A Study On Hintikka's IF First-order Logic

Jaakko Hintikka(1929-),one of philosophy's pre-eminent logicians,proposed a new basic first-order logic--Independence-Friendly first-orderlogic (in short IF first-order logic) after his game-theoretical semantics (in short GTS)in 1990s.He argued that the concept of truth can be expressed on the first-order level in the same language and it is the real basic logic which will prepare the ground for the next revolution(in Jefferson's rather than Lenin's)in the foundation of logic and mathematics. On the basis of first-hand data, this article mostly explore the IF first-order logic from the two aspects of syntax and semantics with the method of modern logic. This paper consists of four parts.The first part analyzes the differences and contacts on syntax between IF first-order logic and classic first-order logic after a discussion about quantifiers.Part two aims to analyze how the GTS is used to explain the first-order logic. At the same time ,this part introduces its philosophical background and demonstrates the incompleteness theorem of IF first-order logic.Part three Based on the profound analysis above, it brings forward some discussion and appraisement on the IF first-order logic. It points out that the truth definition of IF first-order logic is still defined on the second-level in essence and is defined on single model; that the IF first-order logic is destined not to be a system; that it is not the real basic first-order logic. However, GTS can be used to implement the truth-conditional semantics analysis; IF first-order logic links to the second-order logic like a bridge; the expressive strength of IF first-order logic is improved greatly as a consequence.Part four introduces some uses of IF first-order logic in epistemic logic and in the foundations of mathematics. It can deals with the different wh-constructions in epistemic logic and vindicates a controversial axiom in Axiomatic Set Theory-the axiom of choice as a logical rule.