In the Western tradition, at least since the 14th century, the philosophy of knowledge has been built around the idea of knowledge as a representation [BOU 99]. The question of the evaluation of knowledge refers at the same time (1) to the object represented (which one does one represent?), (2) to the process of knowledge formation, in particular with the role of the knowing subject (which one does one represent and how does one represent it?), and finally (3) to the (...) relationship between the representation and the represented object. Criteria of evaluation such as “validity”, “adequacy” or “truth”, as mentioned in [AMB 07], make sense only with respect to these three dimensions. An evaluation can thus (1) depend on the ontological nature of the object of knowledge, (2) relate to the relationship between subject and object—including the structures (cognitive, social) which organize this relationship, or (3) relate to the relation of similarity between the object and its representation as well. The relevant criteria of evaluation thus depend on the points of view adopted on these questions. As there are indeed a plurality of points of view in this field, the goal of this appendix is to summarize, as briefly as possible, the various positions adopted by the philosophers and to refer to the relevant texts of reference for more information (for a first outline [CHA 76, SCH 01]). The first section 1 introduces useful discussions about the philosophy of theoretical knowledge and general epistemology, from a quasi-historical perspective. Section two 2 discusses the intermediary but central notion of models. Section three 3, more exploratory, introduces an approach to simulation as “concrete experiment”. It suggests that such a frequent claim in the literature, when precisely evaluated, can, to some extent, renew both the representational and the linguistic views on simulation. (shrink)

In the Western tradition, at least since the 14th century, the philosophy of knowledge has been built around the idea of knowledge as a representation [Boulnois 1999]. The question of the evaluation of knowledge refers at the same time (1) to the object represented (which one does one represent?), (2) to the process of knowledge formation, in particular with the role of the knowing subject (which one does one represent and how does one represent it?), and finally (3) to the (...) relationship between the representation and the represented object. Criteria of evaluation such as “validity”, “adequacy” or “truth”, as mentioned in chapter 4, make sense only with respect to these three dimensions. An evaluation can thus (1) depend on the ontological nature of the object of knowledge, (2) relate to the relationship between subject and object—including the structures (cognitive, social) which organize this relationship, or (3) relate to the relation of similarity between the object and its representation as well. The relevant criteria of evaluation thus depend on the points of view adopted on these questions. As there are indeed a plurality of points of view in this field, the goal of this appendix is to summarize, as briefly as possible, the various positions adopted by the philosophers and to refer to the relevant texts of reference for more information. The first section introduces useful discussions about the philosophy of theoretical knowledge and general epistemology, from a quasi-historical perspective. Section two discusses the intermediary but central notion of models. Section three, more exploratory, intro-duces an approach to simulation as “concrete experiment”. It suggests that such a frequent claim in the literature, when precisely evaluated, can, to some extent, renew both the representational and the linguistic views on simulation. (shrink)

Drawing on Françoise Dastur’s suggestion that the event is a permanent possibility that shapes lived experience, but also, when it occurs, a distinctive temporal rupture, I argue that the initial weeks of the COVID-19 epidemic constitute an event, in her sense. Connecting this phenomenological point to literatures on the politics of temporality, I suggest that the distinction between event and normal experience maps to that between epidemic and endemic. Understanding some of the political and ethical erasures of death (...) and debility in COVID times can thus be mutually informed by phenomenological analysis. (shrink)

Henry More est le plus connu des Platoniciens de Cambridge et l’Enchiridion Metaphysicum, son dernier ouvrage, représente l’accomplissement de sa pensée. Il s’agit d’une enquête métaphysique dont le principal objectif est d’établir l’existence d’une substance immatérielle, d’une âme du monde, sorte d’intermédiaire entre Dieu et le monde par laquelle les choses agissent. More nous invite ainsi à découvrir la vraie métaphysique qui consiste en la découverte de la nature véritable de l’étendue des êtres spirituels comme Dieu, les anges et les (...) démons, l’espace, les âmes individuelles des hommes ou des bêtes. Ce manuel de métaphysique prend appui sur le mécanisme cartésien pour mieux le contredire et démontre que l’extension spirituelle est la principale qualité des esprits. Cette doctrine conduira More à re-diviniser l’espace pour l’instituer à l’instar des kabbalistes de l’école de Safed, comme lieu de la possibilité de l’existence du monde. More montre ainsi les limites des mécanismes d’Hobbes et de Descartes tout en essayant de composer avec d’autres savants mécanistes tels que Robert Boyle et Robert Hooke. Quelques années plus tard, à Cambridge, Newton, sur les pas d’Henry More, pensera la nature de son espace physique comme un espace de nature divine, comme un Sensorium Dei. ---------------------------------------------------------------------------------------------------- ------------- Biographie de l'auteur: Françoise Monnoyeur est Docent en philosophie (Associate Professor). Elle enseigne la philosophie et l’histoire des sciences en France, aux États-Unis et en Suède. Elle est chercheur associée au centre Jean Pépin, Paris, France. Ses principaux ouvrages portent sur Descartes, l’infini, la matière, la vie. (shrink)

In their book on Descartes’s Changing Mind, Peter Machamer and J. E. McGuire argue that Descartes discarded dualism to embrace a kind of monism. Descartes famously proposed that there are two separate substances, mind and body, with distinct attributes of thought and extension. According to Machamer and McGuire, because of the limitations of our intellect, we cannot have insight into the nature of either substance. After reviewing their argument in some detail, I will argue that Descartes did not relinquish his (...) favorite doctrine but may have actually fooled himself about the nature of his dualism. It is my contention that the problem with Cartesian dualism stems from the definition of mind and body as substances and the role of their respective attributes—thought and extension—in the definition of substances. (shrink)

La querelle qui oppose la sémantique cognitive à la linguistique "orthodoxe" contemporaine: structuralisme et grammaire générative (Claude Vandeloise, ce numéro), éveille, en histoire des sciences du langage, des échos lointains mais familiers. Car, par bien des aspects, se trouve rappelée une querelle épistémologique ancienne de grande envergure, celle qui, dans l'Antiquité grecque, opposa les anomalistes aux analogistes, les anomalistes de l'école stoïcienne de Pergame aux analogistes de l'école aristotélicienne d'Alexandrie.

In book: Infini des mathématiciens, infini des philosophes, Edition: 1992, 1995, 1999, 2002, 2008, 2011 ebook, Chapter: Introduction, Publisher: Belin, Paris, Editors: F. Monnoyeur, pp.9-16.

This article analyzes the value of geometric models to understand matter with the examples of the Platonic model for the primary four elements (fire, air, water, and earth) and the models of carbon atomic structures in the new science of crystallography. How the geometry of these models is built in order to discover the properties of matter is explained: movement and stability for the primary elements, and hardness, softness and elasticity for the carbon atoms. These geometric models appear to have (...) a double quality: firstly, they exhibit visually the scientific properties of matter, and secondly they give us the possibility to visualize its whole nature. Geometrical models appear to be the expression of the mind in the understanding of physical matter. (shrink)

The Mathematical Imagination focuses on the role of mathematics and digital technologies in critical theory of culture. This book belongs to the history of ideas rather than to that of mathematics proper since it treats it on a metaphorical level to express phenomena of silence or discontinuity. In order to bring more readability and clarity to the non-specialist readers, I firstly present the essential concepts, background, and objectives of his book...

This editorial introduces the Journal of Consciousness Studies special issue on "Animal Consciousness". The 15 contributors and co-editors answer the question "How should we study animal consciousness scientifically?" in 500 words or fewer.

Descartes' philosophy contains an intriguing notion of the infinite, a concept labeled by the philosopher as indefinite. Even though Descartes clearly defined this term on several occasions in the correspondence with his contemporaries, as well as in his Principles of Philosophy, numerous problems about its meaning have arisen over the years. Most commentators reject the view that the indefinite could mean a real thing and, instead, identify it with an Aristotelian potential infinite. In the first part of this article, I (...) show why there is no numerical infinity in Cartesian mathematics, as such a concept would be inconsistent with the main fundamental attribute of numbers: to be comparable with each other. In the second part, I analyze the indefinite in the context of Descartes' mathematical physics. It is my contention that, even with no trace of infinite in his mathematics, Descartes does refer to an actual indefinite because of its application to the material world within the system of his physics. This fact underlines a discrepancy between his mathematics and physics of the infinite, but does not lead a difficulty in his mathematical physics. Thus, in Descartes' physics, the indefinite refers to an actual dimension of the world rather than to an Aristotelian mathematical potential infinity. In fact, Descartes establishes the reality and limitlessness of the extension of the cosmos and, by extension, the actual nature of his indefinite world. This indefinite has a physical dimension, even if it is not measurable. La filosofía de Descartes contiene una noción intrigante de lo infinito, un concepto nombrado por el filósofo como indefinido. Aunque en varias ocasiones Descartes definió claramente este término en su correspondencia con sus contemporáneos y en sus Principios de filosofía, han surgido muchos problemas acerca de su significado a lo largo de los años. La mayoría de comentaristas rechaza la idea de que indefinido podría significar una cosa real y, en cambio, la identifica con un infinito potencial aristotélico. En la primera parte de este artículo muestro por qué no hay infinito numérico en las matemáticas cartesianas, en la medida en que tal concepto sería inconsistente con el principal atributo fundamental de los números: ser comparables entre sí. En la segunda parte analizo lo indefinido en el contexto de la física matemática de Descartes. Mi argumento es que, aunque no hay rastro de infinito en sus matemáticas, Descartes se refiere a un indefinido real a causa de sus aplicaciones al mundo material dentro del sistema de su física. Este hecho subraya una discrepancia entre sus matemáticas y su física de lo infinito, pero no implica ninguna dificultad en su física matemática. Así pues, en la física de Descartes, lo indefinido se refiere a una dimensión real del mundo más que a una infinitud potencial matemática aristotélica. De hecho, Descartes establece la realidad e infinitud de la extensión del cosmos y, por extensión, la naturaleza real de su mundo indefinido. Esta indefinición tiene una dimensión física aunque no sea medible. (shrink)

Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together with (...) its main contributors: Archimedes, Cavalieri, Wallis, Hobbes, Pascal, Huygens, Bernoulli, and Nieuwentijt. Many of us know and probably have used the Leibnizian formula: to .. (shrink)

When the benefits of surgery do not outweigh the harms or where they do not clearly do so, surgical interventions become morally contested. Cutting to the Core examines a number of such surgeries, including infant male circumcision and cutting the genitals of female children, the separation of conjoined twins, surgical sex assignment of intersex children and the surgical re-assignment of transsexuals, limb and face transplantation, cosmetic surgery, and placebo surgery.

Résumé – Nous nous intéressons à l’enseignement et l’apprentissage de l’infini en classe de mathématiques en considérant les différences et les relations entre infini potentiel et infini actuel. Nous présentons les principaux éléments de notre étude philosophique, épistémologique et didactique, ainsi que trois situations visant à conduire un travail explicite avec les élèves sur ces questions en début de lycée. ---------------------------------------------------------------------------------------------------- --------------------------------- Abstract – We are interested in the teaching and learning of infinite in mathematics class, taking into account the relations (...) between potential infinite and actual infinite. We report the main elements of our current philosophical, epistemological and didactical study; we also present three mathematical situations that we consider relevant for this purpose and to be explored with 10 and 11 grade students. (shrink)

This essay provides a novel account of iterated epistemic states. The essay argues that states of epistemic determinacy might be secured by countenancing iterated epistemic states on the model of fixed points in the modal $\mu$-calculus. Despite the epistemic indeterminacy witnessed by the invalidation of modal axiom 4 in the sorites paradox -- i.e. the KK principle: $\square$$\phi$ $\rightarrow$ $\square$$\square$$\phi$ -- a hyperintensional epistemic $\mu$-automaton permits fixed points to entrain a principled means by which to iterate epistemic states and account (...) thereby for necessary conditions on self-knowledge. The hyperintensional epistemic $\mu$-calculus is applied to the iteration of the epistemic states of a single agent instead of the common knowledge of a group of agents, and is thus a novel contribution to the literature. (shrink)

I examine what the point of self-ownership might best be thought to be.

In the literature seeking to explain concepts in terms of their point, talk of ‘the point’ of concepts remains under-theorised. I propose a typology of points which distinguishes practical, evaluative, animating, and inferential points. This allows us to resolve tensions such as that between the ambition of explanations in terms of the points of concepts to be informative and the claim that mastering concepts requires grasping their point; and it allows us to exploit connections between types of (...) points to understand why they come apart, and whether they do so for problematic ideological reasons or for benignly functional reasons. (shrink)

I have two objectives in this article. The first is methodological: I elaborate a minimal phenomenological method and attempt to show its importance in studies of infant behavior. The second objective is substantive: Applying the minimal phenomenological approach, combined with Meltzoff’s “like-me” developmental framework, I propose the hypothesis that infants learn the pointing gesture at least in part through imitation. I explain how developments in sensorimotor ability (posture, arm and hand control and coordination, and locomotion) in the first year of (...) life prepare the infant for acquiring the pointing gesture. The former may directly enable the latter by allowing the infant to experience its own body as being “like those” of others, thus allowing it to imitatively appropriate a broader range of adult behavior. My proposal emphasizes the embodiment of mind in the development of cognition, contrary to latent dualistic tendencies in some developmental literature. (shrink)

The definition of a point in geometry is primordial in order to understand the different elements of this branch of mathematics ( line, surface, solids…). This paper aims at shedding fresh light on the concept to demonstrate that it is related to another one named, here, the Primary Geometric Object; both concepts concur to understand the multiplicity of geometries and to provide hints as concerns a new understanding of some concepts in physics such as time, energy, mass….

The definition of a point in geometry is primordial in order to understand the different elements of this branch of mathematics ( line, surface, solids…). This paper aims at shedding fresh light on the concept to demonstrate that it is related to another one named, here, the Primary Geometric Object; both concepts concur to understand the multiplicity of geometries and to provide hints as concerns a new understanding of some concepts in physics such as time, energy, mass….

Recent work in philosophy and cognitive science shows that knowledge is the norm of our social practice of assertion, in the sense that an assertion should express knowledge. But why should an assertion express knowledge? I hypothesize that an assertion should express knowledge because the point of assertion is to transmit knowledge. I present evidence supporting this hypothesis.

Cuneo and Shafer-Landau (2014) argued that there are moral conceptual truths that are substantive in content, what they called ‘moral fixed points’. I argue that insofar as we have some reason to postulate moral fixed points, we have equal reason to postulate epistemic fixed points (e.g. the factivity condition). To this effect, I show that the two basic reasons Cuneo and Shafer-Landau (2014) offer in support of moral fixed points naturally carry over to epistemic fixed points. In particular, epistemic fixed (...) points exhibit the four ‘marks’ of conceptual truths that they identify and can be utilized to address important challenges to epistemic realism. I conclude that insofar as we have some reason to postulate moral fixed points, we have equal reason to postulate epistemic fixed points. -/- . (shrink)

I argue that knowing and having points of view are fundamentally different epistemic states if we assume that having justified true beliefs is necessary for knowledge. Knowers necessarily possess justified true beliefs, but persons holding points of view may, for example, lack justification, have false beliefs, or both. I examine these differences and expose other crucial differentiating patterns between the structure of knowledge and points of view that make the latter more likely to lead to disagreements. I hypothesize that these (...) patterns remain invariant in alternative views of knowledge like contextualism as long as we preserve the classical structure. Yet there is much research to be done on the multiple and contrasting properties that emerge if we consider non‐classical analyses of knowledge and points of view. (shrink)

Loyalty is considered central to people’s moral life, yet little is known about how people think about what it means to be loyal. We used a prototype approach to understand how loyalty is represented in Colombia and the United States and how these representations mediate attributions of loyalty and moral judgments of loyalty violations. Across 7 studies (N = 1,984), we found cross-cultural similarities in the associative meaning of loyalty (Study 1) but found differences in the centrality of features associated (...) with loyalty (Study 2) and the latent structure of loyalty representations (Study 3). Colombians represent loyalty in terms of more general moral characteristics, while US participants represent loyalty in terms of interpersonal commitment, both in contrast with current approaches to loyalty. By comparing representations of loyalty and honesty, we establish that difference in loyalty conceptualizations reflect a different way of thinking about loyalty rather than morality more generally (Study 4). Further, Colombians attributed greater loyalty to individuals with general moral characteristics compared to participants from the United States sample (Study 5) and were more likely to classify non-loyal values as loyalty-related (Study 6). While the centrality of prototypical features predicts categorizing norm violations as loyalty-related, differences in prototypical structure account for differences in the severity of moral judgment for such violations (Study 7), which suggests that loyalty representations have similar functions even though these representations differ in structural characteristics. (shrink)

I seek to advance enquiry into the point of a public higher education institution by drawing on ideals salient in the sub-Saharan African philosophical tradition. There are relational, and specifically communal, values prominently held by African thinkers that I use to ground a promising rival to the dominant contemporary Western, and especially Anglo-American, accounts of what a university ultimately ought to strive to achieve, which focus mainly on autonomy, truth, and citizenship. My aims are not merely comparative, contrasting an (...) Afro-communal approach with other ones that have been more globally influential, but also substantive. Although the theory of a university’s point that I articulate and defend has an African pedigree, I work to show that it should be taken seriously by a global audience, for plausibly capturing a variety of intuitions and claims that are widely shared. (shrink)

An intuitive and widely accepted view is that (a) beliefs aim at truth, (b) many citizens have stable and meaningful political beliefs, and (c) citizens choose to support political candidates or parties on the basis of their political beliefs. We argue that all three claims are false. First, we argue that political beliefs often differ from ordinary world-modelling beliefs because they do not aim at truth. Second, we draw on empirical evidence from political science and psychology to argue that most (...) people lack stable and meaningful political beliefs. Third, we claim that the true psychological basis for voting behavior is not an individual’s political beliefs but rather group identity. Along the way, we reflect on what this means for normative democratic theory. (shrink)

In this paper I introduce Horwich’s deflationary theory of truth, called ‘Minimalism’, and I present his proposal of how to cope with the Liar Paradox. The proposal proceeds by restricting the T-schema and, as a consequence of that, it needs a constructive specification of which instances of the T-schema are to be excluded from Minimalism. Horwich has presented, in an informal way, one construction that specifies the Minimalist theory. The main aim of the paper is to present and scrutinize some (...) formal versions of Horwich’s construction. (shrink)

Numerous evolutionary linguists have indicated that human pointing behaviour might be associated with the evolution of language. At an ontogenetic level, and in normal individuals, pointing develops spontaneously and the onset of human pointing precedes as well as facilitates phases in speech and language development. Phylogenetically, pointing behaviour might have preceded and facilitated the evolutionary origin of both gestural and vocal language. Contrary to wild non-human primates, captive and human-reared nonhuman primates also demonstrate pointing behaviour. In this article, we analyse (...) the debates on pointing and its role it might have played in language evolution from a meta-level. From within an Applied Evolutionary Epistemological approach, we examine how exactly we can determine whether pointing has been a unit, a level or a mechanism in language evolution. (shrink)

The normative mechanics of promising seem complex. The strength and content of promissory obligations, and the residual duties they entail upon being violated, have various prima facie surprising features. We give an account to explain these features. Promises have a point. The point of a promise to φ is a promise-independent reason to φ for the promisee’s sake. A promise turns this reason into a duty. This explains the mechanics of promises. And it grounds a nuanced picture of (...) immoral promises, an argument against promissory bare wrongings, and a constraint on theories of why we have promissory obligations at all. (shrink)

I argue that it’s quite comprehensible to get upset about metaethical nihilism, to indulge what I call nihilistic despair. When we lose the objective moral or normative point of view, we lose the promise of luck-immune guidance and categorical importance, things many of us hope for. This is all quite Williams-friendly, but I reject his puzzling but suggestive remarks that nihilistic despair must be a self-pitying muddle. Finally, I argue that internalism about reasons is even more depressing than outright (...) nihilism, in one way at least. (shrink)

Many philosophers argue that the right of self-determination confers to states a right to exclude would-be migrants. Drawing on the case of anti-colonial struggles of the 20th century, I argue that self-determination should be thought of as fundamentally a claim against intergroup hierarchy. This means that self-determination only grants a right to exclude in cases where immigration poses a genuine oppressive threat. Cases involving immigration into wealthy and powerful states rarely meet this criterion, and so talk of self-determination as grounding (...) a right to exclude in such cases is misguided. (shrink)

We provide a new interpretation of Zeno’s Paradox of Measure that begins by giving a substantive account, drawn from Aristotle’s text, of the fact that points lack magnitude. The main elements of this account are (1) the Axiom of Archimedes which states that there are no infinitesimal magnitudes, and (2) the principle that all assignments of magnitude, or lack thereof, must be grounded in the magnitude of line segments, the primary objects to which the notion of linear magnitude applies. Armed (...) with this account, we are ineluctably driven to introduce a highly constructive notion of (outer) measure based exclusively on the total magnitude of potentially infinite collections of line segments. The Paradox of Measure then consists in the proof that every finite or potentially infinite collection of points lacks magnitude with respect to this notion of measure. We observe that the Paradox of Measure, thus understood, troubled analysts into the 1880’s, despite their knowledge that the linear continuum is uncountable. The Paradox was ultimately resolved by Borel in his thesis of 1893, as a corollary to his celebrated result that every countable open cover of a closed line segment has a finite sub-cover, a result he later called the “First Fundamental Theorem of Measure Theory.” This achievement of Borel has not been sufficiently appreciated. We conclude with a metamathematical analysis of the resolution of the paradox made possible by recent results in reverse mathematics. (shrink)

I offer a novel two-stage reconstruction of Hume’s general-point-of-view account, modeled in part on his qualified-judges account in ‘Of the Standard of Taste.’ In particular, I argue that the general point of view needs to be jointly constructed by spectators who have sympathized with (at least some of) the agents in (at least some of) the actor’s circles of influence. The upshot of the account is two-fold. First, Hume’s later thought developed in such a way that it can (...) rectify the problems inherent in his Treatise account of the general point of view. Second, the proposed account provides the grounds for an adequate and well-motivated modest ideal observer theory of the standard of virtue. (shrink)

A “conceptual spaces” approach is used to formalize Aristotle’s main intuitions about time and change, and other ideas about temporal points of view. That approach has been used in earlier studies about points of view. Properties of entities are represented by locations in multidimensional conceptual spaces; and concepts of entities are identified with subsets or regions of conceptual spaces. The dimensions of the spaces, called “determinables”, are qualities in a very general sense. A temporal element is introduced by adding a (...) time variable to state functions that map entities into conceptual spaces. That way, states may have some permanency or stability around time instances. Following Aristotle’s intuitions, changes and events will not be necessarily instant phenomena, instead they could be processual and interval dependent. Change is defined relatively to the interval during which the change is taking place. Time intervals themselves are taken to represent points of view. To have a point of view is to look at the world as it is in the selected interval. Many important concepts are relativized to intervals, for instance change, events, identity, ontology, potentiality, etc. The definition of points of view as intervals allows to compare points of view in relation to all these concepts. The conceptual space approach has an immediate semantic and structural character, but it is tempting to develop also logics to describe them. A formal language is introduced to show how this could be done. (shrink)

What methodological approaches do research programs use to investigate the world? Elisabeth Lloyd’s Logic of Research Questions (LRQ) characterizes such approaches in terms of the questions that the researchers ask and causal factors they consider. She uses the Logic of Research Questions Framework to criticize adaptationist programs in evolutionary biology for dogmatically assuming selection explanations of the traits of organisms. I argue that Lloyd’s general criticism of methodological adaptationism is an artefact of the impoverished LRQ. My Ordered Factors Proposal extends (...) the LRQ to characterize approaches with sequences of questions and factors. I highlight the importance that ordering one’s investigation plays in approaches at the level of adaptationism by analyzing two research programs in community ecology: competitionists and neutralists. Competitionists and neutralists take opposed starting points and use explanatory and developmental heuristics to consider more factors in due time. On the Ordered Factors Proposal, these approaches are not only the ecological factors they are open to considering but also the order in which they will consider them. My disagreement with Lloyd’s over how to characterize methodological approaches reflects different views about methodological monism and pluralism. (shrink)

We show that any coherent complete partial order is obtainable as the fixed-point poset of the strong Kleene jump of a suitably chosen first-order ground model. This is a strengthening of Visser’s result that any finite ccpo is obtainable in this way. The same is true for the van Fraassen supervaluation jump, but not for the weak Kleene jump.

The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses recently introduced infinite and infinitesimal numbers being in accordance with the principle ‘The part is less than the whole’ observed in the physical world around us. These numbers have a strong practical advantage with respect to traditional approaches: they are representable at a new (...) kind of a computer – the Infinity Computer – able to work numerically with all of them. An introduction to the theory of physical and mathematical continuity and differentiation (including subdifferentials) for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains is developed in the paper. This theory allows one to work with derivatives that can assume not only finite but infinite and infinitesimal values, as well. It is emphasized that the newly introduced notion of the physical continuity allows one to see the same mathematical object as a continuous or a discrete one, in dependence on the wish of the researcher, i.e., as it happens in the physical world where the same object can be viewed as a continuous or a discrete in dependence on the instrument of the observation used by the researcher. Connections between pure mathematical concepts and their computational realizations are continuously emphasized through the text. Numerous examples are given. (shrink)

I defend a novel pragmatist account of truth that I call ‘truth from the agent point of view’ or ‘agential truth’, drawing on insights from Hilary Putnam. According to the agential view, as inquirers, when we take something to be truth-apt, we are taking ourselves and all other thinkers to be accountable to getting right a shared target that is independent of any individual's or community's view of that target. That we have this relationship to truth is what enables (...) our practices of disagreement and agreement, even when subject to the glare of self-conscious reflection, and represents a crucial ingredient in our capacity for rational thought. The resulting account shares elements with Huw Price's and Cheryl Misak's views, but also has important advantages over both. It also yields a surprising conclusion—that our best pragmatist account of truth may well be a version of the correspondence theory of truth. (shrink)

The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality -- these are the so-called "dangerous" directed graphs. Building on Rabern, et. al (2013) we reformulate this problem in terms of fixed points of certain functions, thereby boiling it down to get (...) a purely mathematical problem. (shrink)

While it is known that Euclid’s five axioms include a proposition that a line consists at least of two points, modern geometry avoid consistently any discussion on the precise definition of point, line, etc. It is our aim to clarify one of notorious question in Euclidean geometry: how many points are there in a line segment? – from discrete-cellular space (DCS) viewpoint. In retrospect, it may offer an alternative of quantum gravity, i.e. by exploring discrete gravitational theories. To elucidate (...) our propositions, in the last section we will discuss some implications of discrete cellular-space model in several areas of interest: (a) cell biology, (b) cellular computing, (c) Maxwell equations, (d) low energy fusion, and (e) cosmology modelling. (shrink)