Talk:Propositional function: Difference between revisions

Revision as of 16:06, 7 October 2015

Latest revision as of 03:55, 9 March 2024

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==Inspiration==

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: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. [[Special:Contributions/67.198.37.16|67.198.37.16]] ([[User talk: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 formulafunction, because it occurs in [[propositional logic]], but that is not what "boolean-valued formulasfunctions" 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. [[Special:Contributions/67.198.37.16|67.198.37.16]] ([[User talk:67.198.37.16|talk]]) 15:54, 7 October 2015 (UTC)