Galileo asked in his Dialogue of the Two New Sciences what relationship exists between the size of the set of all natural numbers and the size of the set of all square natural numbers. Although one is a proper subset of the other, suggesting that there are strictly fewer squares than natural numbers, the existence of a simple one-to-one correspondence between the two sets suggests that they have, in fact, the same size. Cantor famously based the modern notion of cardinality (...) on the second intuition, but recent advances in mathematical logic (most notably, numerosity theory) have renewed an interest in the question whether Cantor’s way out of Galileo’s paradox was the only possible one. I present a new solution to Galileo’s paradox and argue that it is a better alternative to the Cantorian solution than numerosity theory. In fact, I argue that it is the best possible way out of Galileo's Paradox that can be based on the "Euclidean" intuition that the whole is always greater than any of its proper parts. (shrink)

Many results in logic and mathematics rely on techniques that allow for concrete, often visual, representations of abstract concepts. A primary example of this phenomenon in logic is the distinction between syntax and semantics, itself an example of the more general duality in mathematics between algebra and geometry. Such representations, however, often rely on the existence of certain maximal objects having particular properties such as points, possible worlds or Tarskian first-order structures. -/- This dissertation explores an alternative to such representations (...) known as possibility semantics. Its core idea is to replace maximal objects with ordered systems of partial approximations. Although it originates in the semantics of modal logic and the representation of abstract ordered structures, I argue that it has far-reaching mathematical, foundational and philosophical significance, especially in the context of semiconstructive mathematics, a foundational framework that does not assume any fragment of the Axiom of Choice beyond the Axiom of Dependent Choices. -/- The dissertation is divided in two main parts. The first part explores various applications of the mathematical framework underlying possibility semantics to lattice theory and non-classical propositional logics. A major theme is the development of constructive dualities for various categories of lattices, which are related to standard non-constructive dualities via Vietoris constructions. -/- The second part of the dissertation explores the alternative foundational setting of semi-constructive mathematics, focusing on three applications of possibility semantics for classical first-order logic to the philosophy of the mathematical infinite. In particular, we introduce generic powers, a semi-constructive analogue of ultrapowers in classical model theory, and we explore the merits of these structures from a foundational, conceptual and historical viewpoint. (shrink)

Although Wilhelm Dilthey and Franz Brentano apparently were pursuing roughly the same objective—to offer a description of our mental functions and of their relations to objects—and both called their respective research programs ‘descriptive psychology’, they seem to have used the term to refer to two different methods of psychological research. In this article, I compare analyses of these differences. Against the reading of Orth but also against a possible application of recent relativist accounts of the epistemology of peer disagreement to (...) this case, I argue that their apparent shared objective is not enough to support an understanding of their views as two alternatives within a given historical or scientific context, or as a mutual peer disagreement. I show that the impression of a shared objective can be explained away as stemming from the influence of their teacher Adolf Trendelenburg, and I stress that the case of introspection strongly suggests that an account in terms of peer disagreement is not plausible. Finally, I conclude that the opposition between two traditions, Austrian philosophy and historicism, might be better suited to account for the dispute and its apparent common historical context. (shrink)

Unlike in physics, the category of thought experiment is not very common in biology. At least there are no classic examples that are as important and as well-known as the most famous thought experiments in physics, such as Galileo’s, Maxwell’s or Einstein’s. The reasons for this are far from obvious; maybe it has to do with the fact that modern biology for the most part sees itself as a thoroughly empirical discipline that engages either in real natural history or in (...) experimenting on real organisms rather than fictive ones. While theoretical biology does exist and is recognized as part of biology, its role within biology appears to be more marginal than the role of theoretical physics within physics. It could be that this marginality of theory also affects thought experiments as sources of theoretical knowledge. Of course, none of this provides a sufficient reason for thinking that thought experiments are really unimportant in biology. It is quite possible that the common perception of this matter is wrong and that there are important theoretical considerations in biology, past or present, that deserve the title of thought experiment just as much as the standard examples from physics. Some such considerations may even be widely known and considered to be important, but were not recognized as thought experiments. In fact, as we shall see, there are reasons for thinking that what is arguably the single most important biological work ever, Charles Darwin’s On the Origin of Species, contains a number of thought experiments. There are also more recent examples both in evolutionary and non-evolutionary biology, as we will show. Part of the problem in identifying positive examples in the history of biology is the lack of agreement as to what exactly a thought experiment is. Even worse, there may not be more than a family resemblance that unifies this epistemic category. We take it that classical thought experiments show the following characteristics: They serve directly or indirectly in the non-empirical epistemic evaluation of theoretical propositions, explanations or hypotheses. Thought experiments somehow appeal to the imagination. They involve hypothetical scenarios, which may or may not be fictive. In other words, thought experiments suppose that certain states of affairs hold and then try to intuit what would happen in a world where these suppositions are true. We want to examine in the following sections if there are episodes in the history of biology that satisfy these criteria. As we will show, there are a few episodes that might satisfy all three of these criteria, and many more if the imagination criterion is dropped or understood in a lose sense. In any case, this criterion is somewhat vague in the first place, unless a specific account of the imagination is presupposed. There will also be issues as to what exactly “non-empirical” means. In general, for the sake of discussion we propose to understand the term “thought experiment” here in a broad rather than a narrow sense here. We would rather be guilty of having too wide a conception of thought experiment than of missing a whole range of really interesting examples. (shrink)

Uncertainty is recognized as a key issue in water resources research, amongst other sciences. Discussions of uncertainty typically focus on tools and techniques applied within an analysis, e.g. uncertainty quantification and model validation. But uncertainty is also addressed outside the analysis, in writing scientific publications. The language that authors use conveys their perspective of the role of uncertainty when interpreting a claim —what we call here “framing” the uncertainty. This article promotes awareness of uncertainty framing in four ways. 1) It (...) proposes a typology of eighteen uncertainty frames, addressing five questions about uncertainty. 2) It describes the context in which uncertainty framing occurs. This is an interdisciplinary topic, involving philosophy of science, science studies, linguistics, rhetoric, and argumentation. 3) We analyze the use of uncertainty frames in a sample of 177 abstracts from the Water Resources Research journal in 2015. This helped develop and tentatively verify the typology, and provides a snapshot of current practice. 4) Provocative recommendations promote adjustments for a more influential, dynamic science. Current practice in uncertainty framing might be described as carefully-considered incremental science. In addition to uncertainty quantification and degree of belief (present in ~5% of abstracts), uncertainty is addressed by a combination of limiting scope, deferring to further work (~25%) and indicating evidence is sufficient (~40%) – or uncertainty is completely ignored (~8%). There is a need for public debate within our discipline to decide in what context different uncertainty frames are appropriate. Uncertainty framing cannot remain a hidden practice evaluated only by lone reviewers. (shrink)

The development of phenomenology in nineteenth‐century German philosophy is that of a particular stream within the larger historical‐philosophical complex of Austro‐German philosophy. As the “grandfather of phenomenology” resp. the “disgusted grandfather of phenomenology,” but also as the key figure on the “Anglo‐Austrian Analytic Axis”, Brentano is at the source of the two main philosophical traditions in twentieth‐century philosophy. This chapter focuses mainly on his place in nineteenth‐century European philosophy and on the central themes and concepts in his philosophy that were (...) determinant in the development of the philosophy of his most gifted student: Edmund Husserl. Despite the variety of stances which Brentano expressed on ontology, metaphysics, and psychology over the course of his career, the five general principles remain central to his whole philosophy throughout: they have an important place in what could be called Brentano's philosophical worldview or system. By extension, they also are essential to his conception of phenomenology. (shrink)

This paper introduces the category of b-frames as a new tool in the study of complete lattices. B-frames can be seen as a generalization of posets, which play an important role in the representation theory of Heyting algebras, but also in the study of complete Boolean algebras in forcing. This paper combines ideas from the two traditions in order to generalize some techniques and results to the wider context of complete lattices. In particular, we lift a representation theorem of Allwein (...) and MacCaull to a duality between complete lattices and b-frames, and we derive alternative characterizations of several classes of complete lattices from this duality. This framework is then used to obtain new results in the theory of complete Heyting algebras and the semantics of intuitionistic propositional logic. (shrink)

Recent developments in generalized probability theory have renewed a debate about whether regularity (i.e., the constraint that only logical contradictions get assigned probability 0) should be a necessary feature of both chances and credences. Crucial to this debate, however, are some mathematical facts regarding the interplay between the existence of regular generalized probability measures and various cardinality assumptions. We improve on several known results in the literature regarding the existence of regular generalized probability measures. In particular, we give necessary and (...) sufficient conditions for the existence of regular generalized probability measures defined on the whole powerset of any sample space. (shrink)

In the present paper, I try to shed some light on the Munich-Göttingen conception of essences, laws of essence, and ideal objects. I first start with a preliminary account of their conception of the synthetic a priori at the basis of their conception of essence (§2); I then offer a first characterization of this conception, which I label as metaphysical realism (§3), highlighting its key concept: foundation (§4). In the last four sections (§§5-8), I discuss different outcomes of this conception (...) of essences: the nature of laws of essences (§5), different categories of essences (§6) and anumericity (§7). (shrink)

Dans son article From Nihilism to Monism, Jonathan Schaffer montre que les partisans du Nihilisme de la Composition ont de bonnes raisons d’accepter le Monisme d’Existence plutôt que le Nihilisme. De manière analogue, nous souhaitons montrer ici que les partisans de l’Universalisme de la Composition ont de bonnes raisons d’accepter le Monisme de Priorité. Pour montrer cela, nous allons proposer et défendre l’argument suivant : Prémisse 1. Si l’Universalisme de la Composition est vrai alors le Cosmos existe. Prémisse 2. Si (...) le Cosmos existe alors le Cosmos est la seule entité concrète basique. Conclusion. Si l’Universalisme de la Composition est vrai alors le Cosmos est la seule entité concrète basique. (shrink)

Many theories about the teaching of logic and critical thinking take for granted that theoretical learning, the learning of formal rules for example, and its practical application are sufficient to master the tools taught and to take the habit of using them. However, this way of teaching is not efficient, a conclusion supported by much work in cognitive science. Approaching cognition evolutionarily with dual-process theories allows for an explanation of these insufficiencies and offers clues on how we could teach critical (...) thinking and logic more efficiently. In this article, we want to present this approach and explore these leads in order to make some pedagogical recommendations and lay the foundations of a framework. We will put forward an example of the application of this research program with philosophy for children. (shrink)

There are empirical grounds to doubt the effectiveness of a common and intuitive approach to teaching debiasing strategies in critical thinking courses. We summarize some of the grounds before suggesting a broader taxonomy of debiasing strategies. This four-level taxonomy enables a useful diagnosis of biasing factors and situations, and illuminates more strategies for more effective bias mitigation located in the shaping of situational factors and reasoning infrastructure—sometimes called “nudges” in the literature. The question, we contend, then becomes how best to (...) teach the construction and use of such infrastructures. (shrink)

Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite sums can be equipped (...) with the rich and original structure of a non-commutative ordered ring, and that Bolzano’s views on the mathematical infinite are, after all, consistent. (shrink)

The low representation (< 30%) of women in philosophy in English-speaking countries has generated much discussion, both in academic circles and the public sphere. It is sometimes suggested (Haslanger 2009) that unconscious biases, acting at every level in the field, may be grounded in gendered schemas of philosophers and in the discipline more widely, and that actions to make philosophy a more welcoming place for women should address such schemas. However, existing data are too limited to fully warrant such an (...) explanation, which therefore will not satisfy those in favor of the status quo or those who argue against the need to address gender imbalance. In this paper, we propose measures to improve the profession that ought to be implemented without referring explicitly to this underrepresentation or to the climate for women and other underrepresented groups. Such recommendations are based on empirical research already carried out in other disciplines and do not rest on whether it is possible to identify the cause of this low representation. We argue that we need not wait for new or better data to ensure that fairer practices are enacted for women, other underrepresented groups, and everybody else, if only out of precaution. (shrink)

Introduction au numéro spécial de la Revue philosophique de la France et de l'étranger en hommage au centenaire de la mort de Franz Brentano.

From the point of view of Husserl's critique of empiricist theories of abstraction in the Logical Investigations, it seems that Brentano and most of his students would have endorsed the presupposition of Locke's theory of abstraction, which Husserl labels as the 'psychological hypostatization of the general'. For Husserl himself, but also for most of his followers, the motivation behind this critique is that the descriptive psychology of the school of Brentano leads to psychologism if one doesn't accept Platonic ideal objects. (...) In the following article, I argue that Husserl's critique doesn't do justice to the accounts of abstraction developed in the school of Brentano. I take here the particular case of Carl Stumpf, showing that not only does Husserl's accusation miss its target, but also that it attributes indirectly to Stumpf a position that he didn't defend. I suggest that even before the Logical Investigations, Stumpf formulated the basis of an account of abstraction in terms of generalization, an account which will later turn out to be in many ways compatible with Husserl's theory of Spezies in the Logical Investigations, and which provide a viable alternative both to Platonism and to empiricism, thereby calling for a reassessment of the positions on abstraction in the School of Brentano. (shrink)

Conscious states—state that there is something it is like to be in—seem both rich or full of detail and ineffable or hard to fully describe or recall. The problem of ineffability, in particular, is a longstanding issue in philosophy that partly motivates the explanatory gap: the belief that consciousness cannot be reduced to underlying physical processes. Here, we provide an information theoretic dynamical systems perspective on the richness and ineffability of consciousness. In our framework, the richness of conscious experience corresponds (...) to the amount of information in a conscious state and ineffability corresponds to the amount of information lost at different stages of processing. We describe how attractor dynamics in working memory would induce impoverished recollections of our original experiences, how the discrete symbolic nature of language is insufficient for describing the rich and high-dimensional structure of experiences, and how similarity in the cognitive function of two individuals relates to improved communicability of their experiences to each other. While our model may not settle all questions relating to the explanatory gap, it makes progress toward a fully physicalist explanation of the richness and ineffability of conscious experience—two important aspects that seem to be part of what makes qualitative character so puzzling. (shrink)

In his Bipartitum in morali philosophia, the Scottish philosopher William of Manderston, a pupil of John Mair, and an Ockhamist philosopher, is quoting a text of Antonin of Padua who distinguishes the factum opened to a juridical qualification from the inner belief, known by God alone. Quoting the same text, the authors of the Malleus maleficarum try hard to distinguish three distinct fields, the inner beliefs which belongs to God, the exterior acts, the facts, which are relevant for the judges, (...) and the third field, which establishes a relation between the fact and the beliefs. This third field is proper to the inquisitors. Against this ethics of imputability, Manderston, relying on Ockham’s ethics, advocates an intentionalist ethics which depends on a sharp separation between interiority and exteriority. The soteriological dimension of the question entirely belongs to the inner life, whereas the exteriority is strictly disciplinary. By his radicality, Manderston appears as a paradigm of the modern dichotomy between conscience and law, Paolo Prodi once pointed out as a cornerstone of the religious modernity. (shrink)

English translation of paper title: Action and Passion in the Renaissance. The Womanly and the Manly in Agrippa, Postel, and Bovelles. This paper uses the philosophy of Nicholas of Cusa and the Querelle des Femmes as historic backgrounds for how Agrippa of Nettesheim, Guillaum Postel, and Charles de Bovelles reconcile the notions of "male" and "female" in their respective philosophies.

This article proposes the thesis that archeofuturism is a postmodern project of the International Alt-Right (IAR). By postmodern project we mean that: i) it is a project for a time after modernity; and ii) it is a project that, due to its content, can be classified as related to the ideas against modernity called postmodernism. As it is part of the IAR, archeofuturism is also a project of a fascist or far-right nature. To prove our thesis, we will first analyze (...) the Archefouturism developed by the French political scientist Guillaume Faye, a member of the IAR. Then what is IAR will be defined and its relationship with postmodernism will be evidenced. Finally, based on that connection called reactionary postmodernism, the existence of other archeofuturists theses that combine fascist rhetoric with postmodernism will be proposed. (shrink)

The first part of this paper will provide a reconstruction of Francis Bacon’s interpretation of Academic scepticism, Pyrrhonism, and Dogmatism, and its sources throughout his large corpus. It shall also analyze Bacon’s approach against the background of his intellectual milieu, looking particularly at Renaissance readings of scepticism as developed by Guillaume Salluste du Bartas, Pierre de la Primaudaye, Fulke Greville, and John Davies. It shall show that although Bacon made more references to Academic than to Pyrrhonian Scepticism, like most (...) of his contemporaries, he often misrepresented and mixed the doctrinal components of both currents. The second part of the paper shall offer a complete chronological survey of Bacon’s assessment of scepticism throughout his writings. Following the lead of previous studies by other scholars, I shall support the view that, while he approved of the state of doubt and the suspension of judgment as a provisional necessary stage in the pursuit of knowledge, he rejected the notion of acatalepsia. To this received reading, I shall add the suggestion that Bacon’s criticism of acatalepsia ultimately depends on his view of the historical conditions that surround human nature. I deal with this last point in the third part of the paper, where I shall argue that Bacon’s evaluation of scepticism relied on his adoption of a Protestant and Augustinian view of human nature that informed his overall interpretation of the history of humanity and nature, including the sceptical schools. (shrink)

Quando la biblioteca diventa un confessionale. Nel 1585, Giordano Bruno ritorna a Parigi dopo il soggiorno londinese, e comincia a frequentare l’abbazia di Saint Victor, famosa per la sua ” libraria “, immortalata da Rabelais. Il bibliotecario, Guillaume Cotin, trasforma lo “scriptorium” in un confessionale, dove il filosofo dà libero sfogo ai suoi ricordi e al suo impetuoso carattere. -/- When the library becomes a confessional. In 1585, Giordano Bruno, returns to Paris after his stay in London, and begins (...) to attend the abbey of Saint Victor, famous for his library, immortalized by Rabelais. The librarian, Guillaume Cotin, transforms the scriptorium into a confessional, where the philosopher gives free rein to his memories and his impetuous character. (shrink)

Psychology considered as a natural science began as Aristotelian "physics" or "natural philosophy" of the soul, conceived as an animating power that included vital, sensory, and rational functions. C. Wolff restricted the term " psychology " to sensory, cognitive, and volitional functions and placed the science under metaphysics, coordinate with cosmology. Near the middle of the eighteenth century, Krueger, Godart, and Bonnet proposed approaching the mind with the techniques of the new natural science. At nearly the same time, Scottish thinkers (...) placed psychology within moral philosophy, but distinguished its "physical" laws from properly moral laws. British and French visual theorists developed mathematically precise theories of size and distance perception; they created instruments to test these theories and to measure visual phenomena such as the duration of visual impressions. By the end of the century there was a flourishing discipline of empirical psychology in Germany, with a professorship, textbooks, and journals. The practitioners of empirical psychology at this time typically were dualists who included mental phenomena within nature. Accordingly, psychology as a natural scientific disciplines was not invented in the 18th and 19th centuries, but *remade* from the extant empirical psychology. (shrink)

Metaphysics and psychology are two of Brentano’s main areas of interest in philosophy. His first writings, the dissertation On the Several Senses of Being in Aristotle (1862) and the habilitation thesis, The Psychology of Aristotle (1867), bear witness to the duality of his concerns. As such, these works were not only significant contributions to the German Aristotelianism of the second half of the XIXth century, but they also played an important role in the development of Brentano’s later philosophy and in (...) defining his school of thought. At the same time, the dissertation, now celebrating the sesquicentennial of its first publication, was received beyond the immediate sphere of the Brentanian school, for its reading played a significant role in young Heidegger’s thought on being, and thus in his development of a new type of phenomenology, distinct from the Husserlian one. The studies comprising this volume examine the relevance of Brentano’s dissertation, of his metaphysics and psychology for contemporary philosophical research. Generally, the papers emphasize a tendency in Brentanian research, which has become more conspicuous in the last two decades, and can be described as a gradual shift in focus from the specific problems of Brentano’s late philosophy, towards his earlier philosophy, especially his first writings and manuscripts. Taking into account both Brentano’s published works, and the manuscripts of the dissertation and the Psychology, the contributions of this volume manage to emphasise unexplored aspects of Brentano’s philosophy and stand witness to the complexity and the historical dimension of a legacy whose richness still awaits full discovery. -/- Table of Contents -/- Ion Tănăsescu, Foreword Edoardo Fugali, Trendelenburg, Brentano und die Aristoteles-Renaissance in der deutschen Philosophie des 19. Jahrhunderts. Die Frage nach dem Ursprung der Kategorien Dale Jacquette, Brentano on Aristotle’s Categories: First Philosophy and the Manifold Senses of Being Klaus Hedwig, „... eine gewisse kongeniale Denkweise“. Brentanos Rückgriffe auf Thomas von Aquin in seiner Dissertation Susan Krantz Gabriel, Heidegger’s Question and the Fundamental Sense of Being in Brentano Ion Tănăsescu, Franz Brentano’s Dissertation and the Problem of Intentionality Josef Seifert, Über das notwendige Dasein Gottes. Eine kritische Antwort auf Franz Brentanos Kritik des ontologischen Gottesbeweises Paul Janssen, Die Gottesrede bei Brentano Robin Rollinger, Brentano's Psychology from an Empirical Standpoint: Its Background and Conception Guillaume Fréchette, Deux aspects de l’intentionnalité dans la Psychologie de Brentano Denis Seron, The Fechner-Brentano Controversy on the Measurement of Sensation Carlo Ierna, Brentano and Mathematics Roberto Poli, Modes and Boundaries Federico Boccaccini, La vérité efficace. L’épistémologie de Brentano entre Evidenzphilosophie et pragmatisme Thomas Binder, Der Nachlass Franz Brentanos. Eine historische Annäherung an einen schwierigen Fall. (shrink)

Mystical Theology and Platonism in the Time of Cusanus engages with the history of mystical theology and Neoplatonic philosophy through the lens of the 15th century philosopher and theologian, Nicholas of Cusa. The volume comprises nineteen essays that break down the barriers between medieval and Renaissance studies, reinterpreting Cusanus’ place in the history of thought by exploring the archive that informed his thinking, while also interrogating his works by exploring them from the standpoint of their later reception by modern philosophers (...) and theologians. The volume also offers tribute to the career of Donald F. Duclow, a leading scholar in the field of Cusanus studies in particular and of the history of mystical theology and Neoplatonic philosophy more generally. (shrink)