The paper discusses the place and the status of fallacies in Arnauld and Nicole’s Port-Royal Logic, which seems to be the first book to introduce a radical change from the traditional Aristotelian account of fallacies. The most striking innovation is not in the definition of a fallacy but in the publication of a new list of fallacies, dropping some Aristotelian ones and adding more than ten new ones. The first part of the paper deals with the context (...) of the book’s publication. We then show the influence of Cartesian and Augustinian/Pascalian philosophy on the whole book, especially their common critical views about logic, dialectic and their traditional academic teaching. The third part of the paper discusses the two chapters on fallacies. It focuses on their place in the book and their relation with its general orientation, before turning to their content, closely connected with some major concerns of the time. (shrink)

La Logique ou L'Art de Penser (LAP), also known as the Port-Royal Logic, is generally presented as a "logic of ideas" in which the idea, the central epistemological entity, is the starting point of this logic based on Cartesian ontology. Structured around the four main operations of the mind - conceiving, judging, reasoning and ordering - the first part of the LAP contains "reflections on ideas". The idea, "the form by which we represent things [objects]", (...) thus takes the place of the concept in Aristotelian-inspired logic. Some of the chapters in this first part deal with the problems raised in scholasticism by the theory of _proprietates terminorum_, which means that it is also a semantics of terms. The word 'term' itself must be understood in its logical and grammatical dimensions. The analyses of the 'Messieurs' of Port-Royal often have a logico-grammatical character, because, according to the anthropology of the authors, men need to make their thoughts heard by one another through language (institutional signs) and, therefore, "it is necessary in logic to consider ideas joined to words, and words joined to ideas". In this text, we shall endeavour to show the importance and innovative character of the semantics of terms in this logic of ideas which makes LAP a pivotal moment in the evolution of the language sciences, reviving the tradition and allowing dialogue with future developments (extension vs. comprehension, explanation, determination of terms, etc.). We will pay particular attention to the chapters on definition, "a remedy for the confusion that arises in our thoughts and speech from the confusion of words". (shrink)

In this study, I intend to show how and why, in the Port-Royal Logic, a singular term can reveal the nature of the logical judgment in the handbook. As I argue, the treatment given to one of thee singular terms, namely, the defined descriptions, in the terminology introduced by Russell, leads to an opening to langage that sounds unexpected and unjustified. Considering the privilege of thinking over langage and also that judgment is the mental act that defines (...) logic, however, we may understand how the authors regard langage, in relation to the epistemic constituents, namely, the mental acts within the terms. In doing so we are compelled to recognize the implications of this step towards pragmatism in fixing the meaning of defined descriptions to the nature of judgment in the handbook. This opening to langage reveals the conception of judgment as a twofold mental act: a formal and a practical (moral and theological) one. (shrink)

Logical reflection in early modern philosophy (EMP) is marked by the instability of the period, although it is more lasting (the Port-Royal Logic was nevertheless used as a handbook in philosophy courses until the end of the nineteenth century). It started in the sixteenth century and ended in the nineteenth century, a period of 300 years during which there were deep transformations in the conceptions of authority and scientific method. For the history of twentieth-century philosophy, it was (...) the period of “classical logic,” which lasted from the Renaissance to the linguistic turn conducted by Gottlob Frege. The period was used to be thought of as centuries of little or no original contribution to logic, in which conceptions of logic were tainted by rhetoric, epistemology, and psychologism in the worst sense (Kneale and Kneale 1962; Michael 1997). From the last decades of the twentieth century, however, scholars began to regard this period more accurately with respect to reflection and changes in logic and semantics. It has recently become a promising field for historical and conceptual research; today we can say that the legacy of early modern logical reformism has a philosophical, logical, and semantic value in itself. (shrink)

In Kant’s logical texts the reference of the form S is P to an “unknown = x” is well known, but its understanding still remains controversial. Due to the universality of all concepts, the subject as much as the predicate is regarded as predicate of the x, which, in turn, is regarded as the subject of the judgment. In the CPR, this Kantian interpretation of the S-P relationship leads to the question about the relations between intuition and concept in judgment. (...) In contrast to intuition, if no concept, due to its universality, refers immediately to an object, how should one understand the relations of S and P to one another, as well as their relations to intuition, which corresponds to the possible individuality of the object in general = x? To answer this question, it is necessary to understand Kant’s notion of extension, and to prove its irreducibility to the Port-Royal notion of extension as well as to the Fregean one. (shrink)

"Language and its Public Features: Reorganizing the Trivium in Locke's Essay and Port-Royal Logic" The new theory of language in the 17th century coincides with the end the traditional order of disciplines in the trivium (grammar, logic and rhetoric), which in the mediaeval times provided a comprehensive view of the problems of discourse. The article focuses on some key passages in Port-Royal Logic and Locke's Essay that provide us with a typical early modern (...) scheme of linguistic representation, characterised by heavily emphasized dualism of ideas and words. Since ideas are also the meanings of words and are ontologically essentially private, one can raise the question, where in this analysis of language is it even possible to locate its public features. The article tries to show that private language is not only possible for Locke and the Port-Royalists, but that it is even a necessary and primary character of language. Language becomes a public medium of communication only on the junctures of private meanings constituted by the “common use” of words. The article then focuses on almost complete marginalisation in the two works of the theory of public speech. Rhetoric, in the 17th century often reduced to mere eloquence, has no place in philosophy, and the duties of making speeches persuasive are taken over by reason alone. To show how the domains of jurisdiction of the trivial disciplines had been transformed in the linguistic theories proposed by the Port-Royal Logic and Locke, one can construct a hypothetical early modern trivium in the light of the following order: idea – word – figure, or, logic – grammar – rhetoric. Rhetoric is found to have kept its structural place only to be singled out as dangerous. (shrink)

One of the most mature achievements of the Cartesian philosophy is the aim to diffuse Descartes’ thought among a wider audience by presenting his philosophy in an encyclopedic way. A relevant contribution in this field is Pierre Sylvain Régis’s Système. Régis’s contribution consists both in reconciling the new scientific discoveries with les principes de Monsieur Descartes by combining them into a scholarly manual whose aim is to stimulate the ars inveniendi and in recognizing the relevance of Arnauld’s and Nicole’s L’art (...) de penser as manual of Cartesian logic. In an article published on the «Annali della Scuola Normale Superiore di Pisa», pp. 517-55: L’«Art de penser» nella logica del «Système» di Régis) I analysed Régis’s logic in order to point out that, even if L’art de penser represents its only source, La logique of the Système has not to be considered as a mere compendium of the Port-Royal Logique, but as a revision of the latter according to a specific philosophical system, characterized by the empirical interpretation of Descartes’s philosophy. In this paper I provide a synopsis of the comparison between the logic of the Système and the Logique of Port-Royal, in order to resume in a schematic way the results of my research. (shrink)

In New Essays on Human Understanding, book II, chapter xxi Leibniz presents an interesting picture of the human mind as not only populated by perceptions, volitions and appetitions, but also by endeavours. The endeavours in question can be divided to entelechy and effort; Leibniz calls entelechy as primitive active forces and efforts as derivative forces. The entelechy, understood as primitive active force is to be equated with a substantial form, as Leibniz says: “When an entelechy – i.e. a primary or (...) substantial endeavour – is accompanied by perception, it is a soul” (NE II, xxi, §1; RB, 170). What about efforts, then? One is certainly the will. In NE, II, xxi, §5 Leibniz argues that volition is the effort (conatus) to move towards what one finds good and away from what one finds bad and that this endeavor arises from the perceptions we are aware of. As an endeavour results in action unless it is prevented, from will (which is always directed to the good) and power together follows action. However, this is not so simple. Leibniz argues that there is also a second class of efforts: “There are other efforts, arising from insensible perceptions, which we are not aware of; I prefer to call these ‘appetitions’ rather than volitions” (NE II, xxi, §5; RB, 173). Although there are appetitions of which one can be aware, usually these appetitions arise from the insensible petite perceptions and are consequently affecting us subconsciously. Now, although all minute perceptions are confused perceptions, they are always related to pleasure and displeasure and also to perfection and imperfection. From this follows that there can be different efforts present in the soul at the same time: the will which is directed to apperceived good and several separate appetitions which lead to different goals, both to those which bring about perfection and pleasure of the mind (joy) and those which bring about displeasure and imperfection (sorrow). These efforts are not only in conflict with each other but may also be in conflict with entelechy. A typical case is perceiving a sensual pleasure. Our entelechy which is always directed to final causes (perfection) may be in conflict with several different appetitions which are related in different ways to the sensual pleasure in question. If our understanding is developed enough, our will resists the temptation posed by the pleasure (agreeing with entelechy), but if the temptation is too strong, the appetitions outweigh the will and the resulting action bring about imperfection and sorrow as it is related to imperfection. In this paper I will argue that deliberation in the human soul is a battle of different endeavors described above: the entelechy in the soul strives according to its law-of-the-series towards its telos (perfection) and the will accompanies it by being automatically directed to the good. This thrust towards the apparent good is aided or hindered by the appetitions which can be thought as derivative forces in the Leibnizian dynamics. Depending on whether the predominant appetitions are related to good or bad desires, the deliberation succeeds or fails in achieving the real good which is the goal of human deliberation. The successs can be facilitated beforehand by developing our understanding so that we are less easily swept away by the derivative forces (NE II, xxi, §19). A central role in this task is played by strong willing. As Martha Bolton has noted in her recent paper, an essential feature of the basic, standing endeavors is that they are continuous – although the power balance in the soul changes from moment to moment, something lingers from our previous volitions. That is why Leibniz argues that we pave way for the future deliberations by our previous voluntary actions (NE II, xxi, §23). In contrast, the appetitions are temporary, fliegende Gedanken as Leibniz says in NE II, xxi, §12. Therefore there is a constant, always changing power balance between two kinds of endeavors in the soul: primitive active force versus derivative forces. I will argue that the behavior of the forces in the soul can be understood with a vectorial model which is related to Leibniz’s early ideas of calculus of variations and which was anticipated by Arnauld and Nicole’s Port-Royal Logic. The central idea in the model is that the options are in tension towards each other and the ratio between them at each moment determines the consequent outcome. The proper relationship between the endeavors is not a simple balance, two options which exhaust each other, but a case where different efforts complement each other: “Since the final result is determined by how things weigh against one another, I should think it could happen that he most pressing disquiet did not prevail; for even If it prevailed over each of the contrary endeavours taken singly, it may be outweighed by all of them together.” Leibniz continues : “Everything which then impinges on us weighs in the balance and contributes to determining a resultant direction, almost as in mechanics” (NE II, xxi, §40; RB, 193). The different endeavors can be understood as vectors leading to different directions and the end result is a certain direction that deliberation takes. The dynamical tension between the different endeavors presents a situation where everything affects everything and the following direction, the resulting volition follows more or less automatically. In Theodicy, §325 Leibniz describes the deliberation as follows: “One might, instead of the balance, compare the soul with a force that puts forth an effort on various sides simultaneously, but which acts only at the spot where action is easiest or there is least resistance” (Huggard, 322) This kind of dynamical tension can be understood in terms of the calculus of variations where there are several possible variations available but where the dynamics of the situation results in the decision taking the “easiest” route which is more or less objectively good depending on the level of the deliberator’s understanding. In his comments to Bayle’s note L of “Rorarius” Leibniz says: “The soul, even though it has no parts, has within it, because of the multitude of representations of external things, or rather because of the representation of the universe lodged within it by the creator, a great number, or rather an infinite number, of variations (Woolhouse & Francks (ed.), ‘New System’ and Associated Texts, 101). This kind of deliberation is comparable to God’s choice of the best world with the difference that God’s understanding is infinite which again results in the fact that the choice is the best possible. Whereas in nature the easiest route taken is always optimal as nature is God’s creation, in men the goodness or badness of men’s actions is dependent on their state of wisdom, that is, how developed their understanding is. The more wise men are, the more metaphysical goodness or perfection follows from their actions. (shrink)

In New Essays on Human Understanding, book II, chapter xxi Leibniz presents an interesting picture of the human mind as not only populated by perceptions, volitions and appetitions, but also by endeavours. The endeavours in question can be divided to entelechy and effort; Leibniz calls entelechy as primitive active forces and efforts as derivative forces. The entelechy, understood as primitive active force is to be equated with a substantial form, as Leibniz says: “When an entelechy – i.e. a primary or (...) substantial endeavour – is accompanied by perception, it is a soul” (NE II, xxi, §1; RB, 170). What about efforts, then? One is certainly the will. In NE, II, xxi, §5 Leibniz argues that volition is the effort (conatus) to move towards what one finds good and away from what one finds bad and that this endeavor arises from the perceptions we are aware of. As an endeavour results in action unless it is prevented, from will (which is always directed to the good) and power together follows action. However, this is not so simple. Leibniz argues that there is also a second class of efforts: “There are other efforts, arising from insensible perceptions, which we are not aware of; I prefer to call these ‘appetitions’ rather than volitions” (NE II, xxi, §5; RB, 173). Although there are appetitions of which one can be aware, usually these appetitions arise from the insensible petite perceptions and are consequently affecting us subconsciously. Now, although all minute perceptions are confused perceptions, they are always related to pleasure and displeasure and also to perfection and imperfection. From this follows that there can be different efforts present in the soul at the same time: the will which is directed to apperceived good and several separate appetitions which lead to different goals, both to those which bring about perfection and pleasure of the mind (joy) and those which bring about displeasure and imperfection (sorrow). These efforts are not only in conflict with each other but may also be in conflict with entelechy. A typical case is perceiving a sensual pleasure. Our entelechy which is always directed to final causes (perfection) may be in conflict with several different appetitions which are related in different ways to the sensual pleasure in question. If our understanding is developed enough, our will resists the temptation posed by the pleasure (agreeing with entelechy), but if the temptation is too strong, the appetitions outweigh the will and the resulting action bring about imperfection and sorrow as it is related to imperfection. In this paper I will argue that deliberation in the human soul is a battle of different endeavors described above: the entelechy in the soul strives according to its law-of-the-series towards its telos (perfection) and the will accompanies it by being automatically directed to the good. This thrust towards the apparent good is aided or hindered by the appetitions which can be thought as derivative forces in the Leibnizian dynamics. Depending on whether the predominant appetitions are related to good or bad desires, the deliberation succeeds or fails in achieving the real good which is the goal of human deliberation. The successs can be facilitated beforehand by developing our understanding so that we are less easily swept away by the derivative forces (NE II, xxi, §19). A central role in this task is played by strong willing. As Martha Bolton has noted in her recent paper, an essential feature of the basic, standing endeavors is that they are continuous – although the power balance in the soul changes from moment to moment, something lingers from our previous volitions. That is why Leibniz argues that we pave way for the future deliberations by our previous voluntary actions (NE II, xxi, §23). In contrast, the appetitions are temporary, fliegende Gedanken as Leibniz says in NE II, xxi, §12. Therefore there is a constant, always changing power balance between two kinds of endeavors in the soul: primitive active force versus derivative forces. I will argue that the behavior of the forces in the soul can be understood with a vectorial model which is related to Leibniz’s early ideas of calculus of variations and which was anticipated by Arnauld and Nicole’s Port-Royal Logic. The central idea in the model is that the options are in tension towards each other and the ratio between them at each moment determines the consequent outcome. The proper relationship between the endeavors is not a simple balance, two options which exhaust each other, but a case where different efforts complement each other: “Since the final result is determined by how things weigh against one another, I should think it could happen that he most pressing disquiet did not prevail; for even If it prevailed over each of the contrary endeavours taken singly, it may be outweighed by all of them together.” Leibniz continues : “Everything which then impinges on us weighs in the balance and contributes to determining a resultant direction, almost as in mechanics” (NE II, xxi, §40; RB, 193). The different endeavors can be understood as vectors leading to different directions and the end result is a certain direction that deliberation takes. The dynamical tension between the different endeavors presents a situation where everything affects everything and the following direction, the resulting volition follows more or less automatically. In Theodicy, §325 Leibniz describes the deliberation as follows: “One might, instead of the balance, compare the soul with a force that puts forth an effort on various sides simultaneously, but which acts only at the spot where action is easiest or there is least resistance” (Huggard, 322) This kind of dynamical tension can be understood in terms of the calculus of variations where there are several possible variations available but where the dynamics of the situation results in the decision taking the “easiest” route which is more or less objectively good depending on the level of the deliberator’s understanding. In his comments to Bayle’s note L of “Rorarius” Leibniz says: “The soul, even though it has no parts, has within it, because of the multitude of representations of external things, or rather because of the representation of the universe lodged within it by the creator, a great number, or rather an infinite number, of variations (Woolhouse & Francks (ed.), ‘New System’ and Associated Texts, 101). This kind of deliberation is comparable to God’s choice of the best world with the difference that God’s understanding is infinite which again results in the fact that the choice is the best possible. Whereas in nature the easiest route taken is always optimal as nature is God’s creation, in men the goodness or badness of men’s actions is dependent on their state of wisdom, that is, how developed their understanding is. The more wise men are, the more metaphysical goodness or perfection follows from their actions. (shrink)

I briefly consider why Descartes stopped work on the _Rules_ towards the end of my paper. My main concern is to accurately characterize the project represented in the _Rules_, especially in its relation to early-modern logic.

In hindsight, it is not surprising that the exegesis of Aristotle’s Sophistici elenchi developed into one of the most substantial parts of the Latin commentary tradition. To make a long story short, in its customary capacity as the art of arts and the science of sciences, medieval logic was primarily concerned with discerning the true from the false in arguments as they occur in natural, ordinary speech as opposed to the more formalised parlance later logicians will resort to. It (...) makes perfect sense, then, that medieval logicians paid special attention to everything that threatens sound reasoning and that prevents us from speaking the truth. Indeed, they were second to none and better than most at exposing and elucidating arguments’ flaws and shortcomings. After all, as John Buridan – faithful to a long and illustrious tradition – aptly put it, «rooting out errors» is logic’s first order of business. As early as the 1140s, Aristotle’s Sophistici elenchi provided the most fertile ground for such keen interest in fallacies; which, in turn, explains etc. This much is uncontroversial or, at any rate, can withstand any amount of scrutiny we care to throw at it. Courtesy – first and foremost – of Sten Ebbesen, whose long-standing interest in medieval writings on bad arguments has turned the Byzantine and Latin aftermath of Aristotle’s Sophistici elenchi into well-charted territory, by all standards. The Anonymus Cantabrigiensis has played no small part in shaping this picture. As a matter of fact, time and again over the last forty years or so, quotes and insights from the anonymous work have kept showing up in Ebbesen’s editions and studies: since he first discovered the commentary in the late 1970s and brought it to the general attention, Ebbesen has routinely drawn on the Anonymus as an early witness of the circulation of Aristotelian logical works and related texts, as a convenient illustration of major trends and distinctive features of the Latin literature on fallacies, and as a sensible interpreter in his own right. (shrink)

Philosophers of the modern period are often presented as having made an elementary error: that of confounding the attitude one adopts toward a proposition with its content. By examining the works of Locke and the Port-Royalians, I show that this accusation is ill-founded and that Locke, in particular, has the resources to construct a theory of propositional attitudes.

In this article, I contend that the three Cuban philosophers/pedagogues of the nineteenth century – Félix Varela y Morales, José de la Luz y Caballero, and Enrique José Varona were responsible for overcoming the teaching of late scholastic at the Royal and Pontifical University of St. Jerome of Havana. Against late scholastic philosophers and pedagogues who preferred syllogistic logic and the authority of tradition over induction, they argued in favor of the latter over the first. Since they defended (...) liberal and republican ideas, they also argued against those who appeal to the authority of tradition rather than to our ordinary experiences. Of course, their liberal spirit challenged not only the tyrannical regime imposed by Spain at the time but any other regime whose authority depends on force rather than on the will of the people. (shrink)

Philosophers typically rely on intuitions when providing a semantics for counterfactual conditionals. However, intuitions regarding counterfactual conditionals are notoriously shaky. The aim of this paper is to provide a principled account of the semantics of counterfactual conditionals. This principled account is provided by what I dub the Royal Rule, a deterministic analogue of the Principal Principle relating chance and credence. The Royal Rule says that an ideal doxastic agent’s initial grade of disbelief in a proposition \(A\) , given (...) that the counterfactual distance in a given context to the closest \(A\) -worlds equals \(n\) , and no further information that is not admissible in this context, should equal \(n\) . Under the two assumptions that the presuppositions of a given context are admissible in this context, and that the theory of deterministic alethic or metaphysical modality is admissible in any context, it follows that the counterfactual distance distribution in a given context has the structure of a ranking function. The basic conditional logic V is shown to be sound and complete with respect to the resulting rank-theoretic semantics of counterfactuals. (shrink)

On sait peu de choses d’Edme Mariotte, membre de l’Académie royale des sciences de 1668 à 1684. Une analyse de son Essai de logique montre cependant que, pour défendre ses pratiques expérimentales, il s’appropria des bribes venues de différentes traditions intellectuelles. Ainsi, ce livre examine ce qu’on entendait par « méthode » à la fin du XVIIe siècle, les épistémologies de la physique qui s’affrontaient alors, quelques débats ouverts par la gestion de l’héritage cartésien. Mais l’essentiel sera peut-être la question (...) suivante : comment reconstituer les idées d’un savant ordinaire, qui n’a ni bouleversé l’ordre des sciences, ni montré une perspicacité épistémologique exceptionnelle ? (shrink)

«Les gens disent encore et encore que la philosophie ne progresse pas vraiment, que nous sommes toujours occupés avec les mêmes problèmes philosophiques que les Grecs. Mais les gens qui disent cela ne comprennent pas pourquoi il doit en être ainsi. C’est parce que notre langue est restée la même et continue de nous séduire à poser les mêmes questions. Tant qu’il continue à y avoir un verbe qui ressemble à s’il fonctionne de la même manière que de manger et (...) de boire, tant que nous avons encore les adjectifs 'identiques', 'faux', 'false', 'possible', tant que nous continuons à parler d’une rivière du temps, d’une étendue d’espace, etc., etc., les gens continueront à trébucher sur les mêmes difficultés déroutantes et se retrouveront à regarder quelque chose qui ne semble pas capable de se dégager. Et qui plus est, cela satisfait un désir pour le transcendant, parce que, dans la mesure où les gens pensent qu’ils peuvent voir les ‘«limites de la compréhension humaine », ils croient bien sûr ce ils peuvent voir au-delà de ceux-ci. Cette citation est de Ludwig Wittgenstein qui a redéfini la philosophie il ya 70 ans (mais la plupart des gens n’ont pas encore de le savoir). Dennett, bien qu’il ait été un philosophe pendant une quarantaine d’années, est l’un d’entre eux. Il est également curieux que lui et son antagoniste principal, John Searle, étudié sous les célèbres Wittgensteiniens (Searle avec John Austin, Dennett avec Gilbert Ryle) mais Searle plus ou moins obtenu le point et Dennett n’a pas, (bien qu’il est étirer les choses à appeler Searle ou Ryle Wittgensteinians). Dennett est un déterministe difficile (bien qu’il essaie de se faufiler la réalité dans la porte arrière), et peut-être cela est dû à Ryle, dont le célèbre livre "Le concept de l’esprit" (The Concept of Mind) (1949) continue d’être réimprimé. Ce livre a fait un excellent travail d’exorciser le fantôme, mais il a quitté la machine. Dennett aime faire les erreurs Wittgenstein, Ryle (et beaucoup d’autres depuis) ont exposé en détail. Notre utilisation des mots conscience, choix, liberté, intention, particule, pensée, détermine, vague, cause, arrivé, événement (et ainsi de suite sans fin) sont rarement une source de confusion, mais dès que nous quittons la vie normale et entrer dans la philosophie (et toute discussion détachée de l’environnement dans lequel la langue a évolué-c’est-à-dire le contexte exact dans lequel les mots avaient un sens) chaos règne. Comme la plupart, Dennett n’a pas un cadre cohérent - que Searle a appelé la structure logique de la rationalité. J’ai développé sur ce considérablement depuis que j’ai écrit cette revue et mes articles récents montrent en détail ce qui ne va pas avec l’approche de Dennett à la philosophie, que l’on pourrait appeler Scientism sur les stéroïdes. Permettez-moi de terminer par une autre citation de Wittgenstein-- «L’ambition est la mort de la pensée. Ceux qui souhaitent un cadre complet à jour pour le comportement humain de la vue moderne de deux systèmes peuvent consulter mon livre 'The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019). Ceux qui s’intéressent à plus de mes écrits peuvent voir «Talking Monkeys --Philosophie, Psychologie, Science, Religion et Politique sur une planète condamnée --Articles et revues 2006-2019 3e ed (2019) et Suicidal Utopian Delusions in the 21st Century 4th ed (2020) et autres. (shrink)

From my ongoing "Metalogical Plato" project. The aim of the diagram is to make reasonably intuitive how the Socratic elenchos (the logic of refutation applied to candidate formulations of virtues or ruling knowledges) looks and works as a whole structure. This is my starting point in the project, in part because of its great familiarity and arguable claim to being the inauguration of western philosophy; getting this point less wrong would have broad and deep consequences, including for philosophy’s self-understanding. (...) -/- (i.) is the first pass at elenchos in which the Socratic interlocutor does not reflect on knowledge being the crux of the problem. (ii.) is the second, rarer, reflective pass in which they are, making the investigation explicitly about knowledge. Its centrality in the Charmides makes that neglected dialogue of superlative importance. This structure is also the gateway through which the discussion/dialectic crosses into the Agathology (discussion of the form of the good) at Republic 505. -/- The problem of elenchos, then, grasped as a whole structure, is that it seems that knowledge can neither satisfactorily be included in nor excluded from its own scope. The development of the ti esti (“what is ---?”) question leads to the introduction of knowledge into its own scope (i. implicitly, as goodness contrasted with blind rule-following ii. explicitly qua knowledge) while the development of the dual peri tinos (“----about what?) question leads to K’s elimination from its own scope. The introductions are motivated to avoid contradiction, but produce regress; the eliminations are motivated to avoid regress, but produce contradiction. In scholarship, and in the history of philosophy, the ti esti question is universally recognized, to the point of being identified with philosophy’s origin and essence; the peri tinos question is neglected textually and never recognized as the equal dual to the ti esti. This, I claim, has blocked the development of a nontrivial logical appreciation of what Plato's Socrates is up to. (One rather disastrous effect of this neglect is taking Aristotle as the beginning of the development of logic, rather than, correctly, for the beginning of logic’s fatal separation from mathematics and dialectic.) -/- Further, because of this monopticism of the ti esti, the function of consistency in the elenchos has not been understood, even with respect to the ti esti. The ti esti is actually in search of completeness, given a norm of consistency; the peri tinos is in search of consistency, given a norm of completeness. Only appreciating the two questions as dual allows space in the structure to clarify these different orientations relative to consistency. (And, dually, to completeness, whose function in the elenchos is generally entirely missed by scholars and relegated to discussions of eros; it's not out of place there, of course, but its significance is secured here.) Recognizing the duality of the ti esti and peri tinos questions is thus the royal road, in the Socratic-Platonic context, to catching sight of what we post-Cantorians can recognize as the metalogical duality of consistency and completeness. (The salutary disruptive effects of this Plato-Cantor proximity have, of course, been traced in complementary ways by Badiou.) -/- Note that the diagram is supposed to provide a relatively accessible orientation, not to stand on its own, and certainly not to be the last word on any subject. An important qualification (telegraphed in the previous paragraph) is that what elenchos shows is not finally circular or paradoxical, though the problem first presents as such (stubbornly, obdurately, as "difficult" Plato's Socrates always says with characteristic understatement). What is depicted here is meant, at a first pass, to be the shape of that first presentation, the form of the problem of elenchos, rather than of its solution. It's not an accident that this problem strongly resembles "Russell's paradox" (not Russell's not a paradox.) Problem is to solution as RP is to the diagonal theorems. (shrink)

We propose to develop the first stage of Max Horkheimer's thought to value the production that him has given to the Marxist thought. The publication of Traditional Theory and critical theory on the part of Max Horkheimer, in 1937, redresses a fundamental importance for Frankfurt's School, provided that in the above mentioned work the elementary points distinguish themselves for the program of the same one. In the following pages we show elements that turn on the false representation that the company (...) has about the scientists who work under the called "traditional theory", as well as the uses that they make regarding the use of the logic or the programs of scientific discovery. The pages of the present article also are accompanied of a methodological offer developed by Horkheimer, to approach the social problematics in a suitable way. We will limit ourselves to cross the text underlining the fundamental differences between a traditional theory, which is necessary to step aside and a new theory, the offer for Horkheimer, which will use him as methodological program to Frankfurt's School, and, that in addition, it is an invitation to approach royal problematics in society. In addition we will develop the economic Marxist elements that Horkheimer thinks fundamental to criticize the supposed neutrality of the science and of the scientific work. to acomplish this we will search on other works from the author. (shrink)

The concept of distributed moral responsibility (DMR) has a long history. When it is understood as being entirely reducible to the sum of (some) human, individual and already morally loaded actions, then the allocation of DMR, and hence of praise and reward or blame and punishment, may be pragmatically difficult, but not conceptually problematic. However, in distributed environments, it is increasingly possible that a network of agents, some human, some artificial (e.g. a program) and some hybrid (e.g. a group of (...) people working as a team thanks to a software platform), may cause distributed moral actions (DMAs). These are morally good or evil (i.e. morally loaded) actions caused by local interactions that are in themselves neither good nor evil (morally neutral). In this article, I analyse DMRs that are due to DMAs, and argue in favour of the allocation, by default and overridably, of full moral responsibility (faultless responsibility) to all the nodes/agents in the network causally relevant for bringing about the DMA in question, independently of intentionality. The mechanism proposed is inspired by, and adapts, three concepts: back propagation from network theory, strict liability from jurisprudence and common knowledge from epistemic logic. (shrink)

Quantifier variance faces a number of difficulties. In this paper we first formulate the view as holding that the meanings of the quantifiers may vary, and that languages using different quantifiers may be charitably translated into each other. We then object to the view on the basis of four claims: (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier variance is not an (...) ontological doctrine; (iv) quantifier variance is not compatible with charitable translation and as such is internally inconsistent. In light of these troubles, we recommend the dissolution of quantifier variance and suggest that the view be laid to rest. (shrink)

This paper reports on an ongoing ARC Discovery Project that is conducting design research into learning in collaborative virtual worlds (CVW).The paper will describe three design components of the project: (a) pedagogical design, (b)technical and graphics design, and (c) learning research design. The perspectives of each design team will be discussed and how the three teams worked together to produce the CVW. The development of productive failure learning activities for the CVW will be discussed and there will be an interactive (...) demonstration of the project's CVW. (shrink)

As hubs of global exchange, port cities are host to inconvenient and contested pasts. Many of these pasts have yet to be fully recognized. In the wake of demonstrations against racial injustices this summer, the PortCityFutures team discussed how our own research practices relate to systemic inequalities within port cities. It was concluded that we need to better understand how these contested and complex pasts, legacies of diversity and segregation, and colonial pasts impact port cities today.

Burgess (1997), building on Quine (1953), convincingly argued that claims in quantified modal logic cannot be understood as synonymous with or logically equivalent to claims about the analyticity of certain sentences. According to modal normativism, metaphysically necessary claims instead express or convey our actual semantic rules. In this paper, I show how the normativist can use Sidelle’s (1992a, 1995) neglected work on rigidity to account for two important phenomena in quantified modal logic: the necessity of identity and the (...) substitutivity of identicals into modal contexts. (shrink)

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of (...) the original pure system with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

There are many domains about which we think we are reliable. When there is prima facie reason to believe that there is no satisfying explanation of our reliability about a domain given our background views about the world, this generates a challenge to our reliability about the domain or to our background views. This is what is often called the reliability challenge for the domain. In previous work, I discussed the reliability challenges for logic and for deductive inference. I (...) argued for four main claims: First, there are reliability challenges for logic and for deduction. Second, these reliability challenges cannot be answered merely by providing an explanation of how it is that we have the logical beliefs and employ the deductive rules that we do. Third, we can explain our reliability about logic by appealing to our reliability about deduction. Fourth, there is a good prospect for providing an evolutionary explanation of the reliability of our deductive reasoning. In recent years, a number of arguments have appeared in the literature that can be applied against one or more of these four theses. In this paper, I respond to some of these arguments. In particular, I discuss arguments by Paul Horwich, Jack Woods, Dan Baras, Justin Clarke-Doane, and Hartry Field. (shrink)

Cinema acts as a significant mediator between urban reality and the imaginary sensory experience of the fictive world. Viewing the city through the lens of a camera enables us to build new narratives. Films have captured port cities within the flows of, goods, people, and ideas, making them ever-present in shared memories, historical narratives, and urban nostalgia. Cultural production plays a role in the on-going construction of local port cultures, whether films, festivals, music, literature, theater, advertisements, or events. (...) Telling the story of the port city – it's past, present, and future; its buildings and its people – contributes strongly to the creation of port city cultures.[i] The big screen can help viewers to perceive complex port city regions, learning from their history, understanding cultural values and developing shared urban narratives to tackle the upcoming challenges. In a broader sense, port city’s ‘Cine-scape’—to use a term coined by Richard Koeck,[ii] puts the cinematic approach to port cities into the spotlight. (shrink)

Gila Sher approaches knowledge from the perspective of the basic human epistemic situation—the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical (...) and abstract, in both mind and world, but the fall of traditional foundationalism has led many to doubt the viability of this ‘classical’ project. Sher challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory of knowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine’s revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind and world. The model of knowledge subjects all disciplines to demanding norms of both veridicality and conceptualization. The correspondence theory is robust and universal yet not simplistic or naive, admitting diverse forms of correspondence. Logic’s grounding in the world brings it in line with other disciplines while preserving, and explaining, its strong formality, necessity, generality, and normativity. (shrink)

Manfred Eigen employs the terms language and communication to explain key recombination processes of DNA as well as to explain the self-organization of human language and communication: Life processes as well as language and communication processes are governed by the logic of a molecular syntax, which is the exact depiction of a principally formalizable reality. The author of the present contribution demonstrates that this view of Manfred Eigen’s cannot be sufficiently substantiated and that it must be supplemented by an (...) approach based on linguistic pragmatics. (shrink)

At least since Aristotle’s famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to the doctrine of the open future--the doctrine that future contingent statements are not true. But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking back) it was the case that it would happen. How can it be that, looking forwards, it isn’t true that there will be a sea battle, while also being true (...) that, looking backwards, it was the case that there would be a sea battle? This tension forms, in large part, what might be called the problem of future contingents. A dominant trend in temporal logic and semantic theorizing about future contingents seeks to validate both intuitions. Theorists in this tradition--including some interpretations of Aristotle, but paradigmatically, Thomason (1970), as well as more recent developments in Belnap, et. al (2001) and MacFarlane (2003, 2014)--have argued that the apparent tension between the intuitions is in fact merely apparent. In short, such theorists seek to maintain both of the following two theses: (i) the open future: Future contingents are not true, and (ii) retro-closure: From the fact that something is true, it follows that it was the case that it would be true. It is well-known that reflection on the problem of future contingents has in many ways been inspired by importantly parallel issues regarding divine foreknowledge and indeterminism. In this paper, we take up this perspective, and ask what accepting both the open future and retro-closure predicts about omniscience. When we theorize about a perfect knower, we are theorizing about what an ideal agent ought to believe. Our contention is that there isn’t an acceptable view of ideally rational belief given the assumptions of the open future and retro-closure, and thus this casts doubt on the conjunction of those assumptions. (shrink)

This paper focuses on the Enkratic principle of rationality, according to which rationality requires that if an agent sincerely and with conviction believes she ought to X, then X-ing is a goal in her plan. We analyze the logical structure of Enkrasia and its implications for deontic logic. To do so, we elaborate on the distinction between basic and derived oughts, and provide a multi-modal neighborhood logic with three characteristic operators: a non-normal operator for basic oughts, a non-normal (...) operator for goals in plans, and a normal operator for derived oughts. We prove two completeness theorems for the resulting logic, and provide a dynamic extension of the logic by means of product updates. We illustrate how this setting informs deontic logic by considering issues related to the filtering of inconsistent oughts, the restricted validity of deontic closure, and the stability of oughts and goals under dynamics. (shrink)

Philosophers of logic are particularly interested in understanding the aims, epistemology, and methodology of logic. This raises the question of how the philosophy of logic should go about these enquires. According to the practice-based approach, the most reliable method we have to investigate the methodology and epistemology of a research field is by considering in detail the activities of its practitioners. This holds just as true for logic as it does for the recognised empirical and abstract (...) sciences. If we wish to systematically understand the aims and epistemology of logic, we are best placed achieving this by looking at what logicians do, rather than reflecting upon the nature of logic itself. In this entry, we outline the motivations for a practice-based approach towards the philosophy of logic and highlight its advantages over more “top-down” approaches, which attempt to infer conclusions about the nature of logic and its methodology on the basis of traditional assumptions about knowledge, metaphysics, or logic itself. We end by addressing several prominent concerns raised against the practice-based approach. (shrink)

George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of (...) thought acquire normative force when constrained to mathematical reasoning. Boole’s motivation is, first, to address issues in the foundations of mathematics, including the relationship between arithmetic and algebra, and the study and application of differential equations (Durand-Richard, van Evra, Panteki). Second, Boole intended to derive the laws of logic from the laws of the operation of the human mind, and to show that these laws were valid of algebra and of logic both, when applied to a restricted domain. Boole’s thorough and flexible work in these areas influenced the development of model theory (see Hodges, forthcoming), and has much in common with contemporary inferentialist approaches to logic (found in, e.g., Peregrin and Resnik). (shrink)

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but (...) the other does not.). (shrink)

A. J. Ayer’s Language, Truth, and Logic had been responsible for introducing the Vienna Circle’s ideas, developed within a Germanophone framework, to an Anglophone readership. Inevitably, this migration from one context to another resulted in the alteration of some of the concepts being transmitted. Such alterations have served to facilitate a number of false impressions of Logical Empiricism from which recent scholarship still tries to recover. In this paper, I will attempt to point to the ways in which LTL (...) has helped to foster the various mistaken stereotypes about Logical Empiricism which were combined into the received view. I will begin by examining Ayer’s all too brief presentation of an Anglocentric lineage for his ideas. This lineage, as we shall see, simply omits the major 19th century Germanophone influences on the rise of analytic philosophy. The Germanophone ideas he presents are selectively introduced into an Anglophone context, and directed towards various concerns that arose within that context. I will focus on the differences between Carnap’s version of the overcoming of metaphysics, and Ayer’s reconfiguration into what he calls the elimination of metaphysics. Having discussed the above, I will very briefly outline the consequences that Ayer’s radicalisation of the Vienna Circle’s doctrines had on the subsequent Anglophone reception of Logical Empiricism. (shrink)

(1) This paper is about how to build an account of the normativity of logic around the claim that logic is constitutive of thinking. I take the claim that logic is constitutive of thinking to mean that representational activity must tend to conform to logic to count as thinking. (2) I develop a natural line of thought about how to develop the constitutive position into an account of logical normativity by drawing on constitutivism in metaethics. (3) (...) I argue that, while this line of thought provides some insights, it is importantly incomplete, as it is unable to explain why we should think. I consider two attempts at rescuing the line of thought. The first, unsuccessful response is that it is self-defeating to ask why we ought to think. The second response is that we need to think. But this response secures normativity only if thinking has some connection to human flourishing. (4) I argue that thinking is necessary for human flourishing. Logic is normative because it is constitutive of this good. (5) I show that the resulting account deals nicely with problems that vex other accounts of logical normativity. (shrink)

이 책자는 형식 논리의 일종인 양상논리에 입문하고 싶으신 분들을 위한 짧은 교재입니다. “양상논리 맛보기” 라는 말마따나, 이 책자는 양상논리에 관심은 있지만 아직 본격적으로 공부를 시작하진 않은 분들께서 ‘맛보기’를 하기에 적합한 안내 책자입니다. 아무쪼록 이 책자가 양상논리를 공부해나가시는데 유용한 첫 발판이 될 수 있기를 바랍니다. / This booklet is a Korean adaptation and translation of Part VIII of forall x: Calgary (Fall 2021 edition), which is intended to be introductory material for modal logic. The original text is based on Robert (...) Trueman's A Modal Logic Primer, which is revised and expanded by Richard Zach and Aaron Thomas-Bolduc in forall x: Calgary. (forall x: Calgary is based on forall x: Cambridge by Tim Button, which is in turn based on forall x by P. D. Magnus, and also includes material from forall x: Lorain County Remix by Cathal Woods and J. Robert Loftis.) This booklet is licensed under a Creative Commons Attribution 4.0 license. (shrink)

This paper deals with the study of the nature of mind, its processes and its relations with the other filed known as logic, especially the contribution of most notable contemporary analytical philosophy Ludwig Wittgenstein. Wittgenstein showed a critical relation between the mind and logic. He assumed that every mental process is logical. Mental field is field of space and time and logical field is a field of reasoning (inductive and deductive). It is only with the advancement in (...) class='Hi'>logic, we are today in the era of scientific progress and technology. Logic played an important role in the cognitive part or we can say in the ‗philosophy of mind‘ that this branch is developed only because of three crucial theories i.e. rationalism, empiricism, and criticism. In this paper, it is argued that innate ideas or truth are equated with deduction and acquired truths are related with induction. This article also enhance the role of language in the makeup of the world of mind, although mind and the thought are the terms that are used by the philosophers synonymously but in this paper they are taken and interpreted differently. It shows the development in the analytical tradition subjected to the areas of mind and logic and their critical relation. (shrink)

The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious (...) obstacle to any such view. (shrink)

A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest in—and endorsement of—justification (...) holism due to the revival of an abductivist approach to the epistemology of logic. This paper presents an argument against holism by establishing a foundational entailment-sentence of deduction which is justified independently of theory choice and outside the context of a whole logical theory. (shrink)

Philosophers have spilled a lot of ink over the past few years exploring the nature and significance of grounding. Kit Fine has made several seminal contributions to this discussion, including an exact treatment of the formal features of grounding [Fine, 2012a]. He has specified a language in which grounding claims may be expressed, proposed a system of axioms which capture the relevant formal features, and offered a semantics which interprets the language. Unfortunately, the semantics Fine offers faces a number of (...) problems. In this paper, I review the problems and offer an alternative that avoids them. I offer a semantics for the pure logic of ground that is motivated by ideas already present in the grounding literature, and for which a natural axiomatization capturing central formal features of grounding is sound and complete. I also show how the semantics I offer avoids the problems faced by Fine’s semantics. (shrink)

Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then (...) describe three additional empirical studies that investigate further claims in the literature on vagueness: the hypothesis that speakers confuse ‘P’ with ‘definitely P’, the relative persuasiveness of different formulations of the inductive premise of the Sorites, and the interaction of vague predicates with three different forms of negation. (shrink)

Rosenkranz has recently proposed a logic for propositional, non-factive, all-things-considered justification, which is based on a logic for the notion of being in a position to know, 309–338 2018). Starting from three quite weak assumptions in addition to some of the core principles that are already accepted by Rosenkranz, I prove that, if one has positive introspective and modally robust knowledge of the axioms of minimal arithmetic, then one is in a position to know that a sentence is (...) not provable in minimal arithmetic or that the negation of that sentence is not provable in minimal arithmetic. This serves as the formal background for an example that calls into question the correctness of Rosenkranz’s logic of justification. (shrink)

The idea that logic is in some sense normative for thought and reasoning is a familiar one. Some of the most prominent figures in the history of philosophy including Kant and Frege have been among its defenders. The most natural way of spelling out this idea is to formulate wide-scope deductive requirements on belief which rule out certain states as irrational. But what can account for the truth of such deductive requirements of rationality? By far, the most prominent responses (...) draw in one way or another on the idea that belief aims at the truth. In this paper, I consider two ways of making this line of thought more precise and I argue that they both fail. In particular, I examine a recent attempt by Epistemic Utility Theory to give a veritist account of deductive coherence requirements. I argue that despite its proponents’ best efforts, Epistemic Utility Theory cannot vindicate such requirements. (shrink)

In this paper I investigate how differences in approach to truth and logic (in particular, a deflationist vs. a substantivist approach to these fields) affect philosophers’ views concerning pluralism and normativity in these fields. My perspective on truth and logic is largely epistemic, focusing on the role of truth in knowledge (rather than on the use of the words “true” and “truth” in natural language), and my reference group includes Carnap (1934), Harman (1986), Horwich (1990), Wright (1992), Beall (...) and Restall (2006), Field (2009), Lynch (2009), and Sher (2016a).1 Whenever possible, I focus on positive rather than negative views on the issues involved, although in some cases this is not possible. (shrink)

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree (...) logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail. (shrink)

Many theories of rational belief give a special place to logic. They say that an ideally rational agent would never be uncertain about logical facts. In short: they say that ideal rationality requires "logical omniscience." Here I argue against the view that ideal rationality requires logical omniscience on the grounds that the requirement of logical omniscience can come into conflict with the requirement to proportion one’s beliefs to the evidence. I proceed in two steps. First, I rehearse an influential (...) line of argument from the "higher-order evidence" debate, which purports to show that it would be dogmatic, even for a cognitively infallible agent, to refuse to revise her beliefs about logical matters in response to evidence indicating that those beliefs are irrational. Second, I defend this "anti-dogmatism" argument against two responses put forth by Declan Smithies and David Christensen. Against Smithies’ response, I argue that it leads to irrational self-ascriptions of epistemic luck, and that it obscures the distinction between propositional and doxastic justification. Against Christensen’s response, I argue that it clashes with one of two attractive deontic principles, and that it is extensionally inadequate. Taken together, these criticisms will suggest that the connection between logic and rationality cannot be what it is standardly taken to be—ideal rationality does not require logical omniscience. (shrink)

This article derives from a project attempting to show that Western formal logic, from Aristotle onward, has both been partially constituted by, and partially constitutive of, what has become known as racism. In the present article, I will first discuss, in light of Frege’s honorary role as founder of the philosophy of mathematics, Reuben Hersh’s What is Mathematics, Really? Second, I will explore how the infamous section of Frege’s 1924 diary (specifically the entries from March 10 to April 9) (...) supports Hersh's claim regarding the link between political conservatism and the (historically and currently) dominant school of the philosophy of mathematics (to which Frege undeniably belongs). Third, I will examine Frege’s attempt at a more reader-friendly introduction to his philosophy of mathematics, The Foundations of Arithmetic. And finally, I will briefly analyze Frege’s Begriffsschrift to see how questions of race arise even at the heights of his logical abstraction. (shrink)