امشب در میانهی گپ و گفتی، بحثی بین دوستان رد و بدل شد دربارهی ارتباط پروژهی براوئر (Brouwer) در ریاضی با طرح هوسرل، اینکه چطور دیدگاه شهودی براوئر به ریاضی، معنای برهان را عوض کرده و آن را به شهود زمان در هوسرل نزدیک میکند.
یاد یادداشتی از هانس اسلوگا دربارهی استادش، اسکار بکر، افتادم. بکر اولا به تحصیل ریاضی پرداخت و آن را تا مدارج عالی دنبال کرد، سپس تحت تاثیر هوسرل و پس از او تحت تأثیر هایدگر در پی فلسفهی ریاضی رفت و میخواست نشان دهد که بنا بر تفسیر هایدگر، ریاضی هم باید تعبیری زمانمند داشته باشد. از مقدمهی متن:
Oskar Becker or the Reconciliation of Mathematics and Existential Philosophy
I begin with a piece of autobiography. When I first heard of symbolic logic I was a schoolboy, about fifteen years old. By chance, I had discovered a little book on the topic in some local bookstore and had found its treatment of the propositional and the predicate calculus an endlessly intriguing subject matter. It was a time when I dreamt at night of sex and truth-tables. I don’t know any more in what order. Then, as a freshman at the University of Bonn, I discovered a course in symbolic logic taught by one Oskar Becker. He turned out to be a charming, elderly, slightly dotty professor who still taught his regular classes even though he was retired and who was scheduled that semester not only for his logic course but also a seminar with the title “The Principle of Reason.” In my innocence I conjectured that this would be more logic and so enrolled in both classes. The seminar, however, turned out to be on the later Heidegger, of whom I had never heard till then, and the text for the course was a small book of lectures entitled “The Principle of Reason,” that quickly intrigued me with its darkly poetic prose. Heidegger was asking himself in the work why calculative reason has become so dominant in our culture and was warning of the limits of all such reasoning. While the principle of sufficient reason tells us that everything has its rational ground, its claim to universal validity was itself mysterious, the human condition remained, in fact, unexplained by it. In short, as Heidegger said at the end, “Being: the Abyss.”
For Becker, as I saw him in that semester, the conjunction of logic and later Heidegger seemed to come naturally. I learned afterwards that he had been a mathematician at first, then a student of Edmund Husserl’s, and finally a personal friend and philosophical associate of Martin Heidegger, that he had written extensively on the history and philosophy of mathematics and had made contributions to modal logic as well as to aesthetics and other parts of philosophy. How interconnected these interests were in Becker’s own mind became clear to me only many years later when I studied his book on “the logic and ontology of mathematical phenomena,” one of his major pieces of writing, published in 1927 under the title Mathematische Existenz. The first thing that struck me about that work was that it had appeared in volume VI of Husserl’s Yearbook for Philosophy and Phenomenological Research side by side with Heidegger’s Being and Time. The two works made up the entire content of that particular yearbook. At first sight, they seemed to have nothing in common. Becker’s treatise belonged, after all, to the philosophy of mathematics: it examined the conflict between L.E.J. Brouwer’s mathematical intuitionism and David Hilbert’s formalism and sought to put mathematics on a new philosophical footing. Heidegger’s work, on the other hand, concerned itself with the conditions of human Dasein and with what its author called the temporality and historicality of Being. But it seemed that Husserl, the editor of the Yearbook, had considered the works as related and complementary. Part of the explanation I found in Husserl’s conviction that Becker and Heidegger represented the two sides of the phenomenological movement in philosophy – the scientific and the humanistic one, for short – and that he hoped his two disciples would bring his own work to further fruition in these two directions.
