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"BOOLE, GEORG - FOUNDING MODERN DIGITAL COMPUTER SCIENCE.
The Calculus of Logic.
Cambridge, Macmillan, Barclay, and Macmillan, 1848. No wrappers as extracted from ""The Cambridge and Dublin Mathematical Journal. Edited by W. Thomson."" Vol. III. Pp. 183-198. Having the titlepage (2) pp. to the entire volume.
Reference : 41705
First printing of this major paper in the founding of mathematical logic and pure mathematics. The paper offered here is a continuation of Boole's ""The Mathematical Analysis of Logic""(1847), pioneering the assimilation of logic to mathematics.Boole showed that how mathematical techniques could be applied to the study of logic, and as such he laid the foundations for the axiomatic and deductive treatment og logic, the Boolean algebra, which find imortent applications in both probability theory and computing. This mathematication of logic was undertaken by Frege and brought to a climax by Whitehead and Russell. Boolean algebra was used for this purpose.Boole's work contains what Bertrand Russell called the greatest discovery of the nineteenth century: the nature of pure mathematics.
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3 book(s) with the same title
On The Calculus Of Relations (In: ""The Journal Of Symbolic Logic"").
(No place), The Association for Symbolic Logic, 1941. Large 8vo. Bound in blue half cloth with silver lettering to spine. In ""Journal of Symbolic Logic"", Volume 5. Small paper label to lower part of spine and upper inner margin of front board. Stamp to title-page and last leaf, otherwise internally fine. Pp. 73-89. (Entire copy: (4), 188 pp.).
First appearance of Tarski's groundbreaking work in mathematical logic. Published in 1941, it revolutionized the study of relations by introducing a formal calculus that provided a rigorous foundation for understanding and reasoning about relations.By introducing a formal calculus, Tarski provided mathematicians with a rigorous framework for reasoning about relations, leading to advancements in diverse fields of mathematics and beyond. His contributions laid the groundwork for the exploration of abstract algebra, order theory, and model theory, and found practical applications in computer science.
Formal Logic; Or the Calculus of Inference Necessary and Probable
General Books 2012 124 pages 1x25x19cm. 2012. Broché. 124 pages.
Comme neuf
Applicazioni geometriche del calcolo infinitesimale. + Calcolo Geometrico secondo l'Ausdehnungslehre di H. Grassmann. Preceduto dalle Operazioni della logica deduttiva. - [THE BEGINNING OF PEANO'S LOGIC AND THE ""GEOMETRICAL CALCULUS""]
Torino, Bocca, 1887 + 1888. Royal 8vo. Bound uncut w. the original wrappers of both works in one very nice a bit later (ab. 1920) red hcalf w. five raied bands to back. Single gilt lines to raised bands and gilt title on spine. A bit of soiling to wrappers, which have minor lacks to the inner hinges, where they are mounted onto hinge-strips. Front-wrappers w. stamp from ""Fratelli Bocca Editori"". A bit of brownspotting, mainly to first work. A very fine and attractive copy of these two works, very finely bound together. XII, 334, (2) + X, (2), 170, (2) pp.
Two rare and important first editions by the famous Italian mathematician, logical philosopher, pioneer of symbolic logic, and a founder of mathematical logic and set theory, Giuseppe Peano, uniting his first publication in logic with his introduction of the basic elements of geometric calculus. The present ""Calcolo geometrico secondo l'Ausdehningslehre de H. Grassmann"" contains a twenty-page long preliminary section on the operations of deductive logic, which constitutes Peano' s very first publication on the subject for which he is most famous, namely logic. This work appeared the year before his seminal ""Arithmetices Principia..."", in which he further improves his logical symbolism, which is introduced in the preliminary section of the present work. ""This section, which has almost no connection with the rest of the text, is a synthesis of, and improvement on, some of the work of Boole, Schröder, Peirce, and McColl."" (D.S.B. X:442).In the other present work, ""Applicazioni geometriche del calcolo infinitesimale"", Peano introduces the basic elements of geometric calculus and gives new definitions for the length of an arc and for the area of a curved surface. This important work (in which not only his geometrical calculus is introduced, but in which he also presented several new geometrical discoveries) is based on his lectures on infinitesimal calculus and its application to geometry from 1885. ""The treatise ""Applicazioni geometriche del calcolo infinitesimal"" (1887) was based on a course Peano began teaching at the University of Turin in 1885 and contains the beginnings of his ""geometrical calculus"" (here still influenced by Bellavitis' method of equipolences), new forms of remainders in quadrature formulas, new definitions of length of an arc of a curve and of area of a surface, the notion of a figure tangent to a curve, a determination of the error term in Simpson's formula, and the notion of the limit of a variable figure. There is also a discussion of the measure of a point set, of additive functions of sets, and of integration applied to sets. Peano here generalized the notion of measure that he had introduced in 1883."" (D.S.B. X:443). Peano (1858 -1932) studied mathematics at the University of Turin, where he was employed just after graduating (1880), and where he stayed almost all of his life, devoting this to mathematics. After having graduated with honours, he was employed to assist first Enrico D'Ovidio, and then the renowned Angelo Genocchi, who possessed the chair of Infinitesimal calculus. In 1890 Peano became extraordinary professor, and in 1895 ordinary professor, of infinitesimal calculus at the Unversity of Turin. Cellerino (Guiseppe Peano e la sua scuola. Catalogo monografico): Nr. 2 + 3. 2: ""Il più alto raggiunto dai matematici del XIX secolo nell'elaborazione della teoria delle funzioni di insiemi, è il V capitolo del libro di Peano..."" F.A. Medvedev.""
