Talk:Propositional function

Inspiration

I would like to thank the User:Logicist for inspiring me to create this new article. Logicist is now banned from editing Wikipedia and blocked from e-mail correspondence and Talk page dialog due to administrative adherence to community-codified rules that govern editorial access to this project. -- Thekohser 15:46, 25 August 2009 (UTC)

Propose merging "Open sentence" article to "Propositional function"

There is an article Open sentence. I believe "open sentences" and "propositional functions" are the same topic. Churchill's Logic: An Introduction states, "Propositional functions are also called open sentences because...". For that matter, I believe "Sentential function", which is currently a redirect to "open sentence" is also a synonym for the same concept. I do not believe the current "open sentence" article is not of high quality, and this shorter article is actually better. In any case, I propose that we merge "open sentence" here. If nobody comments, my strategy would be to mostly just create a redirect from "open sentence" here and just cherry-pick a few choice sentences. This a rather important topic in logic, so it's a shame the articles aren't very good yet. I'll wait for a while (say at least a week) for more opinions. It would be good to know if you oppose the merger and why (I don't anticipate this though) and which phrase you think deserves to be the title (by default I'm assuming "Propositional function" because I've heard it slightly more in use than the other two. Once the merger is performed, it would be good to get the references up-to-speed too. The current ones aren't very good. I have probably four or five books in my personal library that I could use to cite. Jason Quinn (talk) 03:13, 1 February 2013 (UTC)

The articles, as currently written, do seem similar. However, the concept of an open sentence or open term is far more general than a propositional function. An open sentence can be any expression containing free variables; it need not be a function; that is, it need not be evaluatable or satisfiable. Open vs closed occur as a standard definition in lambda calculus and term rewriting and model theory. Anyway, no one has commented in 22 months, I'm removing the merge tag, I guess. 67.198.37.16 (talk) 15:07, 7 October 2015 (UTC)

Also, as I went to make changes, it became clear that open sentence is written in such a way that it's defining something useful for high-school algebra, with talk of "real numbers" in the lead; which is pretty ridiculous for any other field, e.g. theoretical comp sci. 67.198.37.16 (talk) 15:21, 7 October 2015 (UTC)

On further inspection, both articles are "craptastic", and need a large amount of effort to cleanup. So, for example, the second paragraph of 'open sentence' makes a vague attempt to give a general definition, but then the rest of the article reverts to a discussion of high-school algebra. See Talk:Open sentence for more complaints. Meanwhile, this article 'propositional function', fails to mention Predicate (mathematical logic), Boolean-valued function, Formula (logic) or Sentence (logic). How does a propositional function differ from an ordinary predicate or relation or formula? I guess its called a propositional function, because it occurs in propositional logic, but that is not what "boolean-valued functions" are called in predicate logic. Anyway, 'open sentence' uses lots of relations as examples; and while you can think of a relation as a boolean-valued function (thanks to currying), its sort-of misleading to state this in general. I mean we could just say its all a special case of a classifying topos and stop there. I have only one book that even discusses propositional logic, its Dirk van Dalen "Logic and Structure"; he does not define a "propositional function", since that is more appropriately a concept from predicate logic. Thus, I suspect that "propositional function" is maybe an archaic term, no longer widely used, and so this should be more of a history-of-philosophy or history-of-math article? So these are all closely related terms with conflicting usages in different fields, and it would be nice to ... underline the differences and relationships. 67.198.37.16 (talk) 15:54, 7 October 2015 (UTC)