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Morishima, M., 157

Moulines, C. U., 14, 30, 65

Muller, F. A., 1, 4, 6, 9, 11, 13, 25, 55

Maki, U., 64

Nagel, E., 3

Nash, J. F., 83, 124, 126

Newton, I., 2, 18, 37-38, 42, 46, 69

Nicholas, H., 180

Nowak, L., 68

Okishio, N., 158

Oliu, J., 178

Peano, G., 13

Pearson, K., 197, 198

Philosopher, the

see Aristotle, 80

Ponce de Leon, J., 72

Popper, K., 182, 185

Portides, D., 64

Punzo, L. F., 179

Raiffa, H., 128

Ramsey, F. P., 50

Richter, M. K., 23

Robinson, A., 24

Roemer, J. E., 163

Salvadori, N., 178

Samuelson, P. A., 75, 114-115, 130,

148

Schefold, B., 178, 179

Scott, D., 21, 23

Seton, F., 158

Skala, H. J., 19, 21

Skolem, T., 13, 19, 24

Slomson, A. B., 24

Slutsky, E., 75

Smith, A., 79

Sneed, J. D., 14, 30, 35, 48-50

Spanos, A., 80, 82, 182-184, 193,

195-197

Spiegel, M. R., 43

Sraffa, P., 174, 175-181

Stegmuller, W., 39

Stiemke, E., 138, 139

Stiglitz, J. E., 148

Stigum, B., 68

Struik, D. J., 79

Sugar, A. C., 2

Suppe, F., 182

Suppes, P., 1-5, 14, 20-21, 23, 35, 40,

42, 57, 59-60, 69-74, 79-81,

184-185

Sydenham, P. H., 71-72

Symon, K. R., 43

Takayama, A., 173

Tarski, A., 1-3, 13, 16, 19, 24

Truesdell, C., 2

Tverski, A., 3, 69

van der Waerden, B. L., 13

Van Heijenoort, J., 13

Varian, H. R., 67, 75, 81, 130

Velupillai, V., 179

Volterra, W., 59

Wade, H., 11

Walras, L., 63, 65

Whinston, M. D., 91-92

Zermelo, E., 30

Zoubek, G., 55, 68

abstract labor, 132, 134-135, 141, 143, 145, 151, 155-156

structure, 136

as a weak ordering, 135, 137, 143 cancellation law, 135, 137, 144 continuity, 136-137, 144 homotheticity, 136-137, 144 monotonic, 78, 92, 144 monotonicity, 135, 137 reduction, 164, 172

representation theorem, 70, 137, 140 abstraction, 11 added value, 157

admissible approximation, 52

Afriat’s inequalitites, 78

agent behavior, 172 aggregated maximum profit, 162 algebra

modern, 13, 17

σ-, 186, 187

universal, 13, 17

algebraic structure, 13-14

field, 18

group, 18

monoid, 18

ring, 18

semi-group, 18

algebraic topology, 38 algebraic-difference

measurement, 11, 70, 79, 112

structure, 96, 103, 106, 107 geometric representation, 10, 13 numerical representation, 10 representation, 96

theory, 91, 94

allocation of resources

by the market, 87

through distribution, 88 allocation rules, 84 alternative techniques, 145, 172, 175 analytical geometry as numerical representation, 70

Antonelli’s integration problem, 75 approximation, 65

intratheoretical, 51 approximation relation, 52

ARC, 25

ARCU, 25, 30, 40

arithmetic

foundations, 13

Peano’s axioms, 13 arithmetic or elementary class, 23 ars inveniendi, 37

Atwood’s machine, 48 augmented reproduction, 160 axiom

of choice, 83

of class existence, 26

of class separation, 26

of completeness, 25, 28

of extensionality, 26

of regularity, 29

of urelements, 25-26 schema of set existence, 28 axiomatic method, 2 axiomatization kinds, 39

basic theory-element, 39, 41, 65 Berge’s maximum theorem, 166, 168-169 Berkeley University, 2

Bertrand’s game, 125 equilibrium, 114-115, 125, 127,

154-155, 160, 164

pure strategy, 23, 117, 125-126 Book of the Dead, 79

Borel

algebra, 187

set, 187

Bourbaki, N., 14

budget restriction, 85

calculus, differential and integral, 22 capitalist economy, 61, 65 capitalist society, 85

cardinal number, 14

cardinal of the continuum, 22 cardinal preference theory, 113 Carnap’s approach, see scientific theory

L-View, 3 categorical theory, 18 category theory, 25, 30 central planner, 84 characterization, 8-9, 41, 49, 51 choice

action, 83

circumstance, 7

function, 88

structure

unintended consequence of, 62 choice axiom, 25

City College, New York, 1

class, 25

disordered pair, 28

empty, 27

intersection, 29

κ-class, 24

M-homogeneous, 23

M-universal, 23

of all sets, 25

of urelements, 25-26

subclass, 27

classical

equilibrium, 114-115, 125, 127, 154-155, 160, 164

analysis, 2, 5, 23

dynamics, 7, 90

economics, 155

economy, 148, 160, 164, 172 equilibrium, 114-115, 125, 127, 154-155, 160, 164

mechanics, see classical particle mechanics

particle mechanics, 38-39, 48-49 axiomatization, 40

basic theory-element, 8, 40, 114 specialization, 39

sun-earth system, 50 system, 39, 40 theoretical terms, 49 closed convex cone, 160 closed first-order theory, 17 closure under isomorphism, 18

Columbia University, 1 compactness theorem, 19 comparative statics, 115 concept of magnitude, 70 concept of preference, 47 concept of truth, 11 concrete system, 47 concretization, 11, 55, 57, 61, 65, 67-68 as intertheoretical relation, 55 conditional probabilities, 194 conditional-probability structure, 185 Condorcet condition, 8 consequences of a set of sentences, 17 conservative force, 39 consistent set of sentences, 17 constant capital, 157 constraint, 50-51, 53

in game theory, 126, 130 consumer

behavior, 58, 90 choice, 58, 61, 65, 175 concept of, 62 ideal concept, 75 idealized concept of, 63 subsistence, 85 theory, 83, 90, 93, 126 neoclassical, 90 consumption, 68, 83

bundle, see consumption menu final, 84

menu, 83, 85, 88, 93, 160 minimum, 85 productive, 84 countable unions, 186 cutting-off function, 50

data generation process, 80, 82, 183, 193

and random experiments, 184 as a random mechanism, 183 as a real-concrete system, 183 as a source of observable data, 183 data-structure, 6, 9, 58 decidable set of formulas, 18 decision theory, 19 deductive system, 5 demand

theory, 74, 129, 130

as a specialization of game theory, 129

demand function, 75

empirical, 2, 75

Walrasian, 75-76, 81, 92, 173

C¹, 92

derivation relation, 17

derivation rules, 7

dialectical materialism, 37 difference structure, 94, 96

numerical representation, 10

difference relation, 17-18, 94-95 geometric representation, 18, 112 numerical representation, 17 difference structure, 112

geometric representation, 18, 112 differentiable manifold, 93 disjointed set, 29 distribution, 68, 83-84

rule, 85, 86

system, 15, 47, 51-52, 64, 66, 82, 84,

157

Douglas Aircraft Company, 1 dynamic theory, 155 dynamical representation, 46 dynamics, 7-8

econometric structure, 197 econometrics, 12, 57, 79, 182

T-theoretical terms, 178, 181, 196 and probability theory, 197 basic theory-element, 54, 114, 174, 184, 196

density functions, 197

domain of intended applications, 178, 196

empirical claim, 49-51, 53, 178, 198 explanation in, 197 fundamental law, 198 histogram, 196

as a step function, 196 cumulative, 196 dispersion, 196 higher central moments, 196 kurtosis, 196 location, 196 mean, 196 median, 196 mode, 196 shape, 196 skewness, 196

standard deviation, 196 variance, 196 logical foundations, 182 logical structure, 196 observable data, 197 observed data, 193, 195 partial potential models, 197 Pearson frequency curve, 197 probability model, 193-195, 197 random variables, 194

sampling model, 193, 195, 197 statistical model, 195, 197 confidence estimation, 195 hypothesis testing, 195 misspecification, 195 point estimation, 195 prediction, 195 specification, 193

structuralist characterization of, 184 true density function, 198

economic

coordination, 87 by the market, 87

equilibrium, 114-115, 125, 127, 154-155, 160, 164

existence of, 115, 164, 172 methodology, 18, 37-38

and econometrics, 182

system, 15, 47, 51-52, 64, 66, 82, 84, 157

as data generation process, 89 as organic whole, 61, 83 as target system, 89 concept, 82, 123-124 cycle of, 83

disequilibrium, 87 equilibrium, 83, 128-129, 154 feasibility condition, 85 general concept, 66, 79 labor resources, 85

productive cycle, 85 reproduction, 87, 177 total resources, 85

theory, 19, 23

unit, 82

household, 82 production unit, 82

economy, 85, 88, 172 efficient process

existence, 70, 146 elementary

class, 18, 24

in economics, 19

event, 30, 185, 189

elementary or arithmetical class, 17-18, 21

empirical

claim, 61, 64, 66

of classical economics, 172-173 of game theory, 131

of Sraffian economic theory, 180, 181 data, 38, 48, 57, 64, 66, 68, 91, 183 in consumer theory, 130 meaning, 41 observation, 38 phenomenon

as target of game theory, 126 structure, 6, 57-58, 66-67, 74-75 theory, 6

ens rationis, 25 equal-arms balance, 57, 73, 79 measurement, 11, 70, 79, 112 equilibrium

Marxian, see equilibrium, classical equilibrium price as a sink, 155

Euclid’s Archimedian axiom, 112 Eudoxo's theory of proportions, 69 exact value of a magnitude, 42 excess demand, 163 exchange, 68, 83, 84 as a social process, 88 as reallocation of initial endowments, 87, 88

by means of a general equivalent, 87 by means of barter, 87-88 by means of familiar agreements, 87 by means of money, 88 exchange process, 88, 134 exchange-value, 175 expected utility

maximization, 124, 160 of player in a game, 126 explanation

in game theory, 126-130 exploitation rate, 157 extended completeness theorem, 19

factual predicate, 38 feasibility set

for consumers, 162-163

aggregated, 53, 162-163 for firms, 161-162

aggregated, 53, 162-163 feasible choices, 83 final allocation, 88 financial capital market, 155, 160, 164 first-order logic, 1, 5, 13, 40 formalization in, 40 formulation of a theory in, 5 language, 4, 6, 14, 40

cardinality of a, 16

connectives, 16

constants, 16

formulas, 16 individual variables, 16 model of a, 16 notion of satisfaction, 17 notion of truth, 17 parameter, 16 sentences of a, 16 terms of a, 16

theory, 17

formalized language, 35, 40 foundations of measurement, 3, 22 foundations of physics, 2

Fountain of Eternal Youth, 72 Frobenius root, 173 fundamental

measurement, 11, 70, 79, 112 measuring, 71

fundamental law, 67

of game theory, 127-128, 131 of Sraffian economic theory, 177, 179-180

Fundamental Marxian theorem, 156-158,

160 fuzzy set, 52

game

behavioral strategy, 114-115, 117-119 profile, 117-118, 124

concept, 7, 90, 125 definition dynamic, 114, 125 equilibrium, 114-115, 125, 127,

154-155, 160, 164 concept, 82, 123-124 definition, 124 existence of, 115, 164, 172 Nash, 124

feasible action, 117 history, 116 feasible, 123 initial, 117

mixed strategy, 23, 117-118

profile, 117-118, 124 perfect recall, 118 pure strategy, 23, 117, 125-126

profile, 117, 118, 124 strategy profile, 115, 123 temporal horizon, 114, 116 theory, 11, 65, 114-115

T-theoretic term, 127 application to empirical phenomena, 130

basic theory-element, 8, 40, 114 constraint, 115

empirical applicability, 114 empirical claim, 125 equilibrium, 83, 128-129, 154 fundamental law, 114-115, 125, 129 guiding principle, 125, 127 logical reconstruction of, 114 models, 114

problem of lost beings, 115

problem of lost stories, 115 two-person, 23, 65 with discrete time, 125 with finite horizon, 125 with multiple equilibria, 128 zero-sum, 65

Gaussian curvature, 93 general concept vs. theoretical model, 68 general equilibrium, 160 general equilibrium theory, 67 intended applications, 66 general productive system, 175 Generality

I, 36, 38

II, 36, 38

III, 36-37

Genesis, 79 geometric interval, 97, 112

congruence, 97

direction, 97

equivalence class, 97, 98

Abelian group, 99

order relation, 99

order relation, 99

sum, 97-98

geometric-difference

structure, 111 theory, 97

Godel’s completeness theorem, 18

Haavelmo’s methodological foundations of econometrics, 182

Hausdorff η_α-sets, 24

Hegel’s dialectics, 37-38 homogeneous labor, 172, 176 household consumption menu, 84 hypothetical deductive system, 38 Holder

axioms, 18, 97

cuts, 18

theory, 91, 112

ideal

model, 47, 50-53, 57, 59, 172 system, 15, 47, 51-52, 64, 66, 82,

84, 157

type, 63

idealization, 11, 54-55, 57, 61-63,

65-68

as decomposition, 64 as deformation, 64 as intertheoretical relation, 55 as isolation, 64 as stabilization, 64 in economics, 55 in physics, 55 nullifying, 64 stabilizing, 64

idealized concept, 63 imbedding, 6, 58, 60 isomorphical of a data-structure, 9 inclined plane, 42, 46-47, 50 independent producer, 84 indifference

curve

Gaussian curvature of, 92 sets, 92 indifference sets, 92 individual choice, 153

structure, 7-9

similarity type, 9, 15, 33 theory, 7

basic theory-element, 8, 40,

114

inference rule, 18 modus ponens, 18 generalization, 18 informal

mathematics, 7 narrative, 41 initial

distribution, 86 endowment, 86-88

of labor-power, 86

of material resources, 86 resources, 161 instrumentalism, 73 integration method, 67 intended application, 82 interest rate, 160, 171 intertheoretical relation, 67 investment return, 161 isomorphism, 14

joint production, 145, 172, 176, 179 Jonsson’s theorem, 24

Kepler’s laws, 50 kinematic term, 7 kinematic vs. dynamic terms, 7 kinematical

representation, 46

structure, 47

kinematics, 7 Kolmogorov’s axioms for probability theory, 184-185

Kolmogorov-Bochner theorem, 114 Kuhn’s theorem, 118

labor

-power, 85, 87, 134, 176 reproduction, 87, 177

-value, 132, 145, 151

expenditure, 135

allocation, 87, 133-134

as an indispensable input, 146 division, 132

equalization, 134

heterogeneous, 67, 141, 177 homogeneous, 65, 140-141, 177 input, 84, 134

normal, 134, 135, 146

process, 83-85, 87, 135, 156, 175, 184-185

efficient, 145-146, 148 productivity, 146 simple, 21, 141, 156, 187 theory of value, 65, 67, 156, 160 unskilled, 141, 156 labor-power

allocation, 87, 133-134

normal, 134-135, 146 labor-value, 156

as representation of abstract labor, 151-153

market independent, 140 market-dependent, 141-142 law

of excluded middle, 180

of utility maximization, 58, 63

of value, 67, 132-133, 174 in Leontief economies, 173 manifestation form, 132 least squares, 57

Leontief

economy, 148, 160, 164, 172 model, 47, 50-53, 57, 59, 172 Leviticus, 79 lexicographic preferences, 22 Lindenbaum’s theorem, 19 linearly ordered sets, 22 logic

formalized language of, 13, 18

mathematical, 13 logic, methodology and philosophy of science congresses, 2 logical

axioms, 18, 97

calculus, 3

empirical interpretation of, 4 primitive symbols, 4 consequence, 17

Lowenheim-Skolem-Tarski theorem, 19, 24 manifold

C², 92 C^k, 92 differentiable, 70, 90, 92 marginalists, 22 market

participant, 154

price, 142, 145, 151, 155-156, 158-160, 164, 171, 173 Marx’s

dialectics, 37, 38 method of political economy, 11, 37, 89

Marx’s method

of political economy, 55

Marxian economics, see classical economic theory, 12, 154-155 mathematical

logic, 179 method, 65

vs. experimental method, 63 structure, 74

mathematical structure, see set-theoretical structure

maximum profit, 162-163 means of production, 134 measurement, 47

and weak orderings, 71

as an empirical operation, 71 as assignment of numbers, 69 as homomorphism, 72, 80 as isomorphic imbedding, 70-71 as numerical representation, 70 by geometric entities, 69 by real numbers, 69 conjoint, 79 econometric, 79-80 existence, 70, 146 fundamental, 79 in psychology, 72 instrument, 52 of a magnitude, 71 of idealized properties, 69 procedure, 74 representation theorem, 70, 137, 140 representational, 69, 70, 72, 74 as a measuring procedure, 73 set-theoretic structures in, 73 representational theory, 70 uniqueness theorem, 70 utility, 74

without theory, 80, 81 measuring

procedure, 74 structure, 71 fundamental, 72 mechanical law, 39 metaphysical theory, 68 metatheory, 38 method of production, 174, 175, 177 all-engaging, 178-179 of subsistence, 177 of surplus, 177 self-replacing, 177 methodological individualism, 62, 153

metric concept, 47 metrization, 72 of a property, 74 minimum wage, 157 mode of production, 84 model

as a set-theoretical structure, 5, 11 as imaginary system, 11 as set of sentences, 59 characterization of

extrinsic, 35

intrinsic, 35

complete theory, 18 econometric, 79-80 elementary equivalence, 18 elementary extension, 18, 24 extrinsic characterization of, 5 for first-order logic, 13-15 in Tarski’s sense, 172 of a first-order language, 11, 15 of a first-order theory, 35 of a sentence, 16 of a theory, 5, 7 of first-order logic, 30 system, 15, 47, 51-52, 64, 66, 82, 84, 157

theory, 18 model of data, see data-structure model system, 59-61, 63-65, 75 as idealization, 61 as target, 60

monetary value of net product, 157 Mose’s law, 79

motion composition, 95

Nash equilibrium, 126

National Research Council, 2

National Science Foundation, 2 neoclassical economics, 155

basic theory-element, 54, 114, 174, 184, 196

net output, 84

Newton’s laws, 46

Newton’s second law, 38, 42

Newton’s theory of proportions, 18 non-T-theoretical structure, 47 non-T-theoretical term, 50-51

of Sraffian economic theory, 177, 179-180

non-linear programming, 90, 112 non-substitution theorem, 148-149, 151 nonstandard model of real-number

theory, 23 normal science

of game theory, 127-128, 131

of Sraffian economic theory, 177, 179-180

nullifying assumption, 67 numerical conditional-probability representation, 192

numerical representation, 70

observable data, 82, 183 observation sentence, 4, 7 observational vs. theoretical terms, 7 observationally adequate theory, 6 observed behavior of an agent, 47 ontological theory, 68 opportunity set, 7, 8 optimality set

for consumers, 162-163

aggregated, 53, 162-163

for firms, 161, 162

aggregated, 53, 162-163 order

-type, 14

dense strict, 24

isomorphism, 14

strict partial, 21

strict simple, 21-23 ordering, 19, 20

dense simple, 18

linear, 18

partial, 18, 21

quasi-, 20-21

simple, 21, 141, 156, 187

strict partial, 21

strict simple, 21-23

weak, 21

ordinal preference theory, 113

p-representation, 61

Paleolithicum, 79

parametric method, 66, 75, 81 partial ordering, 39 partial potential model, 48, 50, 57 imbedding of a data-structure into, 58 imbedding of an empirical structure into, 58

of consumer theory, 76

of game theory, 127-128, 131 particle mechanics, see classical particle mechanics, 2 perfect

information, 63

knowledge, 115

memory, 115

recall, 63

philosophy of science, 36, 38

Polish school of logic, 2 positive integers, 13 potential model, 49, 51 practice, 35 pre-theoretical thought, 183 preference

as a game-theoretic term, 129 cardinal, 93-94, 97 concept, 7, 90, 125 strength, 91

structure, 8-9, 18, 22, 24 preference ordering, see preference relation

preference relation, 1, 7, 17-19, 23, 47,

61, 63, 74, 85, 88, 90-92, 111-112

cardinal, 93-94, 97

connected, 20, 63

continuous, 25, 78, 90-93, 160, 189 convex, 91

differentiability

condition, 17, 111 empirical meaning of, 18 differentiability condition, 91 empirical meaning, 17

locally nonsatiated, 63, 92, 160 maximization of a, 9 monotonic, 78, 92, 144 nonsatiated, 25, 64, 78, 90

order properties, 91

rational, 21

rationalization of a choice structure by, 8

regular, 8, 21, 63, 90, 160

smooth, see uniform differentiability strictly convex, 63, 90, 160

transitive, 20, 62-63

uniform differentiability empirical meaning of, 18

uniformly differentiable, 19 preference structure

generation of a choice structure by a, 8 in a game, 126

regular, 8, 21, 63, 90, 160

smooth, 18 preference theory, 18, 91, 111

new foundations, 111-112 price system, 157, 161, 179

induced by a reduction, 156

induced by abstract labor, 151 representation of, 142 price-distribution system, 176 prime model, 18

test, 19

private ownership economy, 84, 160 private property, 174

probability

as propensity, 185, 191

as relative frequency, 184-185 probability distribution, 187

simple, 21, 141, 156, 187 probability measure, 185-186

of a countably additive probability space, 188 probability space, 30, 33, 185-186, 193 algebra of events, 185

as formalization of a random experiment, 191

continuous, 25, 78, 90-93, 160, 189 countably additive

discrete, 189

elementary event, 185-186

elementary identities, 187

event, 30, 185, 189

generated by a qualitative conditional probability Archimedian structure, 194

sample point, 185

sample space, 185

continuous, 187 countably infinite, 187

finite, 187

standard, 117 probability theory, 34, 80

in econometrics, 184, 193 problem

of lost beings, 9, 13, 38, 41, 68

of lost content, 9, 11, 13, 38, 41, 68

of theoretical terms, 50

of unavailable stories, 9, 10, 38, 41, 68

producer, 86

production, 68, 83 means, 84 mode, 88 possibility set, 84, 88 price, 142, 145, 151, 155-156, 158-160, 164, 171, 173 equilibrium, 83, 128-129, 154 process, 83-85, 87, 135, 156, 175, 184-185

efficient, 145-146, 148 flow version, 84 global, 163 stock version, 84 structure, 146, 177

activation, 157 activation or state, 149

system, 15, 47, 51-52, 64, 66, 82, 84, 157

as a convex polyhedral cone, 142 profile

of actions, 83

of choices, 83

profit maximization, 175 proletariat, 62, 85 proper class, 14 pure mathematics, 4-5 pure or safe predicate, 25-26 purely mathematical theory, 38

qualitative conditional probability, 192-193

Archimedian structure, 192-194 quantifier elimination, 18

theorem, 19 quantitative relationships, 70

Ramsey sentence, 11, 50-51 Rand, see Rand Corporation

Rand Corporation, 1, 5 random

experiment, 184-185 process, 83-85, 87, 135, 156, 175, 184-185

variable, 187, 189, 190 density function, 193, 195 distribution function, 191 joint distribution function, 193, 195

probability density, 191 probability distribution, 193 probability function, 191 true density function, 195 vector, 193

rate of profit, 142, 156, 158, 161, 173,

177

average, 157 maximum, 157 uniform, 142, 145, 155, 159-160 rate of surplus value, 160 rational

agent, 123

choice, 58, 61, 65, 175

in a game, 126

individual, 90 theory, 90-91 player, 125

rationalization

of data, 58, 81

real

analysis, 2, 5, 23 number system, 23 real-concrete

economic system, 66 objects, 74 system, 15, 47, 51-52, 64, 66, 82, 84, 157

mechanical, 50 reduction, 140

of heterogeneous labor, 145, 151, 154

induced by a price system, 143 standard, 145

relation

antisymmetric, 20

asymmetric, 20 connected, 20, 63 intransitive, 20 irreflexive, 20 reflexive, 20 strongly connected, 20 symmetric, 20, 75 transitive, 20, 62-63

relational structure, 13, 42

M-homogeneous, 24

M -universal, 24

relational system, 14, 18-19 chain of, 24 class of, 21

elementary extension, 18, 24 relative prices, see exchange-value, 175 representational

measurement, 11, 70, 79, 112 theory of measurement, 73 reproducible

economy, 148, 160, 164, 172 social choice, 132 reproduction, 174

response theory, 74

revealed preference

strong axiom, 75, 78, 130 as a constraint, 130

weak axiom, 130 ring of sets, 186 Robinson’s model completeness test, 19, 24

sample space, 30 Samuelson-Houthakker’s strong axiom of revealed preference, 115

Santa Monica, California, 1 satisfaction

difference, 94

interval, 94, 99

level, 93, 113

rate of change, 113

of a first-order formula, 17

of a set of first-order formulas, 17 scale transformations, 71 scientific theory, 3, 5, 38

application, 51, 57, 66, 75, 81 approximated application, 51 as a methodological tool, 74 as a sup-semilattice, 39

as a system of set-theoretical structures, 6, 74

as set of statements, 39 axiomatization of, 40 basic theory-element, 54, 114, 174, 184, 196

empirical claim, 49-51, 53, 178,

198

aggregated, 53, 162-163

empirical content, 3

empirical testing, 38

guiding principle, 126

intended application of, 66

intended scope, see domain of intended applications, see domain of intended applications

logical reconstruction of, 39, 41

L-View, 1, 3-6, 38 metamathematical concept of, 39 metatheory of, 37

model, 47, 50-53, 57, 59, 172

nature, 3

nomological statement of a, 51 observational term, 48

partial potential model, 50, 52-53 positivist conception, 1 potential model, 50

rational reconstruction, 36, 38, 54 regional theory, 53 specialization, 39, 53 standard formalization, 5 S-View, 5-11, 13, 38 problems, 9

testing, 75

T-theoretical term, 48-49 semantic of theories, 55 sentences formulated in a formal

language, 4

set theory, 5-6, 35 term, 25

set-theoretical

analysis, 2, 5, 23 characterization, 33 methods, 2 object, 33

characterization of, 33 predicate, 5-8, 14, 33, 35, 40-41,

49

structure, 11, 57-58, 59, 61, 63-64, 66,

70, 91

in the empirical sciences, 41 similarity type, 9, 15, 33 simple reproduction, 160, 175 Slutsky matrix, 75 negative semi-definite, 75 symmetric, 20, 75 social

equilibrium, 114-115, 125, 127,

154-155, 160, 164 labor, 156 wealth, 163

social choice

feasible, 86 reproducible, 87 social wealth, 174 socially necessary labor-time, 134,

157

society differentiated, 134 undifferentiated, 134

Spanos’ econometrics, 182 specialization, 65, 67 Sraffa’s mathematics, 179 constructivist, 179 intuitionist, 179

Sraffian economic theory, 12, 174,

177

T-theoretical terms, 178, 181, 196 basic theory-element, 54, 114, 174, 184, 196

domain of intended applications, 178,

196

empirical structure, 181 of value, 67, 132-133, 174 standard commodity, 174, 176, 179 standard sequence, 96 Stanford University, 1-3

Department of Economics, 1

Institute for Mathematical Studies in the Social Sciences, 3 model revolution at, 1 statement view of theories, see scientific theory L-View, see L-View statistical inference, 193, 195 Stiemke's theorem, 138 stochastic process, 193 Stone Age, 79 strategic rational behavior, 115 strong axiom of revealed preference

as a constraint, 114 structural claim, see scientific theory empirical claim, 60 structuralism, 1 structuralist theory of economics, 12 structuralist theory of science, see structuralist view of theories structuralist view of theories, 11, 35, 38, 48, 67, 182

view of theoretical progress, 67 structure

Bourbaki’s concept of, 14, 30 domain, 15

enlargement or extension of a, 15 for first-order logic, 13-15 fundamental relations of, 15 homomorphic image of, 15 homomorphism, 15 automorphism, 15 epimorphism, 15 isomorphism, 15 monomorphism, 15

imbedding, 15 M-homogeneous, 22 (M, κ) -universal, 22 M-universal, 22 numerical, 20 of data, 58, 81 of real numbers, 22 order of, 14 set-theoretical, 31-32 auxiliary sets, 30, 31 canonical transformation of, 30 first-order, 33 general concept of, 30 principal sets, 30, 31 similarity type, 9, 15, 33

type of n species, 31-32

similarity, 15

similarity type, 8, 15, 32 substructure of a, 15

theory of a, 17 subsistence basket, 85, see subsistence consumption menu, 161, 177 subsistence consumption menu, 157 Suppe’s semantic view of theories, 182 Suppes’

learning theory, 81

view of theories, 4, 35 surplus rate, 157, 158 synthetic geometry, 70 system reproduction, 87

t-representation, 61, 64 target system, 60-61, 64, 66, 68, 75

as a data generation process, 193

in econometrics, 184, 193

Tarski’s concept of model, 16 tautology, 18

technological, 146

possibility, 87 set, 145

technology, 146 theorem

Afriat, 78 theoretical

idealized model, 68

model, 47, 50-53, 57, 59, 172

practice, 35-36, 38

ideological, 36 pre-scientific, 36 scientific, 36

systematization, 57, 65

terms, 35, 50

T-theoretical, 35, 47, 48 T-theoretical function in economics, 80

theory

confirmation of, 6

core, 51-52

empirical, 2, 75

falsification of, 6

finitely axiomatizable, 18

logical structure of a, 1

net, 53

of classes, 25

of labor-value, 155

of measurement, 21, 47

of science, 37

of theoretical practices, 37

primitive terms, 6

theory-dependence of observation, 183

theory-element, 52-53, 66 idealized, 67 specialization, 39, 53 total

benefit, see total profit labor-power, 88 material resources, 88 profit, 157 resources, 161

trade, 88

union, 155

truth

for formalized languages, 13 of a first-order formula, 17

unavailable stories, problem of, 13

universal numerical system, 23

unlimited computational powers, 115 urelement, 25 utility

as a T-theoretic function, 81

as a game-theoretic term, 129 compared with labor-value, 132 maximization, 124, 160 utility function, 17, 20, 67, 75, 126 as a game-theoretic concept, 130 as a random variable, 190 C², 92 cardinal, 93-94, 97 C^k, 92 concave, 78 continuous, 25, 78, 90-93, 160, 189 continuously differentiable, 19, 63, 90-91, 93, 111-112

C¹, 92

differentiable, 70, 90, 92

integration of, 75

locally nonsatiated, 63, 92, 160 monotonic, 78, 92, 144 monotonically increasing, 90 nonsatiated, 25, 64, 78, 90 quasi-concave, 90 quasiconcave, 63 utility theory, 21, 23

with respect to Q, 22

with respect to a numerical system, 22

validity of a first-order formula, 17 value

substance, 141

variable capital, 157

wage

equilibrium, 114-115, 125, 127, 154-155, 160, 164

rate, 177

system, 15, 47, 51-52, 64, 66, 82, 84, 157

representation of, 142

Walrasian demand, 115, 126 weak order, 18, 21 Wissenschaftstheorie, 38

World War II, 1

ZFC, 14