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Cf. G.W.F. Hegel. 1932. Jenenser Realphilosophie I, Leipzig, Bd. 19 in Sämtliche Werke, eds., Georg Lasson, J. Hoffmeister; or summary thereof in H. Marcuse, Reason and Revolution, Oxford, 1947.
EN v.5.1132b33-1133a3. Abbreviations of Aristotle’s texts used in this article include: Pol.= Aristotle, Politics; EN = Nicomachean Ethics; EE = Eudemian Ethics.
EE 1242b8-10; for an example, cf. EN 1133a32-3.
Cf. EN v.3.
This is true regardless of the value of α/β, i.e., if α/β < 0, then β exploits α. The long form of this analysis is as follows: Since shoes, houses, nourishment and health are incommensurables (cf. EN v.5.1133b18-20; and Robert Gallagher ‘Incommensurability in Aristotle’s theory of reciprocal justice,’ British Journal for the History of Philosophy. 20:4 (2012): 667–701, esp. 669-83), we cannot arrive at an exact exchange ratio of those erga. Therefore,
(A2) δ/γ ≠ N_δ/N_γ ,
where Ni are the quantities of erga γ, δ. Rather, we can only approximate their relative value, i.e.,
(A3) δ/γ ≈ N_δ/N_γ ,
where we use ≈ to indicate the reduction involved in expressing δ/γ as a rational number. From A and A3, we have
(A4) N_δ/N_γ = 〖 P〗_γ/P_δ ≈ α/β,
where Pi is the unit price of ergon δ, γ, for the ratio of the quantity of one good exchanged for the quantity of another is the inverse ratio of their unit prices (cf. Samuelson , p. 58, cited by Soudek). If α/β signifies relative social status, and α/β > 1, then party β hands over to party α more of his product than the product of party α is worth by the factor α/β, for in accordance with A4,
(A5) Nδ ≈ (α/β) Nγ.
That means that party α is materially rewarded through the transaction due to possessing a higher status. That higher relative status skews the exchange ratio. The result is that the price of the ergon of party α is higher than its value, i.e.,
(A6) P_γ/P_δ > V_γ/V_δ ,
where V is the unit value of ergon δ or γ. Here, we take into account the fact that prices as exchange-values may not always reflect the use value of a good. In that way, we distinguish, as does Aristotle, between the proper use of a good and its use as an item for exchange (cf. Pol. i.9), or as Marx did, between use value and exchange value. A complete treatment of these formulae and other used in this article appears in the Author’s “Incommensurability in Aristotle’s theory of reciprocal justice,” British Journal for the History of Philosophy. 20:4 (2012): 667–701.
Cf. Wolff (1982), 86-7, and Robert Gallagher “An Aristotelian Social Welfare Function.” (Forthcoming).
For a more detailed discussion, cf. Robert Gallagher “The role of grace in Aristotle’s theory of exchange,” Methexis 26.
Cf. 1385a32, 33.
Cf. 1385a21, 26, 32; 33.
On contemporary inequality, cf. F. Alvaredo, A.Atkinson, T.Piketty and E. Saez (2013) “The top 1% in international and historical perspective,” Journal of Economic Perspectives, 27(3): 1-21. T. Piketty and E. Saez (2014) “Inequality in the long run,” Science, 344(6186): 838-844.
Marx, K. (1973) Grundrisse, London; reprinted 1993 at pp.487-88.
For a full discussion, cf. Gallagher (2012) ‘Incommensurability in Aristotle’s theory of reciprocal justice,’ cited n.6.
Cf. EN v.5.1133a32f
EN 1133ª1-2; cf. ª3-5; EE 1242b2–21, esp. 1242b15–21.
Cf. EN 1163b7-10.
I draw this suggestion from Aristotle’s Eudemian Ethics. Cf. Gallagher (2012) ‘Incommensurability in Aristotle’s theory of reciprocal justice,’ cited n.6 for a complete discussion.
Data for Fig. 2 from U.S. Census Bureau (n.d.), and for Figs. 3-4 from the World Bank (n.d.), are the ratio of the income share of the poorest 20% of a country’s population to the income share of the wealthiest 20%.
Cf. T. Piketty and E. Saez (2003) “Income inequality in the United States, 1913-1998,” Quarterly journal of economics, vol. 118, no 1, p. 1-39. at Fig. 1, and T. Piketty and E. Saez (2013) “Top incomes and the Great Recession,” IMF economic review, vol.61, n.1, p.456-478.
Documented in Gallagher (forthcoming) “An Aristotelian Social Welfare Function.”
Thailand and Ecuador in recent years also exhibit a positive slope to their graphs of Q_5/Q_1 (Gallagher, unpublished results).