Jon, List,
Thank you, Jon! I don´t think, that unicorns exist in the logical sense, but only their concept. And this fictional concept doesn´t directly interact with matter or energy, while a mathematical law does. And I also think, that modal logic includes classical logic. That is, why I have problems accepting, that there are two different meanings of "exist". Doesn´t logic belong to metaphysics? But maybe I am wrong, I have been before.
Best, Helmut
12. November 2024 um 01:00
"Jon Alan Schmidt" <[email protected]>
wrote: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
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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