The Theory of Plane Area at the Crossroads

Eduardo N. Giovannini is Associate Researcher at the National Scientific and Technological Research Council (CONICET, Argentina) and Assistant Professor at the National University of Litoral (Argentina). He also has held research positions at the Department of Philosophy of the University of Vienna and the University of California at Berkeley (USA). His research areas include the history and philosophy of mathematics, especially in the nineteenth and early twentieth centuries; the history of modern axiomatic geometry, with a particular emphasis on David Hilbert's metatheoretical investigations, and the history and philosophy of modern formal logic, particularly model theory. He has published extensively on Hilbert's foundational work in geometry, the history of the modern axiomatic method, the geometrical roots of model theory. He is the author of David Hilbert y los fundamentos de la geometría (College Publications, 2015).

Edward Hermann Haeusler is Associate Professor of the Department of Informatics at the Pontifical Catholic University of Rio de Janeiro (PUC-Rio, Brazil). His research areas are proof theory, logic, and theory of computation. Besides papers and book chapters, he is the author of Category Theory for Computer Science (Sagra Luzzato and UFRGS), co-editor of Celebration of Dag Prawitz's Work (Springer-Verlag, 2013), co-editor of A Question is More Illuminating than an Answer. A Festschrift for Paulo A. S. Veloso (College Publications, 2021), and co-editor of Why is this a Proof ? Festschrift for Luiz Carlos Pereira (College Publications, 2015). He is also co-editor of the special issue volume 1, number 18 of the Logic Journal of IGPL (Oxford University Press, 2009) and of the special issue of Computación y Sistemas 21(3) (2017).

Abel Lassalle-Casanave is Full Professor of the Department of Philosophy at the Federal University of Bahia (UFBA, Brazil) and Researcher at the National Council of Research and Technological Development (CNPq, Brazil). His area of research is philosophy of formal sciences, with emphasis in verbal, symbolic and diagrammatic proofs, modern philosophy of mathematics and Hilbertian formalism. Beside papers and chapters of books, he is the author of Por construção de conceitos: em torno da filosofia kantiana da matemática (Editora PUC-Rio, 2019), editor of Symbolic Knowledge from Leibniz to Husserl (College Publications, 2012), and co-editor of Visualização nas ciências formais (College Publications, 2012, with Frank Sautter) and of El árbol de los números: cognición, lógica y práctica matemática(Editorial Universidad de Sevilla, 2016, with José Ferreirós).

Chapter 1. From Euclidean to Hilbertean Practice: The Theory of Plane Area.- Chapter 2. De Zolt's Postulate: The Geometrical Path.- Chapter 3. De Zolt's Postulate: The Abstract Approach.- Chapter 4. De Zolt's Postulate in Three-Dimensions.