Hintikka thinks that second-order logic is not pure logic,and because of Godel's incompleteness theorems,he suggests that we should liberate ourselves from the mistaken idea that first-order logic is the foundatio...Hintikka thinks that second-order logic is not pure logic,and because of Godel's incompleteness theorems,he suggests that we should liberate ourselves from the mistaken idea that first-order logic is the foundational logic of mathematics.With this background he introduces his independence friendly logic(IFL).In this paper,I argue that approaches taking Hintikka’s IFL as a foundational logic of mathematics face serious challenges.First,the quantifiers in Hintikka’s IFL are not distinguishable from Linstrom's general quantifiers,which means that the quantifiers in IFL involve higher order entities.Second,if we take Wright’s interpretation of quantifiers or if we take Hale’s criterion for the identity of concepts,Quine’s thesis that second-order logic is set theory will be rejected.Third,Hintikka's definition of truth itself cannot be expressed in the extension of language of IFL.Since second-order logic can do what IFL does,the significance of IFL for the foundations of mathematics is weakened.展开更多
基金Renmin University of China’s 2018 Fund for Building World-Class Universities(Disciplines).
文摘Hintikka thinks that second-order logic is not pure logic,and because of Godel's incompleteness theorems,he suggests that we should liberate ourselves from the mistaken idea that first-order logic is the foundational logic of mathematics.With this background he introduces his independence friendly logic(IFL).In this paper,I argue that approaches taking Hintikka’s IFL as a foundational logic of mathematics face serious challenges.First,the quantifiers in Hintikka’s IFL are not distinguishable from Linstrom's general quantifiers,which means that the quantifiers in IFL involve higher order entities.Second,if we take Wright’s interpretation of quantifiers or if we take Hale’s criterion for the identity of concepts,Quine’s thesis that second-order logic is set theory will be rejected.Third,Hintikka's definition of truth itself cannot be expressed in the extension of language of IFL.Since second-order logic can do what IFL does,the significance of IFL for the foundations of mathematics is weakened.
