This paper argues that in Christian Wolff’s theory of knowledge, logical regimentation does not take the place of experiential justification, but serves to facilitate the application of empirical information and clearly exhibit its warrant. My argument targets rationalistic interpretations such as R. Lanier Anderson’s. It is common ground in this dispute that making concepts “distinct” issues in the premises on which all deductive justification rests. Against the view that concepts are made distinct only by analysis, which is carried out by (...) the understanding independently of experience, I contend that for Wolff some distinct concepts are arrived at through experience. I emphasize that Wolff countenances empirical methods of obtaining distinct concepts even in mathematics. This striking feature of his view indicates how its empiricist elements can be reconciled with his injunction to follow “mathematical” method. (shrink)

This paper considers Kant's understanding of conceptual representation in light of his view of geometry.

J. H. Lambert proved important results of what we now think of as non-Euclidean geometries, and gave examples of surfaces satisfying their theorems. I use his philosophical views to explain why he did not think the certainty of Euclidean geometry was threatened by the development of what we regard as alternatives to it. Lambert holds that theories other than Euclid's fall prey to skeptical doubt. So despite their satisfiability, for him these theories are not equal to Euclid's in justification. Contrary (...) to recent interpretations, then, Lambert does not conceive of mathematical justification as semantic. According to Lambert, Euclid overcomes doubt by means of postulates. Euclid's theory thus owes its justification not to the existence of the surfaces that satisfy it, but to the postulates according to which these "models" are constructed. To understand Lambert's view of postulates and the doubt they answer, I examine his criticism of Christian Wolff's views. I argue that Lambert's view reflects insight into traditional mathematical practice and has value as a foil for contemporary, model-theoretic, views of justification. (shrink)

In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant's 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional (...) applicability of mathematical concepts. (shrink)

Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the putting-together in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity is ultimately related to spatial extension. I (...) use this conception of Newton’s project to explain the organization and proofs of the first theorems of mechanics to appear in the Principia. The placementof Kepler’s rule of areas as the first proposition, and the manner in which Newton proves it, appear natural on the supposition that Newton seeks a measure, in the sense of a moveable spatial quantity, of time. I argue that Newton proceeds in this way so that his reasoning can have the ostensive certainty of geometry. (shrink)

In a crucial passage of the second-edition Transcendental Deduction, Kant claims that the concept of motion is central to our understanding of change and temporal order. I show that this seemingly idle claim is really integral to the Deduction, understood as a replacement for Locke’s “physiological” epistemology (cf. A86-7/B119). Béatrice Longuenesse has shown that Kant’s notion of distinctively inner receptivity derives from Locke. To explain the a priori application of concepts such as succession to this mode of sensibility, Kant construes (...) the mind as receptive to its own activity. As Longuenesse understands Kant’s response to Locke, “motion” becomes little more than a metaphor for the action of understanding on inner sense. For Michael Friedman, in contrast, this passage evidences Kant’s deep concern with the foundations of Newtonian science. He reads it as a reference to inertial motion, the standard by which temporal intervals are measured. I show that Longuenesse’s and Friedman’s interpretations are in fact complementary. Both Locke and Kant are deeply concerned with the quantification of time. So Longuenesse is right that §24 is meant to supplant Locke’s account, and Friedman correctly takes it as the foundation of Kant’s account of the application of quantitative concepts to time. Kant aims, specifically, to explain cognition of time as continuous magnitude. However, Longuenesse leaves Kant without an answer to Locke’s challenge that continuous magnitude cannot be understood on the basis of discrete magnitude. And on Friedman’s view Kant’s account of the understanding’s activity presupposes, and thus cannot explain, the achievements of the mathematical sciences (such as the representation of temporal continuity). On my reading, Kant’s key contention is that we must regard the segregation of temporally ordered representation into units as the work of the understanding, rather than (as Locke views it) of sensibility. By giving the understanding this role, Kant succeeds where he takes Locke to fail. I show how the power to unify temporal representation can be ascribed to the understanding on the basis, not of assumed mathematical or scientific knowledge, but of its characterization as the power of judgment. (shrink)

The main goal of part 1 is to challenge the widely held view that Poincaré orders the sciences in a hierarchy of dependence, such that all others presuppose arithmetic. Commentators have suggested that the intuition that grounds the use of induction in arithmetic also underlies the conception of a continuum, that the consistency of geometrical axioms must be proved through arithmetical induction, and that arithmetical induction licenses the supposition that certain operations form a group. I criticize each of these readings. (...) More fully, I argue that the justification Poincaré offers for the use of the group notion in geometry appears to extend to set-theoretic notions that would suffice to put arithmetic on a logical foundation, thus undermining his own case for the necessity of intuition in arithmetic. In part 2, I offer an interpretation of intuition’s role on which it justifies the use of group-theoretic, but not set-theoretic, notions. (shrink)

Tyler Burge is an American philosopher whose body of work spans several areas of theoretical philosophy in the analytic tradition. While Burge has made important contributions to the philosophy of language and logic, he is most renowned for his work in philosophy of mind and epistemology. In particular, he is known for articulating and developing a view he labels ‘anti-individualism.’ In his later work, Burge connects his views with state-of-the-art scientific theory. Despite this emphasis on empirical considerations, Burge stands in (...) an important relationship to the rationalist tradition in philosophy. This entry surveys Burge’s work and seeks to situate it in the larger philosophical landscape. (shrink)

Part 1 of this article exposed a tension between Poincaré’s views of arithmetic and geometry and argued that it could not be resolved by taking geometry to depend on arithmetic. Part 2 aims to resolve the tension by supposing not merely that intuition’s role is to justify induction on the natural numbers but rather that it also functions to acquaint us with the unity of orders and structures and show practices to fit or harmonize with experience. I argue that in (...) this manner, intuition serves the epistemological function of warranting generalizations and justifying practices. In particular, it justifies the application of group-theoretic notions in geometry but not the use of set-theoretic notions in arithmetic. (shrink)

Kant’s Mathematical World (KMW) is a strikingly original, richly detailed account of Kant’s philosophy of mathematics as a reckoning with the long-held understa.

Kant’s Metaphysical Foundations of Natural Science (MFNS), published in 1786, has proved difficult to situate in the context of eighteenth-century responses to Newton. One point beyond dispute is that Kant is not satisfied with the “metaphysical foundations” thus far proffered by Newton and his followers. He echoes some familiar Leibnizian criticisms (such as those concerning absolute space) and, in a passage we will examine closely, insists that rejecting “the concept of an original attraction” would put Newton “at variance with himself” (...) (4:515). In light of Kant’s robust defense of the immediacy and universality of gravitational attraction, the overall similarity between his three “mechanical laws” and Newton’s “Axioms, or Laws of Motion” has made it the “standard” view that Kant “intends to justify Newtonian science in general and Newtonian mechanics in particular as stated in” Newton’s laws of motion (Watkins 2019, 89). But it is unclear whether the alternative “foundations” he proposes are for Newton’s theory of motion or something more akin to Leibniz’s physics. Recent scholarship has documented the Leibnizian provenance of Kant’s three laws, and argued for the relevance of later figures strongly influenced by Leibniz. (shrink)

_Review of: Anderson, Abraham, _Kant, Hume, and the Interruption of Dogmatic Slumber_, New York, Oxford University Press, 2020, 180+xxii, 978-0-19-009674-8_.

Not a full treatment of Newton’s scientific method, this book discusses his optical research only in passing (342–43). Its subtitle better indicates its scope: it focuses narrowly on the argument for universal gravitation in Book III of the Principia. The philosophical project is to set out an “ideal of empirical success” realized by the argument. Newton claims his method is to “deduce” propositions “from phenomena.” On Harper’s interpretation Newton’s phenomena are patterns of data, which are used to measure “parameters” by (...) which the theory explains them. An example is Kepler’s Area Rule. Its fit to the data confirms the hypothesis that the force maintaining a body in orbit is directed toward the .. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Kant's Transcendental Deduction by Alison LaywineKatherine DunlopAlison Laywine. Kant's Transcendental Deduction. Oxford: Oxford University Press, 2020. Pp. iv + 318. Hardback, $80.00.Alison Laywine's contribution to the rich literature on Kant's "Transcendental Deduction of the Categories" stands out for the novelty of its approach and conclusions. Laywine's declared "strategy" is "to compare and contrast" the Deduction with the Duisburg Nachlaß, an important set of manuscript jottings from the 1770s (...) (10). But her approach is also deeply informed by Kant's writings on metaphysics from the 1750s and 1760s; moreover, she gives attention to ancient Greek geometry and its importance for Kant's thought.I believe Laywine's most important interpretative claim is that the Transcendental Deduction's "final step" addresses "the question of how nature is possible" (210). Here, 'nature' is understood in what Kant calls the "formal sense," as "the totality of rules under which appearances must stand if they are to be thought as joined in one experience" (Prolegomena, §36; cf. B 165). This constitutes a novel answer to the problem posed in Dieter Henrich's landmark 1969 paper "The Proof Structure of the Transcendental Deduction" (Review of Metaphysics 22 [1969]: 640–59): how to understand §§21–26 of the (B-edition) Deduction as proving more than the thesis already stated in §20 (that the manifold in an intuition necessarily stands under the categories).Crucial support for Laywine's interpretation comes from §26 of the Deduction, which claims the possibility of cognizing objects "a priori through categories... as far as the laws of their combination are concerned, thus the possibility of as it were prescribing the law to nature and even making [nature] possible," is now "to be explained" (B 159). Kant does not use the term 'world' in this passage (as he does in Prolegomena §36). But Laywine contends that here the word 'nature' "has unmistakable, deliberate, cosmological connotations," and in fact "means 'world' in the sense of Kant's early cosmology": roughly, a whole unified by means of laws (12–13).The "cosmological" language of §26 does not recur in the following, officially concluding, section of the Deduction. So, we might ask whether Kant's explanation of how the understanding prescribes laws to nature is integral to the Deduction; Henry Allison, for instance, describes this explanation as an "appendix" (Kant's Transcendental Deduction: An Analytical-Historical Commentary [Oxford: Oxford University Press, 2015], 9). The question of whether it belongs integrally has bite because, as Laywine makes clear in her "Conclusion," the universal laws at issue are just the Analogies of Experience. Thus, the passage could be read as the "promissory note with a forward-looking reference to the System of Principles" that she finds missing from the Deduction (289). Laywine meets such worries by arguing that "the reappropriation [from the pre-Critical period] of the general cosmology is actually [End Page 162] doing... a lot of hard work" in the Deduction (13). This sustained argument comes to a head in chapter 4, which contends that each of the two steps into which Laywine divides the first half of the (B-edition) Deduction, treated in chapters 2 and 3 (respectively), relies on cosmological presuppositions.Chapter 2 analyzes the conception of knowledge as relation to an object that is asserted (in §17) to rely on the synthetic unity of apperception. Laywine traces this conception to the Duisburg Nachlaß's account of "exposition," which relates concepts a priori to appearances, in something like the way that geometrical construction relates them to pure intuition. (Laywine further connects the Latin term expositio to the Greek ekthesis, which expositio translates in the context of geometrical proof. She thereby gives the notion of ekthesis broader importance than does Jaakko Hintikka, who noted its relevance to Kant's philosophy of mathematics in "Kant on the Mathematical Method" [Monist 51 (1967): 352–75]. Laywine claims that Borelli's edition of Euclid could have been Kant's source for the term, but I doubt it was known to Kant and his contemporaries, since it is not among the editions cited by Christian Wolff; Commandino seems likelier to me. Chapter 2 is concerned to articulate the notion of... (shrink)

How do things persist? Are material objects spread out through time just as they are spread out through space? Or is temporal persistence quite different from spatial extension? This key question lies at the heart of any metaphysical exploration of the material world, and it plays a crucial part in debates about personal identity and survival. This book explores and compares three theories of persistence — endurance, perdurance, and stage theories — investigating the ways in which they attempt to account (...) for the world around us. Having provided valuable clarification of its two main rivals, the book concludes by advocating stage theory. Such a basic issue about the nature of the physical world naturally has close ties with other central philosophical problems. This book includes discussions of change and parthood, of how we refer to material objects at different times, of the doctrine of Humean supervenience, and of the modal features of material things. In particular, it contains new accounts of the nature of worldly vagueness, and of what binds material things together over time, distinguishing the career of a natural object from an arbitrary sequence of events. Each chapter concludes with a reflection about the impact of these metaphysical debates upon questions about our personal identity and survival. (shrink)

One of Martin Heidegger’s enduring philosophical legacies is his overall vision of what it is to be us. We—whoever that turns out to include—are cases of Dasein, and as such we are distinctively open to entities, including others and ourselves. In this essay, I paint a picture of that openness that aims to capture why Heidegger’s vision has so powerfully gripped so many. Drawing on Heidegger’s thought both early and late, I present a synoptic view of us as open to (...) the encounter with entities' bursting forth into presencing. We can be more or less closed off to this upsurge, but we can also allow it in its full power: in philosophical and poetic openness. I draw on Borgmann, Buber, Plato’s Socrates, Rilke, and others to capture our openness at its Heideggerian best—and we ourselves at our best, showing up radiantly for encounter. (shrink)

We have identified a sample of 53 societies outside of the classical Himalayan and Marquesean area that permit polyandrous unions. Our goal is to broadly describe the demographic, social, marital, and economic characteristics of these societies and to evaluate some hypotheses of the causes of polyandry. We demonstrate that although polyandry is rare it is not as rare as commonly believed, is found worldwide, and is most common in egalitarian societies. We also argue that polyandry likely existed during early human (...) history and should be examined from an evolutionary perspective. Our analysis reveals that it may be a predictable response to a high operational sex ratio favoring males and may also be a response to high rates of male mortality and, possibly, male absenteeism. Other factors may contribute, but our within-polyandry sample limits analysis. (shrink)

The work and ideas of Rudolf Laban, dancer, choreographer and seminal theoretician of movement and dance, have had a profound impact across a range of disciplines. This book explores this impact.

Social groups—like teams, committees, gender groups, and racial groups—play a central role in our lives and in philosophical inquiry. Here I develop and motivate a structuralist ontology of social groups centered on social structures (i.e., networks of relations that are constitutively dependent on social factors). The view delivers a picture that encompasses a diverse range of social groups, while maintaining important metaphysical and normative distinctions between groups of different kinds. It also meets the constraint that not every arbitrary collection of (...) people is a social group. In addition, the framework provides resources for developing a broader structuralist view in social ontology. (shrink)

When William of Ockham lectured on Lombard's Sentences in 1317-1319, he articulated a new theory of knowledge. Its reception by fourteenth-century scholars was, however, largely negative, for it conflicted with technical accounts of vision and with their interprations of Duns Scotus. This study begins with Roger Bacon, a major source for later scholastics' efforts to tie a complex of semantic and optical explanations together into an account of concept formation, truth and the acquisition of certitude. After considering the challenges of (...) Peter Olivi and Henry of Ghent, Part I concludes with a discussion of Scotus's epistemology. Part II explores the alternative theories of Peter Aureol and William of Ockham. Part III traces the impact of Scotus, and then of Aureol, on Oxford thought in the years of Ockham's early audience, culminating with the views of Adam Wodeham. Part IV concerns Aureol's intellectual legacy at Paris, the introduction of Wodeham's thought there, and Autrecourt's controversies. (shrink)

When William of Ockham lectured on Lombard's "Sentences" in 1317-1319, he articulated a new theory of knowledge.

Stereotypes sometimes lead us to make poor judgements of other people, but they also have the potential to facilitate quick, efficient, and accurate judgements. How can we discern whether any individual act of stereotyping will have the positive or negative effect? How Stereotypes Deceive Us addresses this question. It identifies various factors that determine whether or not the application of a stereotype to an individual in a specific context will facilitate or impede correct judgements and perceptions of the individual. It (...) challenges the thought that stereotyping only and always impedes correct judgement when the stereotypes that are applied are inaccurate, failing to reflect social realities. It argues instead that stereotypes that reflect social realities can lead to misperceptions and misjudgements, and that inaccurate but egalitarian social attitudes can therefore facilitate correct judgements and accurate perceptions. The arguments presented in this book have important implications for those who might engage in stereotyping and those who are at risk of being stereotyped. They have implications for those who work in healthcare and those who have mental health conditions. How Stereotypes Deceive Us provides a new conceptual framework-evaluative dispositionalism-that captures the epistemic faults of stereotypes and stereotyping, providing conceptual resources that can be used to improve our own thinking by avoiding the pitfalls of stereotyping, and to challenge other people's stereotyping where it is likely to lead to misperception and misjudgement. (shrink)

Francis Dunlop; Form, Content and Rationality in Morality and Moral Education, Journal of Philosophy of Education, Volume 11, Issue 1, 30 May 2006, Pages 78–97.

Social groups, including racial and gender groups and teams and committees, seem to play an important role in our world. This article examines key metaphysical questions regarding groups. I examine answers to the question ‘Do groups exist?’ I argue that worries about puzzles of composition, motivations to accept methodological individualism, and a rejection of Racialism support a negative answer to the question. An affirmative answer is supported by arguments that groups are efficacious, indispensible to our best theories, and accepted given (...) common sense. Then, I turn to an examination of the features of social groups. I argue that social groups can be divided into two sorts. Groups of Type 1 are organized social groups like courts and clubs. Groups of Type 2 are groups like Blacks, women, and lesbians. While groups of both sorts have some features in common, they also have marked differences in features. Finally, I turn to views of the nature of social groups. I argue that the difference in features provides evidence that social groups do not have a uniform nature. Teams and committees are structured wholes, while race and gender groups are social kinds. (shrink)

Although the principle of fair subject selection is a widely recognized requirement of ethical clinical research, it often yields conflicting imperatives, thus raising major ethical dilemmas regarding participant selection. In this paper, we diagnose the source of this problem, arguing that the principle of fair subject selection is best understood as a bundle of four distinct sub-principles, each with normative force and each yielding distinct imperatives: (1) fair inclusion; (2) fair burden sharing; (3) fair opportunity; and (4) fair distribution of (...) third-party risks. We first map out these distinct sub-principles, and then identify the ways in which they yield conflicting imperatives for the design of inclusion and exclusion criteria, and the recruitment of participants. We then offer guidance for how decision makers should navigate these conflicting imperatives to ensure that participants are selected fairly. (shrink)

Du Châtelet’s 1740 text Foundations of Physics tackles three of the major foundational issues facing natural philosophy in the early eighteenth century: the problem of bodies, the problem of force, and the question of appropriate methodology. This paper offers an introduction to Du Châtelet’s philosophy of science, as expressed in her Foundations of Physics, primarily through the lens of the problem of bodies.

In this paper I argue for a view of groups, things like teams, committees, clubs and courts. I begin by examining features all groups seem to share. I formulate a list of six features of groups that serve as criteria any adequate theory of groups must capture. Next, I examine four of the most prominent views of groups currently on offer—that groups are non-singular pluralities, fusions, aggregates and sets. I argue that each fails to capture one or more of the (...) criteria. Last, I develop a view of groups as realizations of structures. The view has two components. First, groups are entities with structure. Second, since groups are concreta, they exist only when a group structure is realized. A structure is realized when each of its functionally defined nodes or places are occupied. I show how such a view captures the six criteria for groups, which no other view of groups adequately does, while offering a substantive answer to the question, “What are groups?”. (shrink)

Highlighting main issues and controversies, this book brings together current philosophical discussions of symmetry in physics to provide an introduction to the subject for physicists and philosophers. The contributors cover all the fundamental symmetries of modern physics, such as CPT and permutation symmetry, as well as discussing symmetry-breaking and general interpretational issues. Classic texts are followed by new review articles and shorter commentaries for each topic. Suitable for courses on the foundations of physics, philosophy of physics and philosophy of science, (...) the volume is a valuable reference for students and researchers. (shrink)

Introduction -- Anselm's classical theism -- The Augustinian legacy -- The purpose, definition, and structure of free choice -- Alternative possibilities and primary agency -- The causes of sin and the intelligibility problem -- Creaturely freedom and God as Creator Omnium -- Grace and free will -- Foreknowledge, freedom, and eternity : part I, the problem and historical background -- Foreknowledge, freedom, and eternity : part II, Anselm's solution -- The freedom of God.

Symmetry considerations dominate modern fundamental physics, both in quantum theory and in relativity. Philosophers are now beginning to devote increasing attention to such issues as the significance of gauge symmetry, quantum particle identity in the light of permutation symmetry, how to make sense of parity violation, the role of symmetry breaking, the empirical status of symmetry principles, and so forth. These issues relate directly to traditional problems in the philosophy of science, including the status of the laws of nature, the (...) relationships between mathematics, physical theory, and the world, and the extent to which mathematics suggests new physics.This entry begins with a brief description of the historical roots and emergence of the concept of symmetry that is at work in modern science. It then turns to the application of this concept to physics, distinguishing between two different uses of symmetry: symmetry principles versus symmetry arguments. It mentions the different varieties of physical symmetries, outlining the ways in which they were introduced into physics. Then, stepping back from the details of the various symmetries, it makes some remarks of a general nature concerning the status and significance of symmetries in physics. (shrink)

Recently several philosophers have argued that racial, gender, and other social generic generalizations should be avoided given their propensity to promote essentialist thinking, obscure the social nature of categories, and contribute to oppression. Here I argue that a general prohibition against social generics goes too far. Given that the truth of many generics require regularities or systematic rather than mere accidental correlations, they are our best means for describing structural forms of violence and discrimination. Moreover, their accuracy, their persistence in (...) the face of counterexamples, and features of the contemporary socio-political context make generics useful linguistic tools in social justice projects. (shrink)

It has been argued that humans can face an ethical/epistemic dilemma over the automatic stereotyping involved in implicit bias: ethical demands require that we consistently treat people equally, as equally likely to possess certain traits, but if our aim is knowledge or understanding our responses should reflect social inequalities meaning that members of certain social groups are statistically more likely than others to possess particular features. I use psychological research to argue that often the best choice from the epistemic perspective (...) is the same as the best choice from the ethical perspective: to avoid automatic stereotyping even when this involves failing to reflect social realities in our judgements. This argument has an important implication: it shows that it is not possible to successfully defend an act of automatic stereotyping simply on the basis that the stereotype reflects an aspect of social reality. An act of automatic stereotyping can be poor from an epistemic perspective even if the stereotype that is activated reflects reality. (shrink)

Some language encourages essentialist thinking. While philosophers have largely focused on generics and essentialism, I argue that nouns as a category are poised to refer to kinds and to promote representational essentializing. Our psychological propensity to essentialize when nouns are used reveals a limitation for anti-essentialist ameliorative projects. Even ameliorated nouns can continue to underpin essentialist thinking. I conclude by arguing that representational essentialism does not doom anti-essentialist ameliorative projects. Rather it reveals that would-be ameliorators ought to attend to the (...) propensities for our representational devices to essentialize and to the complex relationship between essentialism and prejudice. (shrink)