of knowledge turns up a position more subtle and intriguing than might be expected at first glance.

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)

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)

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)

The goal of this paper is to sketch a distinctive version of naturalism in the philosophy of science, both by tracing historical antecedents and by addressing contemporary objections.

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)

My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, or in (...) social arrangements, governments, power structures, or some such thing, but I resist the full force of this way of thinking, clinging to the old school notion that we have gradually learned more about the world over time, that our opinions on these matters have improved, and that seeing how we reached the point we now occupy may help us avoid falling back into old philosophies that are now no longer viable. In that spirit, it seems to me that once we focus on the general question of how mathematics relates to science, one observation is immediate: the march of the centuries has produced an amusing reversal of philosophical fortunes. Let me begin there. In the beginning, that is, in Plato, mathematical knowledge was sharply distinguished from ordinary perceptual belief about the world. According to Plato’s metaphysics, mathematics is the study of eternal and unchanging abstract Forms,1 while science is uncertain and changeable opinion about the world of mere becoming. Indeed, in Plato’s lights, of the two, only mathematics deserves to be called ‘knowledge’ at all! Of course if sense perception cannot give us knowledge, if mathematics is not about perceivable things, then Plato owes us an account of how we ordinary humans achieve this wonderful insight into the properties of the abstract world of Forms. Plato’s answer is that we do not actually acquire mathematical knowledge at all; rather, we recollect it from a time before birth, when our souls, unencumbered by physical bodies, were free to commune with the Forms, and not just the mathematical ones, either – also Truth, Beauty, Justice, the Good, and so on.2 Whatever appeal this position may have held for the ancient Greeks, it will not begin to satisfy a contemporary, scientifically minded philosopher.. (shrink)

This chapter compares and contrasts Quine’s naturalism with the versions of two post-Quineans on the nature of science, logic, and mathematics. The role of indispensability in the philosophy of mathematics is treated in detail.

Permaculture is primarily a thinking tool for designing low carbon, highly productive systems. It originated in Australia in the 1970s and was conceived by Bill Mollison and David Holmgren as a response to the devastating effects of a temperate European agriculture on the fragile soils of an ancient antipodean landscape. Like the dust bowls of the Great Plains in the USA in the 1930s, an alien agriculture has the capacity to turn a delicately balanced ecology into desert. Their initial response (...) was to design a permanent agriculture with tree crops and other perennials inhabiting all the niches from the canopy to the ground cover and below. The soil is left untilled to establish its own robust micro-ecology. Key to this is that the land must be biodiverse and stable for future generations. From perennial tree crops, permaculture has developed into an integrated system of design that encompasses everything from agriculture, horticulture, architecture, and ecology, as well as economy and legal systems for businesses and communities. (shrink)

What Do Philosophers Do? takes up the leading arguments for radical skepticism from an everyday point of view. A range of philosophical methods are examined and employed, for a revealing portrait of what philosophers do, and perhaps a quiet suggestion for what they should do, for what they do best.

Does V = L? Is the Axiom of Constructibility true? Most people with an opinion would answer no. But on what grounds? Despite the near unanimity with which V = L is declared false, the literature reveals no clear consensus on what counts as evidence against the hypothesis and no detailed analysis of why the facts of the sort cited constitute evidence one way or another. Unable to produce a well-developed argument one way or the other, some observers despair, retreating (...) to unattractive fall-back positions, e.g., that the decision on whether or not V = L is a matter of personal aesthetics. I would prefer to avoid such conclusions, if possible. If we are to believe that L is not V, as so many would urge, then there ought to be good reasons for this belief, reasons that can be stated clearly and subjected to rational evaluation. Though no complete argument has been presented, the literature does contain a number of varied argument fragments, and it is worth asking whether some of these might be developed into a persuasive case.One particularly simple approach would be to note that the existence of a measurable cardinal implies that V ≠ L,1and to argue that there is a measurable cardinal. The drawback to this approach is that its implying V ≠ L cannot then be counted as evidence in favor of MC, as it often is. Indeed, there seems to have been considerable sentiment against V = L even before the proof of its negation from MC,2and this sentiment must either be accounted for as reasonable or explained away as an aberration of some kind. (shrink)

The Logical Must is an examination of Wittgenstein's philosophy of logic, early and late, from an austere naturalistic perspective called "Second Philosophy.".

A plea for natural philosophy --On the question of realism --Hume and Reid --Moore's hands --Wittgenstein on hinges --A note on truth and reference --The philosophy of logic --A Second Philosophy of logic --Psychology and the a priori sciences --Do numbers exist? --Enhanced if-thenism.

Though many working mathematicians embrace a rough and ready form of Platonism, that venerable position has suffered a checkered philosophical career. Indeed the three schools of thought with which most of us began our official philosophizing about mathematics—Intuitionism, Formalism, and Logicism—all stand in fundamental disagreement with Platonism. Nevertheless, various versions of Platonistic thinking survive in contemporary philosophical circles. The aim of this paper is to describe these views, and, as my title suggests, to trace their roots.I'll begin with some preliminary (...) remarks about the big three schools. This seems a reasonable approach to the issues both because most observers are familiar, at least in a general way, with the tenets of Intuitionism, Formalism, and Logicism, and because it is in reaction to these that contemporary Platonism has taken shape. (shrink)

Personality research has functioned under the prevailing influence of middle-level theorizing sufficiently long to justify consideration of the effects of this approach. Despite improvements in precision and testability of hypotheses, with resulting increases in volume of research, the pervasive effect of several practical dangers of middle-level theorizing are identified. These involve the unappreciated failure to test comprehensive theories when concepts from them have been extirpated, overly-weak justification of research methods, a vanity of small differences, and insufficient theoretical precision in framing (...) empirical efforts. Ways of avoiding these dangers are explored, and it is concluded that the most promising is a comparative analytic stance toward inquiry that reconsiders comprehensive theorizing without courting ambiguity and imprecision. (shrink)

Begins with a presentation and elaboration of Benacerraf's epistemic challenge to realism: how can we gain knowledge of an acausal world of non‐spatio‐temporal abstracts? I then outline a theory of perception based in part on neurological theories of Hebb and developmental evidence from Piaget, and I argue in these terms that we can, in fact, perceive sets of medium‐sized physical objects. This account of perception is elaborated into an account of physical and mathematical intuition, faculties that produce various rudimentary beliefs (...) that underlie the simplest physical and set theoretic assumptions. I conclude by comparing and contrasting this epistemology with some controversial passages from Gödel's writings. (shrink)

The early sections describe the pre‐theoretic realism of the mathematician, survey the basic forms of realism in philosophy, and attempt to disentangle the issues of realism from debates over the nature of truth. The final section begins by laying out traditional Platonism, intuitionism, and formalism. Quine's famous critique of Carnap's conventionalism then leads to Quine's realism, and Putnam's developments thereof, while a different sort of mathematical realism is found in Gödel's writings. Set theoretic realism emerges as an effort to build (...) on the strengths of Quine's and Gödel's realisms, while avoiding their weaknesses and filling in their lacunae. (shrink)

There is a paucity of research into the prevalence of academic dishonesty within Canada compared to other countries. Recently, there has been a call for a better understanding of the particular characteristics of educational integrity in Canada so that Canada can more meaningfully contribute to current discussions surrounding academic integrity. Here, we present findings from student and faculty surveys conducted within a medium-sized Canadian university. These surveys probed perceptions towards, and experiences with, academic dishonesty, in which we aimed to understand (...) how students and faculty regarded academically dishonest practices during their postsecondary careers. We also aimed to understand how often students engaged in, and faculty had witnessed, academic dishonesty, whether or not witnessing incidents of academic dishonesty corresponded with gender, year of experience, highest level of educational attainment, discipline, or their personal perceptions towards the importance of academic honesty, and whether students had been adequately taught what constitutes academic dishonesty. We found that an overwhelming majority of students viewed academic honesty as important, and that most students reported not engaging in academic dishonesty themselves despite 45.8% reporting that they had witnessed others engage in academic dishonesty. We also found that students were more likely to witness cheating as their postsecondary experience increased, that witnessing varied across disciplines and educational attainment, and that witnessing varied with student perceptions. However, we found no such patterns in faculty responses, but found that faculty are split on whether or not they believe incidents of academic honesty are increasing. (shrink)

The tenor of much recent work in the philosophy of mathematics has been dictated by the popular assumption that Platonism is defunct. Some embrace that assumption and look for alternatives, others deny it and attempt to revive Platonism, but either way it is the starting point. The fate of Platonism took center stage with the appearance of Paul Benacerraf’s “Mathematical truth”, but a decade has passed since then, and the philosophical climate has changed. Most important, the quarter from which Platonism (...) was to receive its mortal wound—epistemology—has developed considerably; the epistemological theory presupposed by Benacerraf is no longer popular. This makes it difficult to assess the value of work in the philosophy of mathematics done under the influence of Benacerraf’s formulation. (shrink)

My aim in this paper is to propose what seems to me a distinctive approach to set theoretic methodology. By ‘methodology’ I mean the study of the actual methods used by practitioners, the study of how these methods might be justified or reformed or extended. So, for example, when the intuitionist's philosophical analysis recommends a wholesale revision of the methods of proof used in classical mathematics, this is a piece of reformist methodology. In contrast with the intuitionist, I will focus (...) more narrowly on the methods of contemporary set theory, and, more importantly, I will certainly recommend no sweeping reforms. Rather, I begin from the assumption that the methodologist's job is to account for set theory as it is practiced, not as some philosophy would have it be. This credo lies at the very heart of the so-called ‘naturalism’ to be described here.A philosopher looking at set theoretic practice from the outside, so to speak, might notice any number of interesting methodological questions, beginning with the intuitionist's ‘why use classical logic?’, but this sort of question is not a live issue for most practicing set theorists. One central question on which the philosopher's and the practitioner's interests converge is this: what is the status of independent statements like the continuum hypothesis (CH)? A number of large questions arise in its wake: what criteria should guide the search for new axioms? For that matter, what reasons support our adoption of the old axioms? (shrink)

Naturalism in philosophy is sometimes thought to imply both scientific realism and a brand of mathematical realism that has methodological consequences for the practice of mathematics. I suggest that naturalism does not yield such a brand of mathematical realism, that naturalism views ontology as irrelevant to mathematical methodology, and that approaching methodological questions from this naturalistic perspective illuminates issues and considerations previously overshadowed by (irrelevant) ontological concerns.