The insight that the teleological ethicist seems to have is that final causality is a type of the moral law in the Kantian sense (from the second Critique):

... the moral law has no faculty but the understanding to aid its application to physical objects (not the imagination); and the understanding for the purposes of the judgement can provide for an idea of the reason, not a schema of the sensibility, but a law, though only as to its form as law; such a law, however, as can be exhibited in concreto in objects of the senses, and therefore a law of nature. We can therefore call this law the type of the moral law.

For the Aristotelian hybrid, then, we have grounds for conceiving of a type-of-the-law in terms of all four subcategories of causality. But in the system of Aquinas, we don't build a bridge from "is" but we build a bridge between "ought" and "ought" instead, and so this kind of teleological ethics does not suit the purpose(!) of crossing the wider river.

Beatrice rescuing Dante from logical hell: again, we provide a link to the SEP article in which the concept of demi-negation is most explored. But we also generalize to the question of demi-operations besides √¬, to wit √OB (demi-obligation) and √𝓐 (demi-actuality). Since we are, allegorically-speaking, equipped with the powers of Beatrice Portinari, let us suppose that we are free to ask the following kinds of questions (note: we are using a quantified propositional logic in the presentation):

  1. S((√OB√𝓐S) → T)?
  2. S((√𝓐√OBS) → T)?

... where S is some proposition and T is the truth-value True (and the arrow is a generically sufficient mapping arrow, not strictly the conditional connective).

Another way to put it: "Is it true that it is demi-obligatory that it is demi-actually the case that...?" (and so on). Or instead of demi-actuality, have a demi-quantifier √∃,E and then something like √OB(√∃x(Fx)) (and so on...).

Now, for purposes of amusement, suppose that Beatrice is a color-blind neo-logicist. Her vision impairment is not relevant in the allegory. What is important, though, is to assume that we are speaking of the same Beatrice as above, so that her being a neo-logicist is also important. Does Beatrice have the power to compose the questions (1) and (2) so as to cross the river, by building a bridge, between "is" and "ought"? Perhaps the sequences of operations for (1) and (2) are too "small;" perhaps we need something like √𝓐𝓐√OB or OBOB√𝓐, or whatever else does not outpace our normal logical intuitions entirely.

EActually(!), here's another option: normally in predicate logic, we indicate predication just by the adjacency of F and x in Fx. But now suppose that there might be such a thing as demi-predication. From here, we can shift the query about demi-is right into predicate space, so that the "is" from which we are building part of our bridge is not the "is" of existence but of predication.🪜

🪜The obtainment conditions for states-of-affairs being logically distinct from, but coincident with, the truth conditions for fact-theoretic propositions, it follows that the appearance of predicates in states-of-affairs is subtly different compared to their appearance in propositions and facts. This is sufficient to ground Zalta's encodex/exemplar distinction; but since we can ask about quasi-encoding, we can go ahead and ask about demi-encoding, then demi-exemplification, and their interrelations. But is this any different, in the end, than to ask about stipulative definition as a predicate-theoretic operation alongside ostensive definition? Are those already such as are demi-predications, or can they too admit of demification? It would be time-consuming to have to keep breaking operators down and factoring their functions out, so we will stop here on the ladder of logical disquisition, adding from our halted vantage only that we will want to ask down the road about ∜O, for arbitrary operations O, and then n-roots of O (or ω-roots, no less; "and so on..."), and so of our descending kingdom there will be no end.

  • As an aside... I am confused by the use of the radical sign to designate deminegation. Does it have anything to do with square roots in the mathematical sense, or is it just a borrowed symbol? -NN Aug 25 at 5:31
  • @nielsnielsen in the SEP article, they start out by having ##a = not-a, and they read the adjacency of the #'s as logical multiplication, so the theory to that extent ends up being about what they call "the square root of negation." Personally, I did find a way to read the concept of demi-negation more broadly, so as to allow a type correlated with an algebraic/nonstandard truth-value of -1/2, but the core model, so to speak, is more like a correlation with i as the nonstandard truth-value. Aug 25 at 5:44
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    Thanks. You have replaced one mystery with another! ;-) Aug 25 at 5:53


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