formal language. noun. 1. a language designed for use in situations in which natural language is unsuitable, as for example in mathematics, logic, or computer programming. The symbols and formulas of such languages stand in precisely specified syntactic and semantic relations to one another.

That's pretty much all I know.

Can a formal language express ideas which aren't trivial but can be shown to be true by virtue of just content? E.g. (I think) "this sentence is true".

  • In other words, can analytic sentences be non-trivial? Take your pick of what "analytic", a.k.a. "true by virtue of just content", means plato.stanford.edu/entries/analytic-synthetic Frege and Russell intended to derive the whole of mathematics analytically, and we can follow up with Hegel's "the rational is the real" for the rest of it, Quine thought that even logical tautologies aren't analytic.
    – Conifold
    Jul 15 '16 at 4:01
  • not sure what you're asking; i included an example, of something which doesn't seem trivial and pretty clearly is true just cos of what it says. how anyone can claim that logical tautologies can't be demonstrated from their content alone, i don't know @Conifold
    – user6917
    Jul 15 '16 at 5:25
  • Can you say how you distinguish between "trivial" and "true by virtue of just content"? Do you count mathematical truths as true by virtue of just content?
    – Eliran
    Jul 15 '16 at 8:13
  • Think of the law of excluded middle, even realists who accept it know that it depends on a particular conception of truth, which say intuitionists reject along with the law itself rep.routledge.com/articles/intuitionistic-logic-and-antirealism One could still say that it is true or false in virtue of just content but that realists and intuitionists have different ideas of what the content of "or" and "not" is. That I suppose would make it non-trivial.
    – Conifold
    Jul 18 '16 at 21:29

Do formal expressions ever have trivially true content?

No; formal languages can express ideas which are not trivial at all; see:


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy