Biblioteca della Pontificia Università della Santa Croce Library Catalog

Mathematische Schriften: 1804-1810 / Bernard Bolzano ; herausgegeben von Steve Russ und Edgar Morscher.

By: Bolzano, Bernard [autore]Contributor(s): Russ, Steve [curatore [edt]] | Morscher, Edgar [curatore [edt]]Series: Bernard Bolzano-GesamtausgabeReihe 1, Schriften ; 1.Publisher: Stuttgart-Bad Cannstatt : F. Frommann, 2020Description: 187 pagine : illustrazioni, diagrammi : 25 cmContent type: testo (txt) Media type: senza mediazione (n) Carrier type: volume (nc)ISBN: 9783772822902; 3772822908Other title: Bolzano [Cover title]
Contents:
The 'Betrachtungen über einige Gegenstände der Elementargeometrie' marks the beginning of a life-long programme devoted to the re-organisation of geometry, and mathematics in general, according to Bolzano's own far-reaching methodological principles. Rejecting the concepts of motion, and of the plane, in the first part he proposes proofs of the "die ersten Lehrsätze von Dreiecken und Parallellinien" based only on his radical, and largely original second part: "einer künftig aufzustellenden Theorie der geraden Linie". The first main part of the 'Beyträge zu einer begründeteren Darstellung der Mathematik' is devoted to the nature of mathematics and its proper classification. There is an unusually abstract definition of mathematics as "eine Wissenschaft ... die von den allgemeinen Gesetzten (Formen) handelt, nach welchen sich diese Dinge in ihrem Daseyn richten" (I,.8). The second part develops the methodological principles introduced in the 'Betrachtungen' in greater detail and introduces Bolzano's idea that, "in dem Inbegriffe aller wahren Urtheile herrscht ein gewisser Objectiver, von unserer zufälligen Subjectiven Anerkennung derselben unabhängiger Zusammenhang." (II,. 2) This relation [Abfolge] was to become an important theme of his famous later work 'Wissenschaftslehre! (1837). An Appendix criticises Kant's theory of the construction of mathematical concepts through pure intuition.
Item type Current library Call number Copy number Status Date due Barcode
Books Books PUSC
Dip. Filosofia
VB 987.1.1 (Browse shelf (Opens below)) Copy 001 Not For Loan 363014

Titolo in coperta: Bolzano.

Bibliografia: pagine 167-181.

The 'Betrachtungen über einige Gegenstände der Elementargeometrie' marks the beginning of a life-long programme devoted to the re-organisation of geometry, and mathematics in general, according to Bolzano's own far-reaching methodological principles. Rejecting the concepts of motion, and of the plane, in the first part he proposes proofs of the "die ersten Lehrsätze von Dreiecken und Parallellinien" based only on his radical, and largely original second part: "einer künftig aufzustellenden Theorie der geraden Linie". The first main part of the 'Beyträge zu einer begründeteren Darstellung der Mathematik' is devoted to the nature of mathematics and its proper classification. There is an unusually abstract definition of mathematics as "eine Wissenschaft ... die von den allgemeinen Gesetzten (Formen) handelt, nach welchen sich diese Dinge in ihrem Daseyn richten" (I,.8). The second part develops the methodological principles introduced in the 'Betrachtungen' in greater detail and introduces Bolzano's idea that, "in dem Inbegriffe aller wahren Urtheile herrscht ein gewisser Objectiver, von unserer zufälligen Subjectiven Anerkennung derselben unabhängiger Zusammenhang." (II,. 2) This relation [Abfolge] was to become an important theme of his famous later work 'Wissenschaftslehre! (1837). An Appendix criticises Kant's theory of the construction of mathematical concepts through pure intuition.

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