جوزيبه بيانو
رأى بيانو أن الحساب يمكن أن يُبنى على بضع بديهيات للأعداد الطبيعية، وأن الرياضيات والمنطق يمكن أن تُكتبا برمزية دقيقة، وهي ما تبنّاه راسل ووايتهيد لاحقًا.
التموضع
عالم رياضيات إيطالي أعطى الأعداد الطبيعية صورة بديهية موجزة وصمّم رمزية للمنطق تبنّاها راسل ووايتهيد؛ ودافع فريغه عام 1897 عن كتابة مفاهيمه ضدها.
الأفكار الرئيسة
- بديهيات الأعداد الطبيعية
- رمزية للمنطق والرياضيات
التأثير
أثّر في 1
بيرتراند راسل
أثّر في ✓
Russell met Peano at the Paris congress of 1900, and Principia Mathematica adopts Peano’s logical notation. SEP “Bertrand Russell” (A. D. Irvine), chronology; SEP “The Algebra of Logic Tradition” (S. Burris, J. Legris)
التوثيق: مسجّل أيضًا في Wikidata · Wikidata
بيرتراند راسل › 1872–1970
النقد
نقد متبادل 1
غوتلوب فريغه ⇄ متبادل
انتقد مختلف عليها
Peano’s 1895 review of Frege’s Grundgesetze I in the Rivista di matematica prompted Frege’s replies of 1896–97; what exactly Peano objected to was not checked. Bibliographic data from the Frege–Peano literature (G. Besler; Rivista di matematica 5, 1895, 122–128 and 6, 1896–99, 53–61); review text not read
التوثيق: مسودة بالذكاء الاصطناعي
انتقده
In 1897 Frege compared Peano’s logical notation with his own and defended the superiority of his concept-script. Frege, “Über die Begriffsschrift des Herrn Peano und meine eigene” (1897), listed in SEP “Frege’s Logic” (R. Cook, 2023)
التوثيق: مسودة بالذكاء الاصطناعي
غوتلوب فريغه › 1848–1925
الأعمال
رسالة لاتينية قصيرة تصوغ بديهيات الأعداد الطبيعية بالرمزية، وهي الصيغة المعروفة اليوم ببديهيات بيانو.
مجموعة من النظريات الرياضية مكتوبة برمزية بيانو، بدأها عام 1891؛ وصدرت طبعتها الخامسة والأخيرة عام 1908. وقد لفتت رموزها المنطقية انتباه راسل حين التقى بيانو عام 1900.
الموقف
Peano is on the map for two things that shaped logic and the foundations of mathematics: a short axiomatisation of the natural numbers, set out in Latin in Arithmetic Principles (1889) and now called the Peano axioms, and a symbolic notation for logic and mathematics, developed in the Rivista and in the Formulario, a collection of mathematical theorems written in it, of which the fifth and last edition appeared in 1908. At the Paris congress of 1900 he met Bertrand Russell, who was struck by his logical symbols and went on to study his work and that of his school; the Principia Mathematica adopts Peano’s notation. Frege compared Peano’s notation with his own concept-script in a paper of 1897 and defended the superiority of his own; Peano’s review of Frege’s Basic Laws of Arithmetic, vol. 1 (1895), which prompted Frege’s replies of 1896–97, has not been checked in the sources, and the line from Frege to Peano is marked as disputed.
الحياة والسياق
Giuseppe Peano was born on 27 August 1858 in Spinetta near Cuneo in Piedmont. He studied at the University of Turin from 1876, graduated in 1880 with high honours and worked first as assistant to Enrico D’Ovidio and then to Angelo Genocchi. From 1886 he also taught at the Royal Military Academy, which dismissed him later because he neglected calculus in favour of his new symbols, and from 1890 he was a professor at Turin. In 1890 he founded the Rivista di matematica, whose first issue appeared in 1891. In 1903 he announced an auxiliary language based on Latin vocabulary with simplified grammar, Latino sine flexione, in which he wrote most of his later work. He died on 20 April 1932 in Turin.
أعمال رئيسة أخرى
- Rivista di matematica (journal, founded 1890)
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