As a nominalist, Buridan insisted that there is no place for universal things in his nominalist ontology and logic. Every thing in the world is singular; and everything that exists is numerically one and undivided. Indeed, a genus in this way is also one singular term, insofar as it exists just as singularly in my understanding or yours, or in my voice or yours. This nominalist ontology entails that any proposition should be existent by token, whatever they are spoken tokens or written tokens. If the tokens disappear, all the corresponding terms or propositions will disappear, and any proposition that consists of such tokens will be false. However, the existence of proposition token is not the truth carrier for a proposition, neither does the signification of a proposition decide its truth conditions. Any proposition token has two types of significations classified into intramental signification and extramental signification. But the intramental signification obviously does not provide the condition for the truth since its presence is just the precondition of the meaningfulness of the corresponding spoken proposition, and neither does the extramental signification can serve to determine the truth conditions, for the contradictory propositions, having the same categorematic terms, always have the same extramental signification (the syncategorematic terms cannot have extramental signification by themselves). Therefore, it is not sufficient to deal with significations in assigning the truth conditions of a proposition, we have to take into account the suppositions concerned, namely, the cosuppositting of the terms of a proposition from which we can assign the truth conditions of a proposition in terms of the cosupposition (or noncosupposition) of its categorematic terms. According to such semantics, Buridan can consistently handle Liartype paradoxes that are undoubtedly semantically closed sentences. To be sure, Buridans theory of semantics takes the correspondent token of a proposition with reality as a necessary, but not sufficient condition for its truth; the extra conditions he requires are the existence of the proposition we evaluate and the satisfaction of its ″virtual implication,″ i.e., basically, that our proposition in question would fall within the actual extension of a truthpredicate (is true) in a proposition that states its truth, if such a proposition were to be formed. Based on this, given the classic Liartype paradox ″What I am saying is a lie,″ we get: ″What I am saying (A) is a lie″ is true, if and only if (a) this proposition token exists, as it obviously does since I have typed it here; (b) its terms cosupposit (obviously, the intended reference of the subject (A) here is this token itself, and the intended import of the predicate is that this token is not true), i.e., ″A is false″ cosupposit; (c) and that if A refers to this token, and this is obviously not problematic since this is a semantically closed sentence, then the terms of the proposition ″A is true″ cosupposit. However, (b) and (c) cannot be satisfied together, so the original token cannot be true. Therefore, there is no paradox, the evaluation coherently deems the original token not to be true, but to be simply false. Actually, Buridans token based and semantically closed logic which focuses on the virtual implication of a proposition can serve as a general apparatus or device to avoid Liartype paradox. When the terms of an affirmative proposition can cosupposit in a possible situation without placing the proposition itself among what the term ″false″ supposit, Buridan can be sure that the proposition in that situation is true, provided its tokens exists in that situation. By contrast, when the cosupposition of its terms places the proposition itself among what the term ″false″ supposit, Buridan can also be sure that its virtually implied proposition cannot be true, and hence the original proposition cannot be true either. This procedure is entirely effective to resolve any Liartype paradox. Definitely, Buridans solution to the Liartype paradoxes is totally natural. That is to say, he can consistently handle Liartype paradoxes in a semantically closed language without the Tarskian distinction of object language and metalanguage, he merely appealed to the natural language with purely natural analysis that is close to the regular thinking methods of common people.
胡龙彪. 说谎者类型悖论的自然破解----基于布里丹的语义封闭逻辑[J]. 浙江大学学报(人文社会科学版), 2013, 43(3): 53-61.
Hu Longbiao. A Natural Solution to Liartype Paradoxes Based on Buridans Semantically Closed Logic. , 2013, 43(3): 53-61.