Moral Paradigm Equivalence

The paradigms of virtue ethics, deontology, and utilitarianism can each express theories that are equivalent to the other paradigms in this set.

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.

Embedding Sketches

Deontology

Deontology easily embeds the other paradigms thanks to working with logical rules. Take any moral 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 dutifulness¹From 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 vicious²It’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 others³TODO: sketch out how each paradigm motivates the others.. Marta Nussbaum argues that deontology and utilitarianism contain discussions of the virtues⁴Virtue 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)⁵Reasons 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 moral 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))))