NOTES

NOTES TO CHAPTER 1

I From now on, I shall ocassionally refer to this work with the letter C. All quotationsfrom this work are taken from the Penguin edition (1976, 1978, 1981). Since thereare very different editions, instead ofreferring to page numbers in making quotationsI refer to the book, part, chapter and section, in that order. Thus, for instance, anexpression like 'Cl, pi, ch2, s3' denotes the third section of the second chapter, firstpart of book one.

2 Cl, pi, chi, s1.

3 Ibid. The italics are mine.

4 Ibid. My italics.

5 Ibid.

6 Ibid.

7 Ibid. The italics are mine.

8 Cl, pi, chi, s2.

9 Ibid. My italics.

10 Ibid. My italics.

II Ibid.

12 Cl, pi, ch 1, s3. My italics.

13 Ibid.

14 Ibid. My italics.

15 Ibid.

16 Cl, p3, ch7, s1.

17 See Corollary 2 and Theorem 7 in Kempand Kimura (1978), pp. 8-9. The Hawking­Simon condition appears as this theorem.

18 Cl, p3, ch9, s1.

19 Cl, p2, ch8, s1.

20 Morishima (1973), p. 85.

21 Morishima (1973), p. 86.

207

208 NOTES

22 Bohm-Bawerk (1896). I follow the Spanish version published in Argentina in 1974.

NOTES TO CHAPTER 2

] C3,p2,chl0.

2 C3, p2, ch9.

3 Ibid.

4 Ibid.

5 Morishima (1973), pp. 72-74.

6 C3, p2, chlO. My italics.

7 Ibid.

8 C3, p4, chl8.

9 Ibid. The italics are mine.

10 C3, p6, ch37. My italics.

I) C3, p7, ch49.

12 C3, p7, ch5!.

13 Bohm-Bawerk (1974), p. 57.

14 Ibid., p. 54.

15 Ibid.

16 Ibid., p. 58.

17 Ibid., p. 67.

18 Ibid., p. 77.

19 Nuti (1974), p. 43.

20 Ibid.

2] See pp. 8 and 9.

22 Cameron (1952), p. 193.

23 Morishima and Seton (1961), p. 204.

24 Ibid.

25 Op. cit., p. 209.

26 Cf. pp. 297 and 298.

NOTES 209

27 Morishima (1973). Many of the mathematical techniques used by Morishima in thisbook were developed mainly in the fifties by mathematical economists such as Samuel­son, Arrow and Koopmans. See for instance Koopmans (1951).

28 See Theorems 1 and 2 of chapter I.

29 See p. 131.

30 See Morishima (1973), p. 173.

31 Morishima (1974), p. 618.

32 The convexity assumptions have been used to prove the existence of equilibria inneoclassic economics (See Debreu (1956,1959». Roemer uses the convexity assumptionin order to derive the existence of what he calls Marxian reproducible equilibria (seeRoemer (1981».

33 Roemer (1981), p. 38.

34 In fact, Professor H. Scarf has developed illl portant results on the problem ofbuild­ing a theory of (neoclassical) equilibri um on non-convex finitistic assumptions. See Scarf(1981a, 1981b).

NOTES TO CHAPTER 3

I See Enderton (1972), p. 75.

2 See p. 104.

3 See Enderton (1972), p. 79.

4 For a precise definition of decidability see Boolos and Jeffrey (1980).

5 Which can be seen, for instance, in Suppes (1972).

6 Wallace and Findlay (1975), p. 50.

7 See the Susiitz to §31. Wallace and Findlay (1975), p. 51.

8 For a systematic study of the relationships between the philosophy of Hegel and thatof Aristotle, see Mure (1970).

9 See Suarez (1960), Disputation XL, Part VI, §5.

10 See Brown (1984), pp. 153, n. 12. The other "labyrinth" is the problem ofreconcilingGod's foreknowledge with human freewill.

II For a definition of Archimedean, regular, positive, ordered, local semigroup, seeKrantz et al. (1971), p. 44.

NOTES TO CHAPTER 4

1 Wallace and Findlay (1971), §79, p. 113.

210 NOTES

2 Wallace and Findlay (1971), §161Z, p. 224.

3 Findlay (1958), pp. 70-1.

4 Findlay (1958), p. 57.

5 Findlay (1958), p. 74.

6 Findlay (1958), p. 75.

7 For a view of idealization as isolation see Miiki (1991).

8 Findlay (1958), p. 77.

9 Findlay (1958), p. 71-2.

lO Findlay (1958), pp. 72-3. The first italics are mine.

II Miller and Findlay (1971), §382, p. 15.

12 Miller and Findlay (1971), §381, p. 8.

13 Wissenschafl der Logik, p. 44; quoted by Findlay (1958), p. 152.

14 Findlay (1958), p. 32.

15 See "Materialism and Matter in Marxism-Leninism", in r-fcMullin (1978).

16 In the same Postface to the Second Edition.

l7 Elster says: "I find it hard to believe that Marx would have come to accept the lawsof dialectics had he put his mind to them". See pp. 42-3.

l8 Elster (1985), p. 37.

19 Dussel (1990), p. 404. The translation is mine.

20 On 1M Soul, 430' 10-25. See Barnes (1984), volume I. The italics are mine.

21 Aquinatis (1886), p. 455. The translation is mine.

22 In the sections A. Consciousness and B. Self-Consciousness. See Westphal (1989),pp. 154 ff.

23 SCMlling Werke, v. V, p. 198. My translation. lowe to Dussel (1990) his making meaware of Schelling's criticism of Hegel.

24 SCMlling Werke, Book III, Lesson XII.

25 Plotinus, Ennead V, 4.

26 Cfr. Leclerc (1972), p. 66.

27 Holy Bible (The New King James Version). Exodus 3:14-15.

28 Kaufmann (1972), p. 21.

29 See Avineri (1972), chapter 2.

NOTES 211

30 See Dickey (1987) for a thorough study of the historical, political and theologicalcontext in eighteenth century Wurtemberg, the land where Hegel was born and wherehe grew up.

31 See Avineri (1972).

32 See Waszek (1988).

33 See Wood (1990).

34 See Stern (1990).

35 See Westphal (1989).

36 Actually, this is what Stern (1990) does in connection with the Pherwmerwlagy a/Spirit.See pp. 43-54.

37 Stern (1990), pp. 40-1.

38 This quotation is taken from an unpublished paper dated by Van Heijenoort in 1943under the pseudonym ofAlex Barbon. See Van Heijenoort (1943) in the bibliography.

39 Van Heijenoort, op. cit.

40 Ibid.

4l I follow here the German version (1974). Whenever I deem it important, I providethe original German expressions together with their translation.

42 Marx and Engels (1974), p. 630.

43 The value (2000/g) l/2 is obtained by setting - ~gt2 + 1000 = 0 (which is the positionof the particle at the end of the motion), and solving for t.

44 Nowak (1980), p. 95.

45 Nowak (1980), p. 29.

46 Nowak (1980), p. 9.

47 For a detailed, albeit a rather schematic presentation of this process in connectionwith MTV, see Hamminga (1990).

48 See Koopmans (1951) and Leontief(1941).

NOTES TO CHAPTER 5

l Morishima (1973,1974), Okishio (1963), Roemer (1980,1981).

2 Marx (1970), p. 29.

3 Marx (1970), p. 34.

4 Marx (1970), p. 45.

5 Ibid.

212 NOTES

6 In CI, pi, chi, s3.

7 See Rubin (1972).

8 Rubin (1972), p. 139.

9 Rubin (1972), pp. 139-140.

10 See Krause (1979,1980,1981) in the Bibliography.

II Cf. equation 4 of chapter 1. The proviso therein does not apply in the present case,i.e. the vectors 1fT are of dimension m.

12 More precisely, we are requiring x ;::: 0 and

for every (x, 1f. x) E Po.

13 CI, p3, ch7, s2.

14 Ibid.

15 Ibid.

16 See Kemp and Kimura (1978), p. 3.

NOTES TO CHAPTER 6

I See pp. 73-74.

2 Roemer (1981), p. 73.

3 A proofofthe nonemptyness ofA j(p, c) is provided in Lemma 2 of the next chapter.

NOTES TO CHAPTER 8

J Samuelson (1963). p. 233.

2 It would be more correct to write [L(x)T, X(i)T, x T ]. I ask the forgiveness of thereader for this little notational abuse.

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__, Dialectics ofNature, several editions.

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Gale, D., The Theory ofLinear Economic Models, McGraw-Hili, New York,1960.

Gantmacher, E R., Applications of the Theory of Matrices, IntersciencePublishers, New York, 1959.

Garcia de la Sienra, A., "Elementos para una reconstrucci6n 16gica dela teoria del valor de Marx" in C1itica 35, 1980.

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__, "Axiomatic Foundations of the Marxian Theory of Value",Erkenntnis 29, 1988.

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__, Phenomenology ofSpirit, Clarendon Press, Oxford, 1977.

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___, "Abstract Labour in General Joint Systems" in Metmeconomica32,1980.

___, "Heterogeneous Labour and the Fundamental Marxian The­orem" in Review ofEconomic Studies 48, 1981.

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___, "Marx in the Light of Modern Economic Theory" in Economet­1ica 42, 1974.

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Okishio, N., "A Mathematical Note on Marxian Theorems" in Weltwirt­schaftliches Archiv 91,1963.

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___, Analytical Foundations of Marxian Economic Theory, CambridgeUp, Cambridge, 1981.

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___, Introduction to Logic, D. van Nostrand, New York, 1957.

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Wood, A. w., Hegel's Ethical Thought, Cambridge Up, Cambridge, 1990.

NAME INDEX

Alex Barbon 211Alvarez, F. 42,213Aquinas, St Th. 105, 106, 107, 108,

210,Aristotle of Stagira 77, 97, 104, 106,

107,209Arrow,K.J. 123,208,213Augustine, St 108Averroes 105, 106Avineri, S. 109,210,213

Balzer, W. 72,213Barnes,]. 210,213Broncano, E 213Brown, S., 209,213Beethoven, L. v. IIIBirkhoff, G. 72,215Bohm-Bawerk, E. v. 3, 10, 39, 42, 43,

44,49,50,51,52,53,207,208,213Bolzano, B. 76Boolos, G. 209,213Bourbaki, N. 3, 72, 213Brzezinski, J. 213

Caldwell, B. 213Cameron B. 55,208,213Christ Jesus 108, 110

Debreu, G. 128, 185,209,213Dickey, L. 210, 214Dmitriev, V. K. 54,55Dussel, E. 101,102,210,214

Elster,]. 58, 101, 116,210,214Enderton, H. B. 209,214Engels, F. 43,44,51,101,115,210,214Eudoxus ofCnido 76

Fichte,J.G.92,96

219

Findlay,J. N. 93,95,96,209,210,214,215,217

Gale, D. 214Gantmacher, F. R. 214Garcia de la Sienra, A. 214Georgescu-Roegen, N. 55, 214Godel, K. 68Gracia,]. J. E. 214

Haydn, E]. 111Hamminga, B. 116,210,214Hawking-Simon condition 207Hegel, G. W. F. 78, 92, 95, 98, 99, 100,

104, 106, 107, 108, 109, Ill, 113,121, 128, 160,210,214

Jeffre» R. 209, 213

Kakutani, S. 185, 214Kant, E. 78, 96, Ill, 113Kaufmann, W. 108,210,214Kemp, M. C. 207,212,215Kim ura, Y. 207, 212, 215Koopmans, T. C. 123,208,211,215Kosok, M. 92,215Krantz, D. H. 81,89, 150,214Krause, U. 132,133,137,176,211,215Kuipers, Theo A. E 213

Landau,E. 72,215Leclerc, l. 210,215Leibniz, G. W. E 81Lenin, V. l. 99,215LeontiefW. W. 2,54,55,123,211,215Lobkowicz, N. 100,215

Maki, U. 128,210,215

220 NAME INDEX

Marx, K. 1, 2, 3, 4, 7, 8, 9, 10, 11, 12,13, 16, 18, 19, 20, 35, 39, 42, 43, 44,45, 46, 49, 50, 52, 58, 91, 94, 98, 99,100,101,102,104,115,121,123,128129,130,131,156,210,211,215

McLane, S. 72,215McMullin, E. 210McTaggart,j. M. E. 93Miller, A. V. 210,215Morishima M. 2, 3, 29, 39, 42, 45, 47,

48,49,55,56,57,58,59,60,123,124,208,209,211,216

Moses 108Moulines C. U. 72, 213Mure, G. R. G. 209,216

Nikaido, H. 185,216Nowak, L. 116,121,122,125,126,127,

210,213,216Nuti 54,208,216

Okishio, N. 56, 176,211,216

Plotinus 108,210

Quintanilla, M. A. 213

Robinson, A. 68, 216

Roemer,]. E. 57,58,60, 124, 125, 149,171,209,211,212,216

Rubin, 1. 1. 4, 131, 141,211,216

Samuelson, P. 123, 191,208,212,216

Scarf, H. E. 209,216

Seton, F. 55, 56, 176, 208, 216

Schelling, F. W.]. 107,108,210,216

Sneed,]. D. 72,213,216

Stern, R. 114,211,216

Suarez,F. 77,78,80,209,216

Suppes, P. 72,209,216,217

Von Bortkiewicz, j. 217

Van Heijenoort,j.v. 116,211,217

Von Neumann,j. 57,58,60,123

Wallace, W. 209,217

Waszek, N., 210,217

Westphal, K. R. 107,111,210,211,217Wolf, C. 78

Wood, A. W. 211,217

SUBJECT INDEX

absolute mind 98absolute negativity of the notion 97abstract determinations 120, 121, 165activation, intensity or state of an

economy 133, 137, 198active intellect or agent 97, 104, 105,

106, IIIaffine transformation 153, 156alienation 177analytical philosophy 94approximation 121Averroism 4, 105axiomatic systems 125

behavior of the firm 57,160,179,193Bible 109,210,214Buchenwald 110

capital good 18,21,32,53,170,194age of 58industries 22, 26period ofrotation of 19,53,57

Cartesian space 90choice of techniques 1,57Christian faith 105Christianity 109circulation process 46civil or burgeois society 160classical mechanics 113, 118closed economy 19,54,205commensurability 82commodity 8, 102

separately producible 135, 136commodity economy 130commodity exchange 132communism 109competition ofcapitals 159competitive equilibrium 5, 160, 179,

209

221

Marxian 5,57, 124, 159,209competitive market economy 31, 128concentration of multiple

determinations 117, 120concrete concept 127concrete of thought 120concrete thought ll4, ll5concretization 122, 123, 125, 127cone 134, 164

closed 165convex 147, 165convex polyhedral 142, 153, 164,

193constant returns to scale 18, 53, 151,

164constant capital 35, 38consum ption basket of the workingclass 25, 31, 32, 53, 54, 176consumption bundle 165continuum 81,82contradictory concepts 94, 95correspondence 182, 184

lower semicontinuous (lsc) 182upper semicontinuous (usc) 182

cosmology 76, 78credit 162, 163, 166, 168

decidable set ofsentences 69decision function 166decision ofthe firm 164, 170, 204demand 46, 53demand function 164dialectic 128dialectic contradiction 95, 149,205dialectical forms of motion 101dialectical method 79,91, 92ff, 99, ll7,

120, 125, 127, 165formalization of 92, 94Hegelian 4,91, 92ff, 101, 104, llO,

ll5

222 SUBJECT INDEX

Marxian 79, 104, 115, 171Marx's "inversion" of 4,91,99, 100,

104, 110Marx's "breaking of the bottom"

of 102, 104mystical shell of 100rational kernel of 100, 115

division oflabor 12doctrine of the notion 114

eigenvector 33elucidation of concepts 112empirical data 119, 120empiricist philosophy 91, 107ens rationis 75equations for value 25, 36

Leontief's 56equivalence relation 139essential predication 114exchange 129exchange-value 8, 130

valid 140existence of abstract labor 149experience 96exploitation 31,58,161,175,177

factual reality 114faith 108Farkas-Minkowski Lemma 137Father, the 107financial capital 101financial capital market 159, 163,202

clearing of 180financial feasibility function 169

global 170financial resources of the firm 169firm 161, 162, 163, 165fixed point 184foundational problems 91

of MTV 8, 40, 41, 62, 103free lunch 164Frobeniusroot 33,201F-twist 191full employment 204,205fundamental measurement 3, 79, 90,

135, 149

general determination 125general equilibrium theory 139, 179general joint system 133, 142God 108,110Gulag 110

Holy Spirit 107, 108honw politicus 192honw CEconomicus 114, 160, 192honw sapiens 76homomorphism 79human intellect 114human mind 76

Idea 98, 106, 107, 128self-developing 106, 107

idealization 90, 93, 95, 125, 210method of 121, 122, 125, 126idealized concepts 114idealized models 116, 120, 122, 192idealizing assumptions 41, 114imperfect entry 164incommensurability 4

problem of 113individual men 98, 109, 110infinite divisibility 53

of goods 53, 164oflabor amounts 164of production processes 53

initial holdings or endowments 162,163, 166, 192, 205

inner prod uct of vectors 21, 150inputs 20,21isolated notions 114,210interest rate 163, 166, 202international trade 205

Jehovah 97joint production 19, 53, 57, 136, 193,

194, 196

Kingdom of God 109Kolmogorovaxioms 70

labor 12abstract 13, 15, 43, 128, 130, 131,

132, 134, 135, 140, 141, 150, 157,174,202

SUBJECT [NDEX 223

complex 12concrete 15,138,140, [47, 151homogeneous 11 13, 19,31,53,57,

58,60, 129,130, 134, 192homogenization of 134, 135heterogeneous 12, 53,58, 149, 150,

151,176,191indispensable 143, 147, [48, 164instruments of 20, 144live 34,102,103,117,128,175,202necessary 34objects of 20physiologically equal 131process 136, 142productive 143, 147, 148, 164reduction of complex to simple 12,

13, 14, 150red uction of heterogeneous to

homogeneous 14,15,17,19,129,131,135,152,156,157,172,202

simple 12, 31, 130social 42, 130, 139, 140socially equalized 131type of 139,141,164,193unskilled 20, 130, 141value-creating 131

labor-power 12, 20, 101, 131, 144in the physiological sense 131normal 144, 145, 146, 147

Lawof Profit Maximization 161,171,

174,178of Supply and Demand 189of the Cyclical Crises 1of the Tendency of the Profit Rate

to Fall 1scientific 74, 122of Value 3, 4, 5, 15, 16, 17, 39, 40,

41, 42, 43, 44, 46, 47, 48, 49, 50,51,52,53,54,58, 103, 104, 122,123,124,156,157,159,161,171,173,175,176,192,193,202

Leontief economy or technology 5,55,123, 137, 164, 176, 191, 192, 193,194, 198, 199,200,202,203,204

liberty 97linear algebra 72

linear functional 132linear model of MTV 123linear programlning problem 57, 60logic

first order 64formalized 93mathematical 76, 93second order 70

logical consequence 68luxury goods 21,32, 194

manifold of intuitions 111market 130market economy 137,161,191

efficiency of 175Marxian capitalist economy 5,161, 171,

174,175,177,179,193Marxian competitive equilibrium 160,

180Marxian theory of value (MTV) 7, 39,

41,58,115,141,160,179,210foundations of 137foundational problems of 8,40,41,

62,103Marxism 110Marxism-Leninism 100Marx-Von Neumann theory 57,58matrix 29

consumption 26, 165demand 166, 199global 195,198,200,201indecomposable 28,29,33, 196,

198, 200, 203nonpositive 29nonsingular 29of capital goods

ind ustries 23ofcapital and consum ption goods

industries 27, 195,203ofconsum ption goods industries 23ofjoint labor inputs 133, 195ofjoint material inputs 133ofjoint material outputs 133ofjoint net inputs 133, 134oflabor inputs 23quasiproductive 28,203reproducible 28semiproductive 28, 33, 200

224 SUBJECT INDEX

matter 81,99, 107concept of 100

means of production 20,35, 102, 147,193

measurement 77,80additive conjoint 150extensive 81of abstract labor 3, 137, 149

Meinongian economy 128,160,161mereology 81metaphysics 78

Aristotle's 105Hegel's 79, 105, 107, II0, II

model 3,68, 75, 125concrete 126singular 126

model construction 117model representation 126

natural history 76natural theology 78natural world 76nature 97, 98necessary labor 34neoclassic economics 160, 209Newton's second law 119nontriviality 138nous 97, 99, 104, 105, 106, 108

objects in themselves IIIobjects of experience 96, 112ontology 78, 80, 94

of substance 114scholastic 79, 107

optimality function 169organic or value composition of capital

34,44, 129, 159output 21

net 21,135,137,156,175

pantheism 108particular 125passive intellect 105, 106philosophia de enle 77philosophy ofeconomics 192philosophy of nature 97,98philosophy of spirit 97

physics 112point-in put-point-output 19positive hull 146, 147price 31,32

shadow 57price system 30,33, 133, 139, 140, 148,

152, 153, 156, 162, 163admissible or valid 9,134,135,140,

141, 142, 143, 145, 157equilibrium 34,38,46,50,156,199,

201, 202feasible 170,173,175,177,178,

193, 199,200,205private property 109producer 22, 137production plan 137, 139production price 31, 44, 45, 46, 49, 52production process 21, 102, 137, 138,

1-17, 154efficient 143, 174, 196feasible 180global 180indispensable 135, 136, 137

production set 61,139,164,165,193aggregate 164linearly independent 194normal 147, 148, 164

profit 32, 161maximization 57,124,163,179, 180net 32

profit equalizing equilibrium 149profit maximizing function 169

global 170prototype of MTV 17, 18,41,53,54,

55, 128, 156, 159, 160, 191

quantitative concept of value 7, 17, 30,40,41

rate of profit 30,33,34,36,37,43,45,46,52, 142, 177, 178,202,203equilibrium or uniform 34, 35, 44,

47,50,61,142, 143,145,146, 147,156, 159, 174, 176, 179, 193, 199,200, 201

rate of exploitation 30, 34, 35, 36, 45,56,57,60,175,176,178,203,204

rate of surplus value 35

SUBJECT INDEX 225

rate ofsurplus value 35rational psychology 78raw material 144real concrete 117, 120, 121reference 77reflection 100religious freedom 110rent 47representation 4, 63, 77

cardinal 150mathematical 149not fundamental 90ordinal 150theorem 80theory 75of abstract labor 4, 135, 151, 152,

153reproducible global decision (RGD) 5,

179,180,192,200,201,202,203,205existence of 200

reproduction of the econom y 58, 177,179,180,193,204simple 199

restrictive assum ptions 53, 116revealed religion 109Revelation 108Ricardian theory of value 7, 141rigour in science and philosophy 112rising (or passage) to the concrete 116,

117,120,122,125,126,127

salary 32salvation L08, L09satisfiable formula 67,68,75scientific method 117sentence 66set-theoretic predicate 125, 192set of labors or labor inpu ts 140, 141,

148, 170, 174simple commodity production 41, 43,

44,48,49simple Marxian economy 3, L8, 29, 30,

35,38,44,51,52,53,164,192social contradiction 116social division oflabor 46social resources, total or global 162,

166

social science 112socially necessary labor-time II, 17,20,

24,25,40,45,49,50,59, 131, 144Son, the 107soul of man 110Soviet philosophy 99special relativity 113specialist firm 193, 196, 197, 199speculative philosophy 109sphere ofdistribution 43sphere of production 16,43, 130spirit 96, 97, 99, 100, 105, 107, 109,

110, IIIabsolute 108, 110human 108, 110self-conscious 96, 97, 98, 107

standard simplex 162State 109, 160structure 3, 63, 66, 72, 75, 77

abstract labor 135, 148, 150, 153,156, 157

basic Marxian 165idealized 127Aristotelian extensive 83,85first order 70k-type of a - 72, 73numerical 79ontological 79, 135productive 147,147,148,149,151,

152, 156representation theorem of abstract

labor - 150, 151, 152, 153representation theorem of

Aristotelian extensive - 89scientific 75species 72, 74, 75super- 71type ofa - 74

substance-universals 113, 114supply 46surplus-value 7, 17, 30, 34, 35, 46, 47,

52

technology 19alternative 193,194,196,197,199actually chosen by the firms 147,

170

226 SUBJECT INDEX

interconnected 19,25,28, 195, 196,199,200,201

quasiproductive 29reproducible 27,28semiproductive 19,25,27,28, 196,

200,201tensor 150theorem 66

Berge's Maximum 183Compactness 68Coders CompletenessFundamental Marxian (FMT) 2, 30,

36, 37, 53, 56, 57, 59, 124, 161,175,176

Perron-Frobenius 33, 201Stiemke's 153

theory 68, 75axiomatizable 69finitelyaxiomatizable 69of measurement 79of models 69, 76of science 76, 91of sets 76proof 76recursion 76scientific 69, 77, 91Zermelo-Fraenkel - of sets 7 I, 72

topological space 69Totalitarianism 110totality of thought 114, 120trades 20transcendental idealism 113transcendental subject II I, 112transformation problem 4, 37, 39, 47,

124, 129,203true formula 68

understanding (Venliinde) 78,93, 95, 96synthesizing activity of III, 112

unity of apperception 113unity of the diverse 117,120universal in action 104, 106uni versal kinds 96, IIIuniversals, Hegel's theory of III

vague concepts 112

valorization process 17, 144value or labor-value 4, 9, 35, 38, 47,

49,57,59,61,62, 124, 135, 149, 150,156, 157, 175and price, proportionality of 38,39,

40as regulator of prices 40,42,43,45first definition of II, 23, 29, 30, 56form of manifestation of 9, 13, 103,

129, 131individual 48magnitude of II, 13, 131market dependent determination of

17,43, 132market independent determination

of 14, 16, 17,42, 43, 46, 130optimum 57,59,60, 124second definition of 12, 25, 29, 30,

56source of (Quell e) 102substance 10, 13, 130

variable capital 38vector 20

consumption 26,31, 60norm 167n-dimensional 132oflabor inputs 20, 138of material inputs 21,22, 138of material outputs 21, 138of net outputs 21oflabor-values 24, 25, 54of wage goods 26,32representing a prod uction

process 21wage 152

von Neumann economy 176von Neumann golden rule 58,59

wage 30,31,32hourly 151

wage good 19,21,170,194ind ustries 23

wage system 142, 145Word of Cod 107working class 161

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