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Presupposition of the question: the drastic-difference thesis, which is here based on the SEP article on the concept of evil:

Since World War II, moral, political, and legal philosophers have become increasingly interested in the concept of evil. This interest has been partly motivated by ascriptions of ‘evil’ by laymen, social scientists, journalists, and politicians as they try to understand and respond to various atrocities and horrors, such as genocides, terrorist attacks, mass murders, and tortures and killing sprees by psychopathic serial killers. It seems that we cannot capture the moral significance of these actions and their perpetrators by calling them ‘wrong’ or ‘bad’ or even ‘very very wrong’ or ‘very very bad.’ We need the concept of evil.

Now, suppose a category with initial, terminal, and zero objects, a category called Value. Following Kant, if we reverse the appropriate priority of duties/virtues relative to happiness/hypothetical imperatives, we have given ourselves to radical evil. Would this mean that Evil = Valueop, here? Or, to fully capture the essence of the drastic-difference thesis, would we have to go to something more like Metavalue first, with disvalue as an object of some "kind," internally opposite to another object = value, and then take Metavalueop = Evil? Would that be drastic enough, or perhaps too drastic? (As far as interpreting Kant goes, I suppose I should differentiate Diablos Malum from Radix Malum instead of just having generic Malum, here; or then there are diabolical objects and radical objects, as initial, terminal, zero, or otherwise objects, of Evil, but then this makes it seem like Evil is not the opposite of Value or even Metavalue, since reversing the mappings internal to categories of Diablos-objects and Radix-objects together would not give us "good" mappings instead?)

Citation issue: although I have found tantalizing remarks scattered across the Internet about the ethical applicability of category theory, I have yet to find a fuller, broader treatment than this one pertaining to deontic logic in the Canadian legal system. However, as far as I can tell, the word "evil" does not appear anywhere in that article.

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  • Are you trying to postulate a "logical" foundation of evil?
    – Ioannis Paizis
    Commented Nov 5, 2023 at 18:28
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    @IoannisPaizis did I use the word "foundation" anywhere in this OP? I seem to be trying to describe something/interpret other theories (drastic-difference/Kant) on whatever terms. Per Kant, the origins of evil are supposedly inexplicable, though.
    – Kristian Berry
    Commented Nov 5, 2023 at 18:30
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    Deontic calculus modeling 'ought' from 'is' normative reasoning is extremely complicated thus category-theoretic fibration pullback as limit of a diagram is an ideal combining foundation underlying deontic system to give soundness and completeness via trivial monoidal/closed Cartesian structures bi-embeddings as a structure preserving functor between instances of free category for all its fragments such as CNR which is *-autonomous. Ergo at least some fragment has adjunction-like properties such as existence of unit and counit morphisms which may not simply translate to antonyms of ethics...
    – Double Knot
    Commented Nov 6, 2023 at 7:41
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    The problem is that reversing arrows does not produce anything "drastically" different, it is just the same ‘very very wrong’ upside down (like all opposite categories). The point of a separate evil concept is that evil is something distinct from moral wrongness, no matter how significant, and cannot be flashed out in terms of the Value category alone, or some functor thereof. Perhaps, you should pick some subcategory of Value that keeps some sort of "twistedness", while dropping many usual characteristics that determine its arrows as inessential. But which way they go is a formality.
    – Conifold
    Commented Nov 6, 2023 at 9:49
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    This might be better as an answer, but IDK. Anyway: I agree with Conifold's assessment of your approach. I think a more useful approach to a drastic difference between bad and evil is the idea of positive moral obligation to oppose (evil) vs prohibition against (bad). That is bad which one is prohibited to do; that is evil which one is both prohibited to do and obligated to oppose.
    – g s
    Commented Nov 6, 2023 at 14:46

2 Answers 2

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This idea has merit. Value has also been used to connote meaning. So disvalue would be equivalent to meaninglessness. Panpsychism suggests that the universe creates value as it develops. Your idea suggests that evil destroys value and meaning.

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  • I appreciate the upvote, but I should note that by "opposite category" I mean a technical matter of category theory, where mappings are reversed across the board but opposite objects are not so in view. What I need are opposite objects, though... Maybe Alessio Moretti's "logical geometry of opposition" would be helpful?
    – Kristian Berry
    Commented Nov 7, 2023 at 13:05
  • I appreciate your candour. I will return the favour. I had enough of technical matters when I was a scientist. But thanks, you got me thinking.
    – Meanach
    Commented Nov 7, 2023 at 15:44
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Pure evil is actions that are done with the aim of devaluing or disformatting the self. All Counterfeitics and some Realistics reach pure evil. Pure transcendent evil, on the other hand, is synthetic propaganda aimed at eliminating meaning and context. Some Realistics can practice pure transcendent evil.

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  • So which category, or n-category it would turn out, I suppose, do you think that Evil can be reflected out of? Value or even Metavalue seem too low in the hierarchy of categories, except for Radix Malum (per Kant's sense of that phrase, that is).
    – Kristian Berry
    Commented Nov 7, 2023 at 20:53
  • Nothing and space is Counterfeitics. I inverted nothing and there is a universe for ready to exploding. I do it again; Any of the things that aren't. It's not even evil.
    – fkybrd
    Commented Nov 7, 2023 at 23:17

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