Download Empiricism, Logic and Mathematics: Philosophical Papers by Hans Hahn (auth.), Brian McGuinness (eds.) PDF

By Hans Hahn (auth.), Brian McGuinness (eds.)

The function Hans Hahn performed within the Vienna Circle has now not continuously been sufficiently favored. It used to be very important in numerous methods. within the ftrst position, Hahn belonged to the trio of the unique planners of the Circle. As scholars on the college of Vienna and during the fIrst decade of this century, he and his associates, Philipp Frank and Otto Neurath, met kind of frequently to debate philosophical questions. whilst Hahn authorized his fIrSt professorial place, on the collage of Czernowitz within the north­ east of the Austrian empire, and the trails of the 3 pals parted, they determined to proceed such casual discussions at a few destiny time - maybe in a a little bit greater team and with the cooperation of a thinker from the college. a variety of occasions behind schedule the execution of the venture. Drafted into the Austrian military in the course of the first global battle" Hahn used to be wounded at the Italian entrance. towards the tip of the warfare he authorized a suggestion from the collage of Bonn prolonged in attractiveness of his impressive 1 mathematical achievements. He remained in Bonn till the spring of 1921 while he returm:d to Vienna and a chair of mathe­ matics at his alma mater. There, in 1922, the Mach-Boltzmann professorship for the philosophy of the inductive sciences grew to become vacant by means of the loss of life of Adolf Stohr; and Hahn observed an opportunity to achieve his and his pals' outdated plan.

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I have already said that this view is incompatible with a consistent empiricism, and I regard Wittgenstein's and the intuitionists' polemics against this view as fully justified; likewise I regard Ramsey's realist-metaphysical position, which has been attacked by Mr. Carnap, as impossible. But while I do thus attack Russell's philosophical interpretation of his system, I nevertheless believe that the formal side of his system is largely in order as it is and highly suitable for the foundations of mathematics; we must only look for a different philosophical interpretation.

In dreams we experience all sorts of things similar to the things we experience while awake. But dreams are mere shadows: they have no substance, no reality corresponding to them; only what we experience in the waking state has a reality corresponding to it. But it is often extraordinarily difficult to decide whether something was really experienced or merely dreamt. Is our entire life perhaps nothing but a dream? , delirium tremens: everything looks distorted, and some things are seen double; but this is only an illusion.

Certainly not! For they are supposed to serve as justifications for these transformations. What, then, are they? However, in adopting this sceptical position towards Hilbert's point of departure we do not mean to say anything against the significance of his investigations. On the contrary, I am convinced that many of Hilbert's concrete results will enter into the continuation and improvement of Russell's system. What has been said so far about mathematics relates to arithmetic and analysis. The logicization of geometry was carried out in a very different way - with less controversy and at an earlier time.

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