Ethical Paradigm Equivalence

The ethical paradigm equivalence conjecture hypothesizes that each of the paradigms, virtue ethics, deontology, and utilitarianism, can embed the other paradigms: they can express theories that are equivalent to the other paradigms.

For each pair of paradigms A and B and theories a in A and b in B, there exists a translation trans in A such that trans(a) is equivalent to b.

The intuition is that each paradigm provides a formalism and approach to ethical decision theory that is universally expressive.

Discussion

I made this conjecture when investigating ethics for a blog post, Virtue Ethics Qua Learning Theory: there seemed to be features and limitations to each ethical paradigm, and they seemed to be universally expressive if one took liberty to define non-traditional terms (for example, novel virtues or custom utility functions). Fortunately, there are other ethical philosophers with supportive theories: for example, Martha Nussbaum argues that the standard categorizations of ethical theories is confusing and unhelpful and that Virtue Ethics is a Misleading Category because both Kantian deontology and utilitarianism provide accounts of virtues. Thus the suggestion is to focus on the specific theories of philosophers instead of just assigning them to a paradigmatic category. Derek Parfit in On What Matters suggests that Kantian deontology, consequentialist utilitarianism, and Scanlon’s contractualism unify in a single “Triple Theory” because the three theories should generally agree in their recommendations as to when an an act to be wrong. The ethical paradigm equivalence conjecture takes these claims furher by positing that the ideas of ecah paradigm can be treated within the other paradigms; moreover, any theory of one paradigm can be expressed in the others. Furthermore, it may not be uncommon for ethical theories to contain elements of multiple paradigms.

Does this mean paradigmatic categorization is, as Nussbaum suggests, meaningless? No matter which paradigm one starts with, one will likely need to deal with notions of virtues, rules, and utilities (whether as primary or secondary entities). Given that moral perfection is intractable (or undecidable)¹See the analysis in Jakob Stenske’s On the Computational Complexity of Ethics for more details.²This analysis suggests that the Ethical Decidability Conjecture is false, at least for expressive theories that could be applied to diverse real-world domains., one cannot expect any one theory to perfectly cover all moral domains. My hypothesis is that each paradigm captures distinct, important aspects of behaving well (morally), thus there can still be meaning in paradigmatic categorization as well as in mixed theories.

Inter-Paradigmatic Motivations

In this section, I’ll discuss how each paradigm can be natively motivated from within the telos of the other paradigms.

Consequentialist utilitarianism is seen as providing a moral basis in utility, which leads to an optimization approach to attaining this good. However, in practice, brute force optimization is intractable³A Partially Observable Markov Decision Process (POMDP) is PSPACE-hard with finite horizons and undecidable with infinite horizons, thus working with heuristics is necessary. This motivates combined theories such as Hare’s Two-Level Utilitarianism where people are advised to follow rules in the regularly covered cases and to apply utilitarian analysis when in special circumstances. Further, Parfit suggests that people adopting the disposition to love and prioritize care for one’s children may lead to the best consequences (even if locally violating the top-level goal to maximize the quality of the state of afairs)⁴Reasons and Persons. Thus both deontic rules and virtues can be intrinsically motivated within consequentialist utilitarian theories.

Deontological approaches aim to provide a basis of morality via self-evident truths and core principles (such as those pertaining to being a sentient being among others in a society), which indicates reasoning as the means of determining what is good. Parfit argues extensively that optimific (i.e., consequentialist utilitarian) approaches are precisely those whose being universal laws everyone could rationally will. Universal optimific principes also arguably satisfy John Rawls’ original position thought experiment that one should only accept principles that one would select no matter which position in society ends up having⁵This is one way to advocate for sufficiently egalitarian principles.. Kant holds that the single virtue that is good without qualification is posessing a good will, which is a will whose decisions are wholly determined by moral law. More broadly, virtues are the moral stength of the will in adhering to duty against cotnracy inclinations⁶This parallels the target-centered virtue ethics view that virtues correspond to appropriate responses to moral dilemmas, i.e., situations with contrary incentives.: thus while rules such as the categorical imperative determine what is right, virtues are important and represent our capacity to do what is right in practice⁷For example, courage represents one’s strength to uphold moral principles in spite of fear or potential harm..

Virtue ethics focuses on cultivating virtuous character traits, which can take a flourishing life (eudaimonia) as a moral basis⁸However, Kantian good will, utility, status, bonds, or value in general can also be seen as moral bases for the virtues., and suggests that learning is the road to becoming a good person. An overall virtuous person still needs to make practical decisions. For example, take Schopenhauer’s base virtue of “boundless compassion for all beings” (and the related virtue of benificience): perhaps when in a difficult situation, one is likely to follow optimific principles, learning from the consequences of one’s actions, namely, one should act in line with utilitarian analyses. Furthermore, with phronesis (prudence or practical wisdom)⁹An entity has phronesis if ey have good judgment in determining how to act and what is needed for a flourishing life., one will learn how much energy to devote to utilitarian analyses versus employing other strategies. Dutifulness (pietas) is considered a virtue in its own right: thus the virtuous play be the rules. It can be argued that as one develops virtues such as integrity, justice, honesty, and reliability, one will devote oneself to moral principles¹⁰This lines up with Kohlberg’s stages of moral development.

Kinds of Equivalence

Todo: discuss the two kinds of equivalence to explore, the trivial embedding and equivalence of moral guidance.

Embedding Sketches

Deontology

Deontology easily embeds the other paradigms thanks to working with logical rules. Take any ethical theory and assert an obligation to adhere to this theory. QED.

1. “Be virtuous.”
2. “To the best of your knowledge and capacity, act to maximize benefit and minimize harm for all sentient beings.”

Virtue Ethics

Virtues interpreted as character traits are fairly flexible, so this embedding should work similarly to the case of deontology.

1. Pietas: the virtue of dutifulness¹¹From Wikipedia: “The man who possessed pietas “performed all his duties towards the deity and his fellow human beings fully and in every respect,” as the 19th-century classical scholar Georg Wissowa described it¹.”
2. The virtue of “learning from the consequences of one’s actions” combined with benevolence may generate utilitarianism.

Utilitarianism

Utility functions are quite general and can express the degree of adherence to duties or virtues.

1. Assign a utility function for each obligation, permission, prohibition, and right — positive utility for conforming to obligations and negative for prohibitions (including violating permissions and rights).
2. Assign a utility function for each virtue and vice — with positive utility for being virtuous when appropriate and negative for being vicious¹²It’s interesting to note that the universal care aspect of standard utilitarianism is lost here unless a virtue restores it.

Discussion

The simplicity of the embeddings is a feature.

A related question to paradigm embedding is whether each paradigm can be motivated from within standard theories of the others¹³TODO: sketch out how each paradigm motivates the others.. Marta Nussbaum argues that deontology and utilitarianism contain discussions of the virtues¹⁴Virtue Ethics: A Misleading Category?. Derek Parfit gives the example of how on consequentialist utilitarian grounds, one should adopt the disposition to love and prioritize care for one’s children because this results in the best consequences (even if it occasionally violates the top-level goal to maximize the quality of the state of affairs)¹⁵Reasons and Persons.

A corollary of this claim is that disagreements about which paradigm to adopt are reducible to differences in theories. Each paradigm may have practical advantages in handling certain domains of moral situations and weaknesses in others. Furthermore, from the observation that utilitarian theories advocate adopting virtues and virtue ethics theories advocate utilitarian analysis in appropriate circumstances, one can conclude that a holistic approach to pragmatic moral guidance will involve each paradigm and we should examine how they work together.

Isomorphism as Equivalence

In general two objects are considered equivalent if they may be replaced by one another in all contexts under consideration (see also the principle of equivalence).

nLab

If the guidance provided by two ethical theories is the same in all domains, then they can be said to be equivalent. The existence of an isomorphism between two theories suggests that one can substitute one for the other and receive the same guidance.

Under a simple interpretation presented on the deontology page, the value judgment and imerative languages of deontological theories can be seen to be equivalent:

(=> 
  (instance ?S SimpleValueJudgmentSentence)
  (equal ?S 
    (SimpleImperativeToValueJudgmentSentenceFn (ValueJudgmentToImperativeSentenceFn ?S))))

(=> 
  (instance ?S SimpleImperativeSentence)
  (equal ?S
    (ValueJudgmentToImperativeSentenceFn (SimpleImperativeToValueJudgmentSentenceFn ?S))))