User:Tule-hog/Questions
- should redirect shortcuts outside of mainspace be marked with
{{R from modification}}? or is this redundant? - is there a dedicated template for template edit requests when the requester does not know how to perform the modification? Whenever I use
{{TPER}}, someone comes around and marks it as answered and says 'find consensus' or 'perform the modification yourself'. the first doesn't make sense in a number of small cases, and the second is just kind of mean to a less equipped participant...
Article specific
[edit]The lead claims:
A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems.
Most textbooks I have seen approach theories as collections of sentences within a logic. That is, a theory does not "self-contain" an axiomatic system but is formulated within an axiomatic system. Said again, one can investigate multiple theories using the same axiomatic system (in the same formal system).
Have any editors seen the quoted way of presenting theories in mathematical logic (as self-contained systems)? Or should the quote rather be rephrased to something like:
A theory is a consistent collection of sentences contained in an axiomatic system, derivable from an initial collection (sometimes called 'elementary sentences' of the theory) via the rules of the axiomatic system.
19:36, 15 December 2024 (UTC)
- Per pg. 20 of Smith's Logic Study Guide, maybe instead of 'contains' it should use 'presuppose':
21:30, 15 December 2024 (UTC)You will be familiar with the general idea of an axiomatized theory. We are given some axioms and some deductive apparatus is presupposed. Then the theorems of the theory are whatever can be derived from the axioms. Similarly: In an axiomatic logical system, we adopt some basic logical truths as axioms. And then we explicitly specify the allowed rules of inference: usually these are just very simple ones such as the modus ponens rule for the conditional which we will meet in a moment.