Leibniz's ontological proof of the existence of God and the problem of ``impossible objects``
type: Item
instance of: scholarly article
title: Leibniz's ontological proof of the existence of God and the problem of ``impossible objects``
zbMATH Open document ID: 1375.01014
author: Wolfgang Lenzen
published in: Logica Universalis
publication date: 2017-04-20T00:00:00Z
review text: This article examines one of Leibniz's ontological proofs for the existence of God: \textit{Probatio existentiae Dei ex ejus essentia} (1678, now published in AII,1). Leibniz's proof builds on a criticism of the classical ontological proof (hereinafter OA) endorsed, among others, by Descartes: {\parindent=0.7cm\begin{itemize}\item[--] God is, by definition, the most perfect being. \item[--] The most perfect being includes all perfections. \item[--] Existence is a perfection. \item[--] The most perfect being includes existence. \item[--] Existence follows from the idea of God. \item[--] Therefore God exists. \end{itemize}} According to an objection which goes back to Gaunilo of Mormoutiers, this argument is fallacious because it confuses the existence of an idea with the existence of a thing denoted by this idea. Hence, we could, using the formal proof-structure of OA, prove the existence of all sort of non-existing things. Leibniz holds that OA merely proves the conditional: ``if God is possible, then God exists'' and it is incomplete, because it fails to prove that God is possible. A complete proof by OA would follow either of the schemes below, depending on two different conceptions of God as, respectively, ``the most perfect being'' or ``the necessary being'': OA1 {\parindent=0.7cm\begin{itemize}\item[(i)] The most perfect being is possible. \item[(ii)] If most perfect being is possible, then God exists. \end{itemize}} or: OA2 {\parindent=0.7cm\begin{itemize}\item[(i)] The necessary being is possible. \item[(ii)] If the necessary being is possible, then God exists. \end{itemize}} The author's paper considers Leibniz's attempt to prove OA2, analysing it using firstly the formalism of modern modal logic and then using a logic of concepts developed by Leibniz himself. The interpretation of Leibniz's proof through the lens of modal logic brings to light certain ambiguities in Leibniz's own reasoning. In particular, the impossibility of an entity x is understood, in t…
reviewed by: Davide Crippa
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 03Axx
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 6706574
zbMATH Keywords: history of logic
zbMATH Keywords: ontological proof
zbMATH Keywords: modal logic
Wikidata QID: Q56385681
MaRDI profile type: Publication
full work available at URL: s11787-017-0159-2
OpenAlex ID: W2594660368
cites work: Q3999038
DOI: 10.1007/S11787-017-0159-2
description: scientific article; zbMATH DE number 6706574