Mauro, Terry, List: Thanks for your posts. I just sent one of my own in the other thread, which includes some discussion of truth tables for the four-valued modal logic that Łukasiewicz developed, with more to come in the near future. I will be sure to take a look at Nute's book since I still hope ultimately to connect my ongoing study of Peirce's Existential Graphs with his pragmatism, where *subjunctive *conditionals are especially important.
Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Tue, Apr 20, 2021 at 9:42 AM Terry L Rankin <[email protected]> wrote: > Formal conditional logics and corresponding algebras appear to be the best > approach to sorting these matters. Like modal logics, they rely on possible > world semantics, while further invoking “conditional selection functions” > across ranges of possible worlds, in addition to more familiar > “accessibility relations” applied in modal logics. An excellent work on > formal conditional logics and their algebras is Donald Nute’s *Topics in > Conditional Logic <https://www.amazon.com/dp/902771049X/> *(Philosophical > Studies Series, 20) from Kluwer (1980), > https://www.amazon.com/dp/902771049X/. > > > > Terry R. > > > > *From:* [email protected] < > [email protected]> *On Behalf Of *Mauro Bertani > *Sent:* Tuesday, April 20, 2021 3:08 AM > *To:* Helmut Raulien <[email protected]>; Peirce List < > [email protected]>; [email protected] > *Subject:* Re: [PEIRCE-L] Paradisaical logic (was Phaneroscopy... > > > > Hi Helmut and Schmidt, > > I would unify this thread of discussion with this > https://pilot.list.iupui.edu/sympa/arc/peirce-l/2021-04/msg00092.html > <https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpilot.list.iupui.edu%2Fsympa%2Farc%2Fpeirce-l%2F2021-04%2Fmsg00092.html&data=04%7C01%7C%7C31f93843d9134359caf608d903cb104f%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637544992952321054%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=963%2BklUG2hIqi37kxJ4kVGC5CLElF1sdL0JbfHhPTtM%3D&reserved=0> > about modal logic. > > We name it the modality of implication. > > First we can see two truth table: > > *a* > > *b* > > *(a **∧** b)* > > F > > F > > *F* > > F > > T > > *F* > > T > > F > > *F* > > T > > T > > *T* > > > > *a* > > *b* > > *(a → b)* > > F > > F > > *T* > > F > > T > > *T* > > T > > F > > *F* > > T > > T > > *T* > > We can see that these two truth tables have two lines in common. The third > and the fourth and we can see that the first and the second row of the > first table evaluate to false while in the second table they evaluate to > true. > > Now we can compare another two table > > > > *a* > > *b* > > *(a **∧** b)* > > F > > F > > *F* > > F > > T > > *F* > > T > > F > > *F* > > T > > T > > *T* > > > > *a* > > *b* > > *(a **∨** b)* > > F > > F > > *F* > > F > > T > > *T* > > T > > F > > *T* > > T > > T > > *T* > > In these two tables two lines are in common, the first and the fourth. The > others evaluate to false in the first table and evaluate to truth in the > second. > > If we postulate that implication is similar to inclusion we can say that > (a&&b) -> (a->b) and (a&&b)->(a||b). > > In fact a&&b evaluates to false, so is included in the other. > > > > *a* > > *b* > > *((a **∧** b) → (a → b))* > > F > > F > > *T* > > F > > T > > *T* > > T > > F > > *T* > > T > > T > > *T* > > > > *a* > > *b* > > *((a **∧** b) → (a **∨** b))* > > F > > F > > *T* > > F > > T > > *T* > > T > > F > > *T* > > T > > T > > *T* > > > Now we can imagine possibility and necessity as a function of knowledge of > information about the case where the truth table diverges. > > If I know only that a=T and b=T I have the possibility of saying that a->b > but I don't have the necessity to say that a->b. For saying that, I have > to know also that if a=F and b=F or a=F and b=V the proposition a->b is > true. > > Implication is an inclusion of a truth table (possibility) where more > information can bring to the necessity of the conclusion. > > It's similar to intention and extension where more information can change > the proposition. The proposition that I finally evaluate differs in > function of information on a part of the universe that I don't Know and > for this reason I imagine it false. > > regards > > Mauro >
_ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
