Definition talk:Language of Propositional Logic/Formal Grammar/WFF

I still believe there's room for a term like "statement form" or "propositional form" or something, which (I admit: informally) defines the concept of the "shape" of a propositional statement. In the same way we have "argument form" to define the category into which e.g. a Modus Ponendo Ponens argument or a Categorical Syllogism is placed. But beyond the "informal" definition I placed here (copied almost-verbatim from Copi) I'm not sure how we would fit this into the current programme. Perhaps there's room for it at a more abstract "dialectical logic" level? --prime mover (talk) 11:57, 3 December 2013 (UTC)

I feel there's indeed room for a page in the Category:Logic realm that informally discusses the translation of statements to WFFs in a way reminiscent of taxonomy (the Dutch word is "ontleden", lit. dissect or analyse) identifying which parts of the statement correspond to which parts of the WFFs (connectives, variables, etc.).

Does there need to be such a term for PropLog specifically? Not if you ask me. But in writing this, I've come to realise the importance of this in the application of formal logic anywhere -- most importantly, $\mathsf{Pr} \infty \mathsf{fWiki}$-wise, in mathematics. — Lord_Farin (talk) 17:47, 3 December 2013 (UTC)

There is a lot of logic literature which approaches the subject from philosophy and not mathematics, and so the "symbolic manipulation" nature of the subject is subsidiary to the "philosophical" aspects, which focus mainly on translation of natural language into specific statement forms. As such the focus on "statement form", "argument form" have more purpose, being the technique in which the literature in question make that philosophical bridge from a specific series of statements to the abstraction of the symbolic presentation of such. (They go on at great length about how "All men are mortal, Socrates is a man, therefore Socrates is a mortal" is the same argument as "All Cretans are liars, I am a Cretan, therefore I am a liar" and make a big thing about their isomorphism as though it were somehow profound.) Hence their need to find a term which specifies the abstract structure of that sequence, without going into the relative mathematical complexity of the concept of formal languages and WFFs.

Whether we want to go down that route is to be decided by anyone who wants to major in this aspect of logic on this site (note that there has already been some work in that direction, specifically by GFauxPas IIRC who put up such pages as that defining "Amphiboly" and so on.

IMO there *is* room on $\mathsf{Pr} \infty \mathsf{fWiki}$ for this end of logic, but I'm not in a position to document it in detail as I don't have books on logic which are quite that old-fashioned. :-) --prime mover (talk) 03:57, 4 December 2013 (UTC)

I agree. The problem however is that in the current setup, we identify the "shape of a statement"/statement form with a WFF -- but the WFF is more general than its being a (possible) translation of a particular statement. That is, a statement form is a WFF, but a WFF is not necessarily a statement form.

When editing, I'll be changing references to "statement form" which are wrong in the light of these future plans with this term. SourceReview templates will be added as necessary. — Lord_Farin (talk) 15:54, 4 December 2013 (UTC)