唯名论与有穷主义（二） (4-3)

其一，我们要问这样一个问题“我们无法在被给定的语言中为某事物写下一个符号，这种无能的最终意义是什么？”我们会想到给定语言中某些概念的不可表述性，其中包括了Tarski's theorem about the indefinability of truth (in certain types of languages) ，这样即使是墨水资源再充足的世界，只要语言满足了某种条件，“真”就无法在其中定义。

其二，用sequences代替objects的主张已经违反了唯名论的精神。因为sequences是有某种数学结构的class，显然是不适用于Tarski的FN计划的。

3.4 对FN条件的攻击性观点

（1）卡尔纳普认为，FN条件歪曲了算数的本质。

卡尔纳普在讨论的尾声，在评注中对FN有意外很低的评价，尽管他坚持宽容原则：

It seems to me thatthe entire proposal suffers from a mistaken conception of arithmetic: the numbers are reified; arithmetic is made dependent on contingent facts, while in reality it deals with conceptual connections; if one likes: with possible, not with actual facts. (090–16– 23)

作者给出了一个猜想，即宽容原则要求分析句是具有语言相对性的，但区别于其他语言的分析性，数学的分析性是绝对的而不应该是语言相对的。作者猜想这与Foundations中卡尔纳普所谓customary interpretation有关 ，作者将其要旨总结为以下三点：

(i) every formal calculus intended to model inferences in the sciences has a particular interpretation (or family of interpretations), called the ‘customary interpretation,’ associated with it.

(ii) Interpretations can be logico- mathematical or descriptive: for example, an interpretation that takes the universe of discourse to be the natural numbers or the set-theoretic hierarchy is logico-mathematical, while an interpretation whose universe of discourse contains all and only the US presidents (or any other set of physical objects) will be descriptive.

(iii) The customary interpretation for the arithmetical calculus is a logico-mathematical one.

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