December 6-7, 2018
Levi Building, Room 324, E. Safra Campus
09:30-10:30 Burt Hopkins (Université de Lille | UMR-CNRS 8163 STL): “Willard on Husserl’s Early (before 1900) Negative Critique of Mathematical and Logical Formalization”
10:40-11:40 Michael Roubach (The Hebrew University Jerusalem): “Formal Mathematics and Husserl’s Critique of Berkeley”
11:50-12:50 Vincent Gerard (Université Clermont Auvergne): “In the Beginning is the Sign”
12:50-14:20 Lunch Break
14:20- 15:20 Jairo José da Silva (State University of São Paulo): “The Scientific Applicability of Mathematics from a Phenomenological Perspective”
15:30-16:30 Yuval Dolev (Bar Ilan University): “Esse est Percipi – the Case of the Circle”
16:40- 17:40 Tali Leven (Open University Israel): “Robinson’s Monad from a Phenomenological Point of View”
10:00-11:00 Stefania Centrone (TU Berlin): “Husserl and Weyl”
11:10-12:10 Carl J. Posy (The Hebrew University Jerusalem): “Brouwer and Phenomenology”
Burt Hopkins “Willard on Husserl’s Early (before 1900) Negative Critique of Mathematical and Logical Formalization”
Willard’s separation of Husserl’s arguments for the philosophical need to provide an epistemological foundation for symbolic cognition from his psychological account of that foundation in his early work, which extracts those arguments from the psychologism that they are embedded in, is explicated. His apt characterization of them in terms of Husserl’s “negative critique of the ‘extentionalist’ logic of that day (1891-1900) and argument for their “profound relevance . . . to the logical studies of our time” is presented and largely endorsed. It is so, because of its relevance to both contemporary Husserl studies and to the enduring philosophical problem of the theory of symbolic computation.
Michael Roubach “Formal Mathematics and Husserl’s Critique of Berkeley”
In the first part of the talk I will discuss Husserl’s critique of Berkeley and its relevance for Husserl’s own conception of formal mathematics. In the second part I intend to compare Berkeley positive conception of mathematics with Husserl’s.
Vincent Gerard “In the Beginning is the Sign”
In his proof theory of the early 1920s Hilbert acknowledges that, prior to any of the logical inferences we use, there are extra-logical entities that we experience intuitively before any thought process occurs. These entities are “simple signs devoid of any signification”. Paul Bernays has pointed out that this idea of a “sign without signification” had sparked off the reprobation of philosophers. This paper will examine and compare the reactions of two of Husserl’s students: Dietrich Mahnke and Oskar Becker. Both believed that Hilbert’s expression was erroneous, but that it contained a “profound truth”. Which truth was that? This paper will answer this question by showing that Mahnke and Becker had fundamentally different understanding of the meaning of this profound truth of formalism”.
Jairo José da Silva “The Scientific Applicability of Mathematics from a Phenomenological Perspective”
There is a persistent, but wrong, interpretation of mathematized empirical science, popularized by Galileo, for which nature itself is, at its inner core, mathematical; for otherwise, some reason, how mathematics could be so efficient, when not outright indispensable in disclosing the inner secrets of empirical reality?
To dispel the mist clouding the understanding of the true role of mathematics in science one must inquire the inaugural enthronization of mathematical methodology in science. Not as historians, though, but as genetic phenomenologists, and here Husserl, particularly in §9 of his monumental The Crisis of European Sciences and Transcendental Phenomenology, is the perfect guide.
In this work, however, Husserl is not primarily concerned, as I am, with a logical, epistemological and methodological justification of the uses of mathematics in science. Taking Husserl’s analyses as my starting point, I will present my own account of the many roles mathematics play in empirical science, the representative, the instrumental, the predictive and the heuristic, to name them, and how they can be justified.
But I will also ask how my account faces Husserl’s criticism of the “formalist alienation” of science. In fact, as I intend to show, to give free rein to purely symbolic mathematical constructions in science is not only fruitful but methodologically justifiable. Apparently, this conflicts with Husserl’s characterization of the “crisis” of science as consisting essentially in the loss of meaning induced by empty symbolization.
As I read him, however, Husserl does not criticize mathematization per se, no matter how devoid of meaning, but a wrong interpretation of it. I will show how Husserl himself offers ways to cope with mathematization as a methodological strategy by opening to formal logic the realm of formal ontology, where logical relations among empty mathematical structures are investigated that can explain and justify mathematization as a methodological device once mathematical substitutes take the place of perceptual reality as the true objects of immediate scientific concern.
Yuval Dolev “Esse est Percipi – the Case of the Circle”
The term “perceptual constancy” (or “object constancy”) denotes the fact that we see familiar objects as having a fixed shape, size, color, or location despite changes in the angle of perspective, distance, or lighting.
Using perceptual constancy as a platform, in the first part of the talk I discuss the difficulties that arise when an attempt is made to capture geometrically the effect of perspective change on perception. I argue that our grasp of shapes is independent of our success in this endeavor, or, to put it differently, that failure to mathematically represent aspects of experience is not necessarily indicative of weaknesses in our phenomenology.
In the second part of the talk I suggest that the phenomenon of perceptual constancy can also be found in relation to shapes of pure mathematics, such as shapes on the Euclidean plane. This requires expanding the notion of perspective so that it includes changes that are not spatial.
Both parts belong to a broader project aimed at establishing that to be a certain shape is to look that shape, a thesis which, I argue, holds equally for material/imagined shapes and to mathematical shapes.
Stefania Centrone “Husserl and Weyl”
In this paper I will focus on the influence Husserl’s phenomenology had on the ideas of Hermann Weyl and contrast their views on specific issues, in particular those concerning the nature of mathematical knowledge and the ontological status of mathematical objects
Carl J. Posy “Brouwer and Phenomenology”
L.E.J. Brouwer was the founder of mathematical intuitionism. One of his central premises was that mathematical objects are the products of conscious human constructions. In this talk I will assess how Brouwer’s views connect with some classic Husserlian doctrines. To do so, I will look both at Brouwer’s explicit remarks about consciousness and the generation of objects and at how that central premise plays out in actual intuitionistic mathematics. If time permits I will compare these findings with those of other commentators (including some earlier work of my own) who link Brouwer with Husserl.
Tali Leven “Robinson’s Monad from a Phenomenological Point of View”
In this talk I want to present Robinson’s monad as the essence of nonstandard analysis from a phenomenological point of view.
Husserl centered his systematic introduction to phenomenology of 1929, although titled Cartesian meditations, on a version of the Leibnizian notion of monad. In a letter of January 5, 1917, to his former student, Dietrich Mahnke, Husserl confessed that ‘I am in fact, a monadologist myself’. (As appears in Mark Van Atten and Juliette Kennedy 2003, 456(. The importance of monads for Husserl is brought out in the fourth meditation, where it is explained that all phenomenology is essentially a study of the monadic ego. The monadically concrete ego also includes the whole of its actual and potential existence. Although Husserl credits Leibniz for his insights, he faults him for not working them out systematically. The method that Husserl supplied, is the method of the phenomenological reduction of epoch which includes what Husserl calls the ‘eidetic reduction’ which is supposed to help us clarify the essence of the phenomena to be studied.
According to Robinson’s philosophical point of view logic is the basis of epistemology, since Logic according to Robinson deals, among other things, with the question of what makes sense in the eyes of the mathematician and there is a connection between that and what is understandable. According to Robinson’s philosophy of mathematics, there is harmony between epistemology and ontology; what is understandable also exists and therefore logic influences also the ontology of mathematics. The actual acts of consciousness can only come up with contingent truths, for example, the thought that we can talk about the standard real numbers as if they are unique up to isomorphism is an illusion. Robinson was not interested in the way that the real numbers appear to us, he was interested in their ontology and essences. Monad is a central concept in Robinson’s nonstandard analysis. Using reflection principle Robinson showed that everything that ‘is’, in nonstandard analysis, can in the final analysis be reduced to monads and vice versa, that monads reflect everything. Thus Robinson’s monad can be considered as the essence of nonstandard analysis.