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Mathematics and logic present crucial cases in deciding whether the world is of our making or whether some form of realism is true. Edmund Husserl, who was initially a mathematician, discusses this general question extensively, but although his views influenced the Dutch intuitionists and were taken very seriously by Gödel, they have not been widely appreciated among analytical philosophers. In this book Robert Tragesser sets out to determine the conditions under which a realist ontology of mathematics and logic might be justified, taking as his starting point Husserl's treatment of these metaphysical problems. He does not aim primarily at an exposition of Husserl's phenomenology, although many of the central claims of phenomenology are clarified here. Rather he exploits its ideas and methods to show how they can contribute to answering Michael Dummet's question 'Realism or Anti-Realism?'. In doing so he makes a challenging and provocative contribution to the debate.
In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.
This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time.
The primary intent of this volume is to give the English reader access to all the philosophical texts published by Husserl between the appearance of his first book, Philosophie der Arithmetik, and that of his second book, Logische Untersuchungen- roughly, from 1890 through 1901. Along with these texts we have included a number of unpublished manuscripts from the same period and dealing with the same or closely related topics. A few of the texts here translated (the review of Pahigyi, the five "report" articles of 1903-1904, the "notes" in Lalande's Vocabulaire, and the brief discussion. article on Marty of 1910) obviously fall outside this time period, so far as their publication dates are concerned; but in content they seem clearly confined to it. The final piece translated, a set of personal notes that date from 1906 through 1908, provides insight into how Husserl experienced his early labors and their results, and into how he saw their relation to work before him: a phenomenological critique of reason in all of its forms. Thus the texts here translated - which obviously are to be read in conjunction with his first two books - cover the progression of Husserl's Problematik from the relatively narrow one of clarifying the epistemic structure of general arithmetic, to the all-encompassing one of establishing in principle, through phenomenological research, the line between legitimate and illegitimate claims to know or to be rational, regardless of the domain concerned.
called in question, then naturally no fact, science, could be presupposed. Thus Plato was set on the path to the pure idea. Not gathered from the de facto sciences but formative of pure norms, his dialectic of pure ideas-as we say, his logic or his theory of science - was called on to make genuine 1 science possible now for the first time, to guide its practice. And precisely in fulfilling this vocation the Platonic dialectic actually helped create sciences in the pregnant sense, sciences that were consciously sustained by the idea of logical science and sought to actualize it so far as possible. Such were the strict mathematics and natural science whose further developments at higher stages are our modem sciences. But the original relationship between logic and science has undergone a remarkable reversal in modem times. The sciences made themselves independent. Without being able to satisfy completely the spirit of critical self-justification, they fashioned extremely differentiated methods, whose fruitfulness, it is true, was practically certain, but whose productivity was not clarified by ultimate insight. They fashioned these methods, not indeed with the everyday man's naivete, but still with a na!ivete of a higher level, which abandoned the appeal to the pure idea, the justifying of method by pure principles, according to ultimate a priori possibilities and necessities.
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 his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.
Edmund Husserl, founder of the phenomenological movement, is usually read as an idealist in his metaphysics and an instrumentalist in his philosophy of science. In Nature’s Suit, Lee Hardy argues that both views represent a serious misreading of Husserl’s texts. Drawing upon the full range of Husserl’s major published works together with material from Husserl’s unpublished manuscripts, Hardy develops a consistent interpretation of Husserl’s conception of logic as a theory of science, his phenomenological account of truth and rationality, his ontology of the physical thing and mathematical objectivity, his account of the process of idealization in the physical sciences, and his approach to the phenomenological clarification and critique of scientific knowledge. Offering a jargon-free explanation of the basic principles of Husserl’s phenomenology, Nature’s Suit provides an excellent introduction to the philosophy of Edmund Husserl as well as a focused examination of his potential contributions to the philosophy of science. While the majority of research on Husserl’s philosophy of the sciences focuses on the critique of science in his late work, The Crisis of European Sciences, Lee Hardy covers the entire breadth of Husserl’s reflections on science in a systematic fashion, contextualizing Husserl’s phenomenological critique to demonstrate that it is entirely compatible with the theoretical dimensions of contemporary science.
The rift which has long divided the philosophical world into opposed schools-the "Continental" school owing its origins to the phenomenology of Husserl and the "analytic" school derived from Frege-is finally closing. But this closure is occurring in ways both different and in certain respects at odds with one another. On the one hand scholars are seeking to rediscover the concerns and positions common to both schools, positions from which we can continue fruitfully to address important philosophical issues. On the other hand successors to both traditions have developed criticisms of basic assumptions shared by the two schools. They have suggested that we must move not merely beyond the conflict between these two "modem" schools but beyond the kind of philosophy represented in the unity of the two schools and thereby move towards a new "postmodern" philosophical style. On the one hand, then and for example, Husserl scholarship has in recent years witnessed the development of an interpretation of Husserl which more closely aligns his phenomenology with the philosophical concerns of the "analytic" tradition. In certain respects, this should come as no surprise and is long overdue. It is true, after all, that the early Husserl occupied himself with many of the same philosophical issues as did Frege and the earliest thinkers of the analytic tradition. Examples include the concept of number, the nature of mathematical analysis, meaning and reference, truth, formalization, and the relationship between logic and mathematics.
At the turn of the century, Gottlob Frege and Edmund Husserl both participated in the discussion concerning the foundations of logic and mathematics. Since the 1960s, comparisons have been made between Frege's semantic views and Husserl's theory of intentional acts. In quite recent years, new approaches to the two philosophers' views have appeared. This collection of articles opens with the first English translation of Dagfinn Føllesdal's early classic on Husserl and Frege of 1958. The book brings together a number of new contributions by well-known authors and gives a survey of recent developments in the field. It shows that Husserl's thought is coming to occupy a central role in the philosophy of logic and mathematics, as well as in the philosophy of mind and cognitive science. The work is primarily meant for philosophers, especially for those working on the problems of language, logic, mathematics, and mind. It can also be used as a textbook in advanced courses in philosophy.