Heinrich Scholz. Der anselmische Gottesbeweis. In Mathesis universalis. Abhandlungen zur Philosophie als strenger Wissenschaft. Basel: Benno Schwabe 1961. pp. 1-13
Part one of the lecture course Einführung in die Kantische Philosophie (1950-1951).
Studies
Peckhaus Volker, "Logic and metaphysics: Heinrich Scholz and the scientific world view," Philosophia Mathematica 16: 78-90 (2008).
"The anti-metaphysical attitude of the neo-positivist movement is
notorious. It is an essential mark of what its members regarded as the
scientific world view. The paper focuses on a metaphysical variation of
the scientific world view as proposed by Heinrich Scholz and his
Münster group, who can be regarded as a peripheral part of the
movement. They used formal ontology for legitimizing the use of logical
calculi. Scholz's relation to the neo-positivist movement and his
contributions to logic and foundations are discussed. His heuristic
background can be drawn from a set of six methodological 'articles of
faith', formulated in 1942 and published here for the first time."
Karl Barth. Fides quaerens intellectum. Anselm Beweis der Existenz Gottes in Zusammenhang seines theologischen Programms. Münich: C. Kaiser 1931.
Second edition 1958.
Karl Barth. Anselm, Fides quaerens intellectum. Anselm's proof of the existence of God in the context of his theological scheme. London: SCM Press 1960.
Translated by Ian W. Robertson; reprinted Pittsburgh, Pickwick Press, 1975.
Studies
Bouillard Henri. La preuve de Dieu dans le Proslogion et son interprétation par Karl Barth. In Spicilegium Beccense I. Congrés International du IX centenaire de l'arrivée d'Anselme au Bec. Paris: Vrin 1959. pp. 191-207
Potter Vincent G., "Karl Barth and the ontological argument," Journal of Religion 45: 309-325 (1965).
Robin George Collingwood. Speculum Mentis. Oxford: Clarendon Press 1924.
The 1919 Lectures on the Ontological Proof of the Existence of God, Bodleian library, Collingwood dep.
2 (almost 100 pages) are unpublished.
Robin George Collingwood. An essay on metaphysics. Oxford: Oxford University Press 1998.
First edition 1940.
Revised edition, with an introduction by Rex Martin.
Robin George Collingwood. An essay on philosophical method. Oxford: Oxford University Press 2005.
First edition 1933.
Revised edition, with an introduction by James Connelly and Giuseppina D'Oro.
Studies
D'Oro Giuseppina, "On Collingwood's rehabilitation of the ontological argument," Idealistic Studies.An Interdisciplinary Journal of Philosophy 30: 173-188 (2000).
"This paper assesses the nature of Collingwood's rehabilitation of the ontological argument through a close reading of Collingwood's private correspondence with Ryle following the publication of "An Essay on Philosophical Method." The paper asks whether Collingwood's rehabilitation of the ontological proof entails that he is committed to a form of precritical, dogmatic metaphysics, as Ryle suggests. The paper concludes that Collingwood's rehabilitation of the ontological proof is rather unorthodox and does not, contrary to what one might expect, contradict the claim that existence is not a real predicate."
D'Oro Giuseppina. Collingwood and the metaphysics of experience. New York: Routledge 2008.
Chapter 5: Collingwood's 'rehabilitation' of the ontological argument -- pp. 67-78.
"In this chapter I would like to consider a lively debate that took place between Collingwood and Ryle in the aftermath of the publication of An Essay on Philosophical Method (EPM), The debate was prompted by Collingwood's reappropriation of the ontological argument in Chapter 6 of EPM where he defended what he regarded as a neglected kernel of truth in the traditional proof. Ryle launched a fierce attack on Collingwood's attempted rehabilitation of the ontological argument in the pages of Mind, where he accused Collingwood of ignoring crucial philosophical developments which had occurred in the last two hundred years, in particular the thesis that all existential propositions are knowable a posteriori and the corollary that there can be no necessary existential judgements. Collingwood newer took up Ryle's challenge publicly, but did attempt to clarify his own position in a number of private letters.(*) It was Errol Harris who replied to Ryle publicly on Collingwood's behalf, locating Collingwood's defence of the ontological argument in the tradition of Hegel's objective or speculative idealism, thereby adding further fuel to the controversy. As a result of Harris's reply on behalf of Collingwood and the private exchange with Collingwood himself Ryle responded with a further article aimed at reasserting his original position that there can be no necessary existential propositions." p. 67 (some notes omitted).
(*) The Collingwood-Ryle correspondence is deposited in the Bodleian Library in Oxford, Collingwood Department 26/3.
Harris Errol E., "Mr. Collingwood and the ontological argument; reply to G. Ryle," Mind 45: 474-480 (1936).
Reprinted in Hick, John and McGill, Arthur C. (ed.), The many-faced argument. Recent studies on the ontological argument for the existence of God, London, Macmillan, 1967.
Harris Errol E. Collingwood's treatment of the ontological argument and the Categorical Universal. In Critical essays on the philosophy of R. G. Collingwood. Edited by Krausz Michael. Oxford: Clarendon Press 1972. pp. 113-133
O'Neill Michael J., "A peculiar "faith": on R. G. Collingwood's use of Saint Anselm's argument," Saint Anselm Journal 3: 32-47 (2006).
"In this paper, I discuss the role of Anselm's ontological argument in the philosophy of R. G. Collingwood. Anselm's argument appears prominently in Collingwood's Essay on Philosophical Method (1933) and Essay on Metaphysics (1940), as well as in his early work Speculum Mentis (1924). In the proof, Collingwood finds the central expression of the priority of "faith" in the first principles of thought to reason's activities. For Collingwood, it is Anselm's proof that clearly expresses this relationship between faith and reason. The two elements of this analysis that must be understood if one is to understand Collingwood's use of the proof are what he means by "the idea of an object that shall completely satisfy the demands of reason" and the "special case of metaphysical thinking." I analyze both of these elements and conclude by showing how Anselm's proof is essential to Collingwood's historical science of mind."
Ryle Gilbert, "Mr. Collingwood and the ontological argument," Mind: 137-151 (1935).
Reprinted in Hick, John and McGill, Arthur C. (ed.), The many-faced argument. Recent studies on the ontological argument for the existence of God, London, Macmillan, 1967. Also reprinted in: G. Ryle - Collected Papers, Vol. 2, Bristol, Thoemmes Press, 1990.
Ryle Gilbert, "Back to the ontological argument," Mind: 53-47 (1937).
Reprinted in Hick, John and McGill, Arthur C. (ed.), The many-faced argument. Recent studies on the ontological argument for the existence of God, London, Macmillan, 1967. Also reprinted in: G. Ryle - Collected Papers, Vol. 2, Bristol, Thoemmes Press, 1990.
Charles Hartshorne. Man's vision of God and the logic of Theism. Chicago: Willett, Clark and Co. 1941.
Charles Hartshorne, "The formal validity and real significance of the ontological argument," Philosophical Review 53: 225-245 (1944).
Charles Hartshorne, "The logic of the ontological argument," Journal of Philosophy 58: 471-473 (1961).
Charles Hartshorne. The logic of perfection and other essays in neo-classical metaphysics. La Salle: Open Court 1962.
See in particular Chapter 2: Ten ontological or modal proofs for God's existence pp. 28-117.
Charles Hartshorne, "What dis Anselm discover?," Union seminary Quarterly Review 7: 213-222 (1962).
Charles Hartshorne. Anselm's discovery. A re-examination of the ontological proof for God's existence. La Salle: Open Court 1965.
Charles Hartshorne, "Is the denial of existence ever contradictory?," Journal of Philosophy 63: 65-83 (1966).
"This article examines criticisms of the ontological argument proposed
by Plantinga and Alston. The conclusion is reached that the denial of
existence can be contradictory if this denial implies that the ground
of all possibility is itself but a mere possibility, or that an
indispensable predicate -- one whose actualization or being
instantiated is necessary to reality as such -- is yet dispensable. It
is conceded that the argument is a proof for the divine existence only
on the assumption that the idea of God is logically admissible, and not
an absurdity. It is also shown that the argument need not beg the
question by assuming from the outset a subject of predication, God, but
can argue rather from the predicate divine and deduce from this
predicate the necessity of its instantiation in some suitable
actuality."
Charles Hartshorne, "The Prosologion argument. Anselm and Aristotle's First Law of Modality," Anselm Studies.An Occasional Journal 1: 51-58 (1983).
Studies
Connelly Robert J., "The ontological argument: Descartes' advice to Hartshorne," New Scholasticism 43: 530-554 (1969).
Dombrowski Daniel A. Rethinking the ontological argument. A neoclassical Theistic response. Cambridge: Cambridge University Press 2006.
Friedman Joel I., "Necessity and ontological argument," Erkenntnis 15: 301-331 (1980).
"In this paper, I focus on Hartshorne's "de dicto" modal reconstruction of the ontological argument for God's existence. I consider "six" senses of necessity, and for all these senses, I call into question either the truth of at least one of the premises of the reconstructed argument or the truth of at least one of the axioms of modal logic itself. the main conclusion is that it is probably impossible to formalize within a "sound" modal logic any traditional or semi-traditional version of the ontological argument in such a way that it is both formally valid yet has necessarily true, "a priori" known premises. I believe that any claim to the contrary is based on acute modal confusion."
Goodwin George L. The ontological argument of Charles Hartshorne. Missoula: MT Scholars 1978.
With a foreword by Charles Hartshorne.
Goodwin George L., "The ontological argument in neoclassical context: Reply to Friedman," Erkenntnis 20: 219-232 (1983).
Reply to the article published in Erkenntnis, 15, 1980, 301-331.
"Professor Joel Friedman has contended that there is no univocal sense of "de dicto" necessity in terms of which the five axioms of Lewis' S5 system of modal logic and the two premises of Hartshorne's ontological argument can be known "a priori" to be true. Goodwin shows how Friedman's challenge can be met in either Carnap's or Kripke's sense of logical necessity when Hartshorne's temporal interpretation of possibility is taken into account."
Müller Jörn, "Möglichkeit und Notwendigkeit der Existenz Gottes: Anselms ontologischer Gottesbeweis in der modallogischen Deutung von Charles Hartshorne," Veritas.Revista de Filosofia 48: 397-415 (2003).
"The author analyzes the validity of a certain variation of Anselm's "ontological argument", namely the modal-logical version from Charles Hartshorne. He firstly studies the origin of Hartshorne's
arguments, whose starting point is an interpretation of Anselm; secondly, the modal-logical argument from Hartshorne will be presented together with its presuppositions and implications. Finally, the author proposes an evaluation of Hartshorne's approach."
Pailin David A. An introductory survey of Charles Hartshorne's work on the ontological argument. In Analecta Anselmiana. Untersuchungen über Person und Werk Anselms von Canterbury. Edited by Schmitt Franciscus Salesius and Kohlenberger Helmut. Frankfurt: Minerva 1969. pp. 195-221
"The importance of Hartshorne's use of the ontological argument of a God's existence lies not merely in his recognition of the second proof of Anselm's argument but more so in his di-polar Panentheism as in his analyses of the meaning of "necessary existence" which allows it to be significantly attributed to an entity. Nevertheless, Hartshorne's claims that the 'second proof' escapes the earlier criticisms of the ontological argument and that necessary existence implies factual existence are subject to criticism."
Purtill Richard L., "Hartshorne's modal proof," Journal of Philosophy 63: 397-408 (1966).
"This paper restates and criticizes the modal version of the ontological argument given by Charles Hartshorne in The logic of perfection. I show that the argument is valid in modal systems as strong as Lewis' S5 and that it is not subject to some familiar refutations of the ontological argument. I argue that, nevertheless, the ontological argument does not prove what it sets out to, and that the value of Hartshorne's modal version of the argument is that it enables us to state with some precision why this is so."
Purtill Richard L., "Ontological modalities," Review of Metaphysics 21: 297-307 (1967).
"A formal proof, paralleling the argument given by Charles Hartshorne in his reply to my "Hartshorne's modal proof," is given and discussed. His version of the ontological argument in modal logic seemed to offer a modalized ontological argument valid for a system no stronger than Lewis' S3. However, a logical mistake in one of the lemmas to the main proof invalidates this aspect of the argument. (see section 8.5 of my "Logic for philosophers," Harper and Row, 1971). The main critical points of the paper were, however, independent of this proof. The conclusion of the paper is that the ontological argument is redundant if sound."
Shofner Robert D. Anselm revisited. A study of the role of the ontological argument in the writings of Karl Barth and Charles Hartshorne. Leiden: Brill 1974.
"This work traces the dimensions of two independent attempts --- those of Karl Barth and Charles Hartshorne -- to set aside the burden of the Kantian heritage in so far as it has influenced the development of contemporary philosophical-theological thinking. The focal issue throughout is the role that the Anselmian formulation of the ontological argument plays in these respective attempts. Such an issue is raised not out of an historical-critical interest in the writings of the eleventh-century saint, but because both Barth and Hartshorne have found the Proslogion proof for God to be a particularly propitious vantage point from which to gain a fresh perspective on their own professional preoccupations. It is interesting to note, however, that while Barth turns to a discussion of the ontological argument as a phase in the development of a methodological program which entails the rejection of natural theology, Hartshorne undertakes a defense of the same argument in an effort to establish an appropriate basis for the acceptance of natural theology. The scope of the chapters to follow has been shaped by the conviction that there is a pressing need to account for this rather disconcerting difference."
Towne Edgar A., "Semantics and Hartshorne's Dipolar Theism," Process Studies 28: 231-254 (1999).
"The essay examines the syntactical, semantic and philosophical issues raised by Charles Hartshorne's formulation of the ontological argument for the existence of God and by his effort to distinguish his dipolar panentheism from supernatural theism. The essay shows how the argument is invalid, admitted by Hartshorne. It shows Hartshorne's metaphysics employs a natural language, not a modal one. It elucidates the logical structure of dipolar theism. It shows faith need not be contrary to reason though faith cannot expect reason to prove theism. It shows that any non-dogmatic rational inquiry into theistic belief must be open and on-going."
Viney Donald Wayne. Charles Hartshorne and the existence of God. Albany: State University of New York Press 1985.
Chapter IV. The ontological argument pp. 45-57
Vitali Theodore, "The ontological argument: model for neoclassical metaphysics," Modern Schoolman 57: 121-136 (1980).
"The ontological argument of Charles Hartshorne serves as the speculative model for his neoclassical metaphysics. Neoclassicism requires both the necessary existence of God and his maximal relativity if its fundamental ontological principles of world, order, and beauty are to be grounded. The ontological argument proves directly the divine necessary existence and at the same time grounds indirectly the divine relativity which these fundamental principles require. The argument, therefore, is neoclassicism's speculative model in that within this model one is able to discover the structure of Charles Hartshorne's entire metaphysics."
John Niemeyer Findlay, "Can God's existence be disproved?," Mind 57: 176-183 (1948).
Reprinted in:A. Flew and A. MacIntyre (eds.) - New essays in philosophical theology - London: SCM Press, 1957 pp. 47-56, with replies by G. E. Hughes, pp. 56-67, A. C. A. Rainer, pp. 67-71, and a rejoinder by J. N. Findlay, pp. 71-75.J. N: Findlay - Language, truth and value - New York, Humanities Press, 1963 pp. 96-108A. Plantinga (ed.) - The ontological argument from St. Anselm to contemporary philosophers - London, Macmillan, 1965, pp. 111-122.
Studies
Blackman Larry, "Another look at J.N. Findlay's "Ontological Disproof of the Existence of God"," International Journal of the Humanities 3: 23-30 (2005).
"First published in 1948, J.N. Findlay's article, "Can God's Existence
Be Disproved?" remains interesting. Findlay argues that a religious
object possessing unsurpassable superiority (or God), would be one
whose existence is inescapable. By "inescapable" he cannot mean
"psychologically inconceivable", because then the mere fact that there
are unbelievers would make atheism true. But if we interpret
"inescapable" as "logically inconceivable", then God's existence is
inescapable, that is, His nonexistence is logically inconceivable, only
if He is a necessarily existing being. Since, according to Findlay,
there are no necessarily existing beings, it follows that God does not
exist. In effect, he maintains that God is by definition a necessarily
existing being, but there are no such beings. However, this
"ontological disproof of the existence of God" fails, because his claim
that there are no necessarily existing beings is unsupported. This
paper suggests the plausibility of the claim that there are necessarily
existing beings without, however, supposing that God is among them.
Rather than defending theism, the paper considers what would be
required to establish atheism, namely, the unintelligibility of the
concept of God due to certain antinomies. The position being advocated
is not, strictly speaking, atheism but, rather, conceptual skepticism,
that is, skepticism with regard to the very concept. It might be
described as functional atheism, inasmuch as it entails suspending all
matters having to do with God until the conceptual problems are
satisfactorily resolved. This recommendation is different from the one
offered by the logical positivists in a bygone era, since it has
nothing to do with empirical verifiability. The antinomies are to a
great extent "a priori" and therefore rest on a rationalist, not an
empiricist, foundation."
Clarke Bowman, "Modal disproofs and proofs for God," Southern Journal of Philosophy: 247-258 (1971).
"This paper attempts to present J. N. Findlay's ontological disproof of
the existence of God as an extension of Hume and Kant's treatment of
the ontological argument. This modal disproof is presented along side
what is called the Libnizian-Hartshornean modal proof in order to
reveal the modern theistic modal paradox. In order to resolve this
paradox, an interpretation of 'possibility' is presented along the
lines suggested by Charles Hartshorne's justification of the premise
asserting the possibility of the existence of God, that is, in terms of
the other proofs."
Lycan Gregory W., "Hartshorne and Findlay on 'necessity' in the ontological argument," Philosophical Studies (Ireland) 17: 132-141 (1968).
Williams John N., "Ontological disproof," Australasian Journal of Philosophy: 204-210 (1992).
Kurt Gödel. Unpublished essays and letters. Edited by Feferman Solomon et al. New York: Oxford University Press 1995.
First draft written in 1941, revised in 1970; published in: Collected works vol. III - Ontological proof - pp. 403-404.
Kurt Gödel. La prova matematica dell'esistenza di Dio. Edited by Lolli Gabriele and Odifreddi Piergiorgio. Torino: Bollati Boringheri 2006.
Indice: Prefazione di Gabriele Lolli; La prova matematica
dell'esistenza di Dio; Nota introduttiva di Robert Merrihew Adams 23;
Prova ontologica di Kurt Gödel 61; Testi collegati alla prova
ontologica 64; Appendici; A. Una dimostrazione divina di Piergiorgio
Odifreddi; B. Logica e teofilia. Osservazioni su una dimostrazione
attribuita a Gödel di Roberto Magari, con presentazione di Gabrielle
Lolli 95-120.
Studies
Adams Robert Merrihew. Introductory note to *1970. In Kurt Gödel - Collected Works Vol. III: Unpublished essays and lectures. Edited by Feferman Solomon. New York: Oxford University Press 1995. pp. 388-402
Anderson Anthony C., "Some emendations of Gödel's ontological proof," Faith and Philosophy 7: 291-303 (1990).
"Kurt Gödel's version of the ontological argument was shown by J Howard
Sobel to be defective, but some plausible modifications in the argument
result in a version which is immune to Sobel's objection. A definition
is suggested which permits the proof of some of Gödel's axioms."
Anderson Anthony C. and Gettings Michael. Gödel ontological proof revisited. In Gödel '96. Edited by Hájek Petr. Berlin, Heidelberg: Springer 1996. pp. 167-172
"Gödel's version of the modal ontological argument for the existence of
God has been criticized by J. Howard Sobel (5) and modified by C.
Anthony Anderson (1). In the present paper we consider the extent to
which Anderson's emendation is defeated by the type of objection first
offered hy the Monk Gaunilo to St. Anselm's original Ontological
Argument. And we try to push the analysis of this Gödelian argument a
bit further to bring it into closer agreement with the details of
Gödel's own formulation. Finally, we indicate what seems to be the
rnain weakness of this emendation of Gödel's attempted proof."
Bjørdal Frode. Understanding Gödel's ontological argument. In The Logica Yearbook 1998. Edited by Childers Timothy. Praha: Filosofia 1999. pp. 214-217
Cook Roy T. God, the Devil, and Gödel's other proof. In The Logica Yearbook 2003. Edited by Behounek Libor. Prague: Philosophia 2004. pp. 97-109
"Gödel's 1970 proof of the existence of a god-like being (i.e., a being
having all the 'perfective' properties) is investigated. The proof is
streamlined and reformulated within the weakest logic possible - and
intuitionistic version of second-order logic with a modal operator no
stronger than the system K. It is shown that even in this weak context
one can derive that it is necessary that a god-like being is at least
possible. Finally, the prospects for a similar proof of the existence
of the Devil (or, more carefully, a being who lacks all perfective
properties) is investigated. Technical reasons are given for why such a
parallel proof of the existence of an evil being is not forthcoming."
Czermak Johannes. Abriss des ontologischen Argumentes. In Kompendium zum Werk. Edited by Köhler Eckehart et al. Wien: Öbv & Hpt 2002. pp. 309-324
Kurt Gödel. Wahrheit & Beweisbarkeit. Vol.1: Dokumente und historische analysen; Vol. 2: Kompendium zum Werk.
Fitting Melvin. Types, tableaux and Gödel's God. Dordrecht: Kluver Academic Press 2002.
See Part III. Ontological arguments. Chapter 10. Gödel argument, background 133; Chapter 11. Gödel argument, formally 145-172.
"Finally, Part III is devoted to ontological proofs. Chapter 10 gives a
brief history and analysis of arguments of Anselm, Descartes, and
Leibniz. This is followed by a longer, still informal, presentation of
the Gödel argument itself. Formal methods are applied in Chapter 11,
where Gödel's proof is examined in great detail. While Gödel's argument
is formally correct, some fundamental flaws are pointed out. One, noted
by Sobel, is that it is too strong -- the modal system collapses. This
could be seen as showing that free will is incompatible with Gödel's
assumptions. Some ways out of this are explored. Another flaw is
equally serious: Gödel assumes as an axiom something directly
equivalent to a key conclusion of his argument. The problematic axiom
is related to a principle Leibniz proposed as a way of dealing with a
hole he found in an ontological proof of Descartes. Descartes, Leibniz,
and Gödel (and also Anselm) all have proofs that stick at the same
point: showing that the existence of God is possible.
If the Gödel argument is what you are interested in, start with Part
III, and pick up earlier material as needed. Many of the uses of the
formalism are relatively intuitive. Indeed, in Gödel's notes on his
ontological argument, formal machinery is never discussed, yet it is
possible to get a sense of what it is about anyway."
Fuhrmann André. Existenz und Notwendigkeit - Kurt Gödels axiomatische Theologie. In Logik in der Philosophie. Edited by Spohn Wolfgang, Schroeder-Heister Peter, and Olsson Erik J. Heidelberg: Synchron Publishers 2005. pp. 349-374 Gödels ontologischer Beweis pp. 354-360.
Goldman Randolph Rubens, "Gödel's ontological argument", University of California at Berkeley, 2000.
Available at ProQuest Dissertation Express. Order number: 9979637
Gonçalves Gomes Nelson, "Summum Bonum," Analytica.Revista de Filosofia 10: 43-105 (2006).
(The article is in Portuguese).
"This article contains a presentation of Gödel's ontological proof,
from both the intuitive and the formal points of view. Two other
contemporary variations of it are also presented. The article
discusses the philosophical and the theological criticisms of the
proof. The conclusion to be drawn is that the soundness of Gödel's
reasoning is an important logical result, which nevertheless demands
further work of analysis. The metaphysical idea of a positive property (or positive set) for instance needs clarification."
Hazen Allen P., "On Gödel's ontological proof," Australasian Journal of Philosophy 76: 361-377 (1998).
"Gödel, in a cryptic note given to Dana Scott in 1970, introduces the notion of a positive property.
(Thus the formalized version uses a Third-Order constant, the predicate
P(F), expressing the positivity of the property F). The plausibility of
his 'axioms' and the theological relevance of its conclusion depend on
the interpretation of this notion; Gödel says that it means 'positive
in the moral aesthetic sense (independently of the accidental structure of the
world)', but also allows that it may mean 'pure "attribution" as
opposed to "privation".' The evidence available from his notebooks
suggests that he never found an interpretation of this notion
that fully satisfied him, and it is perhaps best to assume that he
thought of his ontological argument not as a conclusive proof of the
existence of God, but as an attempt at a reconstruction of Leibniz's
argument. In any event, he laid down certain axioms concerning the
notion. Any property entailed by a positive property is positive, and
the conjunction of two positive properties (the property, that is, that
an individual has if and only if it has both of the given properties)
is positive. Together, these amount to saying that the positive
properties form a filter on the Boolean algebra of properties.
(Gödel adds in a footnote that the positivity of conjunctions of
positive properties holds for arbitrary numbers of conjuncts,
not just for two: as we shell see, this includes infinite numbers.)
Further, positivity is a non-contingent feature of a property: any
property which is positive is necessarily positive, and no property
which is not positive could be.
Another axiom said that, of any pair of properties consisting of a
property and its negation (the property necessarily holding of all and
only the individuals not possessing the first property), precisely one is
positive. (Positive properties form an ultrafilter.) We are now In a
position to prove our first theorem: positive properties are at least
possibly instantiated, Proof: the contradictory property
(self-non-identity) entails all properties, including Its own negation
(self-Identity), so if it were positive both properties of such a pair
would be positive. (As has been noted by commentators, the proof uses
only part of the strength of the latest axiom: of a pair of a property
and its negation at most one is positive.)
Gödel's remaining axiom is formulated in terms of a defined notion. First define a property to be an essence of
an individual if it is a property, possessed by the individual (Godel
left this clause out in (1), but this appears to have been an oversight
- -it is Included In related manuscripts), which entails every property
the individual has. The terminology is somewhat unfortunate: the notion
defined is close to Leibniz's notion of the complete concept of an
object, but is not at all what current philosophical usage calls an
essence. 'Essence' and 'essentialism' were bad words for most analytic
philosophers of the 1960s -- many found the doctrines of Kripke
downright shocking -- but, with the flowering of modal metaphysics
since, they have come to have well-understood and generally agreed
meanings, defined in terms of de re modal locutions. An individual. x, has a property, F, essentially iff x has F and it is necessarily the case that x, provided it exists, has F. An essence of
x, in this post-1970 sense, is a property which entails all and only
the properties x has essentially. To avoid confusion, therefore, let us
re-christen Gödel's
notion: the property an individual has that entails every property it has is its character." pp. 364-365.
Notes omitted.
Hájek Petr. Magari and others on Gõdel's ontological proof. In Logic and algebra. Edited by Ursini Aldo and Agliani Paolo. New York: Dekker 1996. pp. 125-136
"Gödel's proof of the necessary existence of God is analyzed from the
point of view of modal logic together with related papers by Magari and
Anderson. ln particular, Magari's claim on redundance in axioms is
analyzed and shown to be only true for some extension of Godel's system
(but true for Anderson's modification, as it as shown elsewhere).
Completeness of the underlying modal logic is proved; and it is shown
that the "ontological" proof may use only the logic KD45 (logic of
belief) instead of S5 (logic of knowledge)."
Hájek Petr, "A new small emendation of Gödel ontological proof," Studia Logica 71: 149-164 (2002).
"Two variants of monadic fuzzy predicate logic are analyzed and
compared with the full fuzzy predicate logic with respect to finite
model property (properties) and arithmetical complexity of sets of
tautologies, satisfiable formulas and of analogous notion restricted to
finite models."
Hájek Petr. Der Mathematiker und die Frage der Existenz Gottes. In Kompendium zum Werk. Edited by Köhler Eckehart et al. Wien: Öbv & Hpt 2002. pp. 325-336
Kurt Gödel. Wahrheit & Beweisbarkeit. Vol.1: Dokumente und historische analysen; Vol. 2: Kompendium zum Werk.
Kegler Jeffrey. The God Proof. CreateSpace 2008.
A novel on the ontological proof, useful as a non-technical, but reliable, introduction to Gödel's argument.
Kovac Srecko, "Some weakened Gödelian ontological systems," Journal of Philosophical Logic 32: 565-588 (2003).
"We describe a K B Gödelian ontological system, and some other weak
systems, in a fully formal way using theory of types and natural
deduction, and present a completeness proof in its main and specific
parts. We technically and philosophically analyze and comment on the
systems (mainly with respect to the relativism of values) and include a
sketch of some connected aspect of Gödel's relation to Kant."
Magari Roberto, "Logica e teofilia," Notizie di logica 7: 11-20 (1988).
Ristampato in: Kurt Gödel - La prova matematica dell'esistenza di Dio - Trino, Bollati Boringhieri, 2006, pp. 99-120.
Muck Otto, "Eigenschaften Gottes im Licht des Godelschen Arguments," Theologie und Philosophie 67: 60-85 (1992).
"In his sketch of an Ontological Proof (dated February 10th 1970) Kurt
Gödel introduces the concept of a positive property and proves the
necessary existence of exact one being which instantiates all positive
properties -- he calls it 'summun bonum'.
Special emphasis in the discussion of this argument is put on the
logical structure of positive property and the comparison with the
concept of (pure) perfection as it is used in traditional philosophy of
God for dealing with divine attributes."
Muck Otto, "Religioser Glaube und Gödels ontologischer Gottesbeweis," Theologie und Philosophie 67: 263-267 (1992).
"In discussing the rationality of religious belief, Franz von Kutschera (Vernuft und Glaube,
1990) criticises attempts to clarify divine attributes and to
demonstrate the existence of God, including Gödel's Ontological Proof.
The article argues that the criticism proposed neglects the concept of
pure perfection and that the logical structure of this concept can be
clarified in further developing Gödel's concept of positive property."
Oppy Graham, "Gödelian ontological arguments," Analysis 56: 226-230 (1996).
"The main thesis of this paper is that Gödel's ontological argument is
subject to a kind of objection which has hitherto been overlooked, but
which has often been levelled at other ontological arguments, viz. that
it can be paralleled by apparently equally persuasive proofs of the
existence of beings in which no one should wish to believe. (Compare
Gaunilo's objection to St. Anselm: No one should wish to believe in the
existence of an island than which no greater island can be conceived.) "
Park Woosuk, "On the motivations of Gödel's ontological proof," Modern Schoolman: 144-153 (2003).
"In recent years there has been a surge of interest in Gödel's
ontological proof of the existence of God. Gödel showed his proof
(Gödel *1970) to Scott, and Scott made a note of the proof and
presented it in his seminar at Princeton University in the fall of
1970. From then on, Gödel's proof has become widely circulated. It was
finally published in Sobel 1987 as an appendix and later included in
volume three of Gödel's Collected Works.
Recent discussions of Gödel's proof mostly start from Sobel's
criticisms. As is well known, the most influential criticism of Sobel
is that Gödel's proof leads to a consequence unacceptable to most
philosophers, i.e. that all truths are necessary truths. Anderson 1990
viewed this as the modal collapse of Gödel's assumptions, and tried to
save Gödel's proof by some plausible modifications.
Anderson's emendation secured many interesting responses including Oppy
1996, where a parody of the Gödelian proof reminiscent of Gaunilo's
objection to Anselm's proof is presented. As one might expect, such a
parody has invited friends of ontological proofs to follow in the
footsteps of Anselm.
In spite of all this extensive concern, it is not certain whether there
is any improvement in understanding the motivations of Gödel's
ontological proof. Why was Gödel so preoccupied with completing his own
ontological proof? To the best of my knowledge, no one has dealt with
this basic question seriously enough to answer it.
In this article, I propose to examine Gödel's ideas against a somewhat
larger background in order to understand his motivation for
establishing the ontological proof.
I shall point out that the value of Gödel's proof is to be found in the
possible role of his proof of the existence of God in his philosophy as
a whole as well as in its relative merit as an ontological proof.
Hopefully, my guiding question as to Gödel's motivation will turn out
to be extremely fruitful by enabling us to fathom his mind regarding
God and mathematics."
Perzanowski Jerzy. Ontological arguments II - Cartesian and Leibnizian. In Handbook of metaphysics and ontology. Edited by Burkhardt Hans and Smith Barry. München: Philosophia Verlag 1991. pp. 625-633
Roetti Jorge Alfredo, "El argumento ontológico: La variante de Gödel de la versión de Leibniz," Dialogos.Revista del Departmento de Filosofia Universidad de Puerto Rico 39: 77-105 (2004).
"The paper contains a full version of the well-known Gödel's variant of
the ontological argument. It is based on the Leibniz's version of the
proof, the axiom systems of Gödel 1970 and of Anderson 1990, with some
weakenings. We discriminate between several types of existence; the
form of existence of God we assert is, in a constructive fashion, a
weaker one. Later we deal with Kant's criticism against the predicate
of existence and offer several commentaries on the proof, and on topics
such as perfection and existence."
Scott Dana. Gödel's ontological proof. In On Being and Saying. Essays for Richard Cartwright. Edited by Thomson Judith Jarvis. Cambridge: MIT Press 1987. pp. 257-258
Szatkowski Miroslaw, "Semantic analysis of some variants of Anderson-like ontological proofs," Studia Logica 79: 317-355 (2005).
"The aim of this paper is to prove strong completeness theorems for
several Anderson-like variants of Gödel's theory wrt. classes of modal
structures, in which: (i). 1st order terms receive only rigid
extensions in the constant objectual 1st order domain; (ii). 2nd order
terms receive nonrigid extensions in preselected world-relative
objectual domains of 2nd order and rigid intensions in the constant
conceptual 2nd order domain."
Norman Malcolm, "Anselm's ontological argument," Philosophical Review: 41-62 (1960).
Reprinted in: N. Malcolm - Knowledge and certainty. Essays and lectures - Ithaca, Cornell University Press, 1963, pp. 141-162.
Studies
Morewedge Parviz, "Ibn Sina (Avicenna) and Malcolm and the ontological argument," Monist 54: 234-249 (1970).
"Evidence is presented in support of the following theses: (1) Prior to
Anselm, Ibn Sina formulated a version of the ontological argument which
corresponds to Malcolm's second version of this argument. (2) An
examination of Ibn Sina's formulation permits new criticism of Malcolm's version. The latter makes the unwarranted deduction that in its
metaphysical use "the necessary existent" is identified with "God" in
its ordinary religious use. Further, Malcolm's informal explication of
"the necessary existent" in terms of "dependency on privations"
contains logical confusions. Departing from the same premise as Malcolm, Ibn Sina
deduces a different conclusion, identifying "the necessary existent"
not with a substantial creator, but with the "source of the world's
dependence," analogous to the so-called "principle of sufficient
reason" used by the mystics. To clarify the alledged contentions of the argument,
analytical distinctions are drawn between various metaphysical
categories, e.g., "essence," "existence," and "substance"."
Jan Berg, "An examination of ontological proof," Theoria.A Swedish Journal of Philosophy 27: 99-106 (1961).
Studies
Mann William E., "Definite descriptions and the ontological argument," Theoria 33: 211-229 (1967).
Somewhat revised version, incorporating new translations of the passages of Anselm's works, in: Karel Lambert (ed.) - Philosophical applications of free logic - New York, Oxford University Press, 1991, pp. 257-272.
"Jan Berg has presented, in a painstaking and highly compressed paper,
St. Anselm's Ontological Argument, dressed in the garb of a formal
language, L. L is the first-order predicate calculus with identity and,
particularly, with Russell's theory of descriptions. It is the task of
Berg's paper to reconstruct Anselm's argument in L with an eye towards
(1) preserving historical accuracy and (2) preventing the argument from
begging the question. In this paper I will argue that he has not
completely satisfied either objective, and further, that the reason he
has not is that Russell's theory of descriptions is particularly
unsuitable for Anselm's argument. I will then investigate the
implications of reconstructing the argument in L, supplemented not with
Russell's theory, but with some alternative theories."
Jordan Howard Sobel. Gödel's ontological proof. In On Being and Saying. Essays for Richard Cartwright. Edited by Thomson Judith Jarvis. Cambridge: MIT Press 1987. pp. 241-261
"Notes in Gödel's "Nachlass" contain a sketch of a theory that
culminates in a theorem that says that it is necessary that there is a
being that has every positive property. I observe that in the theory a
being with all positive properties would have only necessarily
instantiated properties, and demonstrate that modalities collapse in
the theory -- in it everything actual or true is so of logical
necessity."
Jordan Howard Sobel. Logic and Theism. Arguments for and against beliefs in God. Cambridge: Cambridge University Press 2004.
Jordan Howard Sobel, "To my critics with appreciation: responses to Taliaferro, Swinburne, and Koons," Philosophia Christi 8: 249-292 (2006).
"This response to critics includes elaboration of ideas and arguments in Logic and Theism
regarding cumulative arguments for theism, probabilities, 'fine-tuning'
and many worlds, and Gödel's ontological proof, probabilities
subjective and objective, and Mackiean doubts concerning the latter,
are explained. There is discussion of 'dividing the evidence' in
Bayesian confirmation exercises, with some of it allowed to target
'priors' of hypotheses, and there is a note on my problems with old
evidence. Tentatively explored are Gödel's considered modal opinions,
which may have included that every truth is necessary, and every
falsehood impossible."
Jordan Howard Sobel. Born Again! Anselm in the Person of Charles Hartshorne. In The Logic Yearbook 2006. Edited by Tomala Ondrej and Honzik Radek. Praha: Filosofia 2007. pp. 223-235
"Charles Hartshorne derives in a sentential modal logic, that
"perfection exists" from the premises that "perfection is not
impossible" and "perfection could not exist contingently." These
premises are, on certain assumptions, equivalent to corollaries to
which Anselm was committed of the premises of the major argument in Proslogion
2, namely, that "(S)omething-than-which-nothing-greater-can-be-thought
exists in the mind" and that
"(T)hat-than-which-a-greater-cannot-be-thought cannot exist in the mind
alone," for the conclusion that "
something-than-which-a-greater-cannot-be-thought exists both in the
mind and in reality," which argument is, on a generous construction,
valid in a quantificational logic for indefinite descriptions."
Jordan Howard Sobel. Born again! Anselm and Gaunilo in the persons of Charles Hartshorne and William Rowe. In Oxford readings in the philosophy of religion. New York: Oxford University Press 2009. pp.
Not yet published; a draft is available at: http://www.scar.utoronto.ca/~sobel/OnL_T/AnselmBornAgain.pdf
Studies
Koons Robert C., "Sobel on Gödel's ontological proof," Philosophia Christi 8: 235-247 (2006).
"Kurt Gödel left with his student Dana Scott two pages of notes in
which he sketched a new version of Anselm's ontological proof of God's
existence. In his most recent book (*), Howard Sobel spends the greater
part of a chapter dedicating his considerable talents to an elucidation
and critique of Gödel's argument, as well as to an emended version of
that argument proposed by Anthony Anderson.
The ontological argument has garnered quite a bit of attention in the
last fifty years. In most cases, philosophers have agreed that the
argument is unsuccessful but have disagreed vigorously over where
exactly the fatal flaw lies.
This paper, will to some extent, follow the familiar pattern. I will
argue that Gödel's argument is unsuccessful, but I hope to show that
Sobel and Anderson have both misdiagnosed its failure, and,
consequently, Anderson's attempted repairs are likewise unsuccessful.
However, I will close with a sketch of my own proposed repair of
Gödel's argument, and I will suggest that, although the repaired
argument is not by itself a successful theistic proof, it may represent
a fruitful matter for future investigation."
(*) Logc and Theism - Cambridge, Cambridge University Press, 2004 - Chapter IV.
Alvin Plantinga, "Kant's objection to the ontological argument," Journal of Philosophy 63: 537-545 (1966). "The Ontological Argument for the existence of God has fascinated and puzzled philosophers ever since it was first formulated by St. Anselm, I suppose most philosophers have been inclined to reject the argument, although it has an illustrious line of defenders extending to the present and presently terminating in Professors Malcolm and Hartshorne. Many
philosophers
have tried to give general refutations of the argument-refutations designed to show that no version of it can possibly succeed-of which the most important is, perhaps, Kant's objection, with its several contemporary variations. I believe that none of these general refutations are successful; in what follows I shall support this belief by critically examining Kant's objection."
Alvin Plantinga. God and other minds. A study of the rational justification of belief in God. Ithaca: Cornell University Press 1967.
Alvin Plantinga. The nature of necessity. Oxford: Clarendon Press 1974.
Alvin Plantinga. God, freedom, and evil. New York: Harper & Row 1974.
Studies
Coburn Robert C., "Animadversions on Plantinga's Kant," Journal of Philosophy: 546-548 (1966).
"The bulk of the paper is devoted to an examination of the 'interpretations' which Alvin Plantinga suggests as to what Kant was saying in his discussion of the ontological argument in the first "Critique." I conclude with an independent account of what Kant was getting at."
Grim Patrick, "Plantinga, Hartshorne, and the ontological argument," Sophia 20: 12-16 (1981).
"R. L. Purtill has claimed that the ontological argument that Plantinga presents in The nature of necessity is basically the same as that offered in Hartshorne's The logic of perfection and that it falls victim to the same criticisms. I argue that Plantinga's ontological argument is different enough "not" to fall victim to Purtill's criticisms. What makes Plantinga's argument different, however, also makes it vulnerable to a different criticism: the God of Plantinga's conclusion is not a being greater than which none can be conceived."
Purtill Richard L., "Plantinga, necessity, and God," New Scholasticism 50: 36-60 (1976).
"This paper is a critical overview of Alvin Plantinga's recent book entitled The nature of necessity. While noting the many virtues of the work, I criticise Plantinga on a number of points, major and minor. In particular I argue that Plantinga's notion of an "essence" is lacking in content and that his formulation of the ontological argument does not advance the question much beyond the stage reached by Hartshorne's formulation of the argument and criticisms of this formulation by myself and others. Plantinga also fails to distinguish sufficiently between narrowly logical necessity and broadly logical necessity and between the direct and inverse probabilities involved in a probabilistic version of the argument from evil. I also criticise Plantinga's strategy of merely defending theistic belief as not disprovable and in that sense rational; in my view this is too modest an aim for the theistic philosopher."
Tooley Michael, "Plantinga's defence of the ontological argument," Mind 90: 422-427 (1981).
"In chapter 10 of his book, The nature of necessity, Alvin Plantinga contends that although many versions of the ontological argument are unsound, there is at least one that is valid, and whose premises may reasonably be accepted. It is argued in this paper that Plantinga's defense of this contention is unsatisfactory, and that the version of the ontological argument which he offers is unacceptable for at least two reasons. In the first place, it involves a form of argumentation which if applied to structurally identical, and equally justified premises, leads to contradictory conclusions. Secondly, the crucial premise in Plantinga's argument can be seen to be necessarily false, given an adequate account of the truth conditions of modal statements."
Van Inwagen Peter, "Ontological arguments," Noûs 11: 375-395 (1977).
"In this paper I shall delimit an infinite class of valid arguments I shall call ontic arguments. These arguments proceed from a premise that asserts of a set of properties that it satisfies certain conditions, to the conclusion that there exists something that exemplifies that set of properties. If the conclusion of an ontic argument can be read as asserting the existence of a Deity, then I call that argument an ontological argument. In the present sense of this term, there are infinitely many ontological arguments, all of them valid. I shall devote special attention to one particular ontological argument, the most modest, since many of its features are shared by all other ontological arguments. I shall argue that anyone who wants to claim either that this argument is sound or that it is unsound is faced with grave difficulties.
I shall take it for granted that the connection between what I call ontological arguments and traditional presentations of "the" ontological argument (there is, of course, no one argument that can be called the ontological argument) is plain. I make the following historical claim without arguing for it: Every well-known "version of the ontological argument" is either, (I) essentially the same as one of the arguments called ontological herein, or (ii) invalid or outrageously question-begging, or (iii) stated in language so confusing it is not possible to say with any confidence just what its premises are or what their relation to its conclusion is supposed to be. I should myself be inclined to place all historical "versions of the ontological argument" in category (iii), but this is a function of the way I read them: I would place many of the arguments certain contemporary philosophers claim to see in the original sources in one of the first two categories. I shall examine one contemporary argument, that presented by Alvin Plantinga in The nature of necessity (Chapter X) and in God, freedom, and evil (pp. 85-112). Plantinga's argument falls into category (I). I shall dispute Plantinga's contention that his argument can be used to show that belief in God is not contrary to reason."
Lewis David, "Anselm and actuality," Noûs 4: 175-188 (1970).
Reprinted in; Philosophical papers - vol. I Oxofrd, Oxford University Press 1983 pp. 10-20 with Postscripts pp. 21-25.
"A version of Anselm's first ontological argument is symbolized in
non-modal logic with explicit reference to conceivable worlds and
beings that exist therein. An ambiguity appears: one symbolization
yields an invalid argument with credible premises while another
symbolization yields a valid argument with premises we have no good,
non-circular reason to accept. The credibility of one premise of the
second version turns on the nature of actuality; I propose that
"actual" is an indexical term closely analogous to 'present'."
Studies
Spade Paul Vincent, "Anselm and ambiguity," International Journal for Philosophy of Religion 7: 433-445 (1976).
"David Lewis' analysis of Anselm's ontological argument shows that
something is wrong with it but not, despite his claim, what is wrong
with it. I offer a further analysis in the spirit of Lewis', taking
account of a four-fold ambiguity in the notion of 'greater'. When the
ambiguity is resolved, it turns out that on some readings the argument
is valid but the premisses are not each more plausible than the
conclusion. On other readings the argument is invalid but the premisses
are trivially true. The argument's illusion of plausibility trades on
the ambiguity."
Maydole Robert, "A modal model for proving the existence of God," American Philosophical Quarterly 17: 135-142 (1980).
"In the first section of this paper I employ an ontological type
argument to show that the mere possibility of God's existence implies,
in a standard system of quantified modal logic, the actual existence of
God. I also show that there is at most one God. In the second section I
argue that the very idea of God is meaningful. In the third section I
use a cosmological argument modeled on St Thomas' Third Way to prove
that God exists. The mediate conclusion is that God exists. In the
final section of the paper I discuss the plausibility of adopting the
modal logic previously employed."
Maydole Robert, "The modal Third Way," International Journal of Philosophy of Religion 47: 1-28 (2000).
Maydole Robert, "The modal perfection argument for the existence of a Supreme Being," Philo.A Journal of Philosophy 6: 299-313 (2003).
"The 'modal perfection argument' (MPA) for the existence of a Supreme
Being is a new ontological argument that is rooted in the insights of
Anselm, Leibniz and Gödel. Something is supreme if and only if nothing
is possibly greater, and a perfection is a property that it is better
to have than not. The premises of MPA are that supremity is a
perfection, perfections entail only perfections, and the negation of a
perfection is not a perfection. I do three things in this paper.
First, I prove that MPA is valid by construction a formal deduction of
it in second order modal logic. Second, I argue that its premises are
true. Third, I defend the argument of the logic used against some
likely objections."
Maydole Robert, "On Oppy's objections to the modal perfection argument," Philo.A Journal of Philosophy 8 (2006).
Maydole Robert, "On Metcalf's objections to the modal perfection argument," Philo.A Journal of Philosophy 8 (2006).
Studies
Metcalf Thomas, "Entailment and ontological arguments: reply to Maydole," Philo.A Journal of Philosophy 8: 131-133 (2005).
"Robert Maydole has recently presented a sophisticated ontological
argument that he calls the modal perfection argument for the existence
of a Supreme Being. While this ontological argument is probably better
than most of its peers, it is nonetheless open to at least one decisive
objection. The purpose of this brief comment is to develop that
objection. I claim that this objection indicates an important further
point about the concept of entailment and its role in ontological
arguments at large, the recognition of which helps to refute other
conceivable ontological arguments."
.Oppy Graham. Ontological arguments and belief in God. Cambridge: Cambridge University Press 1995.
Oppy Graham, "Gödelian ontological arguments," Analysis 56: 226-230 (1996).
"There is now a considerable secondary literature on Gödel's
ontological arguments; in particular, interested readers should consult
Sobel 1987, Anderson 1990 and Adams 1995. In this note, I wish to draw
attention to an objection to these arguments which has hitherto gone
unnoticed. This objection does not depend upon fine details of the
formulation of the arguments; I arbitrarily choose to develop the
objection in connection with the formulation provided by Anderson.
In brief, the argument I shall consider may be summarized thus:
Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive.
Definition 2: A is an essence of x iff for every property B, x has B necessarily iff A entails B. Definition 3: x necessarily exists iff every essence of x is necessarily exemplified.
Axiom 1: If a property is positive, then its negation is not positive.
Axiom 2: Any property entailed by [= strictly implied by] a positive property is positive.
Axiom 3: The property of being God-like is positive.
Axiom 4: If a property is positive, then it is necessarily positive.
Axiom 5: Necessary existence is positive.
Theorem 1: If a property is positive, then it is consistent [= possibly exemplified].
Corollary 1: The property of being God-like is consistent.
Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.
Theorem 3: Necessarily, the property of being God-like is exemplified.
Given a sufficiently generous conception of properties, and granted the
acceptability of the underlying modal logic, the theorems listed do
follow from the axioms. (So say Gödel, Dana Scott, Sobel, Anderson, and
Adams. Who am I to disagree?) Perhaps one might object to the
conception of properties and/or the modal logic. But one doesn't need
to: the proof is demonstrably no good even if these things are accepted.
The problem - as with virtually all ontological arguments known to me -
lies in the fact that there are parallel arguments which can be
constructed, which seem no less acceptable to atheists and agnostics,
but whose acceptance leads to absurd results. (1)" p. 226.
(1) In Oppy (1995, p. 225), I write: 'It may be possible to reinterpret
the (Gödelian) proof in a damaging way, though I have not been able to
see how to do this.' I think that my vision has now improved a little:
hence the present paper.
Oppy Graham, "Response to Gettings," Analysis 60: 363-367 (2000).
In "Gödelian Ontological Arguments" (Analysis
56, 1996), I argue that Gödel's ontological argument is subject to a
Gaunilo-style parody. In the present paper, I provide an emended
version of the argument that avoids objections raised by Mike Gettings
in his "Gödel's Ontological Argument: A Reply to Oppy" (Analysis 59, 1999)."
Oppy Graham. Arguing about Gods. Cambridge: Cambridge University Press 2006.
Chapter 2. Ontological arguments - pp. 49-96.
Studies
Gettings Michael, "Gödel's ontological argument: a reply to Oppy," Analysis 59: 309-313 (1999).
"Graham Oppy has contributed recently to the discussion of Gödel's
ontological argument with an attempted refutation (Oppy 1996). Although
seemingly promising, I will show here that this attempt fails to
undermine Gödel's argument.
Very briefly, Gödel's argument proceeds in the following way. (1) One
begins with the primitive notion of a positive property. A positive
property is a 'great-making' property which entails no defect. The
property of Godlikeness (G) is defined in this way: One is God-like iff
one has as essential properties all and only positive properties. Given
a number of axioms concerning positive properties, one can prove that a
unique possible individual instantiates God-likeness, i.e. that there
is (at least) one possible world inhabited by this unique God-like
being. Furthermore, necessary existence is a positive property. Thus,
in some possible world this unique God-like being necessarily exists,
and so, in SS modal logic, this being exists in the actual world.
Oppy's strategy is the strategy which the monk Gaunilo used to try to
refute Anselm's ontological argument. This strategy attempts to show
that if the theist purports to have proven the existence of God, the
same reasoning may be used to prove the existence of many theologically
repugnant entities, e.g. demi-gods, perfect islands, etc. Oppy's
particular objection is motivated in the following way: since the
theist defines God-likeness, the atheist may define a similar property,
call it 'God*-likeness' ('G*'). Let God*-likeness be the property one
has iff one has as essential properties only and almost all of the
positive properties, including necessary existence (e.g., all positive
properties except omniscience, and only positive properties). Since two
things are identical only if they share the same essential properties,
the definition of God*-likeness ensures that the atheist's being is
distinct from God. Furthermore, a God*-like being must also be
necessarily existent, since necessary existence is a property entailed
by God*likeness.
Oppy cannot draw the conclusion that such a being exists, however.
There is a crucial disanalogy between his argument and the theist's.
This disanalogy becomes evident when we look at Oppy's argument, which
he presents in two formulations. These two formulations are similar,
and I will show that the first is defective, and argue that the second
fails for similar reasons." pp. 309-310.
(1) See Anderson 1990 for details of a strengthened formulation of Gödel's argument. This
is the formulation which both Oppy and I address, although I will also
consider a revision to this argument. For now, 'Gödel's argument' and
'the theist's argument' will refer to the formulation found in Anderson
1990.
Pruss Alexander, "Samkara's principle and two ontomystical arguments," International Journal of Philosophy of Religion 49: 111-120 (2001).
"The S5-based ontological argument assumes (1) possibly there is a
maximally great being (MGB) and (2) that any MGB must be essentially
such and have necessary existence, so that by S5 there is a MGB. The
weakest point is (1). Samkara (788-820 AD) argued that if something is
impossible, then one cannot have a seeming of it. Therefore, by modus
tollens, if a mystic has a (quasi-perceptual) seeming of a MGB, then
possibly there is a MGB, and hence (1) is true, and there is a MGB. A
variant based on a radical dependence ontological argument is also
discussed."
Pruss Alexander, "A Gödelian ontological argument improved," Religious Studies (2008).
Accepted for publication.
Adams McCord Marilyn, "The modal argument for the existence of God", Cornell University, 1969.
Available at ProQuest Dissertation Express. Order number: 6913015.
Adams Robert Merrihew, "Presumption and the necessary existence of God," Noûs 22: 19-32 (1988).
Alston William, "The ontological argument revisited," Philosophical Review 69: 452-474 (1960).
Reprinted in: A. Plantinga (ed.) - The ontological argument from St. Anselm to contemporary philosophers - London, Macmillan, 1968 pp. 86-110.
"The ontological argument has often been criticized on the grounds that it mistakenly supposes "exists" to be a predicate. I am going to argue (1) that the way in which this criticism is usually presented is faulty, (2) that these faults result from overlooking certain basic features of the concept of existence, and (3) that when these features are fully taken into account, new and sounder reasons can be given for denying that "exists" is a predicate and for rejecting the ontological argument. In the first section I shall present the traditional kind of criticism in what I take to be its strongest form; in the second, I shall try to show that it does not hold up; in the third I shall attempt to enrich it so as to avoid those defects.(*)" p. 452
(*) It may be helpful to relate this essay to Professor Norman Malcolm's very interesting article, "Anselm's Ontological Arguments," which recently appeared in the [Philosophical] Review (LXIX, 1960, 41-62). There Malcolm distinguishes two different arguments in Anselm's Proslogion. My treatment of Anselm is restricted to what Malcolm calls the first argument, and is concerned with the sort of considerations which are commonly used in rejecting it. About what Malcolm calls the second argument, I have nothing to say in this essay. My opinion is that the second argument is ultimately dependent on the first, but that is a long story."
Balaban Oded and Avshalom Asnat, "The ontological argument reconsidered," Journal of Philosophical Research 15: 279-310 (1990).
Bausola Adriano, "Per una ripresa dell'argomento ontologico," Rivista di Filosofia Neo-Scolastica 92: 349-362 (2000).
Brown Charles D., "The ontological theorem," Notre Dame Journal of Formal Logic 19: 591-592 (1978).
Duncan Roger, "Analogy and the ontological argument," New Scholasticism 54: 25-33 (1980).
"St Thomas rejects the ontological argument but does not deny that the concept of God entails his essence. Instead, he relies on the distinction between a proposition's being necessary and its being known "a priori", which is related to the problem of knowing God's possibility "a priori", the Achilles heel of contemporary modal arguments. Why can we not know God's possibility "a priori"? The doctrine of analogy claims that God-language is too obscure to authorize such deductions. The rejection of irreducibly analogous language leads to rationalism, which accepts the ontological argument, or to fideism/agnosticism, which reject it. Modern philosophers were in tacit agreement in ignoring the distinction between "a priority" and necessity, and on the irrelevance of analogy. Hence they oscillated between acceptance of the ontological argument, and the total rejection of significant God-talk. Recent trends are favorable to a reconsideration of both points, and to an appreciation of their adumbration in the writings of Aquinas."
Forgie William J., "The modal ontological argument and the necessary a posteriori," International Journal for Philosophy of Religion 29: 129-141 (1991).
"I consider modal ontological arguments of the form, 'God is possible; therefore, God actually exists', which conceive of God in terms of properties"indexed to the actual world. The use of such indexed properties can ensure the validity of these arguments but it also transforms their possibility premisses into a posteriori claims. Because of this, a typical inquirer is not going to be able to get into some desired epistemic position toward the possibility premise (e.g., knowing it, or determining that it is rationally acceptable) without first having to get into that same position toward the conclusion of the argument. Thus it is not clear for whom these arguments could establish even the rationality of their conclusions."
Garcia de la Sienra Adolfo. The ontological argument. In The rationality of theism. Edited by Garcia de la Sienra Adolfo and Araujo Alfredo. Atlanta: Rodopi 2000. pp. 127-142
"Abstract. This paper presents a reconstruction of Anselm's ontological argument within the framework of Meinong's Gegenstandstheorie. It is shown that, within this framework and assuming a certain basic theological view, the argument has some force. Unlike many replies to the argument, the paper concludes undermining the theological view rather than the premise that existence is a predicate.
The ontological argument is an old piece of theological reasoning that has a long and interesting history in the course of Western philosophy. The main author of this argument was the Eleventh-century English friar Anselm of Canterbury, according to Koyré "one of the profoundest and most exalted of spirits," but Descartes' formulation (which he produced without being aware of Anselm's work) is deemed also as one of the standard presentations of the argument.
I shall devote the first part of this chapter to present Anselm's argument. I have found convenient and natural to present the ontological argument within the framework of Meinong's theory of objects, and that is why I shall devote the first section of the first part to present Meinong's doctrine. In the second and last part I will provide a Reformed assessment of the ontological argument."
Goodwin George L., "De Re modality and the ontological argument," Archivio di Filosofia: 607-629 (1990).
Gracia Jorge J.E., "'A supremely great Being'," New Scholasticism 48: 371-377 (1974).
Henle Paul, "Uses of the ontological argument," Philosophical Review 70: 102-109 (1961).
"That anyone should uphold the ontological argument as demonstrative of the existence of God is surprising, yet Professor Norman Malcolm seems perfectly serious in his recent defense of one form of it. (1) He maintains that the argument has two variants, one, which he rejects, concludes that God exists and the other, which he accepts, maintains that God has necessary existence. This acceptance is the more remarkable because Malcolm does not base his contention on any Neoplatonic identification of existence with reality and fullness of being. Granted such a metaphysics, the argument would, seem to follow, but Malcolm does not take this approach and indeed professes to have difficulty in comprehending the doctrine of negation and privation characteristic, of it (p. 59). Without such metaphysical buttressing, the argument is quite weak, but it may be well first to show that something is wrong with it before going on to consider what is wrong."
(1) "Anselm's ontological arguments" Philosophical Review, 69, 1960, pp. 41-62.
Herrschaft Lutz, ""Das was ich mir vorstelle, ist darum doch noch nicht": Der ontologische Gottesbeweis in der neueren Diskussion," Zeitschrift für Philosophische Forschung 47: 461-476 (1993).
Jacquette Dale, "Meinongian logic and Anselm's ontological proof for the existence of God," Philosophical Forum 25: 231-240 (1994).
"The logic of existent and nonexistent objects provides a formal theory of reference and true predication for ordinary discourse, the semantics of ontological commitment, and logic of fiction. The intensional logic proposed in what follows offers a rigorous object theory semantics with nonstandard propositional and predicate inference machinery. The system is distinguished from previous formalizations of object theory by formal criteria for nuclear (constitutive) and extranuclear (nonconstitutive) properties, three-valued propositional semantics for predications of nuclear properties to incomplete nonexistent objects for which the objects ostensibly are undetermined, nonstandard set theory semantics with unrestricted comprehension for object theory predicate semantics (licensed by existence restrictions on abstraction equivalence), demonstrations of internal determinacy, consistency, and Henkin completeness, nonstandard deduction theorem, and consistency considerations in light of free assumption and unrestricted comprehension."
Leftow Brian, "Is God an abstract object?," Noûs 24: 581-598 (1990).
Meixner Uwe, "Der ontologische Gottesbeweis in der Perspektive der Analytischen Philosophie," Theologie und Philosophie 67: 246-262 (1992).
Oppenheimer Paul and Zalta Edward, "On the logic of the ontological argument," Philosophical Perspectives 5: 509-530 (1991).
"In this paper, the authors show that there is a reading of St. Anselm's ontological argument in Proslogium II that is logically valid (the premises entail the conclusion). This reading takes Anselm's use of the definite description "that than which nothing greater can be conceived" seriously. Consider a first-order language and logic in which definite descriptions are genuine terms, and in which the quantified sentence "there is an x such that..." does not imply "x exists". Then, using an ordinary logic of descriptions and a connected greater-than relation, God's existence logically follows from the claims: (a) there is a conceivable thing than which nothing greater is conceivable, and (b) if x doesn't exist, something greater than x can be conceived. To deny the conclusion, one must deny one of the premises. However, the argument involves no modal inferences and, interestingly, Descartes' ontological argument can be derived from it."
Oppenheimer Paul and Zalta Edward, "Reflections on the logic of the ontological argument," Studia Neoaristotelica 4: 28-37 (2007).
"In this paper, the authors evaluate the ontological argument they developed in their 1991 paper as to soundness. They focus on Anselm's first premise, which asserts: there is a conceivable thing than which nothing greater is conceivable. After suggesting reasons why this premise is false, the authors show that there is a reading of this premise on which it is true. Such a premise can be used in a valid and sound reconstruction of the ontological argument. This argument is developed in precise detail, but the authors show that the conclusion, the formal version of which is a reading of the claim that "God exists", doesn't quite achieve the end Anselm desired."
Shaffer Jerome, "Existence, predication, and the ontological argument," Mind 71: 307-325 (1962).
"This is an examination of the ontological argument and its consistency with existential propositions. Clarification of the ontological argument is made in light of Hume, Kant, and Carnap with regard to its empirical, predicative, a priori, a posteriori and linguistic proofs and refutations. A further refinement of the presentation is the establishment of the intensional and extensional character of the ontological argument."
Szatkowski Miroslaw, "Semantic analysis of some variant of Anderson-like ontological proofs," Studia Logica 79: 353-355 (2005).
Van Inwagen Peter. Arguments for God's existence: ontological arguments. In Philosophy of religion: a guide to the subject. Edited by Davies Brian. Washington: Georgetown University Press 1998. pp. 54-58
Vitali Theodore, "The ontological argument: model for neoclassical metaphysics," Modern Schoolman 57: 121-136 (1980).
Wainwright William, "Is necessary existence a perfection?," Noûs 22: 33-34 (1988).
"If God exists, he exists necessarily is a premise in modal versions of the ontological argument. I argue that the proposition isn't clearly entailed by theism. Appeals to intuition aren't conclusive, and alleged proofs place controversial constructions on divine attributes or employ controversial philosophical theses. The proposition is, however, plausible."
(click on the image to see the PDF file)