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在《算术基础》中,弗雷格说:“直线a平行于直线b”与“a的方向=b的方向”的区别在于“我们以一种不同于原来的方式分派了内容”。对弗雷格定义数的逻辑主义方案来说,这种重塑似乎是关键的,但似乎又与他后来的意义和指称的理论不协调。我特地阐述一种对重塑的限制:如果一个名称有可能引入新的无指称,那么它就不能被引入。弗雷格的例子遵守这种限制。这种限制区别了各种依赖于重塑步骤的与“弹弓”论证相关的论证。依据弗雷格的原理,我为该限制提出一种论证,并在A.丘奇(Church)的“意义和指称的逻辑”中把它作了形式化处理,还简单讨论了丘奇的“系统(0)”中各种与重塑不协调的公理。
In Arithmetic Basis, Frege says: “The difference between a straight line a and a straight line b” is the same as “the direction of a = the direction of b.” The difference is that “we assign the content in a different way.” This remodeling seems to be critical to Frege’s definition of logistic scheme, but seems to be incompatible with his later significance and alleged theory. I specifically set out a restriction on remodeling: if a name is likely to introduce a new allegation, it can not be introduced. Frege’s example abides by this restriction. This limitation distinguishes various arguments related to the “slingshot” argument that rely on the remodeling steps. Based on Frege’s principle, I put forward an argument for the restriction and formalized it in A. Church’s “Logic of Meaning and Allegation.” I also briefly discuss Church’s “ System (0) ”in various and remodeled inconsistent axioms.