Rich, (01)
> I'm still reading the Plato paper, but when I finish it, I will
> read those two links as well. (02)
It's not necessary to plow all the way through one article before
switching to another. When you get bogged down in one, you may
find that the each one will clarify obscure points in the other. (03)
The article by Peppas is longer than the one in the Stanford
encyclopedia of philosophy, but the first 7 pages give a good
summary of the issues. In fact, page 6 of the paper by Peppas
emphasizes the importance of the Levi identity. The Stanford
article also mentions it, but does not emphasize it as clearly:
http://pavlos.bma.upatras.gr/papers/8.pdf (04)
> You didn’t mention “any statement that is inconsistent with the laws is
>…” (05)
If a proposition p is provable from the laws, it's necessary.
If p is consistent with the laws, it's possible.
Therefore, if p is inconsistent with the laws, it's impossible. (06)
Qualification: Dunn's semantics can also be used for *deontic*
logics, where the two operators are 'obligatory' and 'permissible'.
For deontic logics, (07)
If a proposition p is provable from the laws, it's obligatory.
If p is consistent with the laws, it's permissible.
Therefore, if p is inconsistent with the laws, it's forbidden.
But as we all know, some people are sinners. (08)
> The symbol "<->" looks like “is equivalent to”... (09)
Yes. Some people use "->" for if-then, and they use the
double arrow for if-and-only-if (AKA iff). (010)
The following statement in the article is badly written: (011)
> A +′ p, the (non-closing) expansion of A by p is the set A∪{p}. (012)
It should have been written (013)
Define A +′ p, the non-closing expansion of A by p,
as the set A∪{p}. (014)
But there is no need for the notation "A+′p" since it's just one
character shorter than the more familiar "A∪{p}". Some people
like to pollute their writing with useless definitions. (015)
I should have cited the paper by Peppas first. (016)
John (017)
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