In a recent paper in this journal, McIntosh ( 2021 ) argues that a modalized version of an epistemic principle of phenomenal conservativism can be used to successfully defend the key possibility premise of the modal ontological argument for the existence of God. I argue, however, that such a defense of the possibility premise is not going to be successful even if one concedes a number of contentious claims to McIntosh.

This paper attacks the modal ontological argument, as advocated by Plantinga among others. Whereas other criticisms in the literature reject one of its premises, the present line is that the argument is invalid. This becomes apparent once we run the argument assuming fictionalism about possible worlds. Broadly speaking, the problem is that if one defines “x” as something that exists, it does not follow that there is anything satisfying the definition. Yet unlike non-modal (...) class='Hi'>ontological arguments, the modal argument commits this “existential fallacy” not in relation to the definition of ‘God’. Rather, it occurs in relation to the modal facts quantified over within a Kripkean modal logic. In brief, we can describe the modal facts by whichever logic we prefer—yet it does not follow that there are genuine modal facts, as opposed to mere facts-according-to-the-fiction. A broader consequence of the discussion is that the existential fallacy is an issue for many projects in “armchair metaphysics.”. (shrink)

The structure of the second, Or so-Called modal version of anselm's ontological argument is discussed in relation to various systems of alethic modal logic. It is argued that there are three current problems standing in the way of acceptance of the argument, Each related to its modal structure, And each an analogue of a traditional objection to anselm's original argument. Two of these problems can probably be solved, But the third remains recalcitrant.

Inspired by the third chapter of Anselm's Proslogion, twentieth century philosophers including Charles Hartshorne and Alvin Plantinga developed “modal” ontological arguments for the existence of God. Such arguments use modal logic to infer God's existence from the premises that (i) God's existence is possible and (ii) if God exists, He exists necessarily. Like other ontological arguments, modal arguments have won few converts to theism; many commentators consider them question‐begging or liable to parody. This article details (...) how recent attempts to defend these arguments have tried to overcome these difficulties by drawing on modern accounts of the epistemology and metaphysics of modality. (shrink)

We formulate a new modal ontological argument; specifically, we show that there is a possible world in which an entity that has at least the property of omnipotence exists. Then we argue that if such an entity is possible, it is necessary as well.

This paper examines the so-called modal ontological argument. It pays special attention to the role that the symmetry and transitivity of the accessibility relation play in the argument, and examines various approaches to a defense of the “possibility premise,” the premise of the argument that states that the existence of a perfect being is metaphysically possible. It contains an analysis of Gödel’s attempt to show that this premise is true, and of a recent formulation by (...) David Johnson of Gödel’s argument. (shrink)

This paper is a critique of a paper by Alex Pruss. I argue that Pruss's attempt to motivate acceptance of the key possiblity premise in modal ontological arguments fails.

This paper deals with some metaphilosophical aspects of the modal ontological argument originating from Charles Hartshorne. One of the specific premises of the argument expresses the idea that the existence of God is not contingent. Several well-known versions of the argument have been formulated that appeal to different ways of clarifying the latter. A question arises: which of the formally correct and relevant versions is proper or basic? The paper points to some criteria of formal (...) correctness, and distinguishes two types of relevance for these versions: strong and weak. Its aim is to furnish a strictly worked out answer to the question, taking into account each of these types. As a result, a very simple, formally correct and relevant version of the modal ontological argument is formulated. The results obtained are also used to criticize a popular belief about the relations in which the main versions of the modal ontological argument stand to one another. (shrink)

The contemporary versions of the ontological argument that originated from Charles Hartshorne are formalized proofs based on unique modal theories. The simplest well-known theory of this kind arises from the b system of modal logic by adding two extra-logical axioms: “If the perfect being exists, then it necessarily exists‘ and “It is possible that the perfect being exists‘. In the paper a similar argument is presented, however none of the systems of modal logic is (...) relevant to it. Its only premises are the axiom and, instead of, the new axiom : “If the perfect being doesn’t exist, it necessarily doesn’t‘. The main goal of the work is to prove that is no more controversial than and -- in consequence -- the whole strength of the modal ontological argument lies in the set of its extra-logical premises. In order to do that, three arguments are formulated: ontological, “cosmological‘ and metalogical. (shrink)

We use a mechanized verification system, PVS, to examine the argument from Anselm’s Proslogion Chapter III, the so-called “Modal Ontological Argument.” We consider several published formalizations for the argument and show they are all essentially similar. Furthermore, we show that the argument is trivial once the modal axioms are taken into account. This work is an illustration of Computational Philiosophy and, in addition, shows how these methods can help detect and rectify errors in (...) modal reasoning. (shrink)

This article shows that the modal ontological argument as proposed by Gottrieb Leibniz was very much anticipated in its logical articulation by John Duns Scotus in his work De Primo Principio. To this end, the author analyzes some of the various versions of the argument present in the philosophical thought of authors such as Scotus, Leibniz, Malcom and Plattinga, and demonstrates that those versions are based on the hidden premise of the possibility of the idea of (...) God. In this respect, the Spanish philosopher Gustavo Bueno defends what he calls an “inverted ontological argument” which, if viable, would prove not so much the non-existence of God but that the idea of God does not exist itself. (shrink)

Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language ar- gument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the existence of God. Our new method, which we call computational hermeneutics, has been particularly conceived for use in interactive-automated proof assistants. It aims at shedding light (...) on the meanings of words and sentences by framing their inferential role in a given argument. By employing automated theorem reasoning technology within interactive proof assistants, we are able to drastically reduce (by several orders of magnitude) the time needed to test the logical validity of an argu- ment’s formalization. As a result, a new approach to logical analysis, inspired by Donald Davidson’s account of radical interpretation, has been enabled. In computational hermeneutics, the utilization of automated reasoning tools ef- fectively boosts our capacity to expose the assumptions we indirectly commit ourselves to every time we engage in rational argumentation and it fosters the explicitation and revision of our concepts and commitments. (shrink)

I argue for modal realism from the following principles:(R1) p just in case there are truth-makers for the proposition that p.(R2) If there are truth-makers for the proposition that p and the proposition that p relevantly entails the proposition that q, then there are truthrmakers for the proposition that q.(M) The proposition that p relevantly entails the proposition that possibly p.(R3) I f there are truth-makers for the proposition that q, then necessarily, if q, there are truth-makers for the (...) proposition that q.All of the above principles are to be read as necessary truths. Also, the propositional variable 'p' is restricted to propositions that necessarily satisfy R1. 'q' is not so restricted.The argument is ontological because I argue that the possibility of modal reaUsm together with R3 entails that modal realism is true. The possibility of modal realism follows from R1, R2 and M. (shrink)

This article aims to provide a new ontological argument for the existence of God. A specific ‘modal’ version of the ontological argument—termed the Modal Realist Ontological Argument—is formulated within the modal realist metaphysical framework of David K. Lewis, Kris McDaniel and Philip Bricker. Formulating this argument within this specific framework will enable the plausibility of its central premise (i.e., the ‘Possibility Premise’) to be established, and allow one to affirm the (...) soundness of the argument—whilst warding off two oft-raised objections against this type of natural theological argument. (shrink)

I set out and explore an argument for God's existence based on the idea that the possibility of God requires the existence of God as a ground. After setting this argument out, I compare it to other arguments for God, concentrating on an argument from Descartes's Third Meditation. I then address various objections and conclude by setting out a non-theistic version of the argument.

This paper discusses a range of modal ontological arguments. It is claimed that these modal ontological arguments fail because they depend upon controversial assumptions about the nature of modal space.

This article aims to provide a new ontological argument for the existence of God. A specific ‘modal’ version of the ontological argument—termed the Modal Realist Ontological Argument—is formulated within the modal realist metaphysical framework of David K. Lewis, Kris McDaniel and Philip Bricker. Formulating this argument within this specific framework will enable the plausibility of its central premise (i.e., the ‘Possibility Premise’) to be established, and allow one to affirm the (...) soundness of the argument—whilst warding off two oft-raised objections against this type of natural theological argument. (shrink)

General discussion of ontological arguments. (Extended the discussion of ontological arguments in the then current version of my SEP entry on ontological arguments.).

Modal ontological arguments argue from the possible existence of a perfect being to the actual (necessary) existence of a perfect being. But modal ontological arguments have a problem of symmetry; they can be run in both directions. Reverse ontological arguments argue from the possible nonexistence of a perfect being to the actual (necessary) nonexistence of a perfect being. Some familiar points about the necessary a posteriori, however, show that the symmetry can be broken in favour (...) of the ontological argument. (shrink)

Latest version of my SEP entry on ontological arguments, which first appeared in 1996. General discussion of ontological arguments. Includes a brief historical overview, a taxonomy of different kinds of ontological arguments, a brief survey of objections to the different kinds of ontological arguments identified in the taxonomy, and more extended discussions of Anselm's ontological argument (Proslogion 2), Godel's ontological argument, and Plantinga's ontological argument.

This chapter contains sections titled: The Validity of Anselm's Ontological Argument The Truth of the Anselmian Premises On Whether Anselm's Ontological Argument Begs the Question On Parodies The Validity of the Ontological Argument of Descartes and Leibniz On the Truth of the Descartes–Leibniz Premises Critiques of the Descartes–Leibniz Ontological Argument Ontological Arguments of the Twentieth Century Gödel's Ontological Argument On Whether Gödel's Argument is Sound The Modal Perfection (...) Argument The Temporal‐Contingency Argument Conclusion References Appendix 1. Logic Matters Appendix 2. Formal Proofs of Some Modal Arguments. (shrink)

Assuming S₅, the main controversial premise in modal ontological arguments is the possibility premise, such as that possibly a maximally great being exists. I shall offer a new way of arguing that the possibility premise is probably true.

This chapter contains sections titled: The History of the Argument The Modal Ontological Argument The Possibility of a Perfect Being: Leibniz The Possibility of a Perfect Being: Gödel The Rationality of Belief in a Perfect Being: Plantinga Summary Works cited.

Assuming S5, the main controversial premise in modal ontological arguments is the possibility premise, such as that possibly a maximally great being exists. I shall offer a new way of arguing that the possibility premise is probably true.

Leibniz's version of the ontological argument, a modal argument for theism on which he worked most intensively in the 1670s, has two stages. The first, an “incomplete” proof, concludes that God can only be a necessary being, and therefore if God's existence is possible, then God exists. The second stage is an a priori argument that the existence of such a necessary God is indeed possible. Leibniz's fullest attempts at a possibility proof turn on his (...) conception of a most perfect being, and the chapter concludes that they are not likely to succeed, in part because of difficulties in connecting the concepts of perfection and necessary existence. (shrink)

This paper is an assessment of Robert Maydole's work on ontological arguments. (Bibliographical details are provided in the text.) I argue that Maydole's ontological arguments are unsuccessful.

Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument the two variants contributed by Anderson and Fitting avoid modal collapse. Although they appear quite different on a cursory reading they are in fact closely related. This has been revealed in the computer-supported formal analysis presented in this article. Key to our formal analysis (...) is the utilization of suitably adapted notions of ultrafilters, and a careful distinction between extensions and intensions of positive properties. (shrink)

An argument for the existence of gods given by the Stoic Diogenes of Babylon and reported by Sextus Empiricus appears to be an ancient version of the ontological argument. In this paper I present a new reconstruction of Diogenes' argument that differs in certain important respects from the reconstruction presented by Jacques Brunschwig. I argue that my reconstruction makes better sense of how Diogenes' argument emerged as a response to an attack on an earlier Stoic (...) argument presented by Zeno of Citium. Diogenes' argument as reconstructed here is an example of a modal ontological argument that makes use of the concept of being of such a nature as to exist. I argue that this concept is a modal concept that is based on the Philonian definition of possibility, and thus that Diogenes' argument is a source of important evidence about the use of non-Stoic modalities in the post-Chrysippean Stoa. I conclude by arguing that the objections made against considering Diogenes' argument as ontological are unfounded and that Diogenes' argument clearly resembles modern versions of modal ontological arguments. (shrink)

There is perhaps no more famous objection to the Ontological Argument than Kant’s contention that existence is not a predicate. However, this is not his only objection against the Ontological Argument. It is rather part of a more comprehensive attack on the OA, one that contains at least four distinct arguments, only one of which involves. It is the purpose of this paper to explore Kant’s case for, consider three contemporary strategies used to reinforce it, assess (...) their merits, and then finally briefly present Kant’s three further arguments. (shrink)

Ontological arguments like those of Gödel (1995) and Pruss (2009; 2012) rely on premises that initially seem plausible, but on closer scrutiny are not. The premises have modal import that is required for the arguments but is not immediately grasped on inspection, and which ultimately undermines the simpler logical intuitions that make the premises seem plausible. Furthermore, the notion of necessity that they involve goes unspecified, and yet must go beyond standard varieties of logical necessity. This leaves us (...) little reason to believe the premises, while their implausible existential import gives us good reason not to. (shrink)

I will offer a defence of Anselm's Ontological Argument, building on some suggestions made by Prior. The defence offered avoids one of the objections commonly levelled against the Ontological Argument. I will not consider whether the use of this objection involves a misinterpretation of the argument as put forward by Anselm. It might, for example, be held that the argument of Proslogion 2 is programmatic, and points forward to Prosiogion 3, and arguments given by (...) Anselm in his Reply to Gaunilo. In particular it might be denied that Anselm holds that what is greater about what exists in reality is just that it exists in reality. While what I have to say will start from points made by Prior, I do not intend to suggest that Prior holds that there is a defence possible for Anselm's argument such as I will offer. What I have to say involves emphasizing modal notions, and treating Anselm's argument as a modal argument. Thus it comes down to defending Anselm's argument in Proslogion 3 in preference to the Proslogion 2 argument. (shrink)

This paper introduces the special issue on Formal Approaches to the Ontological Argument of the Journal of Applied Logics (College Publications). The issue contains the following articles: Formal Approaches to the Ontological Argument, by Ricardo Sousa Silvestre and Jean-Yves Béziau; A Brief Critical Introduction to the Ontological Argument and its Formalization: Anselm, Gaunilo, Descartes, Leibniz and Kant, by Ricardo Sousa Silvestre; A Mechanically Assisted Examination of Begging the Question in Anselm’s Ontological Argument, (...) by John Rushby; A Tractarian Resolution to the Ontological Argument, by Erik Thomsen; On Kant’s Hidden Ambivalence Toward Existential Generalization in his Critique of the Ontological Argument, by Giovanni Mion; The Totality of Predicates and the Possibility of the Most Real Being, by Srećko Kovač; An Even More Leibnizian Version of Gödel’s Ontological Argument, by Kordula Świętorzecka and Marcin Łyczak; A Case Study On Computational Hermeneutics: E. J. Lowe’s Modal Ontological Argument, by David Fuenmayor. (shrink)

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 constructing a formal deduction of it in second order modal logic. Second, I argue that its premises are true. Third, I defend the argument and the logic used against some likely objections. (shrink)

In “On Oppy’s Objections to the Modal Perfection Argument,” Philo 8, 2, 2005, 123–30, Robert Maydole argues that his modal perfection argument—set out in his “The Modal Perfection Argument for a Supreme Being,” Philo 6, 2, 2003, 299–313—“remains arguably sound” in the face of the criticisms that I made of this argument in my “Maydole’s 2QS5 Argument,” Philo 7, 2, 2004, 203–11. I reply that Maydole is wrong: his argument is fatally (...) flawed, and his attempts to avoid the criticisms that I have made of his argument are to no avail. (shrink)

If the words in Spinoza’s Ethics are considered as symbols, then certain words in the definitions of the Ethics can be replaced with symbols from set theory and we can reexamine Spinoza’s first definitions within a logical–mathematical frame. The authors believe that, some aspects of Spinoza’s work can be explained and illustrated through mathematics. A semantic relation between the definitions of the philosopher and set theory is presented. It is explained each chosen symbol. The ontological argument is developed (...) through modal logic. And finally, we present some conclusions drawn from this work. (shrink)

Much of the difficulty surrounding Anselm's ontological argument has been generated by ignoring its metaphysical framework. Examination of the Proslogion and Monologion shows it to be a platonic argument, thus disposing of the 'Lost Island' objection, among others. Contemporary modal interpretations are neither correct versions of, nor advances upon, the original: Hartshorne confuses modal status with truth-value. The Proslogion II argument is valid; it is the sense of Anselm's definition and conclusion which is at (...) issue. Since the argument explicates why God, defined as that which is maximally real, must be real, questions of the logic of 'existence' are irrelevant; however, what 'x is real' means depends on what sort of entity x is, so that Anselm's conclusion remains uncertain until and unless it can be shown in what the non-fictionality of God might consist. Indeed, can God be anything but a fiction? If he can, then he must be real, for, I contend, 'God is eternal and self-sufficient' (which Anselm, as a platonist, claims for him) entails that 'God is real' is necessary. Whether it is necessarily true or necessarily false, then, depends on the coherence of otherwise of 'God', a coherence Anselm assumes. The assumption is disguised by his - and his commentators' - failure to distinguish between the bearer of the name 'God', and the supreme reality described as 'god'. We may thus ask, Can God be god? To discover what sort of entity God is, we must see what may be predicated of him: but neither analogia entis, the language-game theory, nor analogia fidei solve the problem of how attributes may be predicated of a being who is god. The question of God's reality remains unresolved; but Anselm's argument at least shows how and why it is a conceptual question. (shrink)

Oppenheimer & Zalta have re-formulated their non-modal version of the ontological argument, with the help of PROVER9, an automated reasoning engine. The authors end up rejecting the new argument; however, the theist has a rejoinder worth considering. But after presenting the rejoinder, I highlight that the conceivability of the being does not imply its possibility. One lesson is that even non-modal ontological arguments must engage modal matters concerning God. Another lesson is that if (...) PROVER9 is able to derive a conclusion from fewer premises, the proof is sometimes inferior as an argument. (shrink)

According to leibniz, Descartes' ontological argument establishes that if God possibly exists then God exists. To complete the argument a proof that God possibly exists is required. Leibniz attempts a proof-Theoretic demonstration that 'god exists' is consistent and concludes from this that 'god possibly exists is true'. In this paper I formalize leibniz's argument in a system of modal logic. I show that a principle which leibniz implicitly uses, 'if a is consistent then a is (...) possibly true' is either mistaken or useless in completing the ontological argument. (shrink)

In his ontological argument Gödel says nothing about its underlying logic. The argument is modal and at least of second-order and since S5 axiom is used so it is widely accepted that the logic of the argument is the S5 second-order modal logic. However, there is a step in the proof in which Gödel applies the necessitation rule on the assumptions of the argument (see [3]). This is repeated by all of his followers (...) (see [1] and [5]). This application of the necessitation rule can seriously harm the consequence relation of the logic of the ontological argument. It seems that the only way to preserve the modal logic S5 for the ontological argument is to assume some of its axioms in the necessitated form. (shrink)

George L. Goodwin's doctoral dissertation sets out to accomplish two things in Hartshorne scholarship: provide an interpretive tool for understanding the validity of the ontological argument within an Hartshornean perspective and advance the discussion concerning the validity of de re modality considering the challenge posed by W. V. O. Quine. Goodwin attempts to prove that through the doctrine of temporal possibility Hartshorne has provided a means both for understanding the validity of the ontological argument and for (...) meeting Quine's challenge with regard to the possibility of de re modality. (shrink)

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. (shrink)