Making of Mathematics

Carlo Cellucci is emeritus professor of logic at Sapienza University of Rome. He is the author of seven books: Teoria della dimostrazione (Boringhieri, 1978); Le ragioni della logica (Laterza, 1998); Filosofia e matematica (Laterza, 2003); Perché ancora la filosofia (Laterza, 2008); Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method (Springer, 2013); Breve storia della logica: Dall’Umanesimo al primo Rinascimento (with Mirella Capozzi, Lulu Press, 2014); Rethinking Knowledge: The Heuristic View (Springer, 2017).

“Carlo Cellucci … published what can be understood to be one of the most significant books in the philosophy and pedagogy of mathematics in the past century. His erudition and explication are evident on every page, but what makes it most valuable for an understanding and presentation of mathematics is the clarity he brings to the argument … . Such an understanding could transform the way mathematics is presented in journals, textbooks, and classrooms.” (Marshall Gordon, Philosophy of Mathematics Education Journal, Issue 1, February, 2024)“The book is extensive and circumstantial. … The book is well written, based upon sources … with a clear intention to advance the case of ‘heuristic’ philosophy of mathematics. … the book is a valuable position which could start a debate and possible revision of modern philosophy of mathematics.” (Roman Duda, zbMATH 1497.00010, 2022)“The book is an interesting contribution to the new trend in the philosophy of mathematics, the trend in which the attention is paid mainly to the mathematical practice, to making of mathematics and not to mathematics as a finished structure of theorems and proofs.” (Roman Murawski, Mathematical Reviews, November, 2022)

• 1. Introduction.- Part I. Heuristic vs. Mainstream. 2. Mainstream Philosophy of Mathematics.- 3. Heuristic Philosophy of Mathematics.- Part II. Discourse on Method. 4. The Question of Method.- 5. Analytic Method.- 6. Analytic-Synthetic Method and Axiomatic Method.- 7. Rules of Discovery.- 8. Theories.- Part III. The Mathematical Process. 9. Objects.- 10. Demonstrations.- 11. Definitions.- 12. Diagrams.- 13. Notations.- Part IV. The Functionality of Mathematics. 14. Explanations.- 15. Beauty.- 16. Applicability.- Part V. Conclusion. 17. Knowledge, Mathematics, and Naturalism.- 18. Concluding Remarks.- Index.