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: http://plato.stanford.edu/entries/logic-modal/ "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 propositional logic. Necessitation Rule: If A is a theorem of K, then so is ?A. Distribution Axiom: ?(A?B) ? (?A??B). etc. etc. etc. <SNIP> Roger Clough, [email protected] 11/9/2012 "Forever is a long time, especially near the end." -Woody Allen -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
