真值函项理论与怪论

Truth-functional Theory and Paradoxes

真值函项理论对复合命题的解释和刻画与复合命题的直观含义存在着不一致,这种不一致导致的"怪论"既存在于实质蕴涵,也存在于合取和析取。合取和析取仅存在"语法怪论",这种"怪论"是由形式语言和自然语言在语法上的不一致造成的,其表现是将不合法的、无意义的语句当作合法的、有意义的。实质蕴涵则不仅存在"语法怪论",而且存在"语义怪论";后者是由实质蕴涵和"如果……那么……"在语义上的不一致造成的,其表现是将假的充分条件假言命题判定为真的,以及把直观上能确定真假的充分条件假言命题当成无法确定真假的。"语义怪论"的存在表明,用真值函项解释来确定假言命题的真假是不可行的。

The explanation and characterization on compound propositions by truth-functional theory are inconsistent with the intuitive meanings of compound propositions in some respects. This inconsistency can bring about paradoxes in material implication, and in conjunction and disjunction as well. There are only syntactic paradoxes in conjunction and disjunction. The syntactic paradox is caused by the inconsistency between the syntax of formal language and the syntax of natural language. Its performance is to treat illegal and meaningless sentences as legal and meaningful sentences. There are not only syntactic paradoxes, but also semantic paradoxes in material implication. The semantic paradox is caused by the inconsistency between the meaning of material implication and the meaning of ＂if- then..＂ Its performance is to make the false hypothetical propositions under sufficient condition judged as true propositions, and to look upon the hypothetical propositions under sufficient condition whose truth can be determined intuitively as propositions whose truth cannot be determined. The existence of semantic paradoxes shows that it is not feasible to determine the truth of hypothetical propositions according to the truth-functional explanation.