Formalism and Beyond

On the Nature of Mathematical Discourse

Godehard Link

• Publisher: De Gruyter
• Year: 2014
• eBook ISBN: 9781614519966
• Edition: 1
• Topic: Philosophy
• Subtopic: History & Philosophy of Mathematics

The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.

Name Index

Ackermann, Wilhelm, 1, 2, 3–4, 5–6, 7, 8

Aczel, Peter, 1, 2

Adams, William W., 1

Adeleke, Samson A., 1, 2

Angelelli, Ignacio, 1

Apostoli, Peter, 1, 2

Appel, Kenneth, 1

Arai, Toshiyasu, 1, 2

Arana, Andrew, 1–2, 3, 4, 5

Aristotle, 1, 2–3

Atiyah, Michael F., 1

Austin, John, 1, 2, 3

Avigad, Jeremy, 1, 2, 3, 4, 5, 6

Bacon, Francis, 1

Badesa, Calixto, 1

Baer, Reinhold, 1, 2

Bakker, Arthur, 1, 2

Balaguer, Mark, 1, 2

Balbes, Raymond, 1

Banaschewski, Bernhard, 1, 2–3, 4

Bar-Hillel, Yehishua, 1

Barhoumi, Sami, 1, 2

Barr, Michael, 1

Barwise, Jon, 1, 2

Baumann, J. Julius, 1

Beaney, Michael, 1

Becker, James C., 1

Beckmann, Arnold, 1

Bellotti, Luca, 1

Benacerraf, Paul, 1, 2, 3

Berger, Ulrich, 1

Bernays, Paul, 1, 2, 3, 4, 5–6, 7–8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

Bezem, Marc, 1, 2, 3

Biermann, Otto, 1

Birkhoff, Garett, 1

Bishop, Errett, 1, 2, 3, 4, 5, 6

Black, Max, 1

Blanchette, Patricia, 1, 2, 3

Blau, Ulrich, 1

Blumenthal, Otto, 1

Boltzmann, Ludwig, 1

Bolzano, Bernard, 1

Boole, George, 1, 2, 3, 4, 5

Boolos, George, 1, 2, 3

Booth, David, 1

Borchert, Donald M., 1

Borges, Jorge Luis, 1

Bourbaki, Nicholas, 1, 2

Bradley, Francis, 1, 2, 3

Breger, Herbert, 1–2, 3

Bridges, Douglas S., 1, 2, 3

Brouwer, Luitzen E. J., 1, 2, 3, 4, 5

Brown, Bryson, 1

Brown, H. C., 1

Buchholz, Wilfried, 1

Buekenhout, Francis, 1

Bueno, Otávio, 1

Burge, Tyler, 1

Burgess, John, 1, 2, 3

Buss, Sam, 1

Butts, Robert E., 1

Buzzard, Kevin, 1

Byers, William, 1

Cantini, Andrea, 1

Cantor, Georg, 1–2, 3–4, 5–6, 7, 8, 9, 10, 11, 12, 13, 14–15, 16, 17, 18, 19–20, 21, 22, 23, 24, 25, 26

Carnap, Rudolf, 1, 2, 3, 4

Cass, Daniel, 1

Cassirer, Ernst, 1, 2, 3, 4

Cauchy, Augustin-Louis, 1

Cederquist, Jan, 1, 2

Cegielski, Patrick, 1

Chebyshev, Pafnuty, 1

Chevalley, Claude, 1, 2

Chomsky, Noam, 1

Church, Alonzo, 1, 2, 3

Cogdell, James W., 1

Cohen, Hermann, 1, 2, 3

Coolidge, Julian L., 1

Cooper, Robin, 1

Coquand, Thierry, 1, 2, 3, 4, 5, 6, 7, 8, 9

Coste, Michel, 1, 2, 3, 4, 5

Costreie, Sorin, 1

Coxeter, Harold S. M., 1, 2, 3, 4

Crosilla, Laura, 1, 2, 3, 4, 5

Crowell, Richard H., 1

Currie, Gregory, 1, 2, 3, 4, 5

D’Aquino, Paola, 1, 2

Darrigol, Olivier, 1

de la Vallée-Poussin, Charles, 1

De Morgan, Augustus, 1

Dean, Walter, 1

Dedekind, Richard, 1, 2, 3, 4, 5, 6, 7, 8, 9–10, 11, 12, 13

Denton, William W., 1

Derbyshire, John, 1

Desmond, Will, 1

Detlefsen, Michael, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10–11, 12, 13, 14, 15, 16

Dieudonné, Jean, 1, 2

Dirac, Paul, 1

Dirichlet, Johann, 1, 2

Dowling, Linnaeus W., 1

Drake, Frank R., 1

Dreben, Burton, 1

Driesch, Hans, 1

Ducos, Lionel, 1, 2, 3

Duhem, Pierre, 1, 2

Dummett, Michael, 1, 2, 3, 4

Dwinger, Philip, 1

Easwaran, Kenneth, 1

Ebbinghaus, Heinz-Dieter, 1, 2, 3

Ebert, Philip, 1, 2, 3

Edwards, Harold M., 1, 2, 3, 4

Edwards, Paul, 1

Eisenbud, David, 1–2

Enderton, Herbert B., 1

Español, Luis, 1

Euclid, 1, 2, 3, 4, 5, 6, 7

Euler, Leonhard, 1, 2, 3, 4, 5, 6

Evans, E. Graham, 1–2

Ewald, William B., 1, 2, 3

Feferman, Solomon, 1, 2, 3, 4, 5–6

Feynman, Richard P., 1

Field, Hartry, 1, 2, 3

Finsler, Paul, 1–2, 3

Fitting, Melvin, 1

Fontana, Marco, 1, 2, 3, 4

Forster, Otto, 1

Forster, Thomas, 1

Foucault, Michel, 1

Fox, Ralph H., 1

Fraenkel, Abraham, 1, 2, 3, 4, 5, 6

Frege, Gottlob, 1, 2–3, 4–5, 6, 7, 8–9, 10–11, 12, 13–14, 15–16, 17, 18, 19, 20–21, 22–23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38

Friederich, Simon, 1, 2

Friedman, Harvey, 1, 2, 3, 4–5

Friedman, Michael, 1

Furstenberg, Harry, 1, 2, 3–4, 5

Gajda, Adam, 1

Gambino, Nicola, 1

Gandon, Sébastien, 1

Gauss, Carl Friedrich, 1–2, 3, 4, 5

Geach, Peter, 1

Gentzen, Gerhard, 1–2, 3, 4

Gergonne, Joseph D., 1

Gerla, Giangiacomo, 1

Gillies, Donald, 1–2, 3

Glaz, Sarah, 1

Gödel, Kurt, 1, 2, 3, 4, 5, 6–7, 8, 9, 10, 11–12, 13, 14, 15, 16, 17, 18, 19, 20–21, 22, 23, 24

Goldfarb, Warren, 1

Gottlieb, Daniel H., 1

Gottlob, Georg, 1

Gowers, Timothy, 1

Granville, Andrew, 1

Grassmann, Hermann, 1, 2, 3

Grattan-Guinness, Ivor, 1, 2, 3, 4, 5, 6, 7

Griffin, Nicholas, 1

Griffor, Edward R., 1

Grothendieck, Alexander, 1, 2, 3

Gurwitsch, Aaron, 1

Guyer, Paul, 1

Hadamard, Jacques, 1

Haddock, Guillermo E. R., 1

Hahn, Lewis E., 1

Hájek, Petr, 1, 2, 3, 4

Haken, Wolfgang, 1

Halbach, Volker, 1, 2, 3, 4

Hale, Bob, 1

Hallett, Michael, 1, 2, 3

Hamilton, William, 1, 2

Hankel, Hermann, 1–2, 3, 4–5, 6, 7, 8

Hardy, Godfrey H., 1

Har...

Table of contents

• Logos
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Duality, Epistemic Efficiency & Consistency
• Frege on Quantities and Real Numbers in Consideration of the Theories of Cantor, Russell and Others
• Frege on Formality and the 1906 Independence-Test
• Formal Discourse in Russell: From Metaphysics to Philosophical Logic
• On Live and Dead Signs in Mathematics
• Generalization and the Impossible: Issues in the search for generalized mathematics around 1900
• Assumptions of Infinity
• The Interpretation of Classes in Axiomatic Set Theory
• Purity in Arithmetic: some Formal and Informal Issues
• Domain Extensions and Higher-Order Syntactical Interpretations
• Finite Methods in Mathematical Practice
• List of Contributors
• Name Index