I use mechanized verification to examine several first- and higher-order formalizations of Anselm's Ontological Argument against the charge of begging the question. I propose three different but related criteria for a premise to beg the question in fully formal proofs and find that one or another applies to all the formalizations examined. I also show that all these formalizations entail variants that are vacuous, in the sense that they apply no interpretation to "than which there is no greater" and are therefore vulnerable to Gaunilo's refutation. My purpose is to demonstrate that mechanized verification provides an effective and reliable technique to perform these analyses; readers may decide whether the forms of question begging and vacuity so identified affect their interest in the Argument or its various formalizations. This version updates the paper that originally appeared as Chapter 13 in "Beyond Faith and Rationality: Essays on Logic, Religion and Philosophy" published by Springer to respond to criticisms by Oppenheimer and Zalta.
翻译:我用机械化的核查来检查Anselm的Ontical Artical Argument的几处一阶和更高阶的正规化,反对乞讨的问题。我建议三种不同但相关的标准,以完全正式的证明提出问题,发现其中一种或另一种适用于所审查的所有正规化。我还表明,所有这些正规化都包含一些空洞的变体,即它们对Springer为回应Oppenheimer和Zalta的批评而出版的“黄金信仰和理性:关于逻辑、宗教和哲学的理论”的最初第13章更新了这份文件。