2nd Pieri book

[James T Smith]

Colleagues,

With coauthors Elena A. Marchisotto and Francisco Rodríguez-Consuegra I have just published The Legacy of Mario Pieri in Foundations and Philosophy of Mathematics, our second volume on Pieri:  https://www.springer.com/gp/book/9780817648220.  (Marchisotto and I published the first in 2007.)

The new book features our translations of three major papers by Pieri, which pioneered the modern abstract axiomatic approach to higher mathematics:  Principles of the Geometry of Position Composed into a Deductive Logical System (1898, from Italian), On Elementary Geometry as a Hypothetical Deductive System--Monograph on Point and Motion (1900, from Italian), and On Geometry Envisaged as a Purely Logical System ([1900] 1901, from French).

Pieri's approach, which stemmed from the group around Giuseppe Peano in Torino, melded with Hilbert's more famous, more concise, but less clear foundational studies then progressed through the work of the Americans Veblen, Huntington, and others in the next two decades.  The main feature of the modern approach that was still not present is the analysis of the relationship of a mathematical theory and the logic and language used to present it.  That took form during 1920-1940.   One main aspect was the notion of logical consequence, which Pieri employed in a fully modern way.  Seemingly simple, and thus easy to ignore, its neglect by others clouded foundational work until Tarski showed in the 1930s how to relate the mathematics, logic, and language to achieve modern clarity.  There is a clear path leading from Pieri's work to Tarski's concept of logical consequence through a study by Tarski's Warsaw colleague Kazimierz Ajdukiewicz.

For Pieri's biography, a list of his works, and translations of two other major papers on foundations, see our first volume:    http://math.sfsu.edu/smith/Publications/PieriBookI.htm  (updated in appendix 1 of our new book).

The new book contains summaries of all remaining works by Pieri on foundations, and historical surveys of the development of the projective and transformational geometry that he axiomatized.  Pieri's 1898 and 1900 papers were the first rigorous axiomatization of projective geometry of all dimensions in terms of points and lines only, and the first axiomatization of absolute geometry based entirely on isometries.  His [1900] 1901 paper, presented at the famous 1900 Paris congress,  is a summary of that work, emerging from a general discussion of the philosophy underlying the modern axiomatic method.

The new book begins with two chapters by Rodríguez-Consuegra that provide a more concise outline of Pieri's philosophy and logical methods, in particular his formulation and employment of the concept of logical consequence.
--------------------------------------

James T. Smith

Professor Emeritus of Mathematics

San Francisco State University

mailto:smith at sfsu.edu

http://math.sfsu.edu/smith

Sent from Roxane

-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20210422/0b848247/attachment.html>