奎因与量化模态逻辑的发展

On Quine and the Development of Quantified Modal Logic

奎因在20世纪40年代提出解释量化模态逻辑的问题,认为不能把标准量化与模态结合起来。逻辑学家尝试了各种解决方案。由于克里普克语义的广泛应用,逻辑学家找出了一些量化模态逻辑系统,并给出相应语义解释和完全性,使特定的模态系统具有正确的句法和语义,因此部分回答了奎因提出的挑战。另一方面,人们从哲学上提出各种不同的对"模态个体"的说明。我们详细讨论奎因提出的问题,简要说明量化模态逻辑的发展。最后的结论是,虽然关于量化和模态的关系的技术处理取得了大量有意思的结果,但从哲学上看,我们仍然需要一种对模态个体、内涵、同一等概念的恰当解释。

Quine put forward the question of interpreting quantified modal logic, and claimed that standard quantification cannot be combined with modality. Logicians tried lots of solutions. As the wide application of Kripke semantics, logicians found out some quantified modal logical systems, and presented corresponding semantics and completeness such that certain modal systems have fight syntax and semantics. Hence Quine＇s problem is answered partially. On the other hand, various accounts for ＂modal individual＂ have been set forth in philosophy. We discuss Quine＇s problem in detail, and explain the development of quantified modal logic briefly. The final conclusion is that we really need appropriate interpretations of modal individual, intension, identity etc. , although the technical treatment of the relation between quantification and modality leads to many interesting results.