In the paper, I show how two theological axioms in both Christianity and Hindu Vedanta:
- love your neighbour as yourself
- the glory of God surpasses any other gain or loss
generate non-existence of solutions in a mathematical formalization of utilitarianism which cannot be resolved without assumptions on preferences (virtues) and specifying discount rates. The paper formalizes paradoxes arising from the use of mathematical optimization as either a normative or positive methodological framework to study theological issues (for example, Menzies and Hay (2012)). The critique rests on incorporating the above two axioms along with arguments against the social discount rate made by Cowen and Parfit (1992) and the ‘No-Difference View’ (Parfit, 1984)1 into standard economic optimisation problems.
The paper shows non-existence arises in three classes of problems. In each class, pathologies arise from non-compactness of agent spaces and/or discontinuity of welfare functions on the appropriate topology. The three classes of problems are:
- Maximising welfare functions that take into account our responsibility to future generations. In this case, the limit of welfare from consumption paths that approach zero consumption can be shown to approach infinity, but zero consumption drops to zero welfare. In practice, the paradox formalises the Repugnant Conclusion already discussed by Parfit (1984). However, I also argue that any resolution of the Repugnant Conclusion implies breaking one or both of the theological axioms above.
- Choosing a rate at which to weight others’ welfare compared to our own. In this case, the limit of all agents sacrificing consumption for the sake of one measure zero agent approaches infinity, but the single agent consuming everything drops welfare to zero. The paradox implies we will all be better off if each consumed nothing but gained ‘altruistic’ utility from ‘giving’ to a single agent.
- Non-existence of preferences that trade-off salvation with worldly activity. In this case, any attempt to formalise peoples’ decision to choose how much to invest in non-superfluous spiritual activity violates the second theological axiom above.
The results in the paper are abstract and study corner cases when assumptions made by the model are taken to their ‘limit’; nonetheless, the argument I make is that any assumptions made to avoid the corner cases are normative and/or imply that God is ‘finite’. I conclude by suggesting resolution of the paradoxes above requires ‘faith based’ considerations. In particular:
- Utilitarian foundation of ethics is not internally consistent without a set of preferences and discount rates. Not only is utilitarian analysis incompatible with the two axioms suggested above, but there are contradictions if one uses utilitarian methods to ask normative questions without fixed preferences and discount rates.
- Grace of God and leap of faith are the key factors in understanding the path to salvation, not rational cost benefit analysis of people choosing or not choosing to be virtuous/ turning to God (Kierkegaard, 1843).
References
Cowen, T. and Parfit, D. (1992). Against the Social Discount Rate. Philosophy, Politics, and Society, (I):144–161.
Kierkegaard, S. (1843). Fear and Trembling. Penguin Books.
Menzies, G. and Hay, D. (2012). Self and Neighbours. Economic Record, 88(s1):137–148.
Parfit, D. (1984). Reasons and persons. Clarendon Press, Oxford.