Topics Logic

Question Hi, I was thinking about the "This statement is false" paradoxon and so I came to: What about the "This statement is paradox" <err mmh metaparadoxon>? It means that I, the statement, can't be true or false. I find that odd. ..Jumping (1) Layer of statements: "I drink coffee" (2) Layer of statements about statements: "<statement> is true/false" (3) Layer of statements about statements about statements: "<statement> is paradox/not paradox" or is it: "<statement> is true/false-determinable/finite or not" Statements of (1) can state every possibility of language. Statements of (2) state if statements of (1) correspond with reality/each other. Statements of (3) state if statements of (2) are self-referential? finite? Where are my mistakes :p? Or which books do you advise me to read? Err..Which question should i ask? Does (3) "exist"? Is the idea of layers a bad idea? Simon

Accepted:
December 28, 2006

Comments

The idea that there is a hierarchy of statements, each saying something about the level below, but none of the lower ones saying anything about the higher ones, is central to formal work on truth. It originates where such work originates, with Alfred Tarski's great paper "The Concept of Truth in Formalized Languages". In Tarski's work, it doesn't take quite the form you mention. You suggestion regarding (3), in particular, sounds more like the form the hierarchy takes in Saul Kripke's treatment in "Outline of a Theory of Truth". On such treatments, the hierarchy certainly does not end with (3): There are also statements about statements about statements about statements, and so forth; and the hierarchy does not even end with all the finite levels.