Juliet Floyd is Professor of Philosophy at Boston University, researching the interplay between logic, mathematics, and philosophy in late nineteenth and early twentieth centuries.  She has written extensively on Wittgenstein, Gödel and Turing and also published articles on Kant, the history of American philosophy, aesthetics, and eighteenth century philosophy. She taught at the City College of New York and the Graduate Center, City University of New York (1990-1996) and has been a Visiting Professor of Philosophy at the University of Vienna (2007) the University of Paris I Panthéon-Sorbonne (2009), the University of Bordeaux 3, Université Michel de Montaigne (2012) and a Fellow of the Dibner Institute at MIT (1998-9) and the Lichtenberg-Kolleg, Georg August University, Göttingen (2009-10). She has received grants from the American Academy in Berlin, the American Council of Learned Societies, the Fulbright Association, the American Philosophical Society, the National Endowment for the Humanities, the C.U.N.Y. Research Foundation, and Wellesley College. Professor Floyd is currently Associate Senior Editor in Twentieth Century Philosophy at the Stanford Encyclopedia of Philosophy.  She has co-edited (with S. Shieh) Future Pasts: The Analytic Tradition in Twentieth Century Philosophy (Oxford, 2001), (with J.E. Katz) Philosophy of Emerging Media: Understanding, Appreciation, Application (Oxford, 2016) and (with A. Bokulich) Philosophical Explorations of the Legacy of Alan Turing; Turing 100 (Springer, forthcoming, Boston Studies in the Philosophy and History of Science).  See http://www.bu.edu/philo/people/faculty/full-time/juliet-floyd/.Felix Mühlhölzer is Professor of Philosophy at the Georg-August-University of Göttingen since 1997. Before, he taught at the University of Munich from 1989 to 1993 and was Professor of Philosophy of Science and Logic at Dresden University of Technology until 1997. He has published on topics in philosophy of science, especially on space and time, and in philosophy of language. Since 2001 he has written primarily on later Wittgenstein's philosophy of mathematics. His recent works include Braucht die Mathematik eine Grundlegung? Ein Kommentar des Teils III von Wittgensteins "Bemerkungen über die Grundlagen der Mathematik" (2010) and Wissenschaft (2011).He is currently working on a book titled Wittgenstein über Zahlen und Mengen. Mit einem Kommentar des Teils II von Wittgensteins 'Bemerkungen über die Philosophie der Mathematik.

“The book goes far beyond their edition, providing access to important topics in the philosophy of mathematics seen from the special Wittgensteinian perspective.” (Volker Peckhaus, zbMATH 1529.01002, 2024)“There are some books that one learns from them what one expected or hoped to learn; but then there are books that go well beyond the brief laid out in their titles, and the book … is one such. Called Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics, the book is actually an extensive and deeply informed examination of Wittgenstein’s philosophy of mathematics in all of its aspects … .” (Juliette Kennedy, Philosophia Mathematica, Vol. 30 (2), 2022)“The book is very rich in information for the Wittgenstein scholar as well as for students of Wittgenstein's commentaries on the development of mathematics.” (Michael Otte, Mathematical Reviews, May, 2022)

• Part 1. Analysis of the Annotations.- 1. The Context of Wittgenstein’s Annotations.- 2. Wittgenstein’s Non-Extensionalist Point of View.- 3. Irrational Numbers: The Annotations on pp. 2-9, with Commentary.- 4. The Law of the Excluded Middle: A Digression.- 5. The Continuum of Real Numbers: The Annotations on pp. 10-30, with Commentary.- 6. Functions and Limits: The Annotations on pp. 40-47 and 117-121, With Commentary.- Part 2. Applications.- 7. Wittgenstein on Cantor’s Diagonal Method (Felix Mühlhölzer).- 8. Mühlhölzer vs. Putnam on Wittgenstein and the Real Numbers (Juliet Floyd).- Part 3. Images.- 9. Images of Wittgenstein’s Annotations to Hardy’s A Course of Pure Mathematics.

Juliet Floyd is Professor of Philosophy at Boston University, researching the interplay between logic, mathematics, and philosophy in late nineteenth and early twentieth centuries.  She has written extensively on Wittgenstein, Gödel and Turing and also published articles on Kant, the history of American philosophy, aesthetics, and eighteenth century philosophy. She taught at the City College of New York and the Graduate Center, City University of New York (1990-1996) and has been a Visiting Professor of Philosophy at the University of Vienna (2007) the University of Paris I Panthéon-Sorbonne (2009), the University of Bordeaux 3, Université Michel de Montaigne (2012) and a Fellow of the Dibner Institute at MIT (1998-9) and the Lichtenberg-Kolleg, Georg August University, Göttingen (2009-10). She has received grants from the American Academy in Berlin, the American Council of Learned Societies, the Fulbright Association, the American Philosophical Society, the National Endowment for the Humanities, the C.U.N.Y. Research Foundation, and Wellesley College. Professor Floyd is currently Associate Senior Editor in Twentieth Century Philosophy at the Stanford Encyclopedia of Philosophy.  She has co-edited (with S. Shieh) Future Pasts: The Analytic Tradition in Twentieth Century Philosophy (Oxford, 2001), (with J.E. Katz) Philosophy of Emerging Media: Understanding, Appreciation, Application (Oxford, 2016) and (with A. Bokulich) Philosophical Explorations of the Legacy of Alan Turing; Turing 100 (Springer, forthcoming, Boston Studies in the Philosophy and History of Science).  See http://www.bu.edu/philo/people/faculty/full-time/juliet-floyd/.Felix Mühlhölzer is Professor of Philosophy at the Georg-August-University of Göttingen since 1997. Before, he taught at the University of Munich from 1989 to 1993 and was Professor of Philosophy of Science and Logic at Dresden University of Technology until 1997. He has published on topics in philosophy of science, especially on space and time, and in philosophy of language. Since 2001 he has written primarily on later Wittgenstein's philosophy of mathematics. His recent works include Braucht die Mathematik eine Grundlegung? Ein Kommentar des Teils III von Wittgensteins "Bemerkungen über die Grundlagen der Mathematik" (2010) and Wissenschaft (2011).He is currently working on a book titled Wittgenstein über Zahlen und Mengen. Mit einem Kommentar des Teils II von Wittgensteins 'Bemerkungen über die Philosophie der Mathematik.

“The book goes far beyond their edition, providing access to important topics in the philosophy of mathematics seen from the special Wittgensteinian perspective.” (Volker Peckhaus, zbMATH 1529.01002, 2024)“There are some books that one learns from them what one expected or hoped to learn; but then there are books that go well beyond the brief laid out in their titles, and the book … is one such. Called Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics, the book is actually an extensive and deeply informed examination of Wittgenstein’s philosophy of mathematics in all of its aspects … .” (Juliette Kennedy, Philosophia Mathematica, Vol. 30 (2), 2022)“The book is very rich in information for the Wittgenstein scholar as well as for students of Wittgenstein's commentaries on the development of mathematics.” (Michael Otte, Mathematical Reviews, May, 2022)

• Part 1. Analysis of the Annotations.- 1. The Context of Wittgenstein’s Annotations.- 2. Wittgenstein’s Non-Extensionalist Point of View.- 3. Irrational Numbers: The Annotations on pp. 2-9, with Commentary.- 4. The Law of the Excluded Middle: A Digression.- 5. The Continuum of Real Numbers: The Annotations on pp. 10-30, with Commentary.- 6. Functions and Limits: The Annotations on pp. 40-47 and 117-121, With Commentary.- Part 2. Applications.- 7. Wittgenstein on Cantor’s Diagonal Method (Felix Mühlhölzer).- 8. Mühlhölzer vs. Putnam on Wittgenstein and the Real Numbers (Juliet Floyd).- Part 3. Images.- 9. Images of Wittgenstein’s Annotations to Hardy’s A Course of Pure Mathematics.

Juliet Floyd is Professor of Philosophy at Boston University, researching the interplay between logic, mathematics, and philosophy in late nineteenth and early twentieth centuries.  She has written extensively on Wittgenstein, Gödel and Turing and also published articles on Kant, the history of American philosophy, aesthetics, and eighteenth century philosophy. She taught at the City College of New York and the Graduate Center, City University of New York (1990-1996) and has been a Visiting Professor of Philosophy at the University of Vienna (2007) the University of Paris I Panthéon-Sorbonne (2009), the University of Bordeaux 3, Université Michel de Montaigne (2012) and a Fellow of the Dibner Institute at MIT (1998-9) and the Lichtenberg-Kolleg, Georg August University, Göttingen (2009-10). She has received grants from the American Academy in Berlin, the American Council of Learned Societies, the Fulbright Association, the American Philosophical Society, the National Endowment for the Humanities, the C.U.N.Y. Research Foundation, and Wellesley College. Professor Floyd is currently Associate Senior Editor in Twentieth Century Philosophy at the Stanford Encyclopedia of Philosophy.  She has co-edited (with S. Shieh) Future Pasts: The Analytic Tradition in Twentieth Century Philosophy (Oxford, 2001), (with J.E. Katz) Philosophy of Emerging Media: Understanding, Appreciation, Application (Oxford, 2016) and (with A. Bokulich) Philosophical Explorations of the Legacy of Alan Turing; Turing 100 (Springer, forthcoming, Boston Studies in the Philosophy and History of Science).  See http://www.bu.edu/philo/people/faculty/full-time/juliet-floyd/.Felix Mühlhölzer is Professor of Philosophy at the Georg-August-University of Göttingen since 1997. Before, he taught at the University of Munich from 1989 to 1993 and was Professor of Philosophy of Science and Logic at Dresden University of Technology until 1997. He has published on topics in philosophy of science, especially on space and time, and in philosophy of language. Since 2001 he has written primarily on later Wittgenstein's philosophy of mathematics. His recent works include Braucht die Mathematik eine Grundlegung? Ein Kommentar des Teils III von Wittgensteins "Bemerkungen über die Grundlagen der Mathematik" (2010) and Wissenschaft (2011).He is currently working on a book titled Wittgenstein über Zahlen und Mengen. Mit einem Kommentar des Teils II von Wittgensteins 'Bemerkungen über die Philosophie der Mathematik.

“The book goes far beyond their edition, providing access to important topics in the philosophy of mathematics seen from the special Wittgensteinian perspective.” (Volker Peckhaus, zbMATH 1529.01002, 2024)“There are some books that one learns from them what one expected or hoped to learn; but then there are books that go well beyond the brief laid out in their titles, and the book … is one such. Called Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics, the book is actually an extensive and deeply informed examination of Wittgenstein’s philosophy of mathematics in all of its aspects … .” (Juliette Kennedy, Philosophia Mathematica, Vol. 30 (2), 2022)“The book is very rich in information for the Wittgenstein scholar as well as for students of Wittgenstein's commentaries on the development of mathematics.” (Michael Otte, Mathematical Reviews, May, 2022)

• Part 1. Analysis of the Annotations.- 1. The Context of Wittgenstein’s Annotations.- 2. Wittgenstein’s Non-Extensionalist Point of View.- 3. Irrational Numbers: The Annotations on pp. 2-9, with Commentary.- 4. The Law of the Excluded Middle: A Digression.- 5. The Continuum of Real Numbers: The Annotations on pp. 10-30, with Commentary.- 6. Functions and Limits: The Annotations on pp. 40-47 and 117-121, With Commentary.- Part 2. Applications.- 7. Wittgenstein on Cantor’s Diagonal Method (Felix Mühlhölzer).- 8. Mühlhölzer vs. Putnam on Wittgenstein and the Real Numbers (Juliet Floyd).- Part 3. Images.- 9. Images of Wittgenstein’s Annotations to Hardy’s A Course of Pure Mathematics.