Internal Logic : Foundations of Mathematics from Kronecker to Hilbert (Synthese Library)

個数：

Internal Logic : Foundations of Mathematics from Kronecker to Hilbert (Synthese Library)

  • 提携先の海外書籍取次会社に在庫がございます。通常3週間で発送いたします。
    【重要ご説明事項】
    1. 納期遅延や、ご入手不能となる場合が若干ございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。
  • 【入荷遅延について】
    世界情勢の影響により、海外からお取り寄せとなる洋書・洋古書の入荷が、表示している標準的な納期よりも遅延する場合がございます。
    おそれいりますが、あらかじめご了承くださいますようお願い申し上げます。
  • ◆画像の表紙や帯等は実物とは異なる場合があります。
  • ◆ウェブストアでの洋書販売価格は、弊社店舗等での販売価格とは異なります。
    また、洋書販売価格は、ご注文確定時点での日本円価格となります。
    ご注文確定後に、同じ洋書の販売価格が変動しても、それは反映されません。
  • 製本 Hardcover:ハードカバー版／ページ数 237 p.
  • 言語 ENG
  • 商品コード 9781402006890
  • DDC分類 510.1

基本説明

The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof.

Full Description

Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer.

The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.

Contents

1. Introduction. Foundations of Mathematics.- 2. From Hilbert to Kronecker.- 3. The Consistency of Arithmetic Revisited.- 4. The Internal Consistency of Arithmetic with Infinite Descent.- 5. From Kronecker to Brouwer.- 6. Hilbert and the Foundations of Physics.- 7. Conclusion. Internal logic: From Kronecker to Hilbert and Beyond.- References.- Name Index.