Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). -/- By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive (...) way of fleshing out this idea is synonymous with a ZF-like theory. -/- This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974). (shrink)

Tim Button explores the relationship between words and world; between semantics and scepticism. -/- A certain kind of philosopher – the external realist – worries that appearances might be radically deceptive. For example, she allows that we might all be brains in vats, stimulated by an infernal machine. But anyone who entertains the possibility of radical deception must also entertain a further worry: that all of our thoughts are totally contentless. That worry is just incoherent. -/- We cannot, then, (...) be external realists, who worry about the possibility of radical deception. Equally, however, we cannot be internal realists, who reject all possibility of deception. We must position ourselves somewhere between internal realism and external realism, but we cannot hope to say exactly where. We must be realists, for what that is worth, and realists within limits. -/- In establishing these claims, The Limits of Realism critically explores and develops several themes from Hilary Putnam’s work: the model-theoretic arguments; the connection between truth and justification; the brain-in-vat argument; semantic externalism; and conceptual relativity. The book establishes the continued significance of these topics for all philosophers interested in mind, logic, language, or the possibility of metaphysics. (shrink)

There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain first-order formulas. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discrimination have been studied in some detail. (...) However, this paper also introduces grades of relativity, defined in terms of relativeness correspondences. This paper explores the relationships between all the grades of discrimination, exhaustively answering several natural questions that have so far received only partial answers. It also establishes which grades can be captured in terms of satisfaction of object-language formulas and draws connections with definability theory. (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.

Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...) STT are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for CTT. We end by examining an alternative approach to cumulative types due to Florio and Jones; we argue that their theory is best seen as a misleadingly formulated version of STT. (shrink)

This is a short introduction to ontological arguments. It begins with a brief characterization of ontological arguments that proceeds mainly by way of example. The rest of the discussion is given over to consideration of what looks like a very simple ontological argument. This consideration turns up many of the issues that arise when more complex ontological arguments are examined.

Tallant (2007) has challenged my recent defence of no-futurism (Button 2006), but he does not discuss the key to that defence: that no-futurism's primitive relation 'x is real-as-of y' is not symmetric. I therefore answer Tallant's challenge in the same way as I originally defended no-futurism. I also clarify no-futurism by rejecting a common mis-characterisation of the growing-block theorist. By supplying a semantics for no-futurists, I demonstrate that no-futurism faces no sceptical challenges. I conclude by considering the problem of (...) how to interpret the relation 'x is real-as-of y'. -/- (NB: A correction to this article appears in Analysis 68.1.). (shrink)

In “Models and Reality” (1980), Putnam sketched a version of his internal realism as it might arise in the philosophy of mathematics. Here, I will develop that sketch. By combining Putnam’s model-theoretic arguments with Dummett’s reflections on Gödelian incompleteness, we arrive at (what I call) the Skolem-Gödel Antinomy. In brief: our mathematical concepts are perfectly precise; however, these perfectly precise mathematical concepts are manifested and acquired via a formal theory, which is understood in terms of a computable system of proof, (...) and hence is incomplete. Whilst this might initially seem strange, I show how internal categoricity results for arithmetic and set theory allow us to face up to this Antinomy. This also allows us to understand why “Models are not lost noumenal waifs looking for someone to name them,” but “constructions within our theory itself,” with “names from birth.”. (shrink)

Amie Thomasson and Eli Hirsch have both attempted to deflate metaphysics, by combining Carnapian ideas with an appeal to ordinary language. My main aim in this paper is to critique such deflationary appeals to ordinary language. Focussing on Thomasson, I draw two very general conclusions. First: ordinary language is a wildly complicated phenomenon. Its implicit ontological commitments can only be tackled by invoking a context principle; but this will mean that ordinary language ontology is not a trivial enterprise. Second: ordinary (...) language often points in different directions simultaneously, so that a wide variety of existence questions cannot be deflated merely by appealing to ordinary language. (shrink)

Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

Feser (2017) presents and defends five proofs of the existence of God. Each proof is in two stages: the first stage proves the existence of something which, in the second stage, is shown to possess an appropriate range of divine attributes. Each proof is given two presentations, one informal and one formal. In this paper, I critically examine two premises from one of Feser's five first stage proofs. I provide reasons for thinking that naturalists reject both of these premises. In (...) my view, this enough to show that the proof fails: it fails to advance considerations that decide between theism and important competing positions. (shrink)

The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets found before S, we find a set whose members are exactly those sets. We find nothing else at S.' Surprisingly, this story already guarantees that the sets are arranged in well-ordered levels, and suffices for quasi-categoricity. I show this by presenting Level Theory, a simplification of set theories (...) due to Scott, Montague, Derrick, and Potter. (shrink)

No-futurists ('growing block theorists') hold that that the past and the present are real, but that the future is not. The present moment is therefore privileged: it is the last moment of time. Craig Bourne (2002) and David Braddon-Mitchell (2004) have argued that this position is unmotivated, since the privilege of presentness comes apart from the indexicality of 'this moment'. I respond that no-futurists should treat 'x is real-as-of y' as a nonsymmetric relation. Then different moments are real-as-of different times. (...) This reunites privilege with indexicality, but entails that no-futurists must believe in ineliminably tensed facts. (shrink)

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a non-trivial automorphism, distinct indiscernible positions within the structure cannot be shown to be non-identical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include 'irreflexive two-place relations'. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positions that have all the same properties as each other and exactly the same (...) relations to all objects (including themselves). I conclude that realistic structuralists must compromise and treat some structures eliminativistically. (shrink)

I offer a minimal characterization of naturalism, with ontological, epistemological, psychological and evaluative dimensions. I explain why naturalism is attractive. I note that naturalists disagree among themselves about, among other things, the nature of values, beliefs, and abstractions. I close by responding to some standard objections to naturalism.

Hylomorphists claim that substances—human beings, oak trees, chemical compounds—are compounds of matter and form. If a house is a substance, then its matter would be some bricks and timbers and its form the structure those bricks and timbers take on. While hylomorphism is traditionally presented as a theory of change, it only treats the coming-to-be and passing-away of matter-form compounds. But many hylomorphists understand forms to be entities in their own right, as parts or constituents of substances. So, a neglected (...) question arises: how, when, and from where do forms come to be? I take up the view of one prominent and representative hylomorphist, Kathrin Koslicki, and argue that she cannot answer these questions satisfactorily. I close with a proposal for an account of the generation of forms based on machinery many hylomorphists already accept, namely, causal powers, that points to a deflationary metaphysics of form. (shrink)

Tennenbaum's Theorem yields an elegant characterisation of the standard model of arithmetic. Several authors have recently claimed that this result has important philosophical consequences: in particular, it offers us a way of responding to model-theoretic worries about how we manage to grasp the standard model. We disagree. If there ever was such a problem about how we come to grasp the standard model, then Tennenbaum's Theorem does not help. We show this by examining a parallel argument, from a simpler model-theoretic (...) result. (shrink)

This paper discusses a wide range of anti-naturalistic argument from reason due to Balfour, Haldane, Joad, Lewis, Taylor, Moreland, Plantinga, Reppert, and Hasker. I argue that none of these arguments poses a serious challenge to naturalists who are identity theorists. Further, I argue that some of these arguments do not even pose prima facie plausible challenges to naturalism. In the concluding part of my discussion, I draw attention to some distinctive differences between Hasker’s anti-naturalistic arguments and the other anti-naturalistic arguments (...) mentioned above. (shrink)

Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to the (...) problem of many-valued truth-tables for classical sentential logic. I close by outlining the technicalities surrounding nasty connectives on many-valued truth-tables. (shrink)

Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version (...) of the Church–Turing Thesis is unaffected by SAD computation. (shrink)

Can we quantify over everything: absolutely, positively, definitely, totally, every thing? Some philosophers have claimed that we must be able to do so, since the doctrine that we cannot is self-stultifying. But this treats restrictivism as a positive doctrine. Restrictivism is much better viewed as a kind of militant quietism, which I call dadaism. Dadaists advance a hostile challenge, with the aim of silencing everyone who holds a positive position about ‘absolute generality’.

Hylomorphism is the Aristotelian theory according to which substances are composed of matter and form. If a house is a substance, then its matter would be a collection of bricks and timbers and its form something like the structure of those bricks and timbers. It is widely agreed that matter bears a mereological relationship to substance; the bricks and timbers are parts of the house. But with form things are more controversial. Is the structure of the bricks and timbers best (...) conceived as a part of the house, or is it related to the house in some non-mereological fashion? Kathrin Koslicki argues that substances have formal parts, that forms are best conceived as bearing a mereological relation to substances. This paper shows that her argument fails, given the traditional and plausible distinction between substances and accidental unities. I close with a brief suggestion for a non-mereological construal of forms. (shrink)

On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; and a natural (...) extension of BLT is definitionally equivalent with ZF. (shrink)

Bartha (2012) conjectures that, if we meet all of the other objections to Pascal’s wager, then the many-Gods objection is already met. Moreover, he shows that, if all other objections to Pascal’s wager are already met, then, in a choice between a Jealous God, an Indifferent God, a Very Nice God, a Very Perverse God, the full range of Nice Gods, the full range of Perverse Gods, and no God, you should wager on the Jealous God. I argue that his (...) requirement of [strongly] stable equilibrium is not well-motivated. There are other types of Gods, no less worthy of consideration than those that figure in Bartha’s deliberations, which are intuitively no worse wagers than the Jealous God. In particular, I have suggested that one does no worse to wager on a jealous cartel than one does to wager on a Jealous God. Moreover, I argue that there are other types of Gods, no less worthy of consideration than those that figure in Bartha’s deliberations, that make trouble for Pascal’s wager, but not because one would do better to wager on them rather than on a Jealous God. Finally, I argue that, if we suppose that infinitesimal credences are in no worse standing the infinite utilities, then we cannot accept the assumption—built into the relative utilities framework—that there cannot be infinitesimal credences. (shrink)

In this paper, I aim to bring out the implausibility of the claim that there is a class of philosophers of religion—holders of a particular constellation of beliefs about religion—whose religious beliefs are either uniquely rational or uniquely supported by a stock of cogent arguments. My initial focus will be on models of parties to religious disagreements. These models may be simple, but I believe that there is much to be learned from them.

It is a very curious thing that proponents of Idealism have considered it to be a satisfactory counter to ‘scepticism’, ‘nihilism’, and the like. On the contrary, it seems to me that Idealism is a very close cousin to ‘brain-in-a-vat’ scepticism and other anti-naturalistic fantasies. Moreover, it seems to me that Idealism is inferior to Naturalism for much the same kinds of reasons that ‘brain-in-a-vat’ scepticism and other anti-naturalistic fantasies are inferior to Naturalism: a proper weighing of theoretical virtues discloses (...) that Naturalism is the most virtuous worldview. (shrink)

Hylomorphism is the Aristotelian theory according to which objects are composites of form and matter. Form is what unifies the various parts of an object – the matter – into a cohesive whole. Some contemporary hylomorphists argue their theory applies beyond the realm of concreta, and that it explains the unity of various abstract entities. Not everyone agrees. Recent criticism alleges that hylomorphism fails to explain the unity of certain abstract entities, namely, complex properties – properties with other properties as (...) proper parts. Here, I both respond to this criticism and show that and how hylomorphism extends to the domain of complex properties. By discussing hylomorphism’s applicability to the hitherto unchartered domain of complex properties, I hope to defend its credentials as a general mereological theory. (shrink)

Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. For that, we (...) first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

Putnam famously attempted to use model theory to draw metaphysical conclusions. His Skolemisation argument sought to show metaphysical realists that their favourite theories have countable models. His permutation argument sought to show that they have permuted models. His constructivisation argument sought to show that any empirical evidence is compatible with the Axiom of Constructibility. Here, I examine the metamathematics of all three model-theoretic arguments, and I argue against Bays (2001, 2007) that Putnam is largely immune to metamathematical challenges.

This is the concluding chapter of a debate book about the existence of God: *Theism and Atheism: Opposing Arguments in Philosophy* (Gale, 2019). The book has a large number of contributors on both sides. My chapter suggests one way of unifying the contributions that are made on the atheistic side.

In ‘Professor Mackie and the Kalam Cosmological Argument’ , 367–75), Professor William Lane Craig undertakes to demonstrate that J. L. Mackie's analysis of the kalam cosmological argument in The Miracle of Theism is ‘superficial’, and that Mackie ‘has failed to provide any compelling or even intuitively appealing objection against the argument’ . I disagree with Craig's judgement; for it seems to me that the considerations which Mackie advances do serve to refute the kalam cosmological argument. Consequently, the purpose of this (...) paper is to reply to Craig's criticisms on Mackie's behalf. (shrink)

Hylomorphism is the theory that objects are composites of form and matter. Recently it has been argued that form is structure, or the arrangement of an object's parts. This paper shows that the principle of form cannot be ontologically exhausted by structure. That is, I deny form should be understood just as the arrangement of an object's parts. I do so by showing that structure cannot play the role form is supposed to in a certain domain of objects, specifically, in (...) mereological simples. Thus, I show that Hylomorphism does not reduce to Structuralism. I also draw out some important consequences from my argument for Hylomorphism in general. (shrink)

This paper begins with a fairly careful and detailed discussion of the conditions under which someone who presents an argument ought to be prepared to concede that the argument is unsuccessful. The conclusions reached in this discussion are then applied to William Lane Craig’s defense of what he calls “the kalam cosmological argument.” Perhaps unsurprisingly, the chief contention of the paper is that Craig ought to be prepared to concede that “the kalam cosmological argument” is not a successful argument. The (...) paper pays particular attention to Craig’s recent criticisms of Adolf Grünbaum’s contention that “the kalam cosmological argument” presupposes “the normalcy of nothingness”; and it also addresses some methodological issues raised by Craig’s response to my previous criticisms of his replies to critiques of “the kalam cosmological argument” provided by Grünbaum, Hawking, and Davies. (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.

Minimalists, such as Paul Horwich, claim that the notions of truth, reference and satisfaction are exhausted by some very simple schemes. Unfortunately, there are subtle difficulties with treating these as schemes, in the ordinary sense. So instead, minimalists regard them as illustrating one-place functions, into which we can input propositions (when considering truth) or propositional constituents (when considering reference and satisfaction). However, Bertrand Russell's Gray's Elegy argument teaches us some important lessons about propositions and propositional constituents. When applied to minimalism, (...) these lessons show us why we should abandon it. (shrink)

I provide a classification of varieties of pantheism. I argue that there are two different kinds of commitments that pantheists have. On the one hand, there is an ontological commitment to the existence of a sum of all things. On the other hand, there is an ideological commitment: either collectively or distributively, the sum of all things is divine.

Hylomorphism is the Aristotelian theory according to which substances are composites of matter and form. If my house is a substance, then its matter would be a collection of bricks and timbers and its form something like a structure that unites those bricks and timbers into a single substance. Contemporary hylomorphists are divided on how to understand forms best, but a prominent group of theorists argue that forms are emergent powers. According to such views, when material components are arranged appropriately, (...) a novel substance emerges with the power to impose unity on its components through time. I argue that these accounts of form fall prey to a bootstrapping problem, and so, suffer from issues of redundancy, given plausible assumptions about inherence. In their place, I suggest an ontologically minimalist conception of forms as collective manifestations of the powers of matter. (shrink)

We offer two arguments against the halving repose to Sleeping Beauty. First, we show that halving violates the Epistemological Sure-Thing Principle, which we argue is a necessary constraint on any reasonable probability assignment. The constraint is that if hypothetically on C you assign to A the same probability you assign to A hypothetical on not-C, you must assign that probability to A simpliciter. Epistemically, it's a sure thing for you that A has this probability. Second, we show that halving violates (...) solid statistical reasoning (or draws absurdly irrelevant distinctions). (shrink)

According to the Acceptance Principle, a person is entitled to accept a proposition that is presented as true (asserted) and that is intelligible to him or her, unless there are stronger reasons not to. Burge assumes this Principle and then argues that it has an apriori justification, basis or rationale. This paper expounds Burge's teleological reliability framework and the details of his a priori justification for the Principle. It then raises three significant doubts.

In Pascal's Wager: A Study Of Practical Reasoning In Philosophical Theology ,[1] Nicholas Rescher aims to show that, contrary to received philosophical opinion, Pascal's Wager argument is "the vehicle of a fruitful and valuable insight--one which not only represents a milestone in the development of an historically important tradition of thought but can still be seen as making an instructive contribution to philosophical theology".[2] In particular, Rescher argues that one only needs to adopt a correct perspective in order to see (...) that Pascal's Wager argument is a good argument. Moreover, there seems to be a certain amount of contemporary support for Rescher's claim that Pascal's Wager argument can be seen to be a good argument when properly construed .[3] However, despite this recent trend to adopt a more sympathetic stance towards Pascal's Wager argument, I propose to defend the traditional view that Pascal's Wager argument is almost entirely worthless--at least from the theological standpoint. (No doubt, it has historical significance from the standpoint of decision theory; but that's a separate matter.). (shrink)

Bu [makalede], nihai olarak kesin bir sonucu olduğunu iddia etmemekle birlikte, ateizm için geliştirebileceğim en iyi argümanı öne sürmeye çalışacağım ve ortaya koyacağım şeyin, Tanrı’nın varlığına dair yürütülen tartışmaların herhangi bir kısmındaki, en iyi argüman olduğunu iddia edeceğim.

Hilary Putnam’s BIV argument first occurred to him when ‘thinking about a theorem in modern logic, the “Skolem–Löwenheim Theorem”’ (Putnam 1981: 7). One of my aims in this paper is to explore the connection between the argument and the Theorem. But I also want to draw some further connections. In particular, I think that Putnam’s BIV argument provides us with an impressively versatile template for dealing with sceptical challenges. Indeed, this template allows us to unify some of Putnam’s most enduring (...) contributions to the realism/antirealism debate: his discussions of brains-in-vats, of Skolem’s Paradox, and of permutations. In all three cases, we have an argument which does not merely defeat the sceptic; it also shows us that we must reject some prima facie plausible philosophical picture. (shrink)

E.J.Lowe was a prominent and theistically–inclined philosopher who developed and defended a four–category ontology with roots in Aristotle’s Categories. But Lowe engaged in little philosophical theology and said even less about how a divine being might fit into his considered ontology. This paper explores ways in which the reality of a divine being might be squared with Lowe’s ontology. I motivate the exploration with a puzzle that suggests Lowe must reject either divine aseity or the traditional view that God is (...) a substance. After showing that the puzzle cannot be overcome by rejecting one of its premises, I consider ways in which Lowe might try to reject the puzzle wholesale. I argue that the best way to reject the puzzle is to countenance a fifth fundamental category, the category of supernatural substance. (shrink)

Whereas the Platonic-Christian philosophical tradition in the West favours an ”ascent to theory’ and abstract reasoning, east-Asian philosophies tend to be rooted in somatic, or bodily, practice. In the philosophies of Confucius and Zhuangzi in China, and KÅ«kai and Dōgen in Japan, we can distinguish two different forms of somatic practice: developing physical skills, and what one might call ”realising relationships’. These practices improve our relations with others -- whether the ancestors or our contemporaries, the things with which we surround (...) ourselves or the phenomena of nature -- by reducing egocentrism and increasing humility. Because they transform the practitioner’s experience, the major benefit of philosophies grounded in somatic practice is that they help close the gap between beliefs and behaviour, and between ideas and action. (shrink)

This paper outlines an argument for atheism from naturalism that I have developed in more detail elsewhere (in particular, in *The Best Argument against God*). The overall shape of the argument is as follows: first, naturalism is simpler than theism; second, there is no data that naturalism does not explain at least as well as theism; and, third, naturalism entails atheism; so we have good reason to prefer atheism to theism. Note that this statement of the shape of the argument (...) is NOT a statement of the argument itself. (shrink)

This paper is an English version of the paper that was published in German under the title: "Über die Aussichten erfolgreicher Beweise für Theismus oder Atheismus". My English paper was translated into German by Gabriele Schlegel. -/- The aim of this paper is to examine the prospects for proofs or successful arguments for the existence or non-existence of God.

This paper is a response to David Oderberg's discussion of the Tristram Shandy paradox. I defend the claim that the Tristram Shandy paradox does not support the claim that it is impossible that the past is infinite.

Anselmian theists claim (a) that there is a being than which none greater can be conceived; and (b) that it is knowable on purely—solely, entirely—a priori grounds that there is a being than which none greater can be conceived. In this paper, I argue that Anselmian Theism gains traction by conflating different interpretations of the key description ‘being than which no greater can be conceived’. In particular, I insist that it is very important to distinguish between ideal excellence and maximal (...) possible excellence. At the end of my paper, I illustrate the importance of this distinction by applying my discussion to the recent defence of Anselmian Theism in Nagasawa (Philos Q 58:577–591, 2008). (shrink)