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ABSTRACT
This paper investigates Pure Neoclassical economics from a logical standpoint. After discussing validity criteria, it focuses on theoretical individualism, a core foundation of Neoclassical theorizing in all its variants. Careful analysis of this doctrine reveals that, while mathematically valid, it generates many propositional contradictions in all economic and social science theories grounded upon it.
Acknowledgements
I thank Lane Blume, Michael Macklin, and two anonymous referees for helpful comments.
Disclosure Statement
No potential conflict of interest was reported by the author(s).
Notes
1 On SN and its difficulties, see O'Donnell Citation(2022).
2 Large literatures now exist on economic methodology, economic philosophy, logical fallacies, and theoretical individualism. Since only small samples can be cited here, advance apologies are tendered to those whose relevant work is unreferenced.
3 See Debreu (Citation1983 [Citation1992], Citation1986). The assumption goes back to Walras.
4 The only ‘useful’ outcomes are sociological and ideological.
5 For more on the AOC-POC distinction, see O'Donnell Citation(2022). On contraries and contradictions, see any good logic text.
6 For a useful survey of fallacies, see Hansen (Citation2020). As noted below, one recurring fallacy in PN is that of equivocation (or mid-argument meaning change).
7 Although deduction-dependent, the approach is not reliant on the deductive-nomological model of explanation or any of the alternatives surveyed in Woodward and Ross (Citation2021).
8 It also informs Austrian economics.
9 Mathematics and set theory are closely related.
10 The sand-pile example does not imply that everything in physics is TI-based.
11 TI-based equilibria exclude whole-based equilibria — those in which equilibrium of the system (the whole) is independent of every part being in equilibrium (as in Keynes).
12 Despite many attempts, PN theorists have not yet solved (and actually cannot solve) the problem of how to include money. Financial crises/collapses are ongoing embarrassments.
13 A concept viewed as ‘atavistic’ by some free market economists.
14 Similar propositions exist for sand grains.
15 Concerning the members, ‘stable’ here references satisfied, desired or optimal states.
16 Since social theories based on TI-based axioms cannot deliver scientific theorizing, they deliver other messages, such as contradiction-tolerance and ideology.
17 A referee suggested that Wicksell showed that the lower limit must be n > 2 since prices are indeterminate in the n = 2 case. However, Wicksell (Citation1967, pp. 49–51) accepted that n = 2 trades can occur in reality even though OU is absent. A real person in this economy will trade if it brings some benefit, even if not the maximum possible. As my argument concerns reality, not PN-based agents and OU, n = 2 remains the lower limit.
18 Only an abbreviated account of the distortions is given here.
19 Logical contradictions appear elsewhere. Equating n = 1 to a ‘small’ (!) number of agents is unacceptable; n = 1 can never be n > 1, mathematically or logically. The presence of monopoly and monopsony also introduces logical impossibilities.
20 It is even claimed that such axioms can be replaced by axioms positing non-identical families, provided successive generations have, by inheritance, identical mathematical ‘parameter values’ (Becker and Tomes (Citation1979, pp. 1172–1173). Reflection shows that these axioms are basically identical and equally nonsensical.
21 A key example concerns the contradictions exposed by the Sonnenschein-Mantel-Debreu or ‘anything goes’ theorem. Orthodox theorists are aware of the theorem but ignore it, or downplay its consequences, as in Starr (Citation2011, pp. 327–331) and Kreps (Citation2013, pp. 317–318, 353–354).
22 The SN impossibility theorem is a special case of the general theorem since SN is grounded on PN axioms plus extra axioms (see O'Donnell Citation2022). SN is thus doubly compromised: general PN contradictions and SN-specific contradictions.
23 Similarities and differences exist between my approach and Lawson’s critical-realist approach. Both are concerned with reality, science, and improving economics. But while his is primarily ontologically and metaphysically based, mine is primarily based on epistemology and logic. His dismissive stance towards ‘deductivism’ generates internal problems in his account, and removes the possibility of using Neoclassicism’s adopted propositional logic to generate its own internal collapse without debatable ontological theories.
24 When reversed, this pithy, perfect, Ubuntu saying from southern Africa becomes: ‘If we are not, then I am not’. The opposing TI-based aphorism is ‘I am, regardless’, or in Thatcherite form, ‘Only individuals exist; there is no such thing as society’.