James a maintes fois célébré les rencontres philosophiques et l’on sait les efforts de James et de Bergson pour se voir, lors des passages de James en Europe. Proximité physique ne signifie évidemment pas convergence ni capillarité philosophiques, comme l’apprend à ses dépens Agathon dans le Banquet de Platon. Or, le rapprochement, mais aussi les confusions, entre la philosophie de Bergson et celle de James, voire entre « bergsonisme » et « pragmatisme », restent un passage obligé de l’étude des (...) deux hommes. Si cette confusion — peut-être ces familles de confusions — sont caractéristiques du début du XXe siècle , il serait sans doute illusoire de croire que nous en sommes sortis aujourd’hui. C’est en France une expérience encore très répandue chez le jamesien que devoir se justifier par rapport au « bergsonisme », et c’en est une autre pour le « bergsonien » que de devoir dire qu’il n’est pas forcément « pragmatiste ». Ces glissements ont déjà été maintes fois analysés et je tiendrai ici pour acquis que Horace Kallen , Floris Delattre , Ralph Barton Perry et Millic Capek , qui ont procédé à la revue de détail, nous ont donné suffisamment d’éléments pour qu’il ne soit pas nécessaire de reprendre le dossier dans son ensemble. Le propos sera plutôt de décomposer un travers de lecture que l’on inflige généralement aux deux auteurs à partir d’un terrain plus limité : le thème du « courant », ou flux (stream), de conscience, thème prétendument commun aux deux hommes. Je vais pour cela tenter d’identifier, dans la première section, deux grandes manières d’aborder le rapport entre les deux hommes qui ont conduit à méconnaître leur apport propre. L’une interdit tout simplement de les lire comme philosophes, même si elle est couramment pratiquée, ce que j’illustrerai à la lumière de deux exemples. L’autre type de lecture engage, lui, un contresens sur la thèse même de James, et c’est ici que la face critique de ce chapitre se retourne en argument positif. Le cœur de ce contresens est de croire que James aurait introduit le thème du courant de pensée ou de conscience, et que ce serait là son originalité. Or, comme il est normal chez un auteur pragmatiste après tout, l’originalité réside dans l’usage qui est fait de ce thème. En examinant dans la deuxième section les rouages de ce contresens, dont il n’est pas certain que tous les lecteurs de Bergson l’aient totalement évité alors même qu’ils pensaient le déposer, on tentera donc de préciser tout d’abord en quoi le thème lui-même n’est pas spécifiquement jamesien, ensuite en quoi le propos de James n’est pas tant de décrire ce flux pour lui-même que de nous expliquer ce qui nous guette si nous le négligeons systématiquement, enfin quelles sont les fonctions remplies par les passages sur le courant de conscience dans l’argument de James. (shrink)

Behaviorism was a peculiarly American phenomenon. As a school of psychology it was founded by John B. Watson (1878-1958) and grew into the neobehaviorisms of the 1920s, 30s and 40s. Philosophers were involved from the start, prefiguring the movement and endeavoring to define or redefine its tenets. Behaviorism expressed the naturalistic bent in American thought, which came in response to the prevailing philosophical idealism and was inspired by developments in natural science itself. There were several versions of naturalism in American (...) philosophy, and also several behaviorisms. Most behaviorists paid homage to Darwinian functionalism; all forswore introspection and made learned changes in behavior the primary subject matter and explanatory domain of psychology. They differed in their descriptions of behavior, modes of explanation, and attitudes toward mentalistic concepts. Watson was a strict materialist who wanted to eliminate all mentalistic talk from psychology. Edward Chace Tolman (1886-1959) regarded mind as a biological function of the organism. He permitted mentalistic terms such as 'purpose' in behavioral description, and posited intervening processes that included 'representations' of the environment, while requiring such processes be studied only as expressed in behavior. Clark L. Hull (1884-1952) developed a hypothetical-deductive version of behaviorism, akin to Tolman's functionalism in positing intervening variables but without his cognitivist constructs. B. F. Skinner (1904-90) rejected intervening variables and developed his own account of the behavior of the whole organism, based on the laws of operant conditioning. The naturalism in American philosophy of the early twentieth century showed respect for the natural sciences, especially biology and psychology. John Dewey (1896, 1911), George Santayana (1905, 1920), and F. J. E. Woodbridge (1909, 1913) expressed this attitude. It animated the neorealism of E. B. Holt and Ralph Barton Perry, who gave special attention to psychology, and the evolutionary naturalism and critical realism of Roy Wood Sellars. This naturalism differed from Watson's in regarding mind as part of nature from a Darwinian and functionalist perspective, and treating behavior as the product of the mental functioning. It fed Tolman's version of behaviorism. It was not materialistic or physical-reductionist. Only later, with Quine and logical empiricism, was behaviorism seen as essentially physicalistic. (shrink)

LEIBNIZ AND THE TWO SOPHIES is a critical edition of all of the philosophically important material from the correspondence between the philosopher Gottfried Wilhelm Leibniz (1646-1716) and his two royal patronesses, Electress Sophie of Hanover (1630-1714), and her daughter, Queen Sophie Charlotte of Prussia (1668-1705). In this correspondence, Leibniz expounds in a very accessible way his views on topics such as the nature and operation of the mind, innate knowledge, the afterlife, ethics, and human nature. The correspondence (...) also contains the only known philosophical writings by Sophie and Sophie Charlotte, and thus provides a valuable insight into their views and concerns, as well as throwing light on their characters. The texts are accompanied by a substantial introductory essay which sets the context for the correspondence and analyzes its main philosophical themes. (shrink)

Often, when one faces a choice between alternative actions, there are reasons both for and against each alternative. On one way of understanding these words, what one “ought to do all things considered (ATC)” is determined by the totality of these reasons. So, these reasons can somehow be “combined” or “aggregated” to yield an ATC verdict on these alternatives. First, various assumptions about this sort of aggregation of reasons are articulated. Then it is shown that these assumptions allow for the (...) proof of a “Reasons Aggregation Theorem” – parallel to John Harsanyi’s 1955 “Social Aggregation Theorem”. All reasons for action are grounded in reason-providing values; and, for every such reason-providing value, there is in principle a way of measuring how strongly this value counts against each alternative. The theorem tells us that the appropriate measure of how much reason ATC there is against each alternative is simply a weighted sum of the strengths with which these values count against that alternative; the agent ought not ATC to perform an action iff there is ATC more reason against it than against some available alternative. (shrink)

This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.

This volume contains more than 60 original translations of papers written by the German philosopher Gottfried Wilhelm Leibniz (1646-1716). As well as contributing to Leibniz scholarship, it is intended to function as an introductory text for students.

La traduction latine du livre de Maïmonide Moreh Nevukhim | Guide des égarés, a été l'ouvrage juif le plus influent des derniers millénaires (Di Segni, 2019 ; Rubio, 2006 ; Wohlman, 1988, 1995 ; Kohler, 2017). Elle marqua le début de la scolastique, fille du judaïsme élevée par des penseurs juifs, selon l'historien Heinrich Graetz (Geschichte der Juden, L. 6, Leipzig 1861, p. xii). Imprimée par la première presse mécanique de Gutenberg, son influence en Occident s'étendit jusqu'au Vème concile du (...) Latran (1512-1517) « où les savants furent encouragés à lever les difficultés qui semblaient diviser l'ensemble de la théologie et de la philosophie — (Leibniz, Théodicée, 11 ) ». Pendant des siècles, le Guide a révolutionné le programme d'instruction scolaire en réintégrant dans le domaine de la foi les lois de la pensée (dont la quatrième est devenue le principe de la raison suffisante de Leibniz). Cette collection complète de notes qui expose les idées du Guide fournit tous les passages sélectionnés et réécrits par Leibniz. Cette première traduction complète bilingue annotée des manuscrits originaux en latin sert de porte d'entrée à la foi conforme à la Raison. -/- « L'excellent livre du Rabbin Moïse Maïmonide, le Guide des égarés, est plus philosophique que je ne l'avais imaginé et mérite une lecture attentive. L'auteur, distingué par son intelligence en philosophie, était versé dans les mathématiques, l'art médical, et aussi dans la connaissance de Saintes Écritures. » — G. W. LEIBNIZ, 1685, Anthologie de Leibniz du Guide de Maïmonide, Chapitre III. (shrink)

In his _Being Known_ Peacocke sets himself the task of answering how we come to know about metaphysical necessities. He proposes a semantic principle-based conception consisting of, first, his Principles of Possibility which pro­vide necessary and sufficient conditions for a new concept 'admissibility', and second, characterizations of possibility and of necessity in terms of that new con­cept. I focus on one structural feature; viz. the recursive application involved in the specification of 'admissibility'. After sketching Peacocke’s proposal, I intro­duce a fictional (...) protagonist, Cautious Peacocke, whose coherence I claim shows that Peacocke s proposal cannot be made good. I conclude with the conjecture that similar failure will attend any such semantic-based attempts to ground the epistemology of metaphysical necessity. -/- Dans son livre intitulé Being Known, C. Peacocke se propose de repondre à la question de savoir comment nous en venons a connaitre des nécessités métaphysiques. Il développe une conception sémantique reposant sur des principes comprenant, d’une part, ses Principes de Possibilité — qui fournissent les conditions nécessaires et suffisantes pour un nouveau concept, « l’admissibilité » — et d’autre part des caractérisations de la possibilité et de la nécessité a l’aide de ce nouveau concept. Je me concentre sur une caractéristique structurelle, a savoir l’application récursive a l’œuvre dans la spécification de «l’admissibilité ». Apres avoir esquisse la proposition de Peacocke, j’introduis un personnage fictif, Peacocke-prudent. Je soutiens que la cohérence de ce personnage montre que la proposition de Peacocke ne peut pas être satisfaite. Je conclus en conjecturant qu’un échec similaire se présentera pour toutes les tentatives de fonder l’épistemologie de la nécessité métaphysique sur de telles bases semantiques. (shrink)

We defend a functionalist approach to emotion that begins by focusing on emotions as central states with causal connections to behavior and to other cognitive states. The approach brackets the conscious experience of emotion, lists plausible features that emotions exhibit, and argues that alternative schemes are unpromising candidates. We conclude with the benefits of our approach: one can study emotions in animals; one can look in the brain for the implementation of specific features; and one ends up with an architecture (...) of the mind in which emotions are fully accommodated through their relations to the rest of cognition. Our article focuses on arguing for this general approach; as such, it is an essay in the philosophy of emotion rather than in the psychology or neuroscience of emotion. (shrink)

La traducción al latín de la obra de Maimónides Moreh Nevukhim | Guía para Perplejos, ha sido la obra judía más influyente en los últimos milenios (Di Segni, 2019; Rubio, 2006; Wohlman, 1988, 1995; Kohler, 2017). Ésta marcó el comienzo de la escolástica, «hija del judaísmo nutrida por pensadores judíos, » según el historiador Heinrich Graetz (Geschichte der Juden, L. 6, Leipzig 1861, p. xii). Impresa por la primera imprenta mecánica de Gutenberg, su influencia en Occidente se extendió hasta el (...) Quinto Concilio de Letrán (1512-1517) « donde se instó a los eruditos a eliminar las dificultades que parecían dividir el conjunto de la teología y la filosofía (Leibniz, Teodicea, 11 ). » Durante siglos, la Guía revolucionó el currículo de estudios de la instrucción escolar al reintegrar en el ámbito de la fe las leyes del pensamiento (la cuarta de las cuales se convirtió en el principio de la razón suficiente de Leibniz). La colección completa de las notas que exponen las ideas de la Guía incluye todos los pasajes seleccionados y reescritos por Leibniz. Esta primera traducción bilingüe completa y anotada de los manuscritos originales en latín sirve como una puerta de entrada a la fe conforme a la Razón. -/- « El excelente libro del rabino Moisés Maimónides, Guía para perplejos, es más filosófico de lo que había imaginado y merece una lectura atenta. El autor, distinguido por su inteligencia filosófica, fue versado en matemáticas, en el arte de la medicina, y también en el conocimiento de las Sagradas Escrituras. » — GW LEIBNIZ, 1685. Antología de Leibniz de la Guía de Maimónides, Capítulo III. (shrink)

The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French (...) & McKenzie between mathematics and metaphysics to show that the whole field of analytic metaphysics, being useful not only for philosophy but also for science, should continue to exist as a largely autonomous field. (shrink)

This is a book about normativity -- where the central normative terms are words like 'ought' and 'should' and their equivalents in other languages. It has three parts: The first part is about the semantics of normative discourse: what it means to talk about what ought to be the case. The second part is about the metaphysics of normative properties and relations: what is the nature of those properties and relations whose pattern of instantiation makes propositions about what ought to (...) be the case true. The third part is about the epistemology of normative beliefs: how we could ever know, or even have rational or justified belief in, propositions about what ought to be the case. (shrink)

What is the connection between justification and the kind of consequence relations that are studied by logic? In this essay, I shall try to provide an answer, by proposing a general conception of the kind of inference that counts as justified or rational.

Maimonides’ Latin translation of Moreh Nevukhim | Guide for the Perplexed, was the most influential Jewish work in the last millennia (Di Segni, 2019; Rubio, 2006; Wohlman, 1988, 1995; Kohler, 2017). It marked the beginning of scholasticism, a daughter of Judaism raised by Jewish thinkers, according to historian Heinrich Graetz (Geschichte der Juden, L. 6, Leipzig 1861, p. xii). Printed by Gutenberg's first mechanical press, its influence in the West went as far as the Fifth Lateran Council (1512 — 1517) (...) "where scholars were encouraged to remove the difficulties which seemed to divide the whole of theology and philosophy (Leibniz, Théodicée, 11)." For centuries, the Guide revolutionized the curriculum of school instruction by reintegrating the natural laws of thought in the sphere of faith (the fourth of which became Leibniz’ Principle of sufficient reason). This complete collection of notes expounds the ideas of the Guide and features all the passages selected and rewritten by Leibniz. This first complete annotated bilingual translation of the original manuscripts in Latin serves as an entry point to the faith in conformity with Reason. This complete collection of notes expounds the ideas of the Guide as selected and rewritten by Leibniz, the famous mathematician inventor of computer arithmetic, considered the last universal genius. The first complete bilingual translation in three centuries features on the front cover Rembrandt's Philosopher in meditation, and a recommendation from Leibniz's himself on the back: "Rabbi Maimonides' excellent book, A Guide for the Perplexed, is more philosophical than I imagined and worthy of careful reading." According to Malbim’s translator, Noah Rosenbloom, the book’s epigraph indicates that nineteenth-century Rabbi Leibush ben Yehiel Michel Wisser, also known as Malbim, was familiar with Leibniz’ Theodicy. In Leibniz’ anthology of the Guide, the reader can get a detailed glimpse of Leibniz' impressions of Maimonides. The Foreword by Leibniz' translator Lloyd Strickland suggests that there were sympathies and perhaps even overlaps between the thoughts of both universal luminaries. -/- . (shrink)

According to epistemological internalism, the rationality of a belief supervenes purely on "internal facts" about the thinker's mind. But what are "internal facts"? Why does the rationality of a belief supervene on them? The standard answers are unacceptable. This paper proposes new answers. "Internal facts" are facts about the thinker's nonfactive mental states. The rationality of a belief supervenes on such internal facts because we need rules of belief revision that we can follow directly, not by means of following any (...) other rules, and the proximate explanation of any belief revision always consists of such internal facts. (shrink)

An English translation of Leibniz's fragment "Horizon rerum humanarum... " in which he announces a plan to demonstrate "that the number of truths or falsehoods enunciable by humans as they are now is limited; and also that if the present condition of humanity persisted long enough, it would happen that the greatest part of what they would communicate in words, whether by talking or writing, would have to coincide with what others have already communicated in the past; and moreover (...) that new humans would lead an entire life that appears thoroughly the same to the senses as lives that others have already led." . (shrink)

Sometimes, we think of belief as a phenomenon that comes in degrees – that is, in the many different levels of confidence that a thinker might have in various different propositions. Sometimes, we think of belief as a simple two-place relation that holds between a thinker and a proposition – that is, as what I shall here call "outright belief".

Our approach to emotion emphasized three key ingredients. We do not yet have a mature science of emotion, or even a consensus view—in this respect we are more hesitant than Sander, Grandjean, and Scherer or Luiz Pessoa. Relatedly, a science of emotion needs to be highly interdisciplinary, including ecology, psychology, neuroscience, and philosophy. We recommend a functionalist view that brackets conscious experiences and that essentially treats emotions as latent variables inferred from a number of measures. But our version of functionalism (...) is not definitional or ontological. It is resolutely methodological, in good part because it is too early to attempt definitions. (shrink)

Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...) complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

Here is a definition of knowledge: for you to know a proposition p is for you to have an outright belief in p that is correct precisely because it manifests the virtue of rationality. This definition resembles Ernest Sosa’s “virtue theory”, except that on this definition, the only virtue that must be manifested in all instances of knowledge is rationality, and no reductive account of rationality is attempted—rationality is assumed to be an irreducibly normative notion. This definition is compatible with (...) “internalism” about rationality, and with a form of “pragmatic encroachment” on the conditions of rational outright belief. An interpretation is given of this definition, and especially of the sense of ’because’ that it involves. On this interpretation, this definition entails that both safety and adherence are necessary conditions on knowledge; it supports a kind of contextualism about terms like ‘knowledge’; and it provides resources to defend safety, adherence, and contextualism, against some recent objections. (shrink)

Many philosophers working on the branches of philosophy that deal with the normative questions have adopted a " Reasons First" program. This paper criticizes the foundational assumptions of this program. In fact, there are many different concepts that can be expressed by the term 'reason' in English, none of which are any more fundamental than any others. Indeed, most of these concepts are not particularly fundamental in any interesting sense.

Suppose that it is rational to choose or intend a course of action if and only if the course of action maximizes some sort of expectation of some sort of value. What sort of value should this definition appeal to? According to an influential neo-Humean view, the answer is “Utility”, where utility is defined as a measure of subjective preference. According to a rival neo-Aristotelian view, the answer is “Choiceworthiness”, where choiceworthiness is an irreducibly normative notion of a course of (...) action that is good in a certain way. The neo-Humean view requires preferences to be measurable by means of a utility function. Various interpretations of what exactly a “preference” is are explored, to see if there is any interpretation that supports the claim that a rational agent’s “preferences” must satisfy the “axioms” that are necessary for them to be measurable in this way. It is argued that the only interpretation that supports the idea that the rational agent’s preferences must meet these axioms interprets “preferences” as a kind of value-judgment. But this turns out to be version of the neo-Aristotelian view, rather than the neo-Humean view. Rational intentions maximize expected choiceworthiness, not expected utility. (shrink)

What reasons for action do we have? What explains why we have these reasons? This paper articulates some of the basic structural features of a theory that would provide answers to these questions. According to this theory, reasons for action are all grounded in intrinsic values, but in a way that makes room for a thoroughly non-consequentialist view of the way in which intrinsic values generate reasons for aaction.

According to John Broome, akrasia consists in a failure to intend to do something that one believes one ought to do, and such akrasia is necessarily irrational. In fact, however, failing to intend something that one believes one ought to do is only guaranteed to be irrational if one is certain of a maximally detailed proposition about what one ought to do; if one is uncertain about any part of the full story about what one ought to do, it could (...) be perfectly rational not to intend to do something that one believes one ought to do. This paper seeks to remedy this problem, by proposing an anti-akrasia principle that covers cases of uncertainty (as well as cases of such complete certainty). It is argued that this principle is in effect the fundamental principle of practical rationality. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...) to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

According to a widely held view of the matter, whenever we assess beliefs as ‘rational’ or ‘justified’, we are making normative judgements about those beliefs. In this discussion, I shall simply assume, for the sake of argument, that this view is correct. My goal here is to explore a particular approach to understanding the basic principles that explain which of these normative judgements are true. Specifically, this approach is based on the assumption that all such normative principles are grounded in (...) facts about values, and the normative principles that apply to beliefs in particular are grounded in facts about alethic value––a kind of value that is exemplified by believing what is true and not believing what is false. In this chapter, I shall explain what I regard as the best way of interpreting this approach. In doing so, I shall also show how this interpretation can solve some problems that have recently been raised for approaches of this kind by Selim Berker, Jennifer Carr, Michael Caie, and Hilary Greaves. (shrink)

La pertinence de la métaphysique analytique a fait l'objet de critiques : Ladyman et Ross, par exemple, ont suggéré d'abandonner ce domaine. French et McKenzie ont défendu la métaphysique analytique en affirmant qu'elle développe des outils qui pourraient s'avérer utiles pour la philosophie de la physique. Dans cet article, nous montrons dans un premier temps que cette défense heuristique de la métaphysique peut être étendue au domaine scientifique de l'ontologie appliquée, qui utilise des théories et outils issus de la métaphysique (...) analytique. Dans un deuxième temps, nous développons le parallèle que font French et McKenzie entre les mathématiques et la métaphysique pour montrer que l'ensemble du domaine de la métaphysique analytique, étant donné son utilité non seulement pour la philosophie mais également pour la science, devrait continuer à exister en tant que domaine largement autonome. (shrink)

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...) sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation. (shrink)

We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (shrink)

Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...) and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...) the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)

Psychiatric and neurological disorders have historically provided key insights into the structure-function rela- tionships that subserve human social cognition and behavior, informing the concept of the ‘social brain’. In this review, we take stock of the current status of this concept, retaining a focus on disorders that impact social behavior. We discuss how the social brain, social cognition, and social behavior are interdependent, and emphasize the important role of development and com- pensation. We suggest that the social brain, and its (...) dysfunction and recovery, must be understood not in terms of specific structures, but rather in terms of their interaction in large-scale networks. (shrink)

A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...) the status of reflection principles as axioms is left open for the Zermelian. (shrink)

This paper defends the institution of civil marriage against the objection that it is inconsistent with political liberalism, and so should be either totally abolished or else transformed virtually beyond recognition.

An account of Plato’s theory of knowledge is offered. Plato is in a sense a contextualist: at least, he recognizes that his own use of the word for “knowledge” varies – in some contexts, it stands for the fullest possible level of understanding of a truth, while in other contexts, it is broader and includes less complete levels of understanding as well. But for Plato, all knowledge, properly speaking, is a priori knowledge of necessary truths – based on recollection of (...) aspects of the Forms – and so in contemporary terms, it meets the conditions of “safety” and “adherence” (or “indefeasibility”) to the highest degree. This account is defended on the basis of the text of Meno, Phaedo, and the Republic, against some objections – especially objections that are due to Gail Fine. (shrink)

Consciousness and emotion feature prominently in our personal lives, yet remain enigmatic. Recent advances prompt further distinctions that should provide more experimental traction: we argue that emotion consists of an emotion state (functional aspects, including emo- tional response) as well as feelings (the conscious experience of the emotion), and that consciousness consists of level (e.g. coma, vegetative state and wake- fulness) and content (what it is we are conscious of). Not only is consciousness important to aspects of emotion but structures (...) that are important for emotion, such as brainstem nuclei and midline cortices, overlap with structures that regulate the level of consciousness. The intersection of consciousness and emotion is ripe for experimental investigation, and we outline possible examples for future studies. (shrink)

We attribute three major insights to Hegel: first, an understanding of the real numbers as the paradigmatic kind of number ; second, a recognition that a quantitative relation has three elements, which is embedded in his conception of measure; and third, a recognition of the phenomenon of divergence of measures such as in second-order or continuous phase transitions in which correlation length diverges. For ease of exposition, we will refer to these three insights as the R First Theory, Tripartite Relations, (...) and Divergence of Measures. Given the constraints of space, we emphasize the first and the third in this paper. (shrink)

I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...) about this approach. I argue that by comparing them with the `standard' uncountabilist theory, a new approach that brings in arbitrariness rather than the strict controls of forcing is desirable. (shrink)

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...) reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

Phenomenology and physiology become commensurable through a self-organizational physiology and an "enactive" view of consciousness. Self-organizing processes appropriate and replace their own needed substrata, rather than merely being caused by interacting components. Biochemists apply this notion to the living/nonliving distinction. An enactive approach sees consciousness as actively executed by an agent rather than passively reacting to stimuli. Perception does not result from mere stimulation of brain areas by sensory impulses; unless motivated organismic purposes first anticipate and "look for" emotionally relevant.stimuli, (...) brain-sensory processing is not accompanied by perceptual consciousness. To see a soccer ball requires looking for it in the right place. The sell-organizing, emotionally motivated agent instigates this looking-for activity. (shrink)

Proportional relationships of simple numbers were commonly used in architecture during the Renaissance period. These proportional relationships were based on the primary musical consonances of the Greek musical system: the octave (2:1), fifth (3:2), and fourth (4:3). In a similar manner, Obrecht uses the proportional relationships created by periods of rest and the last notes of the cantus firmus segments. These proportional relationships are found in the same voice as the cantus firmus, and appear when the statements of the cantus (...) firmus segments are absent. Together with the statements of the cantus firmus segments, these proportional relationships provide the entire form and structure for the various parts of Obrecht's segmentation masses. (shrink)

In this unpublished Latin fragment (which dates from May 1702) G. W. Leibniz criticizes the Cartesian conception of body and force and develops his own notion of matter, extension and his theory of forces. He argues against Descartes and Cartesians that 1) the essence of corporal bodies cannot be reduced to extension alone but the latter arise from the primitive force itself, 2) consequently Cartesian quantity of motion falls short to account the motive force of a moving body since (...) the true nature of physical bodies which can only be understood through a careful analysis of dynamical forces. -/- Mayıs 1702’de kaleme aldığı ve ölümünden sonra yayımlanan bu Latince fragmanda G. W. Leibniz, Kartezyen felsefenin cisim ve kuvvet anlayışını eleştirir ve kendi madde, uzam ve kuvvetler teorisini geliştirir. Leibniz, Descartes ve Kartezyenlere karşı 1) cisimlerin özünün yalnızca uzama indirgenemeyeceğini, bunun ilksel kuvvetin kendisinden kaynaklandığını, 2) sonuç olarak da Kartezyen hareket miktarının hareket eden bir cismin kuvvetini açıklamakta yetersiz kaldığını, çünkü fiziksel cisimlerin gerçek doğasının ancak dinamik kuvvetlerin dikkatli bir analiziyle anlaşılabileceğini ileri sürer. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective (...) to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

Enactivism has the potential to provide a sense of teleology in purpose-directed action, but without violating the principles of efficient causation. Action can be distinguished from mere reaction by virtue of the fact that some systems are self-organizing. Self-organization in the brain is reflected in neural plasticity, and also in the primacy of motivational processes that initiate the release of neurotransmitters necessary for mental and conscious functions, and which guide selective attention processes. But in order to flesh out the enactivist (...) approach in a way that is plausible and not merely an epiphenomenon, it is necessary to confront the problem of causal closure in a serious way. Atoms and molecules in the brain do not violate the normal causal principles that govern them in other contexts. The theory of self-organizing dynamical systems must be developed in a way that is compatible with causal closure rather than contradicting it. (shrink)