Gödel's ontological argument is related to Gödel's view that causality is the fundamental concept in philosophy. This explicit philosophical intention is developed in the form of an onto-theological Gödelian system based on justification logic. An essentially richer language, so extended, offers the possibility to express new philosophical content. In particular, theorems on the existence of a universal cause on a causal "slingshot" are formulated.

In his "Ontological proof", Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property φ: If φ is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is positive. (...) Given axiom 2, sentences A and B paradoxically cannot be both true or both false, and it is also impossible that one of the sentences is true whereas the other is false. (shrink)

The paper shows that it is possible to obtain a "slingshot" result in Gödel's theory of positiveness in the presence of the theorem of the necessary existence of God. In the context of the reconstruction of Gödel's original "slingshot" argument on the suppositions of non-Fregean logic, this is a natural result. The "slingshot" result occurs in sufficiently strong non-Fregean theories accepting the necessary existence of some entities. However, this feature of a Gödelian theory may be considered not as a (...) trivialisation, but as an intended consequence of Gödel's ontotheological views. (shrink)

This paper discusses: (1) Anselm’s ontological argument and its criticism by Gaunilo; (2) Plantinga’s ontological argument and its criticism by Mackie and Sobel; and (3) a simplified version of Gödel’s ontological argument. It also looks carefully at (4) Kant’s attempt to show that it is impossible for there to be a successful ontological argument.

This paper aims to show that Godel's ontological argument can be parodied in much the same kind of way in which Gaunilo parodied Anselm's Proslogion argument. The parody in this paper fails; there is a patch provided in "Reply to Gettings" (Analysis 60, 4, 2000, 363-7).

This paper discusses recent work on higher-order ontological arguments, including work on arguments due to Gödel, Maydole and Pruss. After setting out a range of these arguments, the paper seeks to highlight the principal difficulties that these kinds of arguments confront. One important aim of the paper is to cast light on Gödel's ontological argument by way of an examination of a range of related higher-order arguments.

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)

This article is a reply to Michael Gettings' criticisms of a previous paper of mine on Godel's ontological argument. (All relevant bibliographical details may be found in the article.) I provide a patch to my previous -- faulty -- attempt to provide a parody of Godel's ontological argument on the model of Gaunilo's parody of Anselm's Proslogion 2 argument.

Anselm’s ontological argument is an argument for the existence of God. This paper presents Iris Murdoch’s ontological argument for the existence of the Good. It discusses her interpretation of Anselm’s argument, her distinctive appropriation of it, as well as some of the merits of her version of the argument. In doing so, it also shows how the argument integrates some key Murdochian ideas: morality’s wide scope, the basicness of vision to morality, moral (...) realism, and Platonism. (shrink)

This paper is my second contribution to the Szatkowski volume. In the first paper, I provide a critical discussion of Bob Maydole's ontological arguments. In this second paper, I respond to Maydole's critical response to my first paper. My overall verdict is that Maydole does not successfully defend his arguments against my critical attack.

After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse (...) of time. As a result, modal collapse should not be conceived in Gödel so much as a deficit, but rather as a kind of the rise of modalities to the “perfect” being. We further show that, in accordance with Gödel’s ontology, the concepts of modality and time should be derived in terms of the “fundamental philosophical concept” of cause. To give an example of how a formalization of such causative Gödelian ontology and ontological proof might look, we propose the transformation of GO into a kind of causally re-interpreted justification logic. (shrink)

First, I suggest that it is possible to make some further improvements upon the Gödelian ontological arguments that Pruss develops. Then, I argue that it is possible to parody Pruss's Gödelian ontological arguments in a way that shows that they make no contribution towards 'lowering the probability of atheism and raising the probability of theism'. I conclude with some remarks about ways in which the arguments of this paper can be extended to apply to the whole family of (...) Gödelian ontological arguments. (shrink)

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with (...) examples such as Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

The ontological argument for the existence of God has enjoyed a recent renaissance among philosophers of religion. Alvin Plantinga's modal version is perhaps the most notable example. This essay critically examines Plantinga's rendition, uncovering both its strengths and weaknesses. The author concludes that while the argument is probably formally valid, it is ultimately unsound. Nonetheless, Plantinga's version has generated much interest and discussion. The author spends some time uncovering the reasons for the argument's powerful intuitive appeal. (...) He concludes his essay by appraising Pruss's recent defence of Plantinga's argument. (shrink)

Gödel’s slingshot-argument proceeds from a referential theory of definite descriptions and from the principle of compositionality for reference. It outlines a metasemantic proof of Frege’s thesis that all true sentences refer to the same object—as well as all false ones. Whereas Frege drew from this the conclusion that sentences refer to truth-values, Gödel rejected a referential theory of definite descriptions. By formalising Gödel’s argument, it is possible to reconstruct all premises that are needed for the derivation of Frege’s (...) thesis. For this purpose, a reference-theoretical semantics for a language of first-order predicate logic with identity and referentially treated definite descriptions will be defined. Some of the premises of Gödel’s argument will be proven by such a reference-theoretical semantics, whereas others can only be postulated. For example, the principle that logically equivalent sentences refer to the same object cannot be proven but must be assumed in order to derive Frege’s thesis. However, different true (or false) sentences can refer to different states of affairs if the latter principle is rejected and the other two premises are maintained. This is shown using an identity criterion for states of affairs according to which two states of affairs are identical if and only if they involve the same objects and have the same necessary and sufficient condition for obtaining. (shrink)

The aim of this essay is twofold. First, it outlines the concept of ontological frame. Secondly, two models are distinguished on this structure. The first one is connected to Kant’s concept of possible object and the second one relates to Leibniz’s. Leibniz maintains that the source of possibility is the mere logical consistency of the notions involved, so that possibility coincides with analytical possibility. Kant, instead, argues that consistency is only a necessary component of possibility. According to Kant, something (...) is possible if there is a cause capable of bringing it into existence; to this end consistency alone is not sufficient. Thus, while the Leibnizian notion of consistency is at the root of the concept of analytical possibility, the Kantian notion of possibility is the source of real possibility. This difference plays an important role in the discussion of Gödel’s ontological proof, which can be formally interpreted on the ontological frame of the pure perfections. While this proof, under some emendation condition, is conclusive in the context of Leibniz’s ontological model, it is not so within the Kantian one. This issue will be the subject of the second part of the present essay. (shrink)

contents -/- ONT vol 1 i. short review: Beyond the Black Rainbow ii. as you die, hold one thought iii. short review: LA JETÉE -/- ONT vol 2 i. maya means ii. short review: SANS SOLEIL iii. vocab iv. eros has an underside v. short review: In the Mood for Love -/- ONT vol 3 i. weed weakens / compels me ii. an Ender's Game after-party iii. playroom is a realm of the dead iv. a precise german History v. short (...) review: STATUES ALSO DIE vi. Kenneth Clark, curator for Fascism vii. a protest poem, in industry lit viii. Lawrence and the English Romance -/- ONT vol 4 i. short review: The Eyes of Tammy Faye ii. vR is efficient R iii. all thru Asia, robes for monks iv. same of God, and of the one God sent v. i thought of the Messiah / muse would be vi. conscience is strong vii. a monk's exalted end -/- ONT vol 5 -/- i. for Shakespeare's Richard the Third ii. the truth is i pass over so many words iii. the boori nazar / nadhar iv. i've awe for jihaad v. short review: Hail, Caesar! vi. a minute of Nothing, gone from YouTube vii. we were rivalrous friends, again viii. my bardo pdf ix. within i'm a weak old mandarin -/- ONT vol 6 i. short review: The Intern ii. the confusion of Chinatown iii. we'll remember water, in Theology iv. Respironics versus ResMed v. i'd bet my life for what vi. the Mad Max deity vii. they'd kill my rat, not heal him -/- ONT vol 7 i. Austen would eroticize all life ii. Merchant/Ivory, a name oddly right iii. Ellie Arroway / Agent Starling iv. abattoir / l’abattoir / laboratoire v. von Neumann's brain an anomaly vi. was terrified of death, delighted in the a-bomb vii. the Greatest Brain is variously named -/- ONT vol 8 i. the day they shot the sacrifice ii. Yay or Nay, on Animal Testing iii. an ought is an is / an is is an ought iv. Behaviorism is for zombies v. a finding from the neuro-lab, on empathy vi. i’ve never had discernible abs vii. a cowardice i'm assenting to perpetually -/- ONT vol 9 i. Day of the Locust / Triffids ii. we're wide on a Paramount soundstage iii. HOLLYWOOD, an ecologic history iv. yet one more site of end-time art v. he's "a bookworm with bulging lobes" vi. apartment is my state of being apart vii. enlightenment means a weight's release -/- ONT lates and xtras i. re Gödel's ontological argument ii. deep in pi's numeric noise iii. from Nothing, something iv. endless in the wrong direction, tragic v. they give you all Eternity to answer vi. what of God's mercy? vii. informed consent and prayer viii. i won't live on. a deed i've done may ix. my selective memory x. Janus means: in close-up foam, two faces xi. a liveable world is a readable world xii. what Supervenes from this? xiii. at each extreme our naming is anachronism xiv. Cat is a collapsing of the wave-function xv. diminishing returns in the history of Experiment xvi. all those undershared Nobels xvii. ice preserves the Cold from heat xviii. a desert spreads xix. Pinker's wit, on jokes xx. Rome surrounds St. Paul / Paul is now the center xxi. each is a gathering Ministry xxii. white boy shot execution-style xxiii. the McDonald's Statement of Claim xxiv. first & last: Don Quixote / Ulysses xxv. The Summer of Rave xxvi. this electro is intrinsically anonymous xxvii. all thru Asia, Drake-Rihanna xxviii. WHO IS BETTER: PLATON OR KANT? (shrink)

In this brief essay, I argue that Anselm's ontological argument for the existence of God achieves its effect through the verbal equivalent of a magician's "sleight-of-hand." More technically, the argument commits the informal fallacy of equivocation. I provide a brief analysis of the argument's text to demonstrate this.

A *very* rough draft of a paper on Anselm's "ontological argument" in which I argue that the argument in the Proslogion rests on a robust notion of having "that then which nothing greater can be thought" in one's mind.

he general theme of this paper is the issue of formalization in philosophy; in a more specific way, it deals with the issue of formalization of arguments in analytic philosophy of religion. One argument in particular – Anselm’s Proslogion II ontological argument – and one specific attempt to formalize it – Robert Adams’ formalization found in his paper “The Logical Structure of Anselm’s Arguments”, published in The Philosophical Review in 1971 – are taken as study cases. The (...) purpose of the paper is to critically analyze Adams’ formalization with the intent to shed some light on the following questions: What are the virtues of formally analyzing arguments and the contributions, if any, of such an enterprise to the debate on Anselm’s argument? Which lessons can Adam’s work teach us about the dangers and limitations of formalization? Do these virtues and dangers teach us something about analysis of arguments in general? (shrink)

This article is a brief overview of major ontological arguments. The most noteworthy feature of this article is the statement of a new parody of the Anselmian and Cartesian arguments that is obviously immune to objections adverting to intrinsic minima and maxima.

In this Introduction, we begin with two relatively uncontroversial matters: the broad contours of the history of discussion of ontological arguments, and the major topics that require discussion in connection with ontological arguments. We then move on to consideration of the much more difficult task of the characterisation of ontological arguments—i.e. the task of saying exactly what ontological arguments are and explaining how they differ from, say, cosmological, teleological, and moral arguments for the existence of God—and (...) then the equally contested question of the provision of general objections to ontological arguments, including, in particular, attempts to show that there could not possibly be a successful ontological argument. Finally, we consider some often-neglected questions about how to assess the merits of arguments, with a particular eye on the assessment of the merits of ontological arguments. (shrink)

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

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 argue that Descartes intended the so-called ontological "argument" as a self-validating intuition, rather than as a formal proof. The textual evidence for this view is highly compelling, but the strongest support comes from understanding Descartes's diagnosis for why God's existence is not 'immediately' self-evident to everyone and the method of analysis that he develops for making it self-evident. The larger aim of the paper is to use the ontological argument as a case study of Descartes's (...) nonformalist theory of deduction and his method of analysis, showing how he conceives the latter as a form of philosophical therapy. (shrink)

The article examines Kant's various criticisms of the broadly Cartesian ontological argument as they are developed in the Critique of Pure Reason. It is argued that each of these criticisms is effective against its intended target, and that these targets include—in addition to Descartes himself—Leibniz, Wolff, and Baumgarten. It is argued that Kant's most famous criticism—the charge that being is not a real predicate—is directed exclusively against Leibniz. Kant's argument for this thesis—the argument proceeding from his (...) example of a hundred thalers—although it may seem to beg the question, in fact succeeds against Leibniz. It does so because the charge of begging the question can be rebutted if one makes certain Leibnizian assumptions. (shrink)

The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no matter whether (...) the proposition is about the past, present or future. In particular, the argument goes, whatever one does or does not do in the future is determined in the present by the truth or falsity of the corresponding proposition. The second argument coming from logic is much more modern and appeals to Gödel's incompleteness theorems to make the case against determinism and in favour of free will, insofar as that applies to the mathematical potentialities of human beings. The claim more precisely is that as a consequence of the incompleteness theorems, those potentialities cannot be exactly circumscribed by the output of any computing machine even allowing unlimited time and space for its work. The chapter concludes with some new considerations that may be in favour of a partial mechanist account of the mathematical mind. (shrink)

This paper is a critique of Stephen Makin's ontological argument. To some extent, the argument of this paper is recapitulated in *Ontological Arguments and Belief in God* (CUP, 1996).

This essay examines how, in the early twentieth century, ontological arguments were employed in the defense of metaphysical idealism. The idealists of the period tended to grant that ontological arguments defy our usual expectations in logic, and so they were less concerned with the formal properties of Anselmian arguments. They insisted, however, that ontological arguments are indispensable, and they argued that we can trust argumentation as such only if we presume that there is a valid ontological (...) argument. In the first section I outline the history of this metalogical interpretation of the ontological argument. In the subsequent sections I explain how Royce and Collingwood each developed the argument, and how this impacted their respective conceptions of both logic and metaphysics. (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.

This paper is a critical examination of Stephen Neale's *The Philosophical Significance of Godel's slingshot*. I am sceptical of the philosophical significance of Godel’s Slingshot (and of Slingshot arguments in general). In particular, I do not believe that Godel’s Slingshot has any interesting and important philosophical consequences for theories of facts or for referential treatments of definite descriptions. More generally, I do not believe that any Slingshot arguments have interesting and important philosophical consequences for theories of facts or for (...) referential treatments of definite descriptions. Friends of facts and referential treatments of definite descriptions can, and should, proceed with the construction of their theories, blithely ignoring the many Slingshots which now litter the landscape. (Of course, there may be other considerations which should give such theorists pause -- but those are other considerations.). (shrink)

There is a philosophical tradition of arguing against presentism, the thesis that only presently existing things exist, on the basis of its incompatibility with fundamental physics. I grant that presentism is incompatible with special and general relativity, but argue that presentism is not incompatible with quantum gravity, because there are some theories of quantum gravity that utilize a fixed foliation of spacetime. I reply to various objections to this defense of presentism, and point out a flaw in Gödel's modal (...) class='Hi'>argument for the ideality of time. This paper provides an interesting case study of the interplay between physics and philosophy. (shrink)

Is there anything new to be said about Anselm's ontological argument? Recent work by Lynne Baker and Gareth Matthews raises some interesting and important questions about the argument. First, Anselm's argument is set in the context of a prayer to God, whose existence Anselm seeks to prove. Is that peculiar or paradoxical? Does it imply that Anselm's prayer is insincere? Baker and Matthews have offered a novel interpretation of Anselm's argument, designed to solve a crucial (...) problem with it. Does their interpretation succeed in solving that problem? This paper addresses both of these questions. (shrink)

We can attend to the logic of Anselm's ontological argument, and amuse ourselves for a few hours unraveling its convoluted word-play, or we can seek to look beyond the flawed logic, to the search for God it expresses. From the perspective of this second approach the Ontological Argument might be seen as more than a mere argument - indeed, as something of a contemplative exercise. One can see in the argument a tantalizing attempt to (...) capture in logical form the devotee’s experience of the presence of God in the contemplation of God. It is a peculiarity of the argument that it can seem hopelessly silly or richly evocative depending upon which of these approaches one takes. In this essay I examine the flawed logic of the Ontological Argument, but then attempt to reflect upon the contemplative experience that may underlie it. (shrink)

Part I argues that ontological arguments, like other classical proofs of the existence of God, are parts of larger arguments in which they are embedded. These larger arguments include reasons supporting the proofs’ premises and responses to them, and to the proofs’ claims to validity and non-circularity, since, in the final analysis, our assessment of the proofs will express our best judgment of the cumulative force of all the considerations bearing on their overall adequacy. Part II illustrates these points (...) by examining contemporary defences of, and attacks on, one of the ontological argument’s central premises, namely, that God’s existence is logically possible. (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)

The ontological argument- proposed by St. Anselm and developed by Descartes, Leibniz, Kant, Hegel, and Marx- furnishes a key to understanding the relationship between thought and reality. In this article, we shall focus on Hegel’s attitude towards the ontological argument as set out in his Science of Logic, where it appears as a paradigm of the relationship between thought and reality. It should be remarked, moreover, that our choice of the subject was not random and that (...) it was selected for the reason that belief in God is a preeminent social reality, inasmuch as faith in God creates His existence. Therefore, an investigation of the concept of God is an inquiry into the most profound recesses of human consciousness. The great opponents of the ontological argument, from Hume down to our day--and even Kant--have based their arguments upon the fundamental empiricist assertion that existential judgments are not analytical. This paper attempts to defend the ontological argument against its opponents. (shrink)

According to standard trope nominalism, there are simple tropes that do not have parts or multiply distinct aspects. Douglas Ehring’s reductio ad absurdum against this standard view concludes that there are no simple tropes. In this paper, we provide a response to Ehring defending the standard view. Ehring’s argument may be refuted by (1) distinguishing the ontological form of tropes from their contribution to the ontological content of the world, and (2) construing tropes as having primitive identity. (...) At the same time, standard trope nominalism is elaborated on by distinguishing between ontological form and content, for which there are also independent reasons. (shrink)

The modal ontological argument (MOA) proceeds from God’s possible existence to God’s actual existence. A prominent objection to the MOA is that it suffers from a symmetry problem: an exactly parallel modal ontological argument can be given for God's non-existence. Several attempts have been made to break the symmetry between the arguments. This draft is a mostly comprehensive survey of those attempts. -/- The draft was initially written as a supplement to the 2024 Summer edition of (...) the SEP entry on Ontological Arguments. However, the draft is not included in the SEP entry. (shrink)

Absolute nothing is the absence of our universe and its laws. Without these rules, nothingness has infinite potential. This implies that within the infinite probability of nothing, infinity can emerge. This would be expressed through infinite universes like our own. Infinite of these universes will differ by several particles, appearing and disappearing for no reason other than fulfilling every possibility. This universe is the product of a greater realisation of infinity and we can test this theory via the measurement of (...) our universe’s most fundamental particles appearing and disappearing for no discernible internal reason (random to our perspective). (shrink)

In this paper, I argue that Kant's famous critique of the Ontological Argument largely begs the question against that argument, and is no better when supplemented by the modern quantificational analysis of "exists." In particular, I argue that the claim, common to Hume and Kant, that conceptual truths can never entail substantive existential claims is false,and thus no ground for rejecting the Ontological Argument.

This book investigates what change is, according to Aristotle, and how it affects his conception of being. Mark Sentesy argues that change leads Aristotle to develop first-order metaphysical concepts such as matter, potency, actuality, sources of being, and the teleology of emerging things. He shows that Aristotle’s distinctive ontological claim—that being is inescapably diverse in kind—is anchored in his argument for the existence of change. -/- Aristotle may be the only thinker to have given a noncircular definition of (...) change. When he gave this definition, arguing that change is real was a losing proposition. To show that it exists, he had to rework the way philosophers understood reality. His groundbreaking analysis of change has long been interpreted through a Platonist lens, however, in which being is conceived as unchanging. Offering a comprehensive reexamination of the relationship between change and being in Aristotle, Sentesy makes an important contribution to scholarship on Aristotle, ancient philosophy, the history and philosophy of science, and metaphysics. (shrink)

Kevin Harrelson's book commences with the following words: This book provides a philosophical analysis of the several debates concerning the "ontological argument" from the middle of the seventeenth to the beginning of the nineteenth century. My aim in writing it was twofold. First, I wished to provide a detailed and comprehensive account of the history of these debates, which I perceived to be lacking in the scholarly literature. Second, I wanted also to pursue a more philosophically interesting question (...) concerning the apparent unassailability of ontological arguments. In pursuit of this latter problem, the driving question that my account addresses is "why has this argument, or kind of argument, been such a constant in otherwise diverse philosophical contexts and periods?" I think that there is no doubt that Harrelson succeeds in the first of these aims. He has, indeed, produced a detailed scholarly account of the history of debates about ontological arguments from the middle of the seventeenth century to the beginning of the nineteenth. His history is engaging and interesting, covering a wide range of authors with diverse philosophical orientations: Descartes, Arnauld, Caterus, Gassendi, Hobbes, Mersenne, More, Geulincx, Cudworth, Locke, Clarke, Malebranche, Huet, Spinoza, Leibniz, Wolff, Baumgarten, Eberhard, Crusius, Kant, Mendelssohn, and Hegel, among others. It seems to me that anyone who works on the treatment of. (shrink)

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 <em>x</em> 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. (shrink)

“Slingshot Arguments” are a family of arguments underlying the Fregean view that if sentences have reference at all, their references are their truth-values. Usually seen as a kind of collapsing argument, the slingshot consists in proving that, once you suppose that there are some items that are references of sentences (as facts or situations, for example), these items collapse into just two items: The True and The False. This dissertation treats of the slingshot dubbed “Gödel’s slingshot”. Gödel argued that (...) there is a deep connection between these arguments and definite descriptions. More precisely, according to Gödel, if one adopts Russell’s interpretation of definite descriptions (which clashes with Frege’s view that definite descriptions are singular terms), it is possible to evade the slingshot. We challenge Gödel’s view in two manners, first by presenting a slingshot even with a Russellian interpretation of definite descriptions and second by presenting a slingshot even when we change from singular terms to plural terms in the light of new developments of the so-called Plural Logic. The text is divided in three chapters, in the first, we present the discussion between Russell and Frege regarding definite descriptions, in the second, we present Gödel’s position and reconstructions of Gödel’s argument and in the third we prove our slingshot argument for Plural Logic. In light of these results we conclude that we can maintain the validity of slingshot arguments even within a Russellian interpretation of definite descriptions or in the context of Plural Logic. (shrink)

This paper argues that Kant’s most famous objection to the ontological argument -- that existence is not a real predicate -- is not, in fact, his most effective objection, and that his ”neglected objection’ to the argument deserves to be better known. It shows that Kant clearly anticipates William Rowe’s later objection that the argument begs the question, and discusses why Kant himself seems to have overlooked the force of this criticism in his attempt to demolish (...) the traditional proofs for God’s existence. (shrink)

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

This chapter gives an exposition and critique of Anselm's Proslogion II argument.

The purpose of this paper is twofold. First, it aims at introducing the ontological argument through the analysis of five historical developments: Anselm’s argument found in the second chapter of his Proslogion, Gaunilo’s criticism of it, Descartes’ version of the ontological argument found in his Meditations on First Philosophy, Leibniz’s contribution to the debate on the ontological argument and his demonstration of the possibility of God, and Kant’s famous criticisms against the (cartesian) (...) class='Hi'>ontological argument. Second, it intends to critically examine the enterprise of formally analyzing philosophical arguments and, as such, contribute in a small degree to the debate on the role of formalization in philosophy. My focus will be mainly on the drawbacks and limitations of such enterprise; as a guideline, I shall refer to a Carnapian, or Carnapian-like theory of argument analysis. (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.