It is proposed that this article be deleted because of the following concern:
If you can address this concern by improving, copyediting, sourcing, renaming, or merging the page, please edit this page and do so. You may remove this message if you improve the article or otherwise object to deletion for any reason. Although not required, you are encouraged to explain why you object to the deletion, either in your edit summary or on the talk page. If this template is removed, do not replace it. The article may be deleted if this message remains in place for seven days, i.e., after 06:55, 5 September 2024 (UTC). Find sources: "Frege's propositional calculus" – news · newspapers · books · scholar · JSTOR Nominator: Please consider notifying the author/project: {{subst:proposed deletion notify|Frege's propositional calculus|concern=Although [[Begriffsschrift]] is certainly notable, this article is a very long list of many of the theorems in it, which are not individually notable. Due to [[WP:NOTDATABASE]], I propose deletion.}} ~~~~ |
![]() | This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)
|
In mathematical logic, Frege's propositional calculus was the first axiomatization of propositional calculus. It was invented by Gottlob Frege, who also invented predicate calculus, in 1879 as part of his second-order predicate calculus (although Charles Peirce was the first to use the term "second-order" and developed his own version of the predicate calculus independently of Frege).
It makes use of just two logical operators: implication and negation, and it is constituted by six axioms and one inference rule: modus ponens.
Axioms | Inference Rule |
---|---|
|
|
Frege's propositional calculus is equivalent to any other classical propositional calculus, such as the "standard PC" with 11 axioms. Frege's PC and standard PC share two common axioms: THEN-1 and THEN-2. Notice that axioms THEN-1 through THEN-3 only make use of (and define) the implication operator, whereas axioms FRG-1 through FRG-3 define the negation operator.
The following theorems will aim to find the remaining nine axioms of standard PC within the "theorem-space" of Frege's PC, showing that the theory of standard PC is contained within the theory of Frege's PC.
(A theory, also called here, for figurative purposes, a "theorem-space", is a set of theorems that are a subset of a universal set of well-formed formulas. The theorems are linked to each other in a directed manner by inference rules, forming a sort of dendritic network. At the roots of the theorem-space are found the axioms, which "generate" the theorem-space much like a generating set generates a group.)
© MMXXIII Rich X Search. We shall prevail. All rights reserved. Rich X Search