Supplement: The logical connection between premiss and rule cannot be symbolized with logical notation including EGs. It is a temporal connection, a relation between past and present. Logic notation merely notes the status of the present. Implication implies this temporal relation, and "not (A and not B)" doesn´t. So both are different, but this difference doesn´t show in logical notation.
Jon, Jon, List
Wikipedia says there are two kinds of "ex falso quod libet": First the contradiction "A and not A", and secondly the counterfactual material implication "If A then B" with A being false. From "every unicorn is pink" follows, that this is true, and anything else also is. These two kinds of quodlibet seem different, but I think they can be connected, by which a hypothesis about implication in general occurs:
Maybe "If A then B" is not only a rule, but also a case, meaning, it includes a premiss: A exists. So "If A then B" does not mean "A exists and if A then B", but it means "If A then B, on the premiss that A is true". Now, if A is false, unicorns donot exist, this falsity also is part of the premiss. The case-part of implication, that part that is not part of the rule, now has a backwards-effect on the premiss. The complete premiss now is: "A exists, and A does not exist", or "A is both true and false". This is the contradictional "ex falso quodlibet", which makes the rule-part´s, the implication´s result true, like anything else as well.
I think, this quibbly argument has the benefit, that one can understand the counterfactual-material-implication-qoudlibet ("Every unicorn is pink" being true), which intuitively is not as easy to understand as the contradiction-quodlibet ("if one nonsense is true, all sense is lost anyway, then say what you want, all is true.": Easy to understand.).
The hypothesis about implication is, that though it is only one term, it adds something to the premiss of itself. Maybe that is what distinguishes "if A then B" from "not (A and not B)".
Best
Helmut
Jon A., List:
Technically, yes, at least in classical logic. Nevertheless, according to Peirce, "it can no longer be granted that every conditional proposition whose antecedent does not happen to be realized is true" (CP 4.580, 1906).
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
On Wed, May 19, 2021 at 6:13 PM Jon Awbrey <[email protected]> wrote:
_ _ _ _ _ _ _ _ _ _ ► 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.
