Self-Reference and Modal Logic

· Springer Science & Business Media
4.0
2 則評論
電子書
333
頁數

關於這本電子書

It is Sunday, the 7th of September 1930. The place is Konigsberg and the occasion is a small conference on the foundations of mathematics. Arend Heyting, the foremost disciple of L. E. J. Brouwer, has spoken on intuitionism; Rudolf Carnap of the Vienna Circle has expounded on logicism; Johann (formerly Janos and in a few years to be Johnny) von Neumann has explained Hilbert's proof theory-- the so-called formalism; and Hans Hahn has just propounded his own empiricist views of mathematics. The floor is open for general discussion, in the midst of which Heyting announces his satisfaction with the meeting. For him, the relationship between formalism and intuitionism has been clarified: There need be no war between the intuitionist and the formalist. Once the formalist has successfully completed Hilbert's programme and shown "finitely" that the "idealised" mathematics objected to by Brouwer proves no new "meaningful" statements, even the intuitionist will fondly embrace the infinite. To this euphoric revelation, a shy young man cautions~ "According to the formalist conception one adjoins to the meaningful statements of mathematics transfinite (pseudo-')statements which in themselves have no meaning but only serve to make the system a well-rounded one just as in geometry one achieves a well rounded system by the introduction of points at infinity.

評分和評論

4.0
2 則評論

為這本電子書評分

請分享你的寶貴意見。

閱讀資訊

智能手機和平板電腦
請安裝 Android 版iPad/iPhone 版「Google Play 圖書」應用程式。這個應用程式會自動與你的帳戶保持同步,讓你隨時隨地上網或離線閱讀。
手提電腦和電腦
你可以使用電腦的網絡瀏覽器聆聽在 Google Play 上購買的有聲書。
電子書閱讀器及其他裝置
如要在 Kobo 等電子墨水裝置上閱覽書籍,你需要下載檔案並傳輸到你的裝置。請按照說明中心的詳細指示,將檔案傳輸到支援的電子書閱讀器。