20 found

Year:

Forthcoming articles
  1. Kai Hauser (forthcoming). Intuition and Its Object. Axiomathes:1-29.
    The view that mathematics deals with ideal objects to which we have epistemic access by a kind of perception (’intuition’) has troubled many thinkers. Using ideas from Husserl’s phenomenology, I will take a different look at these matters. The upshot of this approach is that there are non-material objects and that they can be recognized in a process very closely related to sense perception. In fact, the perception of physical objects may be regarded as a special case of this more (...)
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  2. Teresa Kouri (forthcoming). A Reply to Heathcote's: On the Exhaustion of Mathematical Entities by Structures. Axiomathes:1-13.
    In this article I respond to Heathcote’s “On the Exhaustion of Mathematical Entities by Structures”. I show that his ontic exhaustion issue is not a problem for ante rem structuralists. First, I show that it is unlikely that mathematical objects can occur across structures. Second, I show that the properties that Heathcote suggests are underdetermined by structuralism are not so underdetermined. Finally, I suggest that even if Heathcote’s ontic exhaustion issue if thought of as a problem of reference, the structuralist (...)
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  3. James Trafford (forthcoming). Duality and Inferential Semantics. Axiomathes:1-19.
    It is well known that classical inferentialist semantics runs into problems regarding abnormal valuations :445–467, 2014; Peregrin in J Philos Logic 39:255–274, 2010). It is equally well known that the issues can be resolved if we construct the inference relation in a multiple-conclusion sequent calculus. The latter has been prominently developed in recent work by Restall , with the guiding interpretation that the valid sequent says that the simultaneous assertion of all of Γ with the denial of all of Δ (...)
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  4. Elena Casetta & Jorge Marques da Silva (forthcoming). Biodiversity Surgery: Some Epistemological Challenges in Facing Extinction. Axiomathes:1-13.
    Biological conservation has a long story, but what distinguishes Conservation Biology from previous conservation fields is its multidisciplinary scope and its character as a mission-oriented crisis discipline. These characteristics suggested the introduction of the metaphor of biological conservation as a sort of surgery. This paper is about the initial stages of such surgery. Firstly, some data about the so-called “Big Sixth”—the disease—will be presented together with some information about Conservation Biology—the surgeon. Then epistemic and epistemological difficulties in extinction assessment and (...)
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  5. Noel L. Clemente (forthcoming). A Virtue-Based Defense of Mathematical Apriorism. Axiomathes:1-17.
    Mathematical apriorists usually defend their view by contending that axioms are knowable a priori, and that the rules of inference in mathematics preserve this apriority for derived statements—so that by following the proof of a statement, we can trace the apriority being inherited. The empiricist Philip Kitcher attacked this claim by arguing there is no satisfactory theory that explains how mathematical axioms could be known a priori. I propose that in analyzing Ernest Sosa’s model of intuition as an intellectual virtue, (...)
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  6. L. Dappiano (forthcoming). La holologia come progetto di metafisica descrittiva. Le parti e l'intero nella concezione di Aristotele. I'. Axiomathes.
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  7. Eric Dietrich & Chris Fields (forthcoming). Science Generates Limit Paradoxes. Axiomathes:1-24.
    The sciences occasionally generate discoveries that undermine their own assumptions. Two such discoveries are characterized here: the discovery of apophenia by cognitive psychology and the discovery that physical systems cannot be locally bounded within quantum theory. It is shown that such discoveries have a common structure and that this common structure is an instance of Priest’s well-known Inclosure Schema. This demonstrates that science itself is dialetheic: it generates limit paradoxes. How science proceeds despite this fact is briefly discussed, as is (...)
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  8. Vladimir Drekalović (forthcoming). Some Aspects of Understanding Mathematical Reality: Existence, Platonism, Discovery. Axiomathes:1-21.
    The sum of all objects of a science, the objects’ features and their mutual relations compose the reality described by that sense. The reality described by mathematics consists of objects such as sets, functions, algebraic structures, etc. Generally speaking, the use of terms reality and existence, in relation to describing various objects’ characteristics, usually implies an employment of physical and perceptible attributes. This is not the case in mathematics. Its reality and the existence of its objects, leaving aside its application, (...)
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  9. Kai Hauser (forthcoming). Erratum To: Intuition and Its Object. Axiomathes:1-2.
    Erratum to: Axiomathes DOI 10.1007/s10516-014-9234-yIn the original publication of the article, some of the references were published incorrectly. Please find below the corrected version of these references.
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  10. Wojciech Krysztofiak (forthcoming). Representational Structures of Arithmetical Thinking: Part I. Axiomathes:1-40.
    In this paper, representational structures of arithmetical thinking, encoded in human minds, are described. On the basis of empirical research, it is possible to distinguish four types of mental number lines: the shortest mental number line, summation mental number lines, point-place mental number lines and mental lines of exact numbers. These structures may be treated as generative mechanisms of forming arithmetical representations underlying our numerical acts of reference towards cardinalities, ordinals and magnitudes. In the paper, the theoretical framework for a (...)
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  11. Wojciech Krysztofiak (forthcoming). Algebraic Models of Mental Number Axes: Part II. Axiomathes:1-33.
    The paper presents a formal model of the system of number representations as a multiplicity of mental number axes with a hierarchical structure. The hierarchy is determined by the mind as it acquires successive types of mental number axes generated by virtue of some algebraic mechanisms. Three types of algebraic structures, responsible for functioning these mechanisms, are distinguished: BASAN-structures, CASAN-structures and CAPPAN-structures. A foundational order holds between these structures. CAPPAN-structures are derivative from CASAN-structures which are extensions of BASAN-structures. The constructed (...)
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  12. Seremeti Lambrini & Kameas Achilles (forthcoming). Composable Relations Induced in Networks of Aligned Ontologies: A Category Theoretic Approach. Axiomathes:1-27.
    A network of aligned ontologies is a distributed system, whose components (constituent ontologies) are interacting and interoperating, the result of this interaction being, either the extension of local assertions, which are valid within each individual ontology, to global assertions holding between remote ontology syntactic entities (concepts, individuals) through a network path, or to local assertions holding between local entities of an ontology, but induced by remote ontologies, through a cycle in the network. The mechanism for achieving this interaction is the (...)
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  13. Stathis Livadas (forthcoming). The Subjective Roots of Forcing Theory and Their Influence in Independence Results. Axiomathes:1-23.
    This article attempts a subjectively based approach, in fact one phenomenologically motivated, toward some key concepts of forcing theory, primarily the concepts of a generic set and its global properties and the absoluteness of certain fundamental relations in the extension to a forcing model M[G]. By virtue of this motivation and referring both to the original and current formulation of forcing I revisit certain set-theoretical notions serving as underpinnings of the theory and try to establish their deeper subjectively founded content (...)
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  14. Carlos Lobo, Cleverson Leite Bastos & Carlos Eduardo de Carvalho Vargas (forthcoming). On Essentialism and Existentialism in the Husserlian Platonism: A Reflexion Based on Modal Logic. Axiomathes:1-9.
    Departing from modal logic, Jean-Yves Girard, as a logician interested in philosophy, presented a distinction between essentialism and existentialism in logic. Carlos Lobo reflected about the Girard’s concept to reinterpret the Husserlian Platonism in regard of the status of logical modalities. We start rescuing the notion of modal logic in the Edmund Husserl’s works, especially Formal and Transcendental Logic and First Philosophy. Developing this reflexion, we propose a new contribution to this discussion, reinterpreting the platonic influence in the Husserlian notions (...)
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  15. Dwayne Moore (forthcoming). Supervenient Emergentism and Mereological Emergentism. Axiomathes:1-21.
    In recent years, emergentism has resurfaced as a possible method by which to secure autonomous mental causation from within a physicalistic framework. Critics argue, however, that emergentism fails, since emergentism entails that effects have sufficient physical causes, so they cannot also have distinct mental causes. In this paper I argue that this objection may be effective against supervenient emergentism, but it is not established that it is effective against mereological emergentism. In fact, after demonstrating that two founding emergentists, Samuel Alexander (...)
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  16. Roman Murawski (forthcoming). Cracow Circle and Its Philosophy of Logic and Mathematics. Axiomathes:1-18.
    The paper is devoted to the presentation and analysis of the philosophical views concerning logic and mathematics of the leading members of Cracow Circle, i.e., of Jan Salamucha, Jan Franciszek Drewnowski and Józef Maria Bocheński. Their views on the problem of possible applicability of logical tools in metaphysical and theological researches is also discussed.
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  17. Nicholas Schroeder (forthcoming). A Physicalistic Account of Emergentism. Axiomathes:1-16.
    Jaegwon Kim’s argument against non-reductive physicalism is well known. Many philosophers take Kim’s argument to also apply to emergentism. But this does not necessarily follow. In this paper, I will first briefly show why Kim’s argument against non-reductive physicalism need not apply to emergentism. Next, I will present a physicalistic account of emergentism offered by Jason Megill in his paper “A Defense of Emergence.” This will be followed by an examination of some of the limitations of Megill’s account, in particular, (...)
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  18. Maciej Sendłak (forthcoming). Limits of Hybrid Modal Realism. Axiomathes:1-17.
    The aim of this paper is to point out the limitations of Hybrid Modal Realism as a general theory of modalities, i.e. one that gives an analysis of possibilities as well as impossibilities. To do so we will firstly sketch the goals that theories of impossible worlds should achieve. Secondly we will briefly present the two most popular accounts of impossibilities—Extended Modal Realism and Extended Ersatzism. We will focus on the aspects of both theories which became the motivation for a (...)
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  19. Jairo José Silvdaa (forthcoming). Structuralism and the Applicability of Mathematics. Axiomathes.
    In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.
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  20. Valerio Velardo (forthcoming). Recursive Ontology: A Systemic Theory of Reality. Axiomathes:1-26.
    The article introduces recursive ontology, a general ontology which aims to describe how being is organized and what are the processes that drive it. In order to answer those questions, I use a multidisciplinary approach that combines the theory of levels, philosophy and systems theory. The main claim of recursive ontology is that being is the product of a single recursive process of generation that builds up all of reality in a hierarchical fashion from fundamental physical particles to human societies. (...)
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