“存在问题”再探

Reconsidering the Issue of “Existence”

在自由逻辑系统PFL和NFL中既包含一阶存在谓词,也包含存在量词。通过对普遍存在句和单称存在句的分析,可以看出弗雷格、罗素的存在观与自由逻辑存在观的相同与相异之处。普遍存在句中"存在"是量词,而单称存在句中"存在"是一阶谓词。通过修改PFL和NFL的语义,进而消除其空单称词项,可以得到与经典谓词逻辑等价但包含"存在"谓词的逻辑系统,其中可以将经典谓词逻辑"个体域中对象具有存在性质"这一假定直接表述出来,并能揭示出经典量词与存在谓词之间的联系。

The systems of PFL and NFL include both the first-order predicate "exists" and existential quantifier. By analyzing the general existential statements and the singular existential statements, we can find out the similarities and the differences among Frege, Russell and free logics. "There is" in the general existential statement is an existential quantifier, but the word "exists" in the singular existential statement is a first-order predicate. By changing the model semantics of PFL and NFL and eliminating their empty singular terms, we can get the systems which are equivalent to classical predicate logic and include existential predicate. The new system we get can express the assumption of QC that the objects in the domain have the property of existence, and it can also discover the relations between classical quantifiers and "exists" as a first-order predicate.