Talk:Frege's propositional calculus
 | This article is rated Start-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
| |||||||||||
Unicodify?
editIs space a critical issue on Wikipedia? The last edit brags of the space saved by Unicodify. But is now harder to edit on many browsers... Nahaj 01:50, 27 January 2006 (UTC)
Third axiom unnecessary
editThe article lists the following three axioms of implication:
THEN-1: A → (B → A)
THEN-2: (A → (B → C)) → ((A → B) → (A → C))
THEN-3: (A → (B → C)) → (B → (A → C))
It seems to me that THEN-3 follows from THEN-1 and THEN-2. This is because the first two are enough to prove the deduction theorem. Therefore, in order to prove THEN-3, it is enough to show A → (B → C) ├ B → (A → C). Using the deduction theorem again, it is in turn enough to show A → (B → C), B ├ (A → C), and in turn, A → (B → C), B, A ├ C, which is obvious.
Can anybody confirm that THEN-3 was part of Frege's original axiom system? 136.152.196.167 (talk) 02:27, 3 March 2008 (UTC)
- FWIW, the article on Begriffsschrift, the book where the axioms were originally published, lists THEN-3 as an axiom. I can't read German, nor do I have access to a translation, so I can't personally confirm that. Metamath's entry for the statement also lists it as a Frege axiom, and that page also establishes its derivation from the first two axioms. -happy5214 03:24, 19 October 2019 (UTC)
Standard PC system???
editWhat is the "standard calculus" with 11 axioms? Reference please. — Preceding unsigned comment added by Sciken (talk • contribs) 05:00, 21 April 2017 (UTC)
- @AugPi: As the author, surely you know what this "standard PC" is? I could not find a "standard" PC axiom system with 11 axioms doing a couple of Google searches. Even the work cited (which I found on the author's faculty page and will link shortly) only lists 10 axiom schemata for PC. It really needs to be cited and named something other than "standard", because it clearly isn't a recognized standard axiom system. -happy5214 11:50, 18 October 2019 (UTC)
- Here is the source: Introduction to Mathematical Logic by Vilnis Detlovs and Karlis Podnieks, section 1.3. The appellation “standard” would be my misnomer/misinterpretation. —AugPi 20:36, 1 November 2019 (UTC)
Proof of Theorem 10
editThe justifications for steps 4 and 5 of Theorem 10 seem wrong. — Preceding unsigned comment added by 172.7.163.210 (talk) 21:53, 20 May 2020 (UTC)