Helmut, List: As I have mentioned before, "if necessarily A, then A" is a standard axiom of modal logic called T--if A is true is every possible world, then A is true in the actual world (*alethic *modality). As far as I know, the only commonly used formal systems that *do not* include it are specifically for *deontic *modality, where "obligatory" replaces "necessary" and "permissible" replaces "possible"--"if A is obligatory, then A" is *false *because people can (and often do) fail to behave in accordance with all their obligations. T is replaced by a weaker axiom called D--"if A is necessary/obligatory, then A is possible/permissible." There is also *epistemic *modality, which has to do with states of knowledge rather than states of affairs.
Again, we must distinguish between the metaphysical sense of "exists" as "reacts with other like things in the environment" from the logical sense of "exists" as "belongs within the universe of discourse." Unicorns do not exist in the metaphysical sense, but they do exist in the logical sense, e.g., when we are discussing fictional stories that include them. They are members of Peirce's 1st universe of Ideas, "those airy nothings to which the mind of poet, pure mathematician, or another *might *give local habitation and a name within that mind"; not his 2nd universe of Occurrences, "the Brute Actuality of things and facts" (CP 6.455, EP 2:435, 1908). According to Peirce, the three different kinds of inference produce three different levels of assurance about the resulting conclusion--he associates certainty with deduction, probability with induction, and plausibility with abduction. Formal systems of both classical logic (existence) and modal logic (possibility and necessity) are strictly deductive--as long as all the premisses are true, the conclusion is true. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Mon, Nov 11, 2024 at 10:04 AM Helmut Raulien <[email protected]> wrote: > Edwina, List, > > there was a mistake in my post, I have written a correction afterwards. My > equivalences (poss A = not nec not A, nec A = not poss not A) I now have > looked up at Wikipedia "modal logic", it is correct. What stroke me, is, > that "if nec A, then A". That would mean, if God is necessary, then God > exists. Whether my conclusion with the complete induction is correct, I > should have to dig deeper into modal logic. Meanwhile I assume, that > possibility doesn´t exist, but impossibility may. For example, a homogenous > mixture between a lye and an acid definitely is impossible. About > existence, i think, one has to define the space of discourse, e.g. exists > in this room, on this planet, in the universe. For example, it is incorrect > to say, that unicorns don´t exist in the universe. Maybe once, a from > aliens abducted man made career as a biologist, abducted a horse from the > earth, and gene-manipulated a horn on its head, to have a unicorn for > birthday-present for his daughter. This may be impossible, if aliens don´t > exist, but it is possible-due-to-limited-knowledge, as we don´t know, > whether aliens exist or not. So there are different kinds of possibility > too. I wonder, is there a modal logic, that regards these different kinds > of existence and possibility? I also think, probability should be included, > then it really would become nicely complicated. I think, possibility and > necessity have to do with deduction, existence with induction, and > probability with abduction. > > Best regards, Helmut >
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