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  1. The development of mathematics and the birth of phenomenology.Mirja Hartimo - 2010 - In Phenomenology and mathematics. London: Springer. pp. 107--121.
  • Husserl on axiomatization and arithmetic.Claire Ortiz Hill - 2010 - In Mirja Hartimo (ed.), Phenomenology and mathematics. London: Springer.
  • Phenomenology and mathematics.Mirja Hartimo (ed.) - 2010 - London: Springer.
    This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.
  • A Counterfactual Approach to Explanation in Mathematics.Sam Baron, Mark Colyvan & David Ripley - 2020 - Philosophia Mathematica 28 (1):1-34.
    ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.
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  • Mathematics and its Applications: A Transcendental-Idealist Perspective.Jairo José da Silva - 2017 - Cham: Springer Verlag.
    This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...)
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  • Seemings and Justification: An Introduction.Chris Tucker - 2013 - In Seemings and Justification: New Essays on Dogmatism and Phenomenal Conservatism. New York: Oxford University Press USA. pp. 1-29.
    It is natural to think that many of our beliefs are rational because they are based on seemings, or on the way things seem. This is especially clear in the case of perception. Many of our mathematical, moral, and memory beliefs also appear to be based on seemings. In each of these cases, it is natural to think that our beliefs are not only based on a seeming, but also that they are rationally based on these seemings—at least assuming there (...)
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  • Intuition.Ole Koksvik - 2011 - Dissertation, Australian National University
    In this thesis I seek to advance our understanding of what intuitions are. I argue that intuitions are experiences of a certain kind. In particular, they are experiences with representational content, and with a certain phenomenal character. -/- In Chapter 1 I identify our target and provide some important reliminaries. Intuitions are mental states, but which ones? Giving examples helps: a person has an intuition when it seems to her that torturing the innocent is wrong, or that if something is (...)
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  • Evidence.Earl Conee & Richard Feldman - 2008 - In Quentin Smith (ed.), Epistemology: new essays. New York : Oxford University Press,: Oxford University Press.
  • The mystery of direct perceptual justification.Peter Markie - 2005 - Philosophical Studies 126 (3):347-373.
    In at least some cases of justified perceptual belief, our perceptual experience itself, as opposed to beliefs about it, evidences and thereby justifies our belief. While the phenomenon is common, it is also mysterious. There are good reasons to think that perceptions cannot justify beliefs directly, and there is a significant challenge in explaining how they do. After explaining just how direct perceptual justification is mysterious, I considerMichael Huemers (Skepticism and the Veil of Perception, 2001) and Bill Brewers (Perception and (...)
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  • The Intellectual Given.John Bengson - 2015 - Mind 124 (495):707-760.
    Intuition is sometimes derided as an abstruse or esoteric phenomenon akin to crystal-ball gazing. Such derision appears to be fuelled primarily by the suggestion, evidently endorsed by traditional rationalists such as Plato and Descartes, that intuition is a kind of direct, immediate apprehension akin to perception. This paper suggests that although the perceptual analogy has often been dismissed as encouraging a theoretically useless metaphor, a quasi-perceptualist view of intuition may enable rationalists to begin to meet the challenge of supplying a (...)
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  • Husserl’s Conception of Experiential Justification: What It Is and Why It Matters.Philipp Berghofer - 2018 - Husserl Studies 34 (2):145-170.
    The aim of this paper is twofold. The first is an interpretative one as I wish to provide a detailed account of Husserl’s conception of experiential justification. Here Ideas I and Introduction to Logic and Theory of Knowledge: Lectures 1906/07 will be my main resources. My second aim is to demonstrate the currency and relevance of Husserl’s conception. This means two things: Firstly, I will show that in current debates in analytic epistemology there is a movement sharing with Husserl the (...)
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  • Towards a phenomenological conception of experiential justification.Philipp Berghofer - 2020 - Synthese 197 (1):155-183.
    The aim of this paper is to shed light on and develop what I call a phenomenological conception of experiential justification. According to this phenomenological conception, certain experiences gain their justificatory force from their distinctive phenomenology. Such an approach closely connects epistemology and philosophy of mind and has recently been proposed by several authors, most notably by Elijah Chudnoff, Ole Koksvik, and James Pryor. At the present time, however, there is no work that contrasts these different versions of PCEJ. This (...)
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  • Visualization in Logic and Mathematics.Paolo Mancosu - 2005 - In Paolo Mancosu, Klaus Frovin Jørgensen & S. A. Pedersen (eds.), Visualization, Explanation and Reasoning Styles in Mathematics. Springer. pp. 13-26.
    In the last two decades there has been renewed interest in visualization in logic and mathematics. Visualization is usually understood in different ways but for the purposes of this article I will take a rather broad conception of visualization to include both visualization by means of mental images as well as visualizations by means of computer generated images or images drawn on paper, e.g. diagrams etc. These different types of visualization can differ substantially but I am interested in offering a (...)
     
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  • Hilbert and Bernays on Metamathematics.P. Mancosu - 1998 - In ¸ Itemancosu1998. Oxford University Press. pp. 149--188.
  • Paradox, Harmony, and Crisis in Phenomenology.Judson Webb - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Dordrecht, Netherland: Springer Verlag.
    Husserl’s first work formulated what proved to be an algorithmically complete arithmetic, lending mathematical clarity to Kronecker’s reduction of analysis to finite calculations with integers. Husserl’s critique of his nominalism led him to seek a philosophical justification of successful applications of symbolic arithmetic to nature, providing insight into the “wonderful affinity” between our mathematical thoughts and things without invoking a pre-established harmony. For this, Husserl develops a purely descriptive phenomenology for which he found inspiration in Mach’s proposal of a “universal (...)
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  • Das unendliche in der mathematik und seine ausschaltung.Felix Kaufmann - 1930 - und Wien,: F. Deuticke.
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  • Essays on Husserl’s Logic and Philosophy of Mathematics.Stefania Centrone (ed.) - 2017 - Dordrecht, Netherland: Springer Verlag.
    Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of (...)
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  • From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge,: Harvard University Press.
    The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for ...
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  • What is Wrong with Husserl's Scientific Anti-Realism?Harald A. Wiltsche - 2012 - Inquiry: An Interdisciplinary Journal of Philosophy 55 (2):105-130.
    Abstract Not much scholarly work is needed in order to stumble across many passages where Edmund Husserl seems to advocate an anti-realist attitude towards the natural sciences. This tendency, however, is not well-received within the secondary literature. While some commentators criticize Husserl for his alleged scientific anti-realism, others argue that Husserl's position is much more realist than the first impression indicates. It is against this background that I want to argue for the following theses: a) The basic outlook of Husserl's (...)
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  • Science, Realism and Correlationism. A Phenomenological Critique of Meillassoux' Argument from Ancestrality.Harald A. Wiltsche - 2017 - European Journal of Philosophy 25 (3):808-832.
    Quentin Meillassoux has recently launched a sweeping attack against ‘correlationism’. Correlationism is an umbrella term for any philosophical system that is based on ‘the idea [that] we only ever have access to the correlation between thinking and being, and never to either term considered apart from the other’. Thus construed, Meillassoux' critique is indeed a sweeping one: It comprises major parts of the philosophical tradition since Kant, both in its more continental and in its more analytical outlooks. In light of (...)
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  • Das Kontinuum.H. Weyl - 1960 - Journal of Symbolic Logic 25 (3):282-284.
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  • Construction and Constitution in Mathematics.Mark van Atten - 2010 - New Yearbook for Phenomenology and Phenomenological Philosophy 10 (1):43-90.
    In the following, I argue that L. E. J. Brouwer's notion of the construction of purely mathematical objects and Edmund Husserl's notion of their constitution coincide.
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  • Why did Weyl think that formalism's victory against intuitionism entails a defeat of pure phenomenology?Iulian D. Toader - 2014 - History and Philosophy of Logic 35 (2):198-208.
    This paper argues that Weyl took formalism to prevail over intuitionism with respect to supporting scientific objectivity, rather than grounding classical mathematics, and that this was what he thought was enough for rejecting pure phenomenology as well.
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  • Concept Formation and Scientific Objectivity: Weyl’s Turn against Husserl.Iulian D. Toader - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science 3 (2):281-305.
    This paper argues that Weyl's view that scientific objectivity requires that concepts be freely created, i.e., introduced via Hilbert-style axiomatizations, led him to abandon the phenomenological view of objectivity.
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  • Husserl and Hilbert on completeness, still.Jairo Silva - 2016 - Synthese 193 (6):1925-1947.
    In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...)
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  • Das Unendliche in der Mathematik und seine Ausschaltung.Philosophie der Logik und Arithmetik.Das Problem des Satzes vom Ausgeschlossenen Dritter. [REVIEW]Ernest Nagel, Felix Kaufmann, Hugo Dingler & Paul Hofmann - 1932 - Journal of Philosophy 29 (15):401.
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  • Proofs, pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
    Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs in the Elements in particular, the received view is that Euclid's reliance on geometric diagrams undermines his efforts to develop a gap-free deductive theory. The central difficulty concerns the generality of the theory. How can inferences made from a particular diagrams license general mathematical results? After surveying the history behind the received (...)
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  • Mathematics and phenomenology: The correspondence between O. Becker and H. Weyl.Paolo Mancosu & T. A. Ryckman - 2002 - Philosophia Mathematica 10 (2):130-202.
    Recently discovered correspondence from Oskar Becker to Hermann Weyl sheds new light on Weyl's engagement with Husserlian transcendental phenomenology in 1918-1927. Here the last two of these letters, dated July and August, 1926, dealing with issues in the philosophy of mathematics are presented, together with background and a detailed commentary. The letters provide an instructive context for re-assessing the connection between intuitionism and phenomenology in Weyl's foundational thought, and for understanding Weyl's term ‘symbolic construction’ as marking his own considered position (...)
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  • From Hilbert to Husserl: First Introduction to Phenomenology, Especially that of Formal Mathematics.Dietrich Mahnke - 1977 - Studies in History and Philosophy of Science Part A 8 (1):71.
  • Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
    In many diagrams one seems to perceive necessity – one sees not only that something is so, but that it must be so. That conflicts with a certain empiricism largely taken for granted in contemporary philosophy, which believes perception is not capable of such feats. The reason for this belief is often thought well-summarized in Hume's maxim: ‘there are no necessary connections between distinct existences’. It is also thought that even if there were such necessities, perception is too passive or (...)
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  • The Axiom of Choice.Thomas J. Jech - 1973 - Amsterdam, Netherlands: North-Holland.
    Provability, Computability and Reflection.
  • Formal and transcendental logic.Edmund Husserl - 1969 - The Hague,: Martinus Nijhoff.
    Science in a new sense arises in the first instance from Plato's establishing of logic, as a place for exploring the essential requirements of "genuine" ...
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  • Formal and Transcendental Logic.Edmund Husserl, Dorion Cairns, Suzanne Bachelard & Lester E. Embree - 1971 - Philosophical Review 80 (2):267-273.
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  • Skepticism and the Veil of Perception.Michael Huemer (ed.) - 2001 - Lanham: Rowman & Littlefield.
    This book develops and defends a version of direct realism: the thesis that perception gives us direct awareness, and non-inferential knowledge, of the external..
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  • Compassionate phenomenal conservatism.Michael Huemer - 2007 - Philosophy and Phenomenological Research 74 (1):30–55.
    I defend the principle of Phenomenal Conservatism, on which appearances of all kinds generate at least some justification for belief. I argue that there is no reason for privileging introspection or intuition over perceptual experience as a source of justified belief; that those who deny Phenomenal Conservatism are in a self-defeating position, in that their view cannot be both true and justified; and that thedemand for a metajustification for Phenomenal Conservatism either is an easily met demand, or is an unfair (...)
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  • Experiments in Thought.Walter Hopp - 2014 - Perspectives on Science 22 (2):242-263.
    . What are thought experiments, and how do they generate knowledge? More specifically, what sorts of intentional acts must one perform in order to carry out a thought experiment, what sorts of objects are such acts directed toward, and how are those objects made present in such acts? I argue on phenomenological grounds that the proper objects of thought experiments are, in certain cases, uninstantiated universals and relations among them. I will also argue that, in the best of cases, we (...)
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  • Husserl's Pluralistic Phenomenology of Mathematics.M. Hartimo - 2012 - Philosophia Mathematica 20 (1):86-110.
    The paper discusses Husserl's phenomenology of mathematics in his Formal and Transcendental Logic (1929). In it Husserl seeks to provide descriptive foundations for mathematics. As sciences and mathematics are normative activities Husserl's attempt is also to describe the norms at work in these disciplines. The description shows that mathematics can be given in several different ways. The phenomenologist's task is to examine whether a given part of mathematics is genuine according to the norms that pertain to the approach in question. (...)
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  • Husserl on completeness, definitely.Mirja Hartimo - 2018 - Synthese 195 (4):1509-1527.
    The paper discusses Husserl’s notion of definiteness as presented in his Göttingen Mathematical Society Double Lecture of 1901 as a defense of two, in many cases incompatible, ideals, namely full characterizability of the domain, i.e., categoricity, and its syntactic completeness. These two ideals are manifest already in Husserl’s discussion of pure logic in the Prolegomena: The full characterizability is related to Husserl’s attempt to capture the interconnection of things, whereas syntactic completeness relates to the interconnection of truths. In the Prolegomena (...)
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  • Visual Thinking in Mathematics: An Epistemological Study.Marcus Giaquinto - 2007 - Oxford, England: Oxford University Press.
    Marcus Giaquinto presents an investigation into the different kinds of visual thinking involved in mathematical thought, drawing on work in cognitive psychology, philosophy, and mathematics. He argues that mental images and physical diagrams are rarely just superfluous aids: they are often a means of discovery, understanding, and even proof.
  • Visual Thinking in Mathematics. [REVIEW]Marcus Giaquinto - 2009 - Analysis 69 (2):401-403.
    Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late 19th century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis received much attention in the 19th century. They helped to instigate what Hans Hahn called a ‘crisis of intuition’, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this ‘crisis’ as follows : " Mathematicians had for (...)
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  • In the Light of Logic.Solomon Feferman - 1998 - New York and Oxford: Oxford University Press.
    In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom (...)
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  • Denken über nichts - Intentionalität und Nicht-Existenz bei Husserl.Christopher Erhard - 2014 - Boston: De Gruyter. Edited by Christopher Erhard.
    Ever since Parmenides, one of philosophy's riddles has been how we are able to direct our thoughts to non-being. Erhard uses the problem of non-existence as the starting point for an analysis of Husserl's phenomenology. He examines Husserl's interpretation of judgments about non-being as judgments made "under assumption" and his analysis of "free fantasy." Erhard thus demonstrates that Husserl is compatible with today's non-relational theories.
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  • Husserl and Hilbert on completeness, still.Jairo Jose da Silva - 2016 - Synthese 193 (6).
    In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...)
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  • Husserl and Hilbert on completeness, still.Jairo Jose da Silva - 2016 - Synthese 193 (6):1925-1947.
    In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...)
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  • Awareness of Abstract Objects.Elijah Chudnoff - 2012 - Noûs 47 (4):706-726.
    Awareness is a two-place determinable relation some determinates of which are seeing, hearing, etc. Abstract objects are items such as universals and functions, which contrast with concrete objects such as solids and liquids. It is uncontroversial that we are sometimes aware of concrete objects. In this paper I explore the more controversial topic of awareness of abstract objects. I distinguish two questions. First, the Existence Question: are there any experiences that make their subjects aware of abstract objects? Second, the Grounding (...)
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  • Proofs and pictures.James Robert Brown - 1997 - British Journal for the Philosophy of Science 48 (2):161-180.
    Everyone appreciates a clever mathematical picture, but the prevailing attitude is one of scepticism: diagrams, illustrations, and pictures prove nothing; they are psychologically important and heuristically useful, but only a traditional verbal/symbolic proof provides genuine evidence for a purported theorem. Like some other recent writers (Barwise and Etchemendy [1991]; Shin [1994]; and Giaquinto [1994]) I take a different view and argue, from historical considerations and some striking examples, for a positive evidential role for pictures in mathematics.
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  • Ethics and the Continuum Hypothesis.James Robert Brown - 2019 - In James Robert Brown, Shaoshi Chen, Robert M. Corless, Ernest Davis, Nicolas Fillion, Max Gunzburger, Benjamin C. Jantzen, Daniel Lichtblau, Yuri Matiyasevich, Robert H. C. Moir, Mark Wilson & James Woodward (eds.), Algorithms and Complexity in Mathematics, Epistemology, and Science: Proceedings of 2015 and 2016 Acmes Conferences. Springer New York. pp. 1-16.
    Mathematics and ethics are surprisingly similar. To some extent this is obvious, since neither looks to laboratory experiments nor sensory experience of any kind as a source of evidence. Both are based on reason and something commonly call “intuition.” This is not all. Interestingly, mathematics and ethics both possess similar distinctions between pure and applied. I explore some of the similarities and draw methodological lessons from them. We can use these lessons to explore how and why Freiling’s refutation of the (...)
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  • In Defense of Pure Reason.Laurence Bonjour - 2001 - Philosophy and Phenomenological Research 63 (3):657-663.
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  • Why Husserl is a Moderate Foundationalist.Philipp Berghofer - 2018 - Husserl Studies 34 (1):1-23.
    Foundationalism and coherentism are two fundamentally opposed basic epistemological views about the structure of justification. Interestingly enough, there is no consensus on how to interpret Husserl. While interpreting Husserl as a foundationalist was the standard view in early Husserl scholarship, things have changed considerably as prominent commentators like Christian Beyer, John Drummond, Dagfinn Føllesdal, and Dan Zahavi have challenged this foundationalist interpretation. These anti-foundationalist interpretations have again been challenged, for instance, by Walter Hopp and Christian Erhard. One might suspect that (...)
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  • Why Husserl’s Universal Empiricism is a Moderate Rationalism.Philipp Berghofer - 2018 - Axiomathes 28 (5):539-563.
    Husserl claims that his phenomenological–epistemological system amounts to a “universal” form of empiricism. The present paper shows that this universal moment of Husserl’s empiricism is why his empiricism qualifies as a rationalism. What is empiricist about Husserl’s phenomenological–epistemological system is that he takes experiences to be an autonomous source of immediate justification. On top of that, Husserl takes experiences to be the ultimate source of justification. For Husserl, every justified belief ultimately depends epistemically on the subject’s experiences. These are paradigms (...)
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