Handbook of the History and Philosophy of Mathematical Practice [electronic resource] /
Sriraman, Bharath.editor.
The philosophy of mathematics can be traced back in time to the dawn of mathematics itself. The axiomatization of Euclid in "The Elements" did not hinder innovations in mathematical practice to develop outside the realm of the deductive method. In fact the history of mathematics shows a rich tapestry of practice that include visual, algorithmic, experimental, probabilistic and computational approaches. However the philosophy of mathematics as argued by Imre Lakatos suggests that the innovations and impasses in mathematical practice have remained more or less unacknowledged in philosophy. For instance mathematical argumentation was primarily the domain of theologians and medieval and postmedieval scholastics for over 1700 years after Aristotle. Similarly the study of logic became the purview of mathematical philosophy criticized by Reuben Hersh as "Quinean ping-pong". In two prior Springer books 18 Unconventional Essays on the Nature of Mathematics (Hersh,2006) and Humanizing Mathematics and its Philosophy (Sriraman, 2017), it is sufficiently clear that the philosophy of mathematics is no longer centered around it origins in theology and logic, but influences and is influenced by other domains. Today the philosophy of mathematics can be informed by computer scientists, historians, logicians, linguists, educators, physicists, psychologists, neuroscientists, statisticians and last but not least mathematicians. At the dawn of the 21st century we still have a cadre of scholars influenced first-hand by the likes of Quine and Brouwer, as well as those who were influenced by Imre Lakatos' seminal work Proofs and Refutations (in the 1970s) that espouse the views of practicing mathematicians. Pluralism is the avant-garde term in vogue today suggesting a "post- modern" view of mathematics that would have been frowned upon a century ago. The purpose of this unique Handbook is to unfold the transformation of the philosophy of mathematics from its origins in the history of mathematical practice. In order to do so, chapters will describe different mathematical practices in different time periods of history and contrast it with the development of philosophy. The contributions will include scholars from other disciplines who have contributed to the richness of perspectives that abound the study of philosophy today. The Handbook aims to synthesize what is known, and what has unfolded but also offer directions in which the study of philosophy of mathematics as evident in increasingly diverse mathematical practices is headed. Different sections of the Handbook will offer insights into the origins, debates, methodologies and newer perspectives that characterize the discipline today. This Handbook is curated by an editorial advisory board consisting of leading scholars from the disciplines of mathematics, history and philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute of Technology (USA) Jody Azzouni, Tufts University (USA) Otávio Bueno, University of Miami (USA) William Byers, Concordia University (Canada) Carlo Cellucci, Sapienza University of Rome (Italy) Chandler Davis, University of Toronto (Canada) Paul Ernest, University of Exeter (UK) David Tall, University of Warwick (UK) Michele Friend, George Washington University (USA) Reuben Hersh, University of New Mexico (USA) - (1927-2020) Kyeong-Hwa Lee, Seoul National University (South Korea) Yuri Manin, Max Planck Institute for Mathematics (Germany) Athanase Papadopoulos, University of Strasbourg (France) Ulf Persson, Chalmers University of Technology (Sweden) John Stillwell, University of San Francisco (USA).
Origins [Pythagoreans, Euclid, Apollonius, Diophantus] -- Logic [Aristotelean Logic; Non Aristotelean Logics] -- Enter the natural historians/philosophers -- Non Euclidean Conundrums -- "Experimental" Mathematics -- Constructing the Reals; Paradoxes and Foundations -- Views from Other Domains [Algorithmic, Computational, Bayesian] -- Ontology -- Proof -- Pluralism -- New Perspectives -- Non-western Mathematics -- Mathematical innovations coming from 'practical/real world' problems.
The philosophy of mathematics can be traced back in time to the dawn of mathematics itself. The axiomatization of Euclid in "The Elements" did not hinder innovations in mathematical practice to develop outside the realm of the deductive method. In fact the history of mathematics shows a rich tapestry of practice that include visual, algorithmic, experimental, probabilistic and computational approaches. However the philosophy of mathematics as argued by Imre Lakatos suggests that the innovations and impasses in mathematical practice have remained more or less unacknowledged in philosophy. For instance mathematical argumentation was primarily the domain of theologians and medieval and postmedieval scholastics for over 1700 years after Aristotle. Similarly the study of logic became the purview of mathematical philosophy criticized by Reuben Hersh as "Quinean ping-pong". In two prior Springer books 18 Unconventional Essays on the Nature of Mathematics (Hersh,2006) and Humanizing Mathematics and its Philosophy (Sriraman, 2017), it is sufficiently clear that the philosophy of mathematics is no longer centered around it origins in theology and logic, but influences and is influenced by other domains. Today the philosophy of mathematics can be informed by computer scientists, historians, logicians, linguists, educators, physicists, psychologists, neuroscientists, statisticians and last but not least mathematicians. At the dawn of the 21st century we still have a cadre of scholars influenced first-hand by the likes of Quine and Brouwer, as well as those who were influenced by Imre Lakatos' seminal work Proofs and Refutations (in the 1970s) that espouse the views of practicing mathematicians. Pluralism is the avant-garde term in vogue today suggesting a "post- modern" view of mathematics that would have been frowned upon a century ago. The purpose of this unique Handbook is to unfold the transformation of the philosophy of mathematics from its origins in the history of mathematical practice. In order to do so, chapters will describe different mathematical practices in different time periods of history and contrast it with the development of philosophy. The contributions will include scholars from other disciplines who have contributed to the richness of perspectives that abound the study of philosophy today. The Handbook aims to synthesize what is known, and what has unfolded but also offer directions in which the study of philosophy of mathematics as evident in increasingly diverse mathematical practices is headed. Different sections of the Handbook will offer insights into the origins, debates, methodologies and newer perspectives that characterize the discipline today. This Handbook is curated by an editorial advisory board consisting of leading scholars from the disciplines of mathematics, history and philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute of Technology (USA) Jody Azzouni, Tufts University (USA) Otávio Bueno, University of Miami (USA) William Byers, Concordia University (Canada) Carlo Cellucci, Sapienza University of Rome (Italy) Chandler Davis, University of Toronto (Canada) Paul Ernest, University of Exeter (UK) David Tall, University of Warwick (UK) Michele Friend, George Washington University (USA) Reuben Hersh, University of New Mexico (USA) - (1927-2020) Kyeong-Hwa Lee, Seoul National University (South Korea) Yuri Manin, Max Planck Institute for Mathematics (Germany) Athanase Papadopoulos, University of Strasbourg (France) Ulf Persson, Chalmers University of Technology (Sweden) John Stillwell, University of San Francisco (USA).
Mathematics.
History.
Mathematics—Philosophy.
Mathematical logic.
History of Mathematical Sciences.
Philosophy of Mathematics.
Mathematical Logic and Foundations.