St. Anselm’s Ontological Arguments

Polish Journal of Philosophy 5 (1):7-37 (2011)
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Abstract

In the paper I analyse Anselm’s ontological arguments in favour of God’s existence. The analysis is an explication and formalization of Pavel Tichý’s study‘Existence and God’, Journal of Philosophy, 1979. It is based on Transparent Intensional Logic with its bi-dimensional ontology of entities organized in the ramified hierarchy of types. The analysis goes as follows. First, necessary notions and principles are introduced. They are: existence is not a property of individuals, but of individual offices to be occupied by an individual; the notion of requisite is defined, which is a necessary relation between an office O and a property R: necessarily, if a happens to occupy O then a has the property R. I demonstrate that an argument of the form “R is a requisite of O, hence the holder of O has the property R” is invalid. In order to be valid, it must be of the form “R is a requisite of O, the office O is occupied, hence the holder of O has the property R.” Finally, higher-order offices that can be occupied by individual offices are defined. Their requisites are properties of individual offices. Then the analysis of Anselm’s arguments is presented. The expression ‘God’ denotes an individual office, a ‘thing to be’, rather than a particular individual. Thus the question whether God exists is a legitimate one. I analyze the expression ‘that, than which nothing greater can be conceived’. Since ‘greater than’ is a relation-in-intension between individual offices here, the expression denotes a second-order office, and its requisites are properties of first-order offices suchas necessary existence. The second of Anselm’s assumptions is that individual office that has the property of necessary existence is greater than any other office lacking this property. From these it follows that the first-order holder of the office denoted by ‘that, than which nothing greater can be conceived’ enjoys the property of necessary existence. Thus God exists necessarily, hence also actually. Anselm’s argument is logically valid. If it were also sound, then an atheist would differ from a believer only by the former not believing whereas the latter believing in a tautology, which is absurd. Yet we may doubt the validity of Anselm’s assumption that a necessary existence makes an office greater than any other office lacking this property.

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