Moretti and his colleagues are at the head of a school of logic focused on the tradition of the Square of Opposition and similar graphs/diagrams. Besides a strong thesis of logical form depending on/constituted with geometrical forms, one of the conclusions of the school that is surprising to me is that this constitution would involve infinitely many logical operators.

At least, this is my interpretation of Moretti. It seems that he says logical operators correspond to nodes in graphs in certain sequences. Since he has these sequences spelled out to infinity, there would be an infinity of nodes, hence...

Now with things like the Sheffer stroke in mind, I feel like I have a decent sense of how the general operators could unfold. But what would the infinity of deontic operators mean? Could we use this imagery to outline a "celestial hierarchy," if you will, where entities are ranked according to which level of deontic operators they are "on"? I don't mean to say that "angels exist" or what, here; but as a sort of model of Moretti's conclusions, would (merely possible) "angels" help fill in the semantics of these extra operators?

  • Maybe some more specific reference would help... – Mauro ALLEGRANZA Sep 3 at 18:45
  • Why is it surprising? You can combine the usual connectives into infinitely many "logical operators" and illustrate their nesting by tree graphs. You can get an infinity of deontic operators by simply iterating □ and ◊. How exactly does this relate to the "celestial hierarchy"? – Conifold Sep 3 at 20:51
  • The deontic operators don't seem random and empty, McNamara's more substantiated representation tries to coordinate more than just two operators being iterated. Supererogation is there, but so then there must be infinitely many higher operators. Now agents have to have the ability to act out these operations, so to say, and it seems like agents who could understand the higher and higher operations from the inside, up to an infinite-dimensional structure (or more!), would have to be ordered as possible higher and higher agents (with humans somewhere, perhaps not uniformly, therein). – Kristian Berry Sep 4 at 3:09
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    You sure love you your infinities. I have no interest in celestial hierarchies or other supernaturals, however, your question about infinite syntax and semantics seems closely related to this post. philosophy.stackexchange.com/questions/75675/… – J D Sep 4 at 5:20

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