Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.

José Benardete developed a famous paradox involving a beginningless set of items each member of which satisfies some predicate just in case no earlier member satisfies it. The Grim Reaper version of this paradox has recently been employed in favor of various finitist metaphysical theses, ranging from temporal finitism to causal finitism to the discrete nature of time. Here, I examine a new challenge to these finitist arguments—namely, the challenge of implying that the future cannot be endless. In particular, I (...) develop future-oriented Benardete paradoxes and examine their epistemic symmetry with past-oriented paradoxes. (shrink)

Thought experiments are common where infinitely many entities acting in concert give rise to strange results. Some of these cases, however, can be generalized to yield almost omnipotent systems from limited materials. This paper discusses one of these cases, bringing out one aspect of what seems so troubling about "New Zeno" cases. -/- This paper is in memory of Josh Parsons.

An eternal society with the abilities of ordinary humans in each year of its existence would have had the ability to actualize a logical contradiction. This fact casts doubt on the metaphysical possibility of an infinite past. In addition to using this paradox in an argument against an infinite past, one can also use the paradox mutatis mutandis as a decisive argument against the sempiternality of God.

Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It (...) discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes. (shrink)

The majority of disucssions of Benardete’s Paradox conclude that the traveller approaching the infinite series of gods will be mysteriously halted despite none of the gods erecting any barriers. Using a revision-theoretic analysis of Benardete’s puzzle, four distinct possible outcomes that might occur given Benardete’s set-up are distinguished. This analysis provides additional insight into the puzzle at hand, via identifying heretofore unnoticed possible outcomes, but it also serves as an example of how the revision theoretic framework can be used to (...) construct exhaustive taxonomies of potential outcomes in apparently contradictory situations. (shrink)

The book discusses the structure, content, and evaluation of cosmological arguments. The introductory chapter investigates features essential to cosmological arguments. Traditionally, cosmological arguments are distinguished by their appeal to change, causation, contingency or objective becoming in the world. But none of these is in fact essential to the formulation of cosmological arguments. Chapters 1-3 present a critical discussion of traditional Thomistic, Kalam, and Leibnizian cosmological arguments, noting various advantages and disadvantages of these approaches. Chapter 4 offers an entirely new approach (...) to the cosmological argument - the approach of theistic modal realism. The proper explananda of cosmological arguments on this approach is not change, causation, contingency or objective becoming in the world. The proper explananda is the totality of metaphysical reality - all actualia and all possibilia. The result is the most compelling and least objectionable version of the cosmological argument. (shrink)

In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. I (...) then show how this leads to the Infinity from Nothing paradox, in which we have the spontaneous eruption of infinite mass and energy out of nothing. I conclude by showing how our supertask models at least something of an old conundrum, the question of what happens when the immovable object meets the irresistible force. (shrink)

I trace the relationship between the view that knowledge is stakes sensitive and Laurie Paul’s account of the epistemology of transformative experience. The view that knowledge is stakes sensitive comes in different flavours: one can go for subjective or objective conceptions of stakes, where subjective views of stakes take stakes to be a function of an agent’s non-factive mental states, and objective views of stakes do not. I argue that there is a tension between subjective accounts of stakes sensitivity and (...) Paul’s epistemology of transformative experience. (shrink)

I consider a puzzling case presented by Jose Benardete, and by appeal to this case develop a paradox involving counterfactual conditionals. I then show that this paradox may be leveraged to argue for certain non-obvious claims concerning the logic of counterfactuals.

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of (...) this metaphysical picture, it has important consequences for the debate over absolute generality. It is often thought that ‘indefinite extensibility’ arguments at best make trouble for mathematical platonists; but the contact arguments show that nominalists face the same kind of difficulty, if they recognize even the metaphysical possibility of the picture I sketch. (shrink)

Benardete presents a version of Zeno's dichotomy in which an infinite sequence of gods each intends to raise a barrier iff a traveller reaches the position where they intend to raise their barrier. In this paper, I demonstrate the abstract form of the Benardete Dichotomy. I show that the diagnosis based on that form can do philosophical work not done by earlier papers rejecting Priest's version of the Benardete Dichotomy, and that the diagnosis extends to a paradox not normally classified (...) as a dichotomy. I show how the form is exploited to generate paradox. Introduction The form of the Benardete dichotomy 2.1 The unsatisfiable pair diagnosis Applying the unsatisfiable pair diagnosis 3.1 Perez Laraudogoitia 3.2 Hawthorne 3.3 Angel 3.4 Yablo and Sorensen Exploiting the form. (shrink)

Many philosophers accept a ‘layered’ world‐view according to which the facts about the higher ontological levels supervene on the facts about the lower levels. Advocates of such views often have in mind a version of atomism, according to which there is a fundamental level of indivisible objects known as simples or atoms upon whose spatiotemporal locations and intrinsic properties everything at the higher levels supervenes.1 Some, however, accept the possibility of ‘gunk’ worlds in which there are parts ‘all the way (...) down’ such that there are no simples and insofar as composite objects exist these are composed of smaller objects which in turn are composed of smaller objects, and so on. It may nonetheless still be claimed that the facts about each ontological level supervene on the facts about the lower levels. (shrink)

A novel way of making a non-stick frying pan using a topologically open surface is described. While the article has a slight humorous element to it, it is also intended to contain some serious philosophical points concerning the nature of infinitely divisible matter and the kind of contact that must occur between objects in order for them to interact.

The paper analyses Benardete's paradox of the gods from a more general perspective (the convergence approach) than several of the most important proposals made to date, but in close relation (and sharp contrast) with them. The new theory, based on the notion of limit, is systematically applicable in different possible scenarios involving a denumerable infinity of objects. In particular, it reveals in what way ω-consistency can be compromised in an otherwise consistent description of such "infinitary" situations.

Although the current literature on supertasks concentrates largely on their supposed physical implications (extending the tradition of Zeno’s classical paradoxes of movement), in this study I propose a new model of supertask that explores for the first time some of their information-related consequences and I defend these consequences from a possible criticism.

We argue that not all cases of before-effect involve causation and ask how to demarcate cases of before-effect in which the events that follow exert causal influence over the before-effect from cases in which they do not.

A simultaneous collision that produces paradoxical indeterminism (involving N0 hypothetical particles in a classical three-dimensional Euclidean space) is described in Section 2. By showing that a similar paradox occurs with long-range forces between hypothetical particles, in Section 3, the underlying cause is seen to be that collections of such objects are assumed to have no intrinsic ordering. The resolution of allowing only finite numbers of particles is defended (as being the least ad hoc) by looking at both -sequences (in the (...) context of a very basic supertask, in Section 4) and *-sequences (reversed -sequences, in the form of paradoxical results from the recent literature). Introduction The simultaneous collision The paradox in other contexts The basic problem is N0 things The recent literature Generating N0 things. (shrink)