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Index des noms

Aczel, Peter, 227

Agnesi, Maria Gaetana, 70

Allwein, Gerard, 11, 335

Anderson, John R., 103

Andler, Daniel, 101, 104

Apollonius de Perge, 285-286

Aristarque de Samos, 135, 163

Auchter, Heinrich, 30

Austin, John L., 238, 240, 261

Avigad, Jeremy, 163, 221, 289, 295, 296, 302, 303

Bäuerle, Rainer, 232

Babin, Malte-Ludolf, 29

Bar-Hillel, Yehoshua, 178

Barberousse, Anouk, 145

Barker-Plummer, Dave, 213, 260

Baron, Margaret E., 182

Barwise, Jon, 11, 18, 175-179, 181, 199, 209, 212-223, 225-227, 232-247, 249-253, 255-258, 260, 266-268, 277, 282, 289, 300, 302, 304, 335

Benis-Sinaceur, Hourya, 14, 58

Bernoulli, Jacques, 35, 44, 326

Bernoulli, Jean, 17, 25, 26, 29-31, 35, 36, 40, 42-51, 53-55, 59-72, 75, 79-86, 88-90, 149, 167, 304, 305, 326, 327

Bertin, Jacques, 136, 137

Blanton, John D., 78, 82

Block, Ned, 147

Borgato, Maria Teresa, 70

Bos, Hendrik Jan Maarten, 31-34, 45, 46

Bourbaki, Nicolas, 15-17

Brandom, Robert B., 147, 275, 304

Brechenmacher, Frédéric, 264

Brooks, Rodney, 127

Brown, James Robert, 12

Bullynck, Maarten, 182

Burkhard [Mencke], Johann, 70

Cajori, Florian, 44

Calinger, Ronald S., 182

Carnap, Rudolf, 178, 229-232

Carter, Jessica, 131-133, 163

Cartier, Pierre, 306

Châtelet, Émilie du, 77

Chalmers, David, 126

Chauviré, Christiane, 255

Chemla, Karine, 12, 26, 82

Chernoff, Herman, 139

Chevalley, Claude, 15

Chorlay, Renaud, 82

Clark, Andy, 126

Cohn-Vossen, Stephan, 16

Collins, John, 39
Colyvan, Mark, 12, 27

Cooper, Jacob Lionel Bakst, 80, 81

Cooper, Robin, 227

Corcoran, John, 177, 178

Corry, Leo, 15

Costabel, Pierre, 38

Couturat, Louis, 26, 27, 58, 59

Cresswell, Max J., 232

Crevier, Daniel, 106, 107

Crowther-Heyck, Hunter, 106

Dahan-Dalmedico, Amy, 15, 17

Dale, Nell, 118

Danner, Norman, 181, 194, 196, 199, 206

Davis, Harold T., 29

De Morgan, Augustus, 149

De Risi, Vincenzo, 182

De Toffoli, Silvia, 28, 132, 133

Dean, Edward, 163, 221, 289, 295, 296, 302, 303

Delahaye, Jean-Paul, 142

Descartes, René, 12, 18, 31, 34, 35, 39, 41

Deschamps, Claude, 82

Devlin, Keith, 226, 227

Dowty, David R., 232

Dugowson, Stéphane, 30, 69

Dummett, Michael, 228

Dutilh Novaes, Catarina, 207

Eckes, Christophe, 28

Edwards, A. W. F., 182

Etchemendy, John, 11, 18, 175-179, 181, 199, 209, 212-223, 225-227, 229, 233-238, 240-247, 249-252, 255, 257, 258, 260, 268, 277, 282, 289, 300, 304

Euclide, 12, 18, 134, 158-160, 163, 207, 221, 222, 277, 284-304

Euler, Leonhard, 70-72, 78, 80, 82-84, 166, 167, 181-188, 191, 192, 194, 195, 277-284, 289, 320, 331

Fagnano, Giulio Carlo de' Toschi di, 71, 72, 339

Feigenbaum, Lenore, 30, 43, 47, 59, 65, 70, 81

Fermat, Pierre, 34

Ferraro, Giovanni, 30

Ferreirós, José, 306

Fleckenstein, J.O., 30

Flury, Bernhard, 139, 140

Fodor, Jerry A., 104

Fox, Chris, 232

Frege, Gottlob, 13, 148, 160, 162, 228, 230, 232

Friedlein, Gottfried, 288

Friendly, Michael, 136

Ganis, Giorgio, 103

Gardner, Martin, 142, 143

Gastaldi, Juan Luis, 98

Gawron, Jean Mark, 227

Gelernter, Herbert, 108

Gerhardt, Carl Immanuel, 29, 48

Giaquinto, Marcus, 11, 14

Giardino, Valeria, 11, 28, 189

Gibson, James J., 127, 239

Ginzburg, Jonathan, 227, 228, 238, 239

Goodman, Nelson, 104, 141, 155, 156, 201, 212

Granger, Gilles-Gaston, 27

Grattan-Guinness, Ivor, 14
Gray, Jeremy, 14, 16, 28

Greenberg, Gabriel, 189

Greenberg, Mark, 147

Guedj, Denis, 15, 16

Guicciardini, Niccolò, 78

Guisnée, Nicolas, 62

Høyrup, Jens, 12

Haffner, Emmylou, 14

Hamami, Yacin, 11

Hammer, Eric M., 181, 185, 189, 191, 194, 196, 199, 200, 206, 220, 238, 253, 256, 278, 280, 281

Harman, Gilbert, 147

Hatcher, Allen, 28

Haugeland, John, 101, 102, 104, 127, 160

Heath, Thomas L., 135, 286

Heiberg, J. L., 135, 286–288, 293–295, 297, 300

Hess, Heinz-Jürgen, 29

Hilbert, David, 16

Hintikka, Jaakko, 178, 230

Hoare, C. A. R., 113

Hookway, Christopher, 255

Howse, John, 196, 201, 202, 204, 205

Humphreys, Paul, 145, 161

Hutchins, Edwin, 19, 127

Huygens, Christian, 38, 44, 45, 76, 77

Imbert, Claude, 228

Imbert, Cyrille, 145

Israel, David J., 226, 227, 239

Jamnik, Mateja, 266

Johansen, Mikkel Willum, 16, 19, 27

Kant, Immanuel, 14

Katagiri, Yasuhiro, 227

Katz, Jerrold, 233

Kempson, Ruth, 233

King, Jeffrey C., 179

Kirsh, David, 119, 127

Knobloch, Eberhard, 29, 40, 88, 89

Knuth, Donald E., 115, 116, 118

Koppelman, Elaine, 26, 29, 73

Kosslyn, Stephen M., 103

Kratzer, Angelika, 227

Kripke, Saul, 230

Kulvicki, John, 136, 138, 141, 142, 145, 156, 162, 163, 167

Kuniaki, Mukai, 227

Kutzler, B., 113

L'Hôpital, Guillaume de, 35, 44, 50, 55, 66–70, 72, 80, 83, 89, 305

Lagrange, Joseph-Louis, 70–73, 85, 339

Lang, Serge, 132

Lange, Johann Christian, 182, 282

Lappin, Shalom, 232

Larkin, Jill H., 97, 117–127, 129, 132, 133, 139, 146, 150, 151, 154, 155, 162, 163, 259, 285

Larvor, Brendan, 27, 209

Lee, Meng, 114

Leibniz, Gottfried Wilhelm, 17, 18, 24–91, 165–167, 182, 211, 268, 282, 305, 307, 308, 340, 341

Lemon, Oliver, 181, 188, 189, 191, 281, 289

Leonardo, Anthony M., 120

Lewis, David, 104, 232, 233

Lichtenberger, F., 113

Liskov, Barbara, 113

Lubet, Jean-Pierre, 26, 73
Luengo, Isabel, 221, 253

MacFarlane, John Gordon, 206

MacKenzie, Donald, 105–107, 113

Maglio, Paul, 127

Mancosu, Paolo, 10, 11, 14, 16, 25, 26

Manders, Kenneth, 12, 19, 85, 156, 157, 163, 176, 211, 221–223, 285, 287, 291–294, 296, 299, 302–304, 306

Markowsky, George, 98

Maronne, Sébastien, 35

Martinez, Maricarmen, 177–179, 266

Maurice, Jean Frédéric Théodore, 70

McCarthy, John, 108

McCorduck, Pamela, 105, 106, 108

Mercator, Nicolaus, 61, 62, 86

Merker, Joël, 17

Metzler, Jacqueline, 103, 109

Miller, Nathaniel, 158–160, 199, 208, 221, 285, 289, 304

Minsky, Marvin, 108

Mirowski, Philip, 106

Misfeldt, Morten, 16

Mitchell, W. J. Thomas, 212

Moktefi, Amirouche, 181, 185

Molina, Fernando, 196, 201, 202, 204, 205

Montague, Richard, 230, 232, 233

Morris, Charles W., 229

Mueller, Ian, 300

Mumford, David, 16

Mumma, John, 158–160, 163, 181, 188, 189, 191, 211, 221, 222, 262, 277, 281, 287–289, 295, 296, 302, 303

Neth, Hansjörg, 12, 148

Netz, Reviel, 134–136, 163, 285, 286, 302

Newell, Allen, 102, 105, 107, 127

Newton, Isaac, 39, 53, 54, 61, 76–79, 81, 86

Nieuwentijt, Bernard, 66

Oldenburg, Henry, 39

Pólya, George, 107

Pallavicini, Josephine, 16

Palsky, Gilles, 136

Panza, Marco, 30, 43, 70, 73, 76, 77, 86, 285, 292, 295, 297

Parmentier, Marc, 29, 52, 75

Parnas, David L., 113

Partee, Barbara H., 230, 231

Peirce, Charles Sanders, 148, 181, 187–189, 196, 212, 255, 256, 258, 346

Pepe, Luigi, 70

Perry, John, 176, 225–227, 232, 233, 238–240

Peters, Stanley, 227, 232

Petkovšek, Marko, 17

Pietarinen, Ahti-Veikko, 187

Plotkin, Gordon, 227

Poesio, Massimo, 227

Pomerantz, James R., 103

Priestley, Mark, 113, 117

Pringsheim, A., 30

Proclus, 288

Putnam, Hilary, 126

Pylyshyn, Zenon W., 103, 105, 125

Qin, Yulin, 120

Rabouin, David, 19, 82, 264, 291, 302, 303

Rashed, Roshdi, 286

Raussen, Martin, 133

Recanati, François, 231
Reyneau, Charles-René, 38, 70

Riedwyl, Hans, 139, 140

Risse, Wilhelm, 182

Robic, Marie-Claire, 136

Ross, Bertram, 29

Ruskey, Frank, 187

Sag, Ivan A., 227

Saito, Ken, 288, 293–295, 297, 298

Schafheitlin, Paul, 35

Schlimm, Dirk, 12, 148–149, 164

Schroeder-Heister, Peter, 179, 267

Scotto di Luzio, Patrick, 196, 203, 204

Seligman, Jerry, 253, 260, 302

Sellars, Wilfrid, 147

Sequoiah-Grayson, Sebastian, 178, 179

Serfati, Michel, 27, 40, 44, 75, 84, 85, 88, 89

Series, Caroline, 16

Serre, Jean-Pierre, 133

Serres, Michel, 27

Shannon, Claude E., 98, 156, 157

Shaw, J. Clifford, 107

Shepard, Roger N., 103, 109

Sher, Gila Y., 229

Shimojima, Atsushi, 11, 19, 176, 226, 253, 257–268, 306

Shin, Sun-Joo, 11, 18, 175, 181, 182, 185, 187–189, 191–209, 212, 221, 225, 237, 251–253, 257–260, 277, 278, 280–282, 289

Short, T. L., 255

Sidoli, Nathan, 294

Simon, Herbert A., 17, 18, 97, 101–129, 131–134, 138, 139, 141, 145, 146, 148, 150, 151, 153–156, 161–164, 176, 208, 259, 285, 308, 351, 352

Skau, Christian, 133

Soames, Scott, 179, 228

Speaks, Jeff, 179, 228

Speiser, Andreas, 182

Stalnaker, Robert C., 237

Stapleton, Gem, 266

Stein, Myron L., 142–144

Stenning, Keith, 185, 256, 268

Stepanov, Alexander, 114

Stjernfelt, Frederik, 256, 257, 259

Stojanovic, Isidora, 227

Sturm, Johann Christoph, 182

Sundholm, Göran, 179

Suppes, Patrick, 213

Szczeciniarz, Jean-Jacques, 17

Tabachneck-Schijf, Hermina J. M., 120

Takahashi, Nobuo, 106

Tappenden, Jamie, 89

Tarski, Alfred, 229, 230, 354

Taylor, Brook, 30, 70, 76, 79–81

Taylor, John, 196, 201, 202, 204, 205

Tefera, Akalu, 17

Thompson, William L., 103

Tschirnhaus, Ehrenfried Walther von, 44

Tucker, John V., 113

Tufte, Edward R., 136

Tukey, John W., 136, 142

Tutiya, Syun, 227

Ulam, Stanislaw M., 142–144

Van Benthem, Johan, 177–179, 266

Varignon, Pierre, 70, 71, 83, 85, 86, 304, 305

Venn, John, 181, 182, 185, 186, 211
Vera, Alonso H., 127

Volkert, Klaus Thomas, 14

Vorms, Marion, 145–147, 156, 161, 162

Wagner, Pierre, 101

Wagner, Roi, 306

Walker, Henry Mackay, 118

Wall, Robert E., 232

Wallis, John, 62, 69, 78, 86

Waring, Edward, 79, 80

Warusfel, André, 82

Waszek, David, 277

Weil, André, 15

Wells, Mark B., 142–144

Weston, Mark, 187

Wilf, Herbert S., 17

Wilson, Mark, 139, 289, 290, 306

Wilson, Robert A., 126

Wittgenstein, Ludwig, 211, 230

Woodhouse, Robert, 80

Wright, David, 16

Yeung, Raymond W., 98

Zeilberger, Doron, 17

Zilles, Stephen, 113

Zimmermann, Thomas Ede, 230
LES REPRÉSENTATIONS EN MATHÉMATIQUES

**Résumé** : Pour résoudre un problème de mathématiques ou comprendre une démonstration, une figure bien choisie est parfois d'un grand secours. Ce fait souvent remarqué peut être vu comme un cas particulier d'un phénomène plus général. Utiliser une figure plutôt que des phrases, reformuler un problème sous la forme d'une équation, employer telles notations plutôt que telles autres : dans tous ces cas, en un sens, on ne fait que représenter sous une nouvelle forme ce qu'on sait déjà, et pourtant, cela peut permettre d'avancer. Comment est-ce possible ? Pour répondre à cette question, la première partie de cette thèse étudie ce qu'apporte un changement notationnel précis introduit par Leibniz à la fin du XVIIe siècle. La suite de ce travail analyse, et confronte à l'exemple précédent, plusieurs manières de penser les différences représentationnelles proposées dans la littérature philosophique récente. Herbert Simon, étudié dans la deuxième partie, s'appuie sur le modèle informatique des structures de données : deux représentations peuvent être « informationnellement » équivalentes, mais « computationnellement » différentes. Les logiciens Barwise et Etchemendy, étudiés dans la troisième partie, cherchent à élargir les concepts de la logique mathématique (en particulier ceux de syntaxe et de sémantique) aux diagrammes et figures. Enfin, certains philosophes des mathématiques contemporains, comme Kenneth Manders, remettent en cause la notion même de représentation, en soutenant qu'elle n'est pas éclairante pour comprendre l'usage de figures, formules ou autres supports externes en mathématiques. C'est à ces critiques qu'est consacrée la quatrième et dernière partie.

REPRESENTATIONS IN MATHEMATICS

**Abstract:** When solving a mathematical problem or reading a proof, drawing a well-chosen diagram may be very helpful. This well-known fact can be seen as an instance of a more general phenomenon. Using a diagram rather than sentences, reformulating a problem as an equation, choosing a particular notation rather than others: in all these cases, in a sense, we are only representing in a new form what we already knew; and yet, it can help us make progress. How is this possible? To address this question, the first part of this thesis explores the benefits afforded by a specific notational change introduced by Leibniz in the late seventeenth-century. The rest of this work analyses, and puts to the test of the preceding case study, several ways of understanding representational differences which have been put forward in the recent philosophical literature. Herbert Simon, studied in the second part, relies on a comparison with the notion of data structures in computer science: two representations, he writes, can be “informationally” equivalent yet “computationnally” different. The logicians Barwise and Etchemendy, studied in the third part, try to broaden the concepts of mathematical logic (in particular those of syntax and semantics) to cover diagrams and figures. Finally, some contemporary philosophers of mathematics, for instance Ken Manders, argue that the notion of representation itself is not helpful to understand the use of diagrams, formulas or other external reasoning tools in mathematics. Such arguments are the focus of the fourth (and last) part.

**Mots-clés** : Philosophie des mathématiques – Histoire des mathématiques – Logique – Notation – Représentation – Figure – Diagramme – Signe

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