Formalization and Assessment of Lowe’s Modal Ontological Argument

Concrete Necessary Numbers God Contingent Fiction Stuff Our experiments in Isabelle/HOL confirm that the conclusion C: ∃x.Necessary x ∧ Concrete x follows from premises P2: ∃x.Necessary x ∧ Abstract x, P3: ∀x.Abstract x → Dependent x, P4: ∀x.Dependent x → (∃y.Independent y ∧ x dependsOn y) and P5: ∀x.Necessary x → (∀y.x dependsOn y → Necessary y). Here, Necessary and Concrete are uninterpreted constant symbols and Contingent x and Abstract x are abbreviations for ¬(Necessary x) and ¬(Concrete x), respectively. Dependent, Independent and dependsOn are modeled analogous to before. The ambiguity of natural language for different formalizations of the same argument, two of which we have formalised in Isabelle/HOL as outlined above. The first variant tries to capture the essentialist nature of the concreteness predicate, and the second exploits the very idiosyncratic meaning given by the author to the terms necessity and contingency inside his argument. The full details of our formalisations and experiments are available online. Note that in both of our formalisations only a subset of Lowe’s premises is needed to justify the conclusion. Moreover, in both variants the consistency of the premises was confirmed. We invite the readers to inspect and adapt our formalisations, and to eventually contribute further alternative formal interpretations of Lowe’s natural language argument. The work presented here is a result of a student project of the (awarded) lecture course on Computational Metaphysics at held in Summer 2016 at FU Berlin. In this lecture course we pioneered the rigorous, deep logical assessment of rational arguments in philosophy on the computer; for more details see [1]. 2See http://christoph-benzmueller.de/papers/2017-Lowe-OntologicalArgument.zip