Set-theoretic pluralism and the Benacerraf problem

Philosophical Studies - Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer in Platonism and anti-platonism in mathematics, Oxford University...     

论模态逻辑的集合论语义

引入非良基集合可以为模态逻辑提供一种新的语义学。这种语义是在集合上解释模态语言,使用集合中作为元素的集合之间的属于关系解释模态词,并在集合中采用命题变元作为本元,从而解释原子命题的真假。在这种新的语义下,从模型构造的角度看可以引入几种非标准的集合运算：不交并、生成子集合、p-态射、树展开等等,证明模态公式在这些运算下的保持或不变结果。利用这些结果还可以证明一些集合类不是模态可定义的。     

模态逻辑的集合论语义与互模拟不变性

含有命题变元的非良基集合能够被看作解释模态语言的模型。任给非良基集合a,一个命题变元p在a上真当且仅当p属于a。命题联结词的解释与古典命题逻辑相同。一个公式3A在a上真当且仅当存在集合b属于a,使得A在b上是真的。在一个集合中,属于关系被看作可及关系。在这种思想下,我们可以定义从模态语言到一阶集合论语言的标准翻译。对任意模态公式A和集合变元x,可以递归定义一阶集合论语言的公式ST(A,x)。在关系语义学下,van Benthem刻画定理是说,在带有唯一的二元关系符号R的一阶语言中,任何一阶公式等价于某个模态公式的标准翻译当且仅当这个一阶公式在互模拟下保持不变。因此,模态语言是该一阶关系语言的互模拟不变片段。同样,我们可以在集合上定义互模拟关系,证明van Benthem刻画定理对于集合论语义和集合上的互模拟不变片段成立,即模态语言是一阶集合论语言的集合互模拟不变片段。     

Immoral realism

Philosophical Studies - Non-naturalist realists are committed to the belief, famously voiced by Parfit, that if there are no non-natural facts then nothing matters. But it is morally objectionable...     

Wittgenstein and moral realism

Presidential Address, American Society for Value Inquiry, 1987.     

Inconsistency and scientific realism

I erect a framework within the semantic view of theories for explaining the empirical success of internally inconsistent models and theories, with scientific realism in mind. The framework is an instance of the ‘content-driven’ approach to inconsistency, advocated by both Norton (Philos Sci 54:327–350, 1987) and Smith (Stud Hist Philos Sci 19:429–445, 1988a, In: Fine A, Leplin J (eds) PSA1988, 1988b), whose ideas my analysis aims to clarify and substantiate.     

Heidegger and scientific realism

This paper describes Heidegger as a robust scientific realist, explains why his view has received such conflicting treatment, and concludes that the special significance of his position lies in his insistence upon linking the discussion of science to the question of its relation with technology. It shows that Heidegger, rather than accepting the usual forced option between realism and antirealism, advocates a realism in which he embeds the antirealist thesis that the idea of reality independent of human understanding is unintelligible. This reading is defended against Rorty's antirealist interpretation, as well as Dreyfus' depiction of him as a deflationary realist, and his assessment of background realism is contrasted with Fine's. Further, the robustness of Heidegger's realism is laid out across several texts from 1912 to 1976, in order to show that he is neither an instrumental realist nor an internal realist. Finally, the point is made that the development of his view concerning realism gives rise to a critique of objectivity that is now being similarly advocated by numerous thinkers from a variety of disciplines, and that this critique is inevitably ethical and political.