Cardinal and ordinal numbers, and ethics

[Mighara Sovmadhi]

So there is supposed to be this important distinction in types of ethical thought, namely between deontological and teleological systems. In the one case, people define their concept of goodness in terms of rightness, and in the other case they order these concepts reversewise. Or so the theory goes.

A while back (and I might have posted about it here), I thought the difference could be traced to that between orientation and destination in imperatives. That is, {go left, up, left, left, up, up} and {go to square X} are both satisfied by going to square X, but one is from a 1st-person perspective, so to say, whereas the other is more 3rd-personish, maybe. So I thought goodness was destination and rightness was orientation, so the question of deontology and teleology was whether all rational orientation was to be derived from rational destination or not or whatever.

However, I also think that moral information involves some kind of special mathematics. I noticed that there's a way to pair goodness/value as a concept, with cardinal numbers, i.e. there's the idea of cardinal utility. But a categorical imperative is an unconditional one, or one of ultimate priority. So deontological information is couched in terms of ordinal numbers, as it were. Whether deontological or teleological information is prior to the other depends, then, on whether the normative relationship between the categories of cardinal and ordinal numbers, is hierarchical or not.

Also, though, what if there's a third "use" of numbers, besides cardinally or ordinally, and this third "use" pertains to ethics? So there'd be the deontic numbers, so to speak. Could these be a harmony or fusion or whatever, between cardinal and ordinal enumation? IDK...

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One of the things I always liked about discussing ethics was that no mathematics was involved. Now you're threatening that?

--A

[Mighara Sovmadhi]

Well, perhaps. But perhaps the computations would be simple enough. Let's say ethics depends on free will and free will has a different mathematics of probability than other comparable (relevant) things. That is, it is not 50% probable that an agent faced with only two choices, will ever choose one or the other, if given infinite chances. That is, free will is not like rolling dice. But so then what probability is involved? There's also supposed to be a difference between chance and randomness:

https://plato.stanford.edu/entries/chance-randomness/

So if free will has a "random" element, then maybe there is no probability function for it. In fact, I do not think that the usual, "People probably will do what they want/desire to do," is true. Or, it might be true accidentally, but not in the way that a fair dice has probabilities (per its own function). OTOH I feel like, "If I intend to do X, this increases the probability that I will," where intent is distinguished from desire.

There's also the issue of transfinite numbers, like, what if people are not to be counted for "one and only one" but infinitely? That is, instead of assigning each person a unit of cardinal value, each person is assigned an infinite number of them. But in that event "the greatest good for the greatest number" becomes a quite different problem to solve...

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I think there's always a random element, because humans are sometimes moved by random things. On one day the choice may go one way, on another, a different way. It might be possible to chart the probability of it going one way or another, but probably not the specific outcome in any given attempt.

--A