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Wiki MarkupI more and more see the need to consider carefully just how the following three things are both similar to and different from one another:

1. _'Hartshorne's threefold division of "knowledge" into "\[1\] mathematics, dealing with various '_possible_ _worlds,' or better, various_ _possible_ _logical structures; \[2\] natural and social science, dealing with the one_ _actual_ _world; \[3\] metaphysics, dealing with what is common and_ _necessary_ _to all possible states of affairs and all possible truth, including adjudication of the question of whether 'there is no world at all' represents a conceivable truth or is mere nonsense or contradiction"_ (_(The Divine Relativity_:_ _xiii)._ _false in other possible "{uorlds";_ _(2) "conditionally necessary truths" that are "necessarily true in some possible worlds and_ _false in no possible worlds"_ _and therefore are also "nonexistential necessary truths"; and (3) "unconditionally necessary truths" whose criterion is not only_ _''falsity in no possible world,"_ _but_ _"truth in all possible worlds"_ _and which therefore are_ _"existential"_ _as well as_ _"necessary" (The Ontological Argument of Charles Hartshorne:_ _14, 17 f., 19_ _f.)._ _3. Nygren's threefold distinction of forms of "scientific," or "objective:' argumentation into (1) "axiomatic," where the method is "deduction";_.

2. Goodwin's threefold distinction of "truths" into (1) "contingent truths" that are "true in some possible worlds and false in other possible worlds"; (2) "conditionally necessary truths" that are "necessarily true in some possible worlds and false in no possible worlds" and therefore are also "nonexistential necessary truths"; and (3) "unconditionally necessary truths" whose criterion is not only "falsity in no possible world," but "truth in all possible worlds"  and which therefore are "existential" as well as "necessary" (The Ontological Argument of Charles Hartshorne: 14, 17 f., 19 f.).

3. Nygren's threefold distinction of forms of "scientific," or "objective," argumentation into (1) "axiomatic," where the method is "deduction"; (2) "empirical," where the method involves "induction" as well as "deduction"; and (3) "philosophical," where the method, again, is "deduction," albeit in the different sense of "presuppositional analysis," i.e., deduction from X of its necessary presuppositions or conditions of possibiltypossiblity, as distinct from deduction of X from certain axioms that necessarily imply it (Meaning and Method: 65-125, et passim).

22 March 1999

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Hartshorne's threefold division of "knowledge" into "\[1\] mathematics, dealing with various

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