Agnar, S. 45n20
‘Algorithme of Algebra’ (Petty, W.) 22
algorithms, economic theorising and: Brouwer, L.E.J. 190; Church, Alonzo 187–189; Debreu, Gerard 189, 190; Gödel, Kurt 187–188; Herbrand, Jacques 188; Kaldor, Nicholas 190; Kleene, S.C. 187; Mirowski, Philip 191; Simon, Herbert 190–191; Turing, Alan Mathison 187, 188–189, 190, 191; Velulillai Vela, Kumaraswamy 189–191; von Neumann, John 187, 191; Zambelli, Stefano 189, 190
algorithms, mathematisation of economics and: Hilbert, David 183, 185, 186; Turing, Alan Mathison 183–187
Allais, Maurice 41
Amati, F. and Aspromourgos, T. 19
Anderson, G., Goff, B. and Tollison, R. 12
argumentation, grammar of 135–136
Aristotle 81, 82, 169; mathematics, philosophy of 205–206
Arithmetic, Foundations of (Frege, G.) 205
Arrow, Kenneth J. 80–81, 98, 102n10, 130; constructive and computable mathematics, emergence of 175, 176; neo-Walrasian formalisation of economics 135, 139, 142; philosophical reflections 197, 202
Arthur, Brian 70
Aspromourgos, T. 19, 20, 22, 44n13
Aubrey, John 44n9
Aumann, R.J. 162n2
Auxier, R.E. and Hahn, L.E. 193n18
axiomatic method, economics and 105–128; applied mathematical sciences, axiomatisation and 111–114; commodity and price, concepts of 115; Debreu, Gerard 105–106, 109–110; distillation of axiomatic method 107–108; economic analysis, assets of Debreu’s formalist philosophy of 123–128; economic domain, axioms in 117; economic theory, Debreu’s formalist mathematisation of 114–118; Élements d’economie politique pure (Walras, L.) 105, 114; Euclidean axiomatisation 105–106, 107–108, 112–114, 117, 123–124, 126; formalist philosophy of applied mathematics, indispensable steps in 113; General Equilibrium Theory, axiomatisation of 105–106; Hahn, F.H. 114, 123, 127; Hilbert, David 106, 107, 110, 111–112, 113, 123, 129n14; Hilbertian principle of uniformity of axiomatic method 111–112; ideology-free economics, Debreu’s ideal of 124; image of economic theory, body of knowledge and 117–118; logic, basic tool of any axiomatic system 108; logico-mathematical structures 112–113; mathematical form, semanticist conception of 119; mathematical model of Debreu, formalist or semanticist? 118–123; metamathematics, Hilbert’s notion of 110; pathology of the paradoxes in, formalist remedy for 109–110; Poincaré, Henri 109, 110, 120, 121, 122, 123; Poincaré malaise, concerns raised by 120–122; pure formalism, domain of 112; pure mathematics, mathematical content and 119–120; rigour, axiomatisation and 107–110; semantical domination, semanticism and 108–109, 110, 112, 113, 118, 119–120, 121–122, 123, 126, 129n13; Theory of Value (Debreu, G.) 105–106, 110, 114–115, 116, 117, 118, 119, 121, 123, 124, 128n2, 128n11; Walras, Leon 105, 114, 116, 117, 126; Weintraub, Steven H. 110, 117, 128n1–3
axiomatisation 3, 6, 87, 132, 136, 143n2, 161, 176, 193n20, 208; aesthetic code of 125; of arithmetic and of logic 108–109; axioms, assumptions and grammar of argumentation 136–140; of economic theory 2; formalist conception of 7; non-Euclidean geometries and 107–108; philosophical admiration for 105, 125–126
Backhouse, R.E. 12
Bacon, Francis 16, 17, 19–20, 21, 23, 44n6, 44n8, 44n12
Baker, K. 30
Barnard, T.C. 44n10
Bastiat, Frédéric 33
Bathurst, Ralph 44n8
Baumol, W.J. and Goldfeld, S.M. 37
Benacerraf, P. and Putnam, H. 212n1
Bennett, Kate 44n9
Berkeley, George 148
Bernays, P. 106, 111–112, 114–115, 128–129n12, 128n10
Bishop, Errett 42
bivalence, doctrine of 176, 177, 193n20, 206, 209
Blanché, R. 105
Boolos, G. 212n2
Bostock, D. 212n1
Bourbaki, Nicholas 175, 192n12; critique of Brouwerian intuitionism 172–174
Bowen, H.R. 12
Boylan, T.A. and O’Gorman, P.F. 45n30, 72n23, 104n24, 143n1, 162, 162n6, 164n25, 164n33
Bridel, P. 45n29
Bridel, P. and Momati, F. 71n14
Brouwer, L.E.J. 2–3, 41, 42, 162n3, 163n7; algorithms, economic theorising and 190; Brouwer-Hilbert controversy 167; constructive and computable mathematics, emergence of 165, 182, 183, 187, 192–193n15, 192n5, 192n7, 192n11, 193n16; formalisation of economics and Debreu’s philosophy of mathematics 77, 86, 87, 93, 98, 101, 102n7, 102n9, 103n15, 103n20–21, 104n27; formalism and economic theorising, internal critique of 181; intuitionism of, Bourbaki’s critique of 172–174; intuitionistic mathematics of 168, 193n18, 193n23, 194n27; mathematics, philosophy of 204, 208–209, 212, 212n4; neo-Walrasian formalisation of economics 110, 116, 119–120, 121, 122, 130n25; philosophical reflections 196, 197, 198, 199; pragmatic intuitionism, economic theorising and 178, 180; strict intuitionism, Dummett’s philosophical reconstruction of 174–175, 177; strict intuitionism, neo-Walrasian programme and 170, 171
Brown, J.R. 212n1
Brown, Robert 11
Canard, Nicholas-Francois 37, 39
Cantor, Georg 169, 172, 185, 187, 192n6; formalisation of economics and Debreu’s philosophy of mathematics 74–75, 88, 89, 90, 92, 93, 98, 103n20; mathematics, philosophy of 205, 206–207, 209, 211, 212; neo-Walrasian formalisation of economics 110, 121, 122, 129n23
Carnap, Rudolf 5, 71n7, 72n17, 105, 111, 159, 164n26
Cartesian deductive method 26, 58
Cartesian tradition 107, 147, 168
Cassirer, Ernst 27
Church, Alonzo 3, 4, 42, 103n18, 129n14, 166, 183, 184; algorithms, economic theorising and 187–189; Church-Turing thesis 194n26–27, 197, 201; formalism and economic theorising, internal critique of 181; mathematics, philosophy of 208, 209; post Gödel-Church-Turing view of classical mathematics 3–4
classical mathematics 1, 2, 3–4, 82, 110, 165–167, 171–172, 175; constructive mathematics and, choice between 178–179; economic modelling and 199–200; excluded middle and 170; logical basis of 176; post Gödel-Church-Turing view of 3–4; pure calculus of 129n13; strict intuitionism and 168–169, 173–174; transfinite domain of 202–203
Cohen, B.I. 27
Colander, D., Follmer, H., Hans, A. et al. 13
Colyvan, M. 212n1
Commerce en Géneral (Cantillon, R.) 25
The Elements of Commerce (Tucker, J.) 25
Condorcet, Marie Jean, marquis de 30–32; social sciences, ambitions for 30–31
constructive and computable mathematics, emergence of 165–191; algorithmetic revolution in economic theorising? 187–191; Arrow, Kenneth J. 175, 176; Bourbaki critique of Brouwerian intuitionism 172–174; Brouwer, L.E.J. 165, 182, 183, 187, 192–193n15, 192n5, 192n7, 192n11, 193n16; constructive or intuitionistic mathematics 165–166; Debreu, Gerard 165, 166–167, 169, 170–172, 176, 180, 184–185, 186, 192n9; Dummett, Sir Michael 168, 178, 187, 193n18, 193n21, 194n27; economic content and computable mathematics, fit between 166–167; excluded middle, Aristotlan principle of 169–170, 192n8, 193n20, 194n27; extensionality 175, 176, 206; external and internal critiques of Hilbert programme 165–166; formalisation of economics, choice in 166; formalism and economic theorising, internal critique of 181; Frege, Gottlob 169, 175, 192n10, 193n18, 193n23; Gödel, Kurt 166, 176–177, 184, 186; Hahn, F.H. 165, 185; Hilbert, David 165, 166, 168, 171, 174, 175, 180, 192n11–12; Kaldor, Nicholas 165, 169, 172; Kant, Immanuel 168, 192n5, 193n23; mathematical discourse, infinite nature of 168; neo-Walrasian programme, poverty of prognosis for 166–167; Poincaré, Henri 168, 178, 185–186, 192–193n15, 192n5, 192n12; pragmatic intuitionism and economic theorising 178–181; Russell, Bertrand 167, 169, 175; strict intuitionism, classical mathematics and 168–169; strict intuitionism, Dummett’s philosophical reconstruction of 174–177; strict intuitionism, neo-Walrasian programme and 167–172; theorems of Gödel, Debreu’s philosophy of economic theorising and 182–183; Turing, algorithms and mathematisation of economics 183–187; Velulillai Vela, Kumaraswamy 185, 193–194n25, 193n19, 194n27–28; Weyl, Hermann 171, 172, 192n11
convention: custom and convention, relationship between 147; Keynes’ notion of, rationality in context of radical uncertainty and 5; Lewis’ six conditions for 153–154; in mathematical physics, indispensable role of 159; neo-classical rationality and 152–155; post-Keynesians on uncertainty and 155–158; promises, convention and 151; see also rationality, convention and economic decision-making
Convention (Lewis, D.) 5
Copeland, J. 183
Corry, L. 106, 111, 128n2, 129n16
Courcelle-Seneuil, Jean Gustave 33
Cournot, Augustin 37–39, 41, 45n26, 76; mathematician-economist in tradition in France 38–39
Courtault, J.M., Kabunov, Y., Bru et al. 50, 51
Crillo, R. 39
Cunningham Wood, J. and McLure, M. 39
D’Alembert, Jean le Rond 26
Dasgupta, P. 128n2
Davidson, Paul 157–158, 159, 161, 196
Dawson, J.W. Jr. 182
Debreu, Gerard 2, 4, 6–7, 12, 40–41; algorithms, economic theorising and 189, 190; axiomatic method in foundations of mathematics 105–106, 109–110; constructive and computable mathematics, emergence of 165, 166–167, 169, 170–172, 176, 180, 184–185, 186, 192n9; on contemporary period of economic formalism 76–78; equilibrium, proof of existence of, Poincaré malaise and 97–99, 102; equilibrium, Walras and proof of existence of 99–102; formalism and economic theorising, internal critique of 181; formalist mathematisation of economic theory 114–118; formalist philosophy of economic analysis, assets of 123–128; generality, achievement of 84–89; Kaldor on achievement and legacy of 140–143; mathematical economics, ‘scientific accidents’ theory of the growth of 40–41; mathematical model, formalist or semanticist? 118–123; mathematical model of a private ownership 4; mathematisation of economics, global view on 94–97; neo-Walrasian formalisation of economics 131–132, 133, 134, 135–136, 139; philosophical reflections 195–196, 198–199; philosophy of economic theorising, Gödel’s theorems and 182–183; philosophy of mathematics, formalisation of economics and 73–74, 75–76, 102n6–8, 104n30–31, 104n35; rigour, achievement of 79–84; simplicity and existence proofs 90–94
Della Moneta (Galiani, F.) 25
demarcation 102n4
Dennehy, C.A. 44n10
Descartes, Rene 16, 26, 62, 66, 107, 168
Destutt de Tracy, Antoine 33
disciplinary boundaries, Petty’s disregard for 16–17
Dobbs, B.J.T. and Jacob, M. 45n18
Dreyfus, Captain Alfred 48, 71n1
Dummett, Sir Michael 2, 88, 198; constructive and computable mathematics, emergence of 168, 178, 187, 193n18, 193n21, 194n27; intuitionism of 193n23–24; philosophical reconstruction of strict intuitionism 174–177
Düppe, T. and Weintraub, E.R. 45n27
Dupré, L. 45n14
Durlauf, S.N. and Blume, L.E. 45n28
Dynamic Stochastic General Equilibrium (DSGE) model 1
Eatwell, T., Milgate, M. and Newman, P. 45n29
Foundation of Economic Analysis (Sameulson, P.) 41
Economic Journal 12
economic theorising: algorithmetic revolution in? 187–191; dynamic process of general equilibrium theorising 135; Gödel’s theorems, Debreu’s philosophy of economic theorising and 182–183; image of economic theory, body of knowledge and 117–118; philosophy of, Gödel’s theorems and 182–183; pragmatic intuitionism and 178, 180; simplification of assumptions in 138–139; theoretical economics as science, Hahn’s opposition to 134; Walras’ contribution to history of 46
economics: axiomatisation of economic theory 2, 6–7; balance in curriculum, issue of seeking 13; Classical Situation in 15; commitment to use of mathematics and quantification in 20; curriculum structure and design 13; economic domain, axioms in 117; economic policy, debates about 133; economic theorising, developments in philosophy of mathematics and 11; engineer-economist tradition in France 36–37; formalisation of 1–2; formalism in, issue of 10, 35–43; general equilibrium formalisation of, radical questioning of 132; general equilibrium theory, neo-classical economics and 142; historical development of mathematisation of 15–16; ideology-free economics, Debreu’s ideal of 124; intellectual contextualisation for study of 13; laws of society, existence of 11; mathematical economics, Debreu’s ‘scientific accidents’ theory of the growth of 40–41; mathematical modelling in 2; mathematics and, relationship between 9–11; mathematics in, contentious nature of 10–11; mathematics in, intensification of use of 12; mathematisation of economics 2–3, 5–6, 11–14; methodological basis for Petty’s political arithmetic 22–23; methodology in, implications of Gödel’s theorems for 4; momentum for mathematisation of 14; neo-classical economics, scientific theory of value in 133; normative economics, distinction between positive economics and 133; numerical analysis, commitment to ‘spirit of’ 15–16; Petty’s economic writings 18–19; political arithmetic in 14–24; quantification of socio-economic phenomena 13; scientific investigations of actual economies 131–132; social laws of development, existence of 11; socio-economic domain, Pareto’s contribution 39; socio-economic phenomena, emergence of quantification of 14–24; socio-economic phenomena, Petty’s quantification and analysis of 20–21; specificity as social science of 11; theoretical economics, applied mathematical science and 2, 5–6, 11–14; theoretical economics, mathematical science and 2; Walras as central figure in evolution of 39–40
How Economics became a Mathematical Science (Weintraub, S.H.) 42
Edgeworth, Francis Ysidro 40
Einstein, Albert 72n21, 111, 164n31
Ekelund, R.B. and Hébert, R.F. 36, 45n28
Élements de Statiques (Poinsot, L.) 52, 71n6
Élements d’economie politique pure (Walras, L.) 4, 105, 114; equilibrium, proof of existence of 99–100, 101, 102n2; formalisation of economics, Debreu’s philosophy of mathematics and 73, 74–75, 77; Walras-Poincaré correspondence, reassessment of 40, 46, 48–51, 54–59, 68, 70
Eltis, W. 45n21
empirical objects, status and quantification of 21
empirical sciences as ‘mixt mathematical arts’ 22
Epstein, R.L. and Carnielli, W.A. 182
equilibrium: Debreu and proof of existence of 99–102; mathematical modelling of 2; near equilibrium state as causal factor in real world 140–141; Poincaré malaise and proof of existence of 97–99, 102; proof of existence of 99–100, 101, 102n2; Walras and proof of existence of 99–102
Esprit des Lois (Montesquieu) 24, 28
Euclid 6–7, 75, 85–86; applied mathematical sciences, axiomatisation and 112, 113, 114; axiomatic method in foundations of mathematics 105, 106, 123, 124, 126; Debreu’s formalist mathematisation of economic theory and 114, 117; Euclidean geometry 63, 75, 85, 107, 160, 204; neo-Walrasian formalisation of economics and 132, 136; ontological-epistemic indeterminacy and 159–160; rigour, axiomatisation and 107–108
excluded middle, Aristotlan principle of 93, 108, 128n6, 169–170, 192n8, 193n20, 194n27, 209–210, 211
explanation, Kaldor on Debreu’s conception of 141
extensionality: constructive and computable mathematics, emergence of 175, 176, 206; formalisation of economics, Debreu’s philosophy of mathematics and 80, 81, 82, 83, 98, 102n10, 104n30
Faccarello, G. 45n23
Fanning, B. 44n10
Fermat, Pierre de 16
Ferrone, V. 45n14
Fisher, Irving 40
Fleetwood, S. 45n30
Forget, E.L. 45n23
formalisation of economics, Debreu’s philosophy of mathematics and 73–102; Brouwer, L.E.J. 77, 86, 87, 93, 98, 101, 102n7, 102n9, 103n15, 103n20–21, 104n27; Cantor, Georg 74–75, 88, 89, 90, 92, 93, 98, 103n20; core theses 74–76; Cours d’Economie Politique (Pareto, V.) 77; Critique of Pure Reason (Kant, I.) 85; economic formalism, Debreu on contemporary period of 76–78; economy, Debreu’s perspective on an 96; Élements d’economie politique pure (Walras, L.) 73, 74–75, 77; equilibrium, Debreu, Walras and proof of existence of 99–102; equilibrium, Debreu’s proof of existence of 97–99; extensionality 80, 81, 82, 83, 98, 102n10, 104n30; fixed point theorem (Brouwer) 77, 79–80, 86, 93, 94, 97, 98, 100, 101, 102n7, 104n27; formalism, rejection of semantical philosophy of mathematics variables 86–87; The Foundations of Arithmetic (Frege, G.) 81; Frege, Gottlob 75, 79, 81, 86, 87, 90, 91–92, 103n12, 104n23; generality, Debreu and achievement of 84–89; Hilbert, David 77, 87, 89, 90, 103n18, 103n20–21, 104n35; Marginalist Revolution, Walras as key figure in 73; mathematisation of economics, Debreu’s global view of 94–97; Poincaré, Henri 79, 86, 87, 89, 90, 93, 102n1–2, 102n9, 104n33–4; Poincaré malaise, Debreu’s proof of existence of equilibrium and 97–99; Recherches sur les Principes Mathématiques de la Théorie des Richesse (Cournot, A.) 76–77; rigour, Debreu and achievement of 79–84; simplicity and existence proofs, Debreu and 90–94; Theory of Games and Economic Behaviour (von Neumann, J. and Morgenstern, O.) 77; Theory of Value (Debreu, G.) 73–74, 76, 77, 79, 89, 90, 93, 94–95, 96, 99–100, 101–102, 102n7, 104n30; truth-tables 83–84, 118; Walras, Leon 74–76, 76–77, 98, 99, 102n1–2; Weintraub, Steven H. 74, 76, 77, 78
formalism 1; applied mathematics in context of 75–76; Debreu on contemporary period of economic formalism 76–78; economic theorising and, internal critique of 181; economic theorising and internal critique of 181; formalist mathematisation of economic theory, Debreu and 114–118; formalist philosophy of applied mathematics, indispensable steps in 113; pathology of the paradoxes in axiomatic method, formalist remedy for 109–110; philosophy of economic analysis, assets of 123–128; pure formalism, domain of 112; pure mathematics and metamathematics in 129n13
Fox, A. 44n10
Frege, Gottlob 152, 196, 197; constructive and computable mathematics, emergence of 169, 175, 192n10, 193n18, 193n23; formalisation of economics and Debreu’s philosophy of mathematics 75, 79, 81, 86, 87, 90, 91–92, 103n12, 104n23; mathematics, philosophy of 204, 205, 206–207, 208, 209, 211; neo-Walrasian formalisation of economics 108–109, 110, 113, 128n9
French Liberal School, emergence of 36
Friedman, M. 133, 134, 137, 139, 141
Fullbrook, E. 45n30
Galiani, Ferdinando 25
game theory 5, 9, 77, 145, 153–155, 162, 163n10, 164n24
Garnier, Josselin 33
Gassendi, Pierre 16
general equilibrium theory 71n6, 86, 105, 106, 127, 131–132, 141, 187, 188–189; abstraction and 143; dynamic process of general equilibrium theorising 135; mathematics, economics and 14, 25, 36, 37, 39, 41, 45n25, 45n29; methodological approach to 133–134; neo-classical economics and 142
generality, achievement of 84–89
Gloria-Palermo, S. 102n7
Gödel, Kurt 3–4, 104n33, 129n13–14, 129n24, 201; algorithms, economic theorising and 187–188; constructive and computable mathematics, emergence of 166, 176–177, 184, 186; formalism and economic theorising, internal critique of 181; incompleteness theorem (second) 176; mathematics, philosophy of 208, 209; post Gödel-Church-Turing view of classical mathematics 3–4; theorems of, Debreu’s philosophy of economic theorising and 182–183
gold and silver as measures of exchange 151–152
Gossen, Hermann Heinrich 40
Greffe, J-L., Heinzmann, C. and Lorentz, K. 72n21
Groenewegen, P. 45n22
Grubel, H. and Boland, L. 12
Grünbaum, A. 164n30
Guerlac, H. 45n18
Hahn, F.H. 4, 45n27, 101, 104n24; axiomatic method in foundations of mathematics 114, 123, 127; constructive and computable mathematics, emergence of 165, 185; grammar of argumentation, first step 135–136; neo-Walrasian formalisation of economics 131–132, 133–134, 136–140, 141, 142, 143; philosophical reflections 196–197, 198–199
Hands, Wade 133
Hartlib, Samuel 17
Heck, R. 212n2
Heinzman, G. and Nabonnard, P. 192–193n15
Herbrand, Jacques: algorithms, economic theorising and 188; Herbrand-Gödel general recursiveness 188
Heyting, Arend 168, 170, 172, 179–180, 192n7; mathematics, philosophy of 204, 211, 212n4
Hicks, John 41
hierarchy of reservations, notion of 54–58
Hilbert, David 2–3, 6, 7, 51, 71n5, 74, 75; algorithms and mathematisation of economics 183, 185, 186; axiomatic method in foundations of mathematics 106, 107, 110, 111–112, 113, 123, 129n14; Brouwer-Hilbert controversy 167; constructive and computable mathematics, emergence of 165, 166, 168, 171, 174, 175, 180, 192n11–12; economic theorising, Gödel’s theorems and Debreu’s philosophy of 182; formalisation of economics and Debreu’s philosophy of mathematics 77, 87, 89, 90, 103n18, 103n20–21, 104n35; formalism, economic theorising and internal critique of 181; formalism and economic theorising, internal critique of 181; mathematics, philosophy of 204, 207–208; neo-Walrasian formalisation of economics 131, 132, 136; philosophical reflections 196, 197
Hobbes, Thomas 16, 19, 20, 21, 22, 44n6, 44n12
Hochstrasser, T.J. 45n22
Hodgson, Geoffrey M. 9–10, 43n1
Hollander, S. 45n23
Hoppit, J. 44n13
Hughes, G.E. and Cresswell, M.J. 102–103n11
Hume, David 5, 25, 145, 155, 161–162, 163n11–17, 196; convention and foundations of justice 146–152; Human Nature, Treatise on (1739) 146–147
Husserl, Edmund 193n16
Hutchison, T. 16, 18, 19, 24, 25, 45n20
incompleteness theorem (second) 176
Ingrao, B. and Israel, G. 25, 26, 27, 28, 29, 30–31, 33, 37, 38, 45n29, 58, 71n3, 140
intuitionism 2, 3, 204, 208–212, 211–212, 212n1; Bourbaki’s critique of 172–174; Brouwer’s intuitionistic mathematics 168, 193n18, 193n23, 194n27; critique of Brouwerian intuitionism 172–174; Dummett and 193n23–24; economic theorising, pragmatic intuitionism and 178–181; formalism and intuitionism, conflict between 2–3; philosophical reconstruction of strict intuitionism 174–177; pragmatic intuitionism 178–181, 198–199; see also strict intuitionism
Isnard. Achylle-Nicolas 36, 39, 45n25
Jaffé, William 45n25, 45n27; Walras-Poincaré correspondence 47, 49, 50, 52–53, 54–55, 56, 58, 62, 67, 71n6, 72n18
James I of England 19
Jevon, William Stanley: Memorial Fund Lecture 135
Jevons, William Stanley 40, 49
Jolink, A. 45n27
Jordan, T.E. 44n10
Journal of Political Economy 12
Kakutani, S. 93, 97, 101, 102n7, 104n32
Kaldor, Nicholas 96, 125; on achievement and legacy of Debreu 140–143; algorithms, economic theorising and 190; constructive and computable mathematics, emergence of 165, 169, 172; neo-Walrasian formalisation of economics 131, 132, 133, 136
Kant, Immanuel 79, 85–86, 160; constructive and computable mathematics, emergence of 168, 192n5, 193n23; mathematics, philosophy of 204–205
Kates, S. 45n23
Kenny, Anthony 81; mathematics, philosophy of 207
Keynes, John Maynard 2, 5, 44n11, 139, 196; convention notion, rationality in context of radical uncertainty 5; post-Keynesian decision-making 5; and post-Keynesians on uncertainty and conventions 155–158; rationality, convention and economic decision-making 144–145, 146–147, 154–155, 162, 162n5
Kirkhoff, Gustav 62
Kleene, S.C. 182, 183; algorithms, economic theorising and 187
Kornai, János 136
Kronecker, Leopold 89
Kuczynski, M. and Meek, R. 45n21
Kuhn, Thomas 127
language: ideal language, construction of 206; logico-philosophical and socio-historical views of 152–153; natural language, logical reasoning and 82–83, 84, 86, 202
Lansdowne, H.W.E. Petty-Fitzmaurice, marquis of 23
Laplace, Pierre-Simon 31, 33, 36
Larson, B.D. 37
Latsis, J. 146
Laurent, Hermann 49, 51, 52–53
Lawson, Tony 42, 45n30, 144, 145, 155, 161, 162n5
Leibniz, Gottfried Wilhelm 164n28
Leontief, W. 29
Levasseur, Pierre Émile 40
Lewis, C.I. 82
Lewis, C.I. and Langford, C.H. 102–103n11
Lewis, David 5, 196; convention and neo-classical rationality 152–155; rationality, convention and economic decision-making 145, 146, 158–159, 161–162, 163–164n21–22, 163n9, 163n19, 164n24
Linnebo, Ø. 212n1
MacBride, F. 212n2
McCormick, T. 44n10
McGuinness, B. and Oliveri, G. 193n18
McLure, M. 39
Malcolm, N. and Stedall, J. 16
Malthus, Thomas R. 34
Marginalist Revolution 1, 4, 6
Marsenne, Father Marin 16
Marshall, Alfred 40
Martinich, A.P. 44n6
Mas-Collel, A. 45n27
mathematics: classical logic, calculus of 179–180; convention in mathematical physics, indispensable role of 159; economics, Debreu’s global view on mathematisation of 94–97; in economics, quantification of extent of 12–13; economics and, Newton and 14, 25–28, 30, 31, 32, 33, 37, 39; general equilibrium theory, economics and 14, 25, 36, 37, 39, 41, 45n25, 45n29; intuitionistic mathematics of Brouwer 168, 193n18, 193n23, 194n27; logico-mathematical structures 112–113; mathematical discourse, infinite nature of 168; mathematical economics, formulation of 14, 24, 35, 36, 37, 39–40, 41, 45n25; mathematical economics, ‘scientific accidents’ theory of the growth of 40–41; mathematical model, formalist or semanticist? 118–123; mathematical physics as deductive a priori science, response to Poincaré critique 62–68; ‘mathematical reasoning’; methodological framework for 23–24; metamathematics, Hilbert’s notion of 110; philosophy of, formalisation of economics and 73–74, 75–76, 102n6–8, 104n30–31, 104n35; physico-mathematical approach 25–28, 32–33; Poincaré’s critique of mathematical physics as deductive a priori science, Walras’ response to 62–68; post Gödel-Church-Turing view of classical mathematics 3–4; precision in 9–10; private ownership, mathematical model of 4; quantification of socio-economic phenomena 13; rational inquiry and 22; social mathematics, Concordet’s notion of 30, 31–32; social sciences, mathematisation of 36; in socio-economic inquiry, employment of 11
mathematics, philosophy of 2, 204–212; algorithm application 210; algorithmatically decidable and undecidable theorems 3–4; Aristotle 205–206; arithmatic 204, 205; arithmetic, foundations of 205–207; axiomatisation of mathematics 207–208; bivalence, philosophical thesis of 176, 177, 193n20, 206, 209; Brouwer, L.E.J. 204, 208–209, 212, 212n4; Cantor, Georg 205, 206–207, 209, 211, 212; Church, Alonzo 208, 209; classical logic 204–205, 209–210, 211; classical mathematics 2, 3–4; classical mathematics, post Gödel-Church-Turing view of 3–4; completeness 208; computable mathematics 3; computable mathematics, orthodox modelling of rationality and 4–5; constructive existence proof 210; decidability 208; economic methodologies, creative destruction of 7–8; empiricism 204; Euclidean geometry 204; Euclid’s parallel postulate 210; excluded middle, principle of 93, 108, 128n6, 169–170, 192n8, 193n20, 194n27, 209–210, 211; finite systems, meta-empirical law of 210; formal axiomatic system, development of 207–208; formalism 204, 207–208, 211–212, 212n1; formalism and intuitionism, conflict between 2–3; formulae, symbols and 208; Frege, Gottlob 204, 205, 206–207, 208, 209, 211; geometry 205; Gödel, Kurt 208, 209; Heyting, Arend 204, 211, 212n4; Hilbert, David 204, 207–208; ideal language, construction of 206; infinity, actual or potential 209–210, 211; intuitionism 2, 3, 204, 208–212, 211–212, 212n1; Kant, Immanuel 204–205; Kenny, Anthony 207; logic, reasoning and 205–206, 209; logic, set theory and 206–207; logicism 204–207, 207–208, 211–212, 212n1; logico-mathematical analysis 3; logico-philosophical analysis 2, 8, 75, 152; logico-semantics 206; mathematical infinity 209; mathematical proofs 210–211; natural number system 205; natural numbers 209; a posteriori truth 205; a priori truth 204–205; pure mathematics 207–208; rational number system 205; rationalism 204; rationality, mathematical modelling of 4–5; real number system 205; reasoning, logic and 205–206, 209; reductio ad absurdum method 210; Russell, Bertrand 204, 206–208, 209, 211; sense and reference, distinction between 205; set theory 205, 206, 207–208, 209; set theory, logic and 206–207; symbolism, construction of 206; theorems 208; totality 209; Turing, Alan Mathison 208, 209; Walras, Leon 206
Mathematics and Modern Economics (Hodgson, G.) 9
Maxwell, James Clerk 71n8
Menger, K. 49
Mill, John Stuart 192–193n15, 192n7
Miller, A. 164n31
Mirowski, P. Cook, P. 46, 47, 58, 60, 62
Mirowski, Philip 6, 12, 42, 72n23, 166, 194n28; algorithms, economic theorising and 191
modus ponens rule of inference 193n22
Introduction to Moral Philosophy (Smith, A.) 24–25
moral sciences, Walrasian programme in context of 47–49
morality, Hume’s philosophical foundations of 148–150
Moravia, S. 33
Morishima, M. 45n27
An Essay Concerning the Multiplication of Mankind (Petty, W.) 19
Nagel, E. Newman, J.R. 122
Napoleonic political order 31, 32
Nash equilibrium 162n2–3, 163n19
Natural and Political Observations mentioned in a following Index, and made upon the Bills of Mortality (Graunt, J.) 19
The Nature of Social Laws (Brown, R.) 11
neo-Walrasian formalisation of economics 131–143; Arrow, Kenneth J. 135, 139, 142; axioms, assumptions and grammar of argumentation 136–140; Brouwer, L.E.J. 110, 116, 119–120, 121, 122, 130n25; Cantor, Georg 110, 121, 122, 129n23; Debreu, Gerard 131–132, 133, 134, 135–136, 139; Debreu’s formalisation, economists’ reception of 131–132; economic policy, debates about 133; economic theorising, simplification of assumptions in 138–139; economic theory, role of 132–134; equilibrium, near equilibrium state as causal factor in real world 140–141; explanation, Kaldor on Debreu’s conception of 141; Frege, Gottlob 108–109, 110, 113, 128n9; general equilibrium theory, methodological approach to 133–134; general equilibrium theory, neo-classical economics and 142; Hahn, F.H. 131–132, 133–134, 136–140, 141, 142, 143; Hahn’s grammar of argumentation 135–136; Hilbert, David 131, 132, 136; Invisible Hand thesis, Smith and 135–136; Kaldor, Nicholas 131, 132, 133, 136; Kaldor on Debreu’s achievement and legacy 140–143; neo-classical economics, scientific theory of value in 133; normative economics, distinction between positive economics and 133; rational agent axiom 137–138; theoretical economics as science, Hahn’s opposition to 134; Theory of Value (Debreu, G.) 131–132, 133, 136, 140, 141, 142, 143
neo-Walrasian programme 3–4, 6, 7, 73–74, 123, 129n19, 131–143, 200–201, 202–203; constructive and computable mathematics, emergence of 165, 166, 167–172, 175–176, 177, 178, 179–181, 183, 185, 186; formalisation of mathematics 131, 140, 142; formalism and economic theorising, internal critique of 181; poverty of prognosis for 166–167; prices,xplanation of 4; strict intuitionism and neo-Walrasian programme 167–172; trajectory and development of 41–42
New Mathematics and Natural Computation 45n31
Newton, Elements de la Philosophie de (Voltaire) 26, 27
Newton, Isaac 62, 65–66, 72n21, 75, 85; mathematics, economics and 14, 25–28, 30, 31, 32, 33, 37, 39; mechanics of 160, 164n31; physico-mathematical approach 25–28
Newtonian analysis, infinitesimal calculus of 30
Newtonian natural science 26–28
Newtonian rational mechanics 39
non-ergodicity 158, 159, 162, 196
non-Euclidean geometries 74, 107, 160, 205
Ockham’s razor 69
ontological-epistemic indeterminacy: conventions and philosophy of mathematics and 158–161; Euclid and 159–160; rationality, convention and economic decision-making 145–146
ontological lock-in, Walras and 68–70
Pagden, A. 45n14
Pareto, Vilfredo 39, 41, 49, 77, 185; Pareto optimality 140, 141, 143
Pascal, Blaise 16
Pasinetti, L.L. 34
Pell, John 16
Petri, F. and Hahn, F. 45n29
Pettit, P. 154–155, 161, 163–164n21, 164n23
Petty, William 14, 15–24, 25, 30, 43–44n5, 44n7–13; ‘Algorithme of Algebra’ 22; disciplinary boundaries, disregard for 16–17; economic writings 18–19; economics, commitment to use and application of mathematics and quantification in 20; empirical objects, status and quantification of 21; empirical sciences as ‘mixt mathematical arts’ 22; ‘mathematical reasoning’; methodological framework for 23–24; mathematics, rational inquiry and 22; methodological basis for political arithmetic of 22–23; methodological commitments 19–20; Political Arithmetic (1690) 23; Sir William Petty’s Quantulumcunque concerning Money, 1682 (1695) 19; socio-econimic phenomena, quantification and analysis of 20–21; Treatise of Taxes and Contributions (1662), production models in 21–22
philosophical reflections 195–203; algorithmetic mathematics, economic modelling and 201–202; Arrow, Kenneth J. 197, 202; axiomatised mathematics 201; Brouwer, L.E.J. 196, 197, 198, 199; Church-Turing thesis 194n26–7, 197, 201; classical mathematics, economic decision-making and 197–198; classical mathematics, economic modelling and 199–200; classical mathematics, transfinite domain of 202–203; computer/digital age, emergence of 201; conventions, reflections on 196; Debreu, Gerard 195–196, 198–199; Élements d’economie politique pure (Walras, L.) 195; geometrical conventionalism, Poincaré’s thesis of 196; Hahn, F.H. 196–197, 198–199; hermenuetics 195; Hilbert, David 196, 197; Hilbertian mathematico-philosophical climate 196; intuitionistic mathematics, economic modelling and 200–201, 202–203; intuitionistic philosophy of mathematics, formalisation of economics and 200–201; logico-mathematical concepts, disputed nature of 196–197; mathematico-economic commitments of Debreu 196; non-constructive mathematics, economic modelling and 199–200, 202–203; non-ergodic economic world 196; orthodox formalisation of economics 198; philosophy of mathematics, new formalisation of economic theorising? 197–203; Poincaré, Henri 195, 196; Poincaré’s philosophy of applied mathematics 195–196; post-Keynesian economic decision-making 196; pragmatic intuitionism 198–199; pragmatic intuitionism, mathematical modelling and 199; praise for philosophy of mathematics 195–197; problems, methods and 202; Russell, Bertrand 196, 197; strict intuitionism 198; theoretical economics, experimental resources of 199; theoretical economics, predictive success of 198–199; Theory of Value (Debreu, G.) 195–196; Walras, Leon 195–196; Walras’s scientific realist defence of theoretical economics 195–196
physico-mathematical approach of Newton 25–28
Piccard, Antoine Paul 71n3
Plato 192n10
Platonic philosophy 58–59, 61, 62, 70
Platonic realism 58–59, 61, 62, 192n10; Platonic-scientific realism 58–62
pleasure, Hume’s analysis of abstract idea of 148
Poincaré, H. Darboux, G. and Appell, P. 48
Poincaré, Henri 2, 4, 5, 6, 40, 71n1–2, 71n5, 71n8–9, 72n16, 72n21; axiomatic method i foundations of mathematics 109, 110, 120, 121, 122, 123; constructive and computable mathematics, emergence of 168, 178, 185–186, 192–193n15, 192n5, 192n12; critique of mathematical physics as deductive a priori science, Walras’ response to 62–68; Debreu’s proof of existence of equilibrium, Poincaré malaise and 97–99, 102; formalisation of economics and Debreu’s philosophy of mathematics 79, 86, 87, 89, 90, 93, 102n1–2, 102n9, 104n33–4; hierarchy of reservations, notion of 54–58; philosophical reflections 195, 196; rationality, convention and economic decision-making 145–146, 158–159, 160–161, 161–162, 163n8, 164n31–2; Walras and 46–47, 60–61, 68–70, 73; Walras-Poincaré correspondence, mathematisation of economics 49–51; Walras-Poincaré correspondence, measurement of utility 52–54; Walras-Poincaré correspondence, Poincaré’s hierarchy of reservations 54–58
Political Anatomy of Ireland (Petty, W.) 19, 23
Political Arithmetic (Petty, W.) 23
Another Essay in Political Arithmetic (Petty, W.) 19
Political Discourses (Hume, D.) 25
political economy 24–35; construction of, Say’s perspective on 33; Down Survey, quantitative surveying and 18; foundations of 16–20; historical development of 15–16; philosophical framework for 24–25
Poovey, Mary 20
Porter, T.M. 48
post-Keynesian analysis 5, 145, 146, 154, 159, 161, 162, 165
post-Keynesian economics 196
post-Keynesian uncertainty and conventions 155–158
Potter, M. 129n14
Potts, J. 13
pragmatic intuitionism, economic theorising and 178, 180
Pribam, K. 45n20
Priest, G. 212n4
promises, convention and 151
Pufendorf, Samuel von 28
Putnam, Hilary 111
Pythagoras 204
Quarterly Journal of Economics (QJE) 12, 156, 157
Quesnay, Francois 28–29, 34, 45n21; methodological approach 28–29; Tableau Économique 29
rationality, convention and economic decision-making 144–162; appetites, emotions, passions and sentiments, interplay of 147–148; convention, Lewis’ six conditions for 153–154; custom and convention, relationship between 147; deductive system of pure mathematics 144; equilibrium, commitments to 144; game theory 153–155; General Theory (Keynes, J.M.) 144–145, 156, 157; geometrical conventionalism, Poincaré and 145–146; gold and silver as measures of exchange 151–152; goods, species of 150–151; Hume, convention and foundations of justice 146–152; Keynes, John Maynard 144–145, 146–147, 154–155, 162, 162n5; language, logico-philosophical and socio-historical views of 152–153; Lewis, convention and neo-classical rationality 152–155; Lewis, David 145, 146, 158–159, 161–162, 163–164n21–2, 163n9, 163n19, 164n24; mathematical modelling of rationality 2; morality, Hume’s philosophical foundations of 148–150; non-ergodicity 158, 159, 162; ontological-epistemic indeterminacy 145–146; ontological-epistemic indeterminacy, conventions and philosophy of mathematics and 158–161, 162; pleasure, Hume’s analysis of abstract idea of 148; Poincaré, Henri 145–146, 158–159, 160–161, 161–162, 163n8, 164n31–2; Poincaré’s conventionalist reading of principles of mechanics 158–160, 162; probability theory 144; promises, convention and 151; rational agent axiom 137–138; rational conduct in face of radical uncertainty, possibility of 145–146; rationality, commitments to 144; Risk, Uncertainty and Profits (Knight, F.H.) 156–157; society, Hume’s thesis on development of 150; Treatise on Human Nature (Hume, D.) 146–147; uncertainty and conventions, Keynes and post-Keynsians on 155–158; Walras, Leon 144, 158, 159
Rattansi, P.M. 26
A la recherche d’une discipline économique (Allais, M.) 41
reservations, notion of hierarchy of 54–58
Revue D’Economie Politique 12
Ricardo, David 34–35; deductivist argumentation of 34–35
Riemann, Bernhard 85, 107, 160
Risk, Uncertainty and Profits (Knight, F.H.) 156–157
Robbins, L. 45n20
Rosser, Barkley J. Jr. 194n28
Rosso, Giovanni 33
Russell, Bertrand 51, 71n5, 75, 90, 152, 164n27; constructive and computable mathematics, emergence of 167, 169, 175; mathematics, philosophy of 204, 206–208, 209, 211; philosophical reflections 196, 197
Samuelson, Paul A. 12–13, 41, 43n2
Say, Jean-Baptiste 32–33, 34–35, 36, 37, 45n23
Scarf, H. 100–101; algorithms, economic theorising and 189
Schmid, A.M. 71n5
Schumpeter, J.A. 15, 43–44n5, 43n4, 45n20
Screpanti, E. and Zamagni, S. 45n20
Shank, J.B. 26
Simon, Herbert 2, 4–5, 158; algorithms, economic theorising and 190–191
simplicity, existence proofs and 90–94
Skinner, Quentin 20
Skyrms, B. 162n2, 163–164n21, 164n24
Small, A. 45n15
Smith, Adam 24, 32, 33–34, 96, 99, 135, 140, 182
society, Hume’s thesis on development of 150
socio-economic phenomena, Petty’s quantification and analysis of 20–21
Socratic-Platonic tradition 147
Solow, R. 202
Staatwissenschaft (von Justi, J.) 25
Steiner, P. 45n23
Stewart, L. 45n19
Stigler, G.T., Stigler, S.M. and Friedland, C. 12
Stirwell, J. 164n29
strict intuitionism: classical mathematics and 168–169; Dummett and philosophical reconstruction of 174–175, 177; neo-Walrasian programme and 170, 171; philosophical reconstruction of 174–177
Sugden, Robert 146
Sutherland, I. 44n7
Tableau Économique (Quesnay, F.) 29
Tait, Peter Guthrie 62
Tarascio, V. 39
A Treatise of Taxes and Contributions (Petty, W.) 19; production models in 21–22
Theocharis, R.D. 45n25
Théorie de la Spéculation (Bachelier, L.) 50
Theory of Games and Economic Behaviour (von Neumann, J. and Morgenstern, O.) 41
Theory of Value (Debrue, G.) 6, 7
Topoi 163n20
Touffut, J.P. 38
Traité des Richesses (Isnard, A.-N.) 36
Tribe, K. 15
Troelstra, A.S. and van Dalen, D. 191n1, 192–193n15, 192n8
Tucker, Josiah 25
Turgot, Anne Robert Jacques 29–30, 45n22
Turing, Alan Mathison 3, 4, 42, 129n14, 166, 184, 186–187; algorithms, economic theorising and 187, 188–189, 190, 191; algorithms and mathematisation of economics 183–187; Church-Turing thesis 194n26–7, 197, 201; formalism and economic theorising, internal critique of 181; mathematics, philosophy of 208, 209; post Gödel-Church-Turing view of classical mathematics 3–4
Vaggi, G. 45n21
Value and Capital (Hicks, J.) 41
Van Daal, J. and Jolink, A. 45n27, 71n6
Van der Berg, R. 45n25
Van Heijenoort, J. 212n1
Van Stigt, W.P. 167–168, 173, 192n4, 192n7, 192n14
Vanderschraaf, P. 146, 163n10, 163n17
Velulillai Vela, Kumaraswamy 4–5, 13, 42, 45n31; algorithms, economic theorising and 189–191; constructive and computable mathematics, emergence of 185, 193–194n25, 193n19, 194n27–28
Verbum Sapienti (Petty, W.) 19
Vilks, A. 192n12
von Justi, Johann 25
von Neumann, J. and Morgenstern, O. 163n10
von Neumann, John 41, 42, 77, 102n7, 182, 212n2; algorithms, economic theorising and 187, 191
von Thünen, Johann Heinrich 40
Wakefield, A. 45n15
Wald, A. 41
Walker, Donald A. 45n27
Wallis, John 44n8
Walras, Leon 2, 4, 5–7, 71n2–3, 71n15, 72n18–20, 185; axiomatic method in foundations of mathematics 105, 114, 116, 117, 126; economic thought, contribution to history of 46; equilibrium, Debreu and proof of existence of 99–102; formalisation of economics and Debreu’s philosophy of mathematics 74–76, 76–77, 98, 99, 102n1–2; mathematical economics, formulation of 14, 24, 35, 36, 37, 39–40, 41, 45n25; mathematical physics as deductive a priori science, response to Poincaré critique 62–68; mathematics, philosophy of 206; moral sciences, Walrasian programme in context of 47–49; neo-Walrasian formalisation of mathematics 131, 140, 142; ontological lock-in 68–70; philosophical reflections 195–196; platonic-scientific realism of, ‘Economics and Mechanics’ in context of 58–62; Poincaré and 46–47, 73; rationality, convention and economic decision-making 144, 158, 159; Walras-Poincaré correspondence, mathematisation of economics 49–51; Walras-Poincaré correspondence, measurement of utility 52–54; Walras-Poincaré correspondence, Poincaré’s hierarchy of reservations 54–58; see also neo-Walrasian theory
Walras-Poincaré correspondence 40; cardinal magnitude concepts 53; causal scientific realism 58, 62, 63, 67; consistency, pure mathematics and concern for 54; deductive method (Cartesian) 58, 62, 68; ‘Economique et Mechanique’ (Walras, L.) 46, 58–62; empirical-conventional account of principles of mathematical physics 58, 63–64; essentialist scientific realism 58, 59, 62, 69; hierarchy of reservations, Poincaré’s notion of 54–58; human action, dimensions of 47; infinite clairvoyance, Walras’ hypothesis of 56, 57–58; interpersonal comparison of utility, issue of 55, 57; intuition, Poincaré’s perspective on guidance by 51; Jaffé, William 47, 49, 50, 52–53, 54–55, 56, 58, 62, 67, 71n6, 72n18; linguistic-conceptual scheme of science 64–65, 66–67, 69, 158–159; logical validity, pure mathematics and concern for 54; mathematical physics as deductive a priori science, Walras’ response to Poincaré critique 62–68; mathematisation of economics 49–51; moral sciences, Walrasian programme in context of 47–49; ontological lock-in to Walras’ principles of mathematical economics 68–70; platonic-scientific realism, ‘Economique et Mechanique’ in context of 58–62; Poincaré’s hierarchy of reservations 54–58; principles and laws, Poincaré’s view of relationship between 65–66; probability theory, applicability of 50; probability theory, exposure of errors in use of 48; reassessment of 46–70; reassessment of, Élements d’economie politique pure (Walras, L.) and 40, 46, 48–51, 54–59, 68, 70; rebustness of principles 58, 60–61, 65–66, 67, 69; rigour, Poincaré’s quest for 51; Science and Hypothesis (Poincaré, H.) 55–56, 62, 67; scientific causality 64, 65; scientific conceptual schemes 64, 66–67; utility, measurement of 52–54
Walrasian-Poincaré correspondence: measurement of utility 52–54
Wang, H. 129n13
Ward, Seth 44n8
Wealth of Nations (Smith, A.) 32, 33–34
Reflections on the Production and Distribution of Wealth (Turgot, A.R.J.) 29–30
Weintraub, E.R. and Mirowski, P. 73, 96, 192n13
Weintraub, Steven H. 12, 41, 42, 131, 157, 192n13; axiomatic method in foundations of mathematics 110, 117, 128n1–3; formalisation of economics and Debreu’s philosophy of mathematics 74, 76, 77, 78
Weir, A. 212n2
Weyl, Hermann 75, 79, 90, 93, 103n21, 104n27–8, 104n35; constructive and computable mathematics, emergence of 171, 172, 192n11
Whatmore, R. 45n23
Wicksell, Knut 40
Wilkin, John 44n8
Willis, Thomas 44n8
Wittgenstein, Lugwig J.J. 152, 193n18
Worsley, Benjamin 18
Wren, Christopher 44n8
Wren, Matthew 44n8
Wright, C. 193n21
Young, H. Peyton 146
Zambelli, Stefano 45n31, 193–194n25, 194n27–28; algorithms, economic theorising and 189, 190
Zermelo, Ernst 185