No doubt Bruno has already figured out the relationship
between the necessary and the contingent, perhaps
in his levels of sigma, but at any rate, some logician
has done this, where below
the necessary (Platonia?):  or it is necessary that.. and
the possible (world ?) <> or it is possible that....
At any rate, there are a number of other forms of existence
given by modal logic as indicated next which provide a
sort of theology of existence:
"What is Modal Logic? (a theology of existence)
Narrowly construed, modal logic studies reasoning that involves the use of the
expressions ‘necessarily’ and ‘possibly’.
However, the term ‘modal logic’ is used more broadly to cover a family of
logics with similar rules and a variety of different symbols.
A list describing the best known of these logics follows.
LogicSymbols Expressions Symbolized
Modal Logic?It is necessary that ..
?It is possible that …
Deontic LogicOIt is obligatory that …
PIt is permitted that …
FIt is forbidden that …
Temporal LogicGIt will always be the case that …
FIt will be the case that …
HIt has always been the case that …
PIt was the case that …
Doxastic Logic Bxx believes that …
2. Modal Logics
The most familiar logics in the modal family are constructed from a weak logic
called K (after Saul Kripke). Under the narrow reading, modal logic concerns
necessity and possibility. A variety of different systems may be developed for
such logics using K as a foundation. The symbols of K include ‘~’ for ‘not’,
‘?’ for ‘if…then’, and ‘?’ for the modal operator ‘it is necessary that’. (The
connectives ‘&’, ‘?’, and ‘?’ may be defined from ‘~’ and ‘?’ as is done in
propositional logic.) K results from adding the following to the principles of
Necessitation Rule: If A is a theorem of K, then so is ?A.
Distribution Axiom: ?(A?B) ? (?A??B).
etc. etc. etc.
Roger Clough, rclo...@verizon.net
"Forever is a long time, especially near the end." -Woody Allen
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