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Just to record some references, prodded by discussion in another thread (here).
From people’s question around the fora (e.g. Physics.SE:q/15339) I gather that the principle is referenced prominently in popular physics books by “Penrose, Hawking, Greene, etc.”, but I haven’t tracked those paragraphs down yet.
Anything that is not compulsory is forbidden
But Kragh points out (p. 3) that this is the converse of what one wants:
The statement Gell-Mann associated with a totalitarian state is not what is usually known as the TP. On the contrary, it is the converse of it.
We want
Anything that is not forbidden is compulsory.
Although, perhaps one should see them as equivalent (classically) ($\neg C \to F$ iff $\neg F \to C$).
In modal terms, we might have
not compulsory $A$ implies forbidden $A$, as $\neg \Box A \to \Box \neg A$
and
not forbidden $A$ implies compulsory $A$, as $\neg \Box \neg A \to \Box A$
The latter, classically, is $\lozenge A \to \Box A$, which tallies with the possibility = necessity idea.
Not the converse, but the contrapositive. [edit: oh, we overlapped]
(I have added that term, and a few more references.)
Re #3:
I’ll want to add the formulation in linear-modal-logic to this and related entries, but first to finish polishing up the entry quantum circuits via dependent linear types which will provide the justification.
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