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The “Second Version” of Anselm's Ontological Argument
Published online by Cambridge University Press: 01 January 2020
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Chapter III of Anselm's Proslogion is quite naturally interpreted as presenting a second version of the ontological argument (the first version having been presented in Chapter II). In recent discussions it has been so interpreted by Charles Hartshorne and by Norman Malcolm. Other writers, however, have rejected this interpretation, maintaining that Anselm intended Chapter Ill, not as a second proof of God's existence (by way of showing that it is necessary that God exist), but only as a demonstration that the kind of existence which God (already proved to exist in Chapter II) has is necessary existence. Perhaps the latter writers are correct on this exegetical point, but even so, it does not follow that there is anything improper about an inquiry into the character of the distinct, modal version of the ontological argument which can be derived from this passage.
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References
1 Hartshorne, Charles The Logic of Perfection(La Salle, III. :Open Court, 1962Google Scholar), ch. 2, sec. 6, as rpt. in The Many-Faced Argument, ed. Hick, John and McGill, A. C. (New York: Macmillan, 1967), pp. 334–340;Google Scholar and Anselm's Discovery (La Salle, lll.: Open Court, 1965), pp. 85–106.
2 Malcolm, Norman “Anselm's Ontological Arguments,” Philosophical Review, 69 (1960), 41-62CrossRefGoogle Scholar, as rpt. in Hick and McGill, pp. 301–320. See especially pp. 305– 310.
3 E.g., Henry, D. P. The Logic of Saint Anselm(Oxford: Clarendon Press, 1967), pp. 143-149.Google Scholar
4 St. Anselm's, Proslogion,trans. Charlesworth, M. J. (Oxford: Clarendon Press, 1965), p. 119.Google Scholar
5 To allow for the significant use of non-designating singular terms, however, is to presuppose certain restrictions on the use of the quantificational rules of inference, EG and U I. That is, if’ a’ is an individual constant and ‘S’ is a sentence containing ‘a', we can generalize from S by EG only if 
is true. Likewise, we can instantiate to ‘S’ by ⋃l only if the same condition is met.
6 For a further elaboration of the notions of conceptual possibility and necessity, see Snyder, D.P. Modal Logic and Its Applications (New York: Van Nostrand, 1971)Google Scholar, ch. 6, sec. 2.
7 A useful critical discussion of the thesis that all existence assertions are contingent [a standard sort of objection to (P3)] is to be found in Adams, R. M. “Has It Been Proved That All Real Existence Is Contingent?” American Philosophical Quarterly, 8 (1971), 284-291.Google Scholar
8 That the modal proof enjoys this advantage over the proof of Proslogion, Chapter II, has been claimed both by Hartshorne and by Malcolm. See also Adams, R. M. “The logical Structure of Anselm's Arguments,” Philosophical Review, 80 (1971), 28-54CrossRefGoogle Scholar, especially 44-45.
9 This is my formulation of the principle introduced in Chapter II of the Proslogion in the following terms: “For if it exists solely in the mind even, it can be thought to exist in reality also, which is greater.” (Charlesworth, p. 117) It seems clear in context that Anselm's notion of existence solely in the mind is equivalent to the standard notion of possible, but not actual, existence; and that his notion of existence in reality also is equivalent to the standard notion of actual existence.
10 Most of the contemporary discussion of this thesis has, of course, centered around Kant's famous objections to Descartes’ formulation of the argument. See, for instance, Malcolm's positive assessment of Kant's objections in “Anselm's Ontological Arguments,” rpt. in Hick and McGill, pp. 303–305. Negative assessments of the Kantian criticisms have been made by Shaffer, Jerome “Existence, Predication and the Ontological Argument,” Mind, 71 (1962), 307-325Google Scholar, rpt. in Hick and McGill, pp. 226–245; and by Plantinga, Alvin “Kant's Objection to the Ontological Argument,” Journal of Philosophy, 63 (1966), 537-546.CrossRefGoogle Scholar
11 Lewis, David”Anselm and Actuality,” Nous, 4 (1970), 175-188CrossRefGoogle Scholar; see especially sec. 9.
12 Hume, David A Treatise of Human Nature,ed. Selby-Bigge, L. A. (Oxford: Clarendon Press, 1958), pp. 66–67.Google Scholar
13 Danto, A. C. Analytical Philosophy of Knowledge(Cambridge: Cambridge Univ. Press, 1968), p. 165Google Scholar, n. 1.
14 See above, p. 666.
15 I assume that the relational predicate ‘is greater than’ has the logical properties of being irreflexive, asymmetrical, and transitive.
16 line (6) follows from line (1) by way of assumption (c) on p. 671.
17 line (9) comes from line (3) via Ul; the restriction on Ul being observed here is satisfied by line (4) and assumption (c) on p. 671.
18 This presupposes the logical equivalence of 
and 
', which is provable in a modal system as strong as S5. I assume throughout that such a system will be available to Anselm to justify the inferences involved in the modal proof.
19 To see that these claims are correct, one need only note that if we assume that 
are all true (a consistent assumption), it turns out that (a) 
will be true and 
will be false, and (b) 
and 
will both be true and 
will be false.
20 To see that 
does not follow from (P1), (P3), and (P4’), one need Only note that if we assume that both of 
are true (a consistent assumption), it turns out that (P4’) cannot be used to derive anything inconsistent with (P1) from (P3) and the relevant reductio premise 
Nor can (P4’) be strengthened to permit such a derivation without at the same time ruling out the possibility of an affirmative answer to question (a) on p. 666 above. (See the discussion of (P4) on pp. 668–670. above.]
21 Malcolm, op. cit., p. 310.Google Scholar
22 For an extensive discussion of Hartshorne's proof, see Purtill, R. L. “Hartshorne's Modal Proof,” Journal of Philosophy, 63 (1966), 397-409.CrossRefGoogle Scholar
23 Hartshorne, The Logic of Perfection, ch. 2, sec. 6, as rpt. in Hick and McGill, pp. 334–335. R. M. Adams has shown that it is possible to derive ‘Eg’ from these premises in the Brouwerian modal system (where the alternativeness relation is taken to be reflexive and symmetrical, but not transitive, in the model system). See Adams, op. cit., pp. 43–44.
24 As a case of apparent failure to appreciate the difference, see the discussion of Proslogion, Chapter III, by Adams, pp. 49–53.
25 Hartshorne, in Hick and McGill, p. 335.
26 Hartshorne, Anselm's Discovery, p. 97.
27 The equivalence of these propositions is provable in a modal system as strong as S5.
28 Charlesworth, p. 171.
29 Adams, p. 41.
30 Malcolm, pp. 308–309.
31 Ibid., p. 309.
32 Charlesworth, pp. 169–171.
33 Plantinga, Alvin “A Valid Ontological Argument?” Philosophical Review, 70 (1961), 93-101.CrossRefGoogle Scholar
34 Charlesworth, p. 171.
35 Adams, p. 47. For the sake of notational consistency, I have modified the symbolic forms used by Adams to bring them into line with my own usage.
36 Ibid., pp. 47–48.
37 Begging the question (i.e., assuming something which is tantamount to the assumption of the conclusion to be demonstrated) is clearly a matter of degrees. That is, one can readily imagine cases ranging from the explicit assumption of the conclusion as part of the premises to ones which are highly disputable. I take it to be a clear-cut case of begging the question where the following conditions are satisfied: (1) A proposition ø is assumed as a premise for the demonstration of a proposition 
(3) There is another proposition X, which adequately expresses that part of what ø expresses which is independently defensible. (4) It is not the case that 
.
38 Of course, 
do not entail 
. Alli mean here is that one who grants that ‘Eg’ is true only if it is necessarily true should, for the sake of the argument, allow that it could be necessarily true, if he is going to allow that it could be true at all.
39 See Snyder, Modal Logic and Its Applications, pp. 180–184.Google Scholar