A patch to the possibility part of Gödel’s Ontological Proof
Kurt Gödel’s version of the Ontological Proof derives rather than assumes the crucial (yet controversial) Possibility Claim, that is, the claim that it is possible that somethingGod-like exists. Gödel’s derivation starts off with a proof of the Possible Instantiation of the Positive, that is, the principle that, if a property is positive, it is possible that there exists something that has that property. I argue that Gödel’s proof of this principle relies on some implausible axiological assumptions. Nevertheless, I present a proof of the Possible Instantiation of the Positive which only relies on plausible axiological principles. Nonetheless, Gödel’s derivation of the Possibility Claim also needs a substantial axiological assumption, which is still open to doubt. In its classic modal form, the Ontological Proof runs as follows:1 The Possibility Claim It is possible that something God-like exists. p. 230 The Necessity Claim That something God-like exists strictly entails that it is necessary that something God-like exists. Therefore, something God-like exists. Given some standard principles of modal logic, the proof is valid.2 Yet the Possibility Claim is questionable. Maybe the properties needed to be * Published in Analysis 80 (2): 229–240, 2020, https://dx.doi.org/10.1093/analys/an z024. † I would be grateful for any thoughts or comments on this paper, which can be sent to me at johan.eric.gustafsson@gmail.com. 1 See, for example, Hartshorne 1962: 51, Plantinga 1974a: 111, 1974b: 214 and Sobel 2004: 115. 2 More precisely, the proof is valid given normal modal logic and the Brouwerian principle q ⊃ ♦q. God-like are inconsistent. And, if they are, it’s impossible that something God-like exists. Notably, Kurt Gödel does not assume the Possibility Claim in his version of the Ontological Proof. Rather, his proof demonstrates the possibility of there being something God-like.3 He does this by first proving the following principle, which—in addition to any potential theistic implications—is interesting in its own right: The Possible Instantiation of the Positive If a property is positive, then it is possible that there exists something that has that property. A positive property, in Gödel’s terms, is a property that is ‘positive in the moral aesthetic sense’.4 Presumably, a positive property in this sense is a good-making property (but not necessarily a basic good-making property), that is, a property such that the properties it entails together rate, on balance, the possessor a plus.5 Gödel (1995b: 435) also suggests that positive properties can be interpreted as perfective properties, that is, “purely good”-making properties. A positive property in this alternative sense is, presumably, a property such that it entails some basic good-making properties and no other properties except those entailed by the basic goodmaking properties. Given thePossible Instantiation of the Positive and the further premise that the property of being God-like is positive, we have that it is possible that there exists something God-like. p. 231 There are two versions of Gödel’s Ontological Proof. One version is contained in two pages of handwritten notes by Gödel from February 1970, and a more elaborate version is contained in three pages written by Dana Scott, who discussed the proof with Gödel that same month (Adams 1995: 388). 3 In this respect, Gödel is following Leibniz (1969: 167–68). 4 Gödel 1987: 257, 1995a: 404. Gödel (1987: 257, 1995a: 404, 1995b: 435) also suggests that ‘positive’ could, alternatively, be understood as ‘attribution’ (as opposed to ‘privation’). See Hazen 1998: 375–76 for an objection to Gödel’s proof given the ‘attribution’ interpretation. In this paper, I focus on Gödel’s main, ‘moral aesthetic’ interpretation. 5 It’s not obvious how the overall value-making of a non-basic property should be calculated based on the the properties it entails. See Carlson 1997 for a discussion of how to calculate the intrinsic value of non-basic states of affairs. The calculation for properties is probably analogous to the one for states of affairs.