"Monoids", you keep using that word. I don't think it means what you think it means. You've basically said "use monoids" without a word of elaboration how to interpret ethics, or really anything, in this formalism.
Yes of course we can get away from defining any new systems of logic by simply taking working with different kinds of relations or functions in our classical logic. This doesn't show that non-classical logics are useless but that classical logic and classical mathematics are incredibly powerful and can describe practically anything.
Note that this article is very far from the wishy washy hippie claims like "Everything is connected! And you have your truth man and I have my truth". Instead it gives a popular-science description of some non-classical systems of logic, their historical background and how they relate to Buddhist philosophy and certain problems of reference. Personally I don't really think the logics presented solve these problems in a satisfactory way, but they are definitely of philosophical interest (o/w Cambridge University Press wouldn't have published his "An Introduction to Non-Classical Logic").
The goal of the post seems to be a curriculum for Computer Science, the chapters 13 and 14 in the list seem to cover most of this. Though I would approach the matter quite differently depending on if I wanted to learn all the CS in a certain degree or all the CS needed/useful for practical Software Engineering.
Sorry to give a minor correction to a little quibble, but it is the ordinals, not the cardinals, that are a special case of Conway numbers. The cardinals are equivalence classes of these of the form [א_a,א_(a+1))
(Also you can get infinitesimals from Conway's construction as well)
Actually you'd want to save it as (1 . (2 . (4 . (8 . NIL)))) since o/w you'd still get quadratic time complexity as you need to unpack your whole list when you add the next value.