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The article is a comparative critical discussion of the views of Brentano and Husserl on intentional objects and on perception. Brentano's views on intentional objects are first discussed, with special attention to the problems connected with the status of the intentional objects. It is then argued that Husserl overcomes these problems by help of his notion of noema. Similarly, in the case of perception, Brentano's notion of physical phenomena is argued to be less satisfactory than Husserl's notion of hyle, whose (...) |
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The article is a comparative critical discussion of the views of Brentano and Husserl on intentional objects and on perception. Brentano's views on intentional objects are first discussed, with special attention to the problems connected with the status of the intentional objects. It is then argued that Husserl overcomes these problems by help of his notion of noema. Similarly, in the case of perception, Brentano's notion of physical phenomena is argued to be less satisfactory than Husserl's notion of hyle, whose (...) |
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Darstellung des Noema in 12 Thesen.\nverwendete Textstellen: Ideen 1: S. 203, 22-23; S. 204, 20-21; S. 357, 19-20: Handlungen sind zielgerichtet. Dabei bedarf eines keines physischen Objekts. Husserl setzt and diese Stelle das Noema. Somit wird auch zielgerichtetes Handeln aufgrund einer Halluzination m{ö}glich, Zielgerichtet zu sein bedeutet ein Noema zu haben.\n1. Follesdal´sche These: Noema ist eine intensionale Entit{ä}t, eine Generalisierung des Begriffs Sinn/Bedeutung.\n2. These: Das Noema hat zwei Bestandteile, a) der noematische Sinn, der allen thetischen Handlungen (erinnern, sich vorstellen usw.) (...) |
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Part of the ambiguity lies in the various points of view from which this question might be considered. The crudest di erence lies between the point of view of the working mathematician and that of the logician concerned with the foundations of mathematics. Now some of my fellow mathematical logicians might protest this distinction, since they consider themselves to be just more of those \working mathematicians". Certainly, modern logic has established itself as a very respectable branch of mathematics, and there (...) |
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Brains, it has recently been argued, are essentially prediction machines. They are bundles of cells that support perception and action by constantly attempting to match incoming sensory inputs with top-down expectations or predictions. This is achieved using a hierarchical generative model that aims to minimize prediction error within a bidirectional cascade of cortical processing. Such accounts offer a unifying model of perception and action, illuminate the functional role of attention, and may neatly capture the special contribution of cortical processing to (...) |
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An exciting theory in neuroscience is that the brain is an organ for prediction error minimization. This theory is rapidly gaining influence and is set to dominate the science of mind and brain in the years to come. PEM has extreme explanatory ambition, and profound philosophical implications. Here, I assume the theory, briefly explain it, and then I argue that PEM implies that the brain is essentially self-evidencing. This means it is imperative to identify an evidentiary boundary between the brain (...) |
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We investigate both iteration hypotheses and extender models at the level of one supercompact cardinal. The HOD Conjecture is introduced and shown to be a key conjecture both for the Inner Model Program and for understanding the limits of the large cardinal hierarchy. We show that if the HOD Conjecture is true then this provides strong evidence for the existence of an ultimate version of Gödel's constructible universe L. Whether or not this "ultimate" L exists is now arguably the central (...) |
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The view that mathematics deals with ideal objects to which we have epistemic access by a kind of perception 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 universal (...) |
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The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture known as the Mouse Set Conjecture. One particular motivation for resolving MSC is that (...) |
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Charles Parsons; X*—Mathematical Intuition, Proceedings of the Aristotelian Society, Volume 80, Issue 1, 1 June 1980, Pages 145–168, https://doi.org/10.1093/ari. |
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Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...) |
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Different cognitive functions recruit a number of different, often overlapping, areas of the brain. Theories in cognitive and computational neuroscience are beginning to take this kind of functional integration into account. The contributions to this special issue consider what functional integration tells us about various aspects of the mind such as perception, language, volition, agency, and reward. Here, I consider how and why functional integration may matter for the mind; I discuss a general theoretical framework, based on generative models, that (...) |
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One of the standard ways of postulating large cardinal axioms is to consider elementary embeddings,j, from the universe,V, into some transitive submodel,M. See Reinhardt–Solovay [7] for more details. Ifjis not the identity, andκis the first ordinal moved byj, thenκis a measurable cardinal. Conversely, Scott [8] showed that wheneverκis measurable, there is suchjandM. If we had assumed, in addition, that, thenκwould be theκth measurable cardinal; in general, the wider we assumeMto be, the largerκmust be. |
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Convinced that the classically undecidable problems of mathematics possess determinate truth values, Gödel issued a programmatic call to search for new axioms for their solution. The platonism underlying his belief in the determinateness of those questions in combination with his conception of intuition as a kind of perception have struck many of his readers as highly problematic. Following Gödel's own suggestion, this article explores ideas from phenomenology to specify a meaning for his mathematical realism that allows for a defensible epistemology. |
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This paper explores the metaphysical roots of Cantor’s conception of absolute infinity in order to shed some light on two basic issues that also affect the mathematical theory of sets: the viability of Cantor’s distinction between sets and inconsistent multiplicities, and the intrinsic justification of strong axioms of infinity that are studied in contemporary set theory. |
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In den Bernauer Forschungsmanuskripten nimmt Husserl seine frühere, in Husserliana Band X dokumentierte Phänomenologie der formalen Struktur des inneren Zeitbewusstseins neu auf. Dabei stehen die Fragen, welche die Anwendung des Schemas `Auffassung - Auffassungsinhalt' auf das Zeitbewusstein und die Gefahr des unendlichen Regresses betreffen, noch immer im Vordergrund. Es ergeben sich aber auch entscheidende neue Einsichten. Diese betreffen vor allem das auf die Zukunft gerichtete `protentionale' Zeitbewusstsein in seiner Verflechtung mit der `Retention' der Vergangenheit sowie eine spezifisch noematische Bestimmung der (...) |
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Offers a glimpse into the world of science and technology between 1950 and 1990 as seen through the eyes of a mathematician, and debunks various myths of scientific philosophy. Portrays some of the great scientific personalities of the period, including Stanislav Ulam, who patented the hydrogen bomb, and Jack Schwartz, one of the founders of computer science. Also discusses phenomenology of mathematics, and philosophy and computer science. Includes book reviews. For students and academics. Annotation copyright by Book News, Inc., Portland, (...) |
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