Abstract
In the Logic of Perfection, Charles Hartshorne developed what has come to be known as the modal ontological proof for the existence of God.1 That proof relies on two premises, the first of which is that God’s existence is not contingent (rendered in modal logic as), 1| ~CG, and the second of which is that God’s existence is possible, 2| MG (where ‘G’ is some version of the assertion “God exists”, ‘C’ is a modal operator representing “it is contingent that…”, and ‘M’ is the model operator for representing possibility). In modal logic, ‘Cp’ is defined as
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Charles Hartshorne, The Logic of Perfection (LaSalle: Open Court Publishing Co., 1962).
The above is a variant of Hartshorne’s proof. Hartshorne takes’ God existence is not contingent’ to be ‘G ⊃ NG’ No matter which version is chosen, the effect will be the same.
John O. Nelson, “What the Ontological Proof Does Not Do,” Review of Metaphysics 18/4 (June 1964): 608–609.
Bowman L. Clarke, “God, Modality, and Ontological Commitment”, Ontological Commitment, ed. Robert H. Severns (Athens, Georgia: The University of Georgia Press, 1974).
J.N. Findlay, “Can God’s Existence be Disproved?”, New Essays in Philosophical Theology eds. Anthony Flew and Alasdair MacIntyre (London: SCM Press Ltd., 1958).
Charles Hartshorne, Anselm’s Discovery (LaSalle: Open Court Publishing Co., 1965).
Donald R. Keyworth, “Modal Proofs and Disproofs of God,” The Personalist L (1969): 33–52.
Clarke, “Philosphical Arguments for God”, Sophia 3/3 (October 1964): 3–14.
Clarke, “Modal Disproofs and Proofs for God”, Southern Journal of Philosophy IX (1971): 247–258 and “God, Modality, and Ontological Commitment”.
Clarke, “Modal Disproofs and Proofs for God”.
For the sake of simplicity, here, and in the sequal, I will use ‘G’ to represent Clarke’s longer expression ‘(∃x)x=God’
Clarke, “God, Modality, and Ontological Commitment”.
This is essentially the same argument as given by Clarke, ibi., p. 56.
For a discussion of standard and non-standard modal logic see Saul A. Kripke, “Semantical Analysis of Modal Logic I, Normal Prepositional Calculu”, Zeitschrift für mathematische Logik und Grundlagen der Mathematik IX (1963): 67-96 and “Semantical Analysis of Modal Logic II, Non-normal Prepositional Calculi”, The Theory of Models, eds. J.W. Addision, L. Henkin, and A. Tarski (Amsterdam: North Holland Publishing Co., 1965).
Clarke, p. 247.
Kripke, “A Completeness Theorm in Modal Logic”, The Journal of Symbolic Logic XXIX (1959): 1–14. “Semantical Analysis of Modal Logic I, Normal Propositional Calculi”. “Semantical Analysis of Modal Logic I, Normal Propositional Calculi”. “Semantical Analysis of Modal Logic II, Non-normal Propositional Calculi”.
One might argue that atheistic worlds are inaccessible from theistic worlds and vice versa. This is, in a different language Hartshorne’s response to Findlay. But given the general character of possible worlds and the arbitrary restrictions that need to be put on accessibility (e.g., how close can one get to an atheistic world from a theistic world?), the effort is futile.
If one chooses to treat possible worlds in a manner different from the intended interpretation, then my objection is moot. But since a choice would be tantamount to turning possible worlds into what I am calling contexts.
Non-normal systems pose special problems which normal modal systems do not. For example an S3 model must contain at least one context in which the proposition ‘MM-G’ is true, but since ‘MM-G’ is not reducible to ‘M-G’ in S3,I do not see how this could affect T.
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Dunlap, J.T. (1992). Models, Modality, and Natural Theology. In: Harris, J.F. (eds) Logic, God and Metaphysics. Studies in Philosophy and Religion, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2670-0_8
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