Arrhenius’s impossibility theorems purport to demonstrate that no population axiology can satisfy each of a small number of intuitively compelling adequacy conditions. However, it has recently been pointed out that each theorem depends on a dubious assumption: Finite Fine-Grainedness. This assumption states that there exists a finite sequence of slight welfare differences between any two welfare levels. Denying Finite Fine-Grainedness makes room for a lexical population axiology which satisfies all of the compelling adequacy (...) conditions in each theorem. Therefore, Arrhenius’s theorems fail to prove that there is no satisfactory population axiology. In this paper, I argue that Arrhenius’s theorems can be repurposed. Since all of our population-affecting actions have a non-zero probability of bringing about more than one distinct population, it is population prospect axiologies that are of practical relevance, and amended versions of Arrhenius’s theorems demonstrate that there is no satisfactory population prospect axiology. These impossibility theorems do not depend on Finite Fine-Grainedness, so lexical views do not escape them. (shrink)

By recourse to the fundamentals of preference orderings and their numerical representations through linear utility, we address certain questions raised in Nover and Hájek 2004, Hájek and Nover 2006, and Colyvan 2006. In brief, the Pasadena and Altadena games are well-defined and can be assigned any finite utility values while remaining consistent with preferences between those games having well-defined finite expected value. This is also true for the St Petersburg game. Furthermore, the dominance claimed for the Altadena game (...) over the Pasadena game, and that would have been claimed for the St Petersburg game over the Altadena, can be contradicted without fear of inconsistency with the axioms of utility theory. However, insistence upon dominance can be made to yield a contradiction of the Archimedean axiom of utility theory. CiteULike Connotea Del.icio.us What's this? (shrink)

This paper formulates a new argument against the received view in the philosophy of poetry. The received view consists of three tenets: the unity of poetic form and poetic content; the impossibility of paraphrasing and translating poetry; and the hyperintensionality of poetry. We will explore the same detour via direct quotation that has been used by proponents of the received view. We will argue that the hyperintensionality and unity of quotation do not guarantee its untranslatability, and thus that the inference (...) of untranslatability from hyperintensionality and unity is not universally valid. As a consequence, the claim that poetry cannot be translated is left without much support, since it relies on the same kind of inference. However, this does not mean that poetry is translatable; it means only that if it is not translatable, this is due to something other than the combination of hyperintensionality and unity. (shrink)

This chapter discusses why the grounding idiom does not perform as well as we have been led to believe in providing a plausible approach to relative fundamentality. Grounding suffers from some of same deficiencies as supervenience: most prominently, grounding also fails to be sufficiently fine-grained to do its intended explanatory work. In addition, there is doubt as to whether the phenomena collected together under the rubric of grounding are really unified by the presence of a single relation. Grounding turns (...) out not to be helpful in capturing and illuminating what is philosophically important about the traditional substance/non-substance distinction. Although grounding performs better than supervenience in some ways, it does not solve all of the problems to which a supervenience-based approach to relative fundamentality falls prey. (shrink)

McGrew, McGrew and Vestrup (MMV) have argued that the fine-tuning anthropic principle argument for the existence of God fails because no probabilities can be assigned to the likelihood that physical constants fall in some finite interval. In particular, the fine-tuning argument that, say, some constant must lie in the range (1.000,1.001) in order for intelligent life to be possible is no better than a seemingly absurd coarse-tuning argument based on the need for that constant to lie in (...) the range (0.001, 10000000). The author of this piece defends the coarse tuning argument as a rational piece of reasoning, and, further, argues that the countable additivity assumption in the MMV paper can be dropped in favor of finite additivity. (shrink)

The challenge of giving a semantics for relevance logic in terms of worlds or situations intrigued several logicians. As a solution, Fine gave a two-sorted semantics. We overview the semantics as well as some further work of Fine in the area of relevance logic. Then we show that beyond supplying technical results such as soundness, completeness and the finite model property (fmp) for many logics, the operational–relational semantics provides footing for an informal interpretation and it naturally leads (...) to an interpretation in terms of relevance. (shrink)

Dariusz Łukasiewicz has investigated in depth the “Argument from Chance” which argues that the data revealing chance in the world are incompatible with Divine Providence. Łukasiewicz agrees that these data undermine the traditional model of Providence—a fine-grained model in which every single detail is controlled by God—but maintains that they are not incompatible with a coarse-grained model—in which God leaves to chance many aspects of history (including some horrendous evils). Furthermore, Łukasiewicz provides independent reasons to prefer this coarse-grained model. (...) Even though I agree that a maximally fine-grained model is undermined by the scientific data, I argue that this is no sufficient reason to adopt a model as coarse-grained as Łukasiewicz’s. I propose a model of intermediate level of fine-grainedness which could avoid the drawbacks of both extremes, and seems to me to provide a more traditional approach to the problem of evil. (shrink)

I begin by examining a recent debate between John McDowell and Christopher Peacocke over whether the content of perceptual experience is non-conceptual. Although I am sympathetic to Peacocke’s claim that perceptual content is non-conceptual, I suggest a number of ways in which his arguments fail to make that case. This failure stems from an over-emphasis on the "fine-grainedness" of perceptual content - a feature that is relatively unimportant to its non-conceptual structure. I go on to describe two other (...) features of perceptual experience that are more likely to be relevant to the claim that perceptual content is non-conceptual. These features are 1) the dependence of a perceived object on the perceptual context in which it is perceived and 2) the dependence of a perceived property on the object it is perceived to be a property of. (shrink)

This paper obtains the weak completeness and decidability results for standard systems of modal logic using models built from formulas themselves. This line of work began with Fine (Notre Dame J. Form. Log. 16:229-237, 1975). There are two ways in which our work advances on that paper: First, the definition of our models is mainly based on the relation Kozen and Parikh used in their proof of the completeness of PDL, see (Theor. Comp. Sci. 113-118, 1981). The point is (...) to develop a general model-construction method based on this definition. We do this and thereby obtain the completeness of most of the standard modal systems, and in addition apply the method to some other systems of interest. None of the results use filtration, but in our final section we explore the connection. (shrink)

This paper presents a generalization of Fine’s completeness theorem for transitive logics of finite width, and proves the Kripke completeness of transitive logics of finite “suc-eq-width”. The frame condition for each finite suc-eq-width axiom requires, in rooted transitive frames, a finite upper bound of cardinality for antichains of points with different proper successors. The paper also presents a generalization of Rybakov’s completeness theorem for transitive logics of prefinite width, and proves the Kripke completeness of transitive (...) logics of prefinite “suc-eq-width”. The frame condition for each prefinite suc-eq-width axiom requires, in rooted transitive frames, a finite upper bound of cardinality for antichains of points that have a finite lower bound of depth and have different proper successors. We will construct continuums of transitive logics of finite suc-eq-width but not of finite width, and continuums of those of prefinite suc-eq-width but not of prefinite width. This shows that our new completeness results cover uncountably many more logics than Fine’s theorem and Rybakov’s theorem respectively. (shrink)

This paper deals with two different problems in which infinity plays a central role. I first respond to a claim that infinity renders counting knowledge-level beliefs an infeasible approach to measuring and comparing how much we know. There are two methods of comparing sizes of infinite sets, using the one-to-one correspondence principle or the subset principle, and I argue that we should use the subset principle for measuring knowledge. I then turn to the normalizability and coarse tuning objections to (...) class='Hi'>fine-tuning arguments for the existence of God or a multiverse. These objections center on the difficulty of talking about the epistemic probability of a physical constant falling within a finite life-permitting range when the possible range of that constant is infinite. Applying the lessons learned regarding infinity and the measurement of knowledge, I hope to blunt much of the force of these objections to fine-tuning arguments. (shrink)

Locally finite omega languages were introduced by Ressayre [Formal languages defined by the underlying structure of their words. J Symb Log 53(4):1009–1026, 1988]. These languages are defined by local sentences and extend ω-languages accepted by Büchi automata or defined by monadic second order sentences. We investigate their topological complexity. All locally finite ω-languages are analytic sets, the class LOC ω of locally finite ω-languages meets all finite levels of the Borel hierarchy and there exist some locally (...) finite ω-languages which are Borel sets of infinite rank or even analytic but non-Borel sets. This gives partial answers to questions of Simonnet (Automates et Théorie Descriptive, Ph.D. Thesis. Université Paris 7, March 1992) and of Duparc et al. [Computer science and the fine structure of Borel sets. Theor Comput Sci 257(1–2):85–105, 2001]. (shrink)

We show that there exist 2 ℵ 0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any first-order definable class of relational structures. Using a variant of this construction, we resolve a long-standing question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any first-order definable class of Kripke frames (a monomodal example can then be obtained using simulation results (...) of Thomason). The constructions use the result of Erd $\H{o}$ s that there are finite graphs with arbitrarily large chromatic number and girth. (shrink)

This text unites the logical and philosophical aspects of set theory in a manner intelligible both to mathematicians without training in formal logic and to logicians without a mathematical background. It combines an elementary level of treatment with the highest possible degree of logical rigor and precision. Starting with an explanation of all the basic logical terms and related operations, the text progresses through a stage-by-stage elaboration that proves the fundamental theorems of finite sets. It focuses on the Bernays (...) theory of finite classes and finite sets, exploring the system's basis and development, including Stage I and Stage II theorems, the theory of finite ordinals, and the theory of finite classes and finite sets. This volume represents an excellent text for undergraduates studying intermediate or advanced logic as well as a fine reference for professional mathematicians. (shrink)

In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet contraction over that theory. The purpose (...) of the present paper is to study the relationship more finely, by seeking an explicit map between the component orderings involved in each of the two kinds of contraction. It is shown that at least in the finite case a suitable map exists, with the consequence that the relational, transitively relational, and antisymmetrically relational partial meet contraction functions form identifiable subclasses of the safe contraction functions, over any theory finite modulo logical equivalence. In the process of constructing the map, as the composition of four simple transformations, mediating notions of bottom and top contraction are introduced. The study of the infinite case remains open. (shrink)

Are there, in addition to the various actual objects that make up the world, various possible objects? Are there merely possible people, for example, or merely possible electrons, or even merely possible kinds? We certainly talk as if there were such things. Given a particular sperm and egg, I may wonder whether that particular child which would result from their union would have blue eyes. But if the sperm and egg are never in fact brought together, then there is no (...) actual object that my thought is about. Or again, in the semantics for modal logic we presuppose an ontology of possibilia twice over. For first, we countenance various possible worlds, in addition to the actual world; and second, each of these worlds is taken to be endowed with its own domain of objects. These will be the actual objects of the world in question, but they need not be actual simpliciter, i.e., actual objects of our world. What are we to make of such discourse? There are four options: (i) the discourse is taken to be unintelligible; (ii) it is taken to be intelligible but nonfactual, i.e. as not in the business of stating facts; (iii) it is taken to be factual but reducible to discourse involving no reference to possibilia; (iv) it is taken to be both factual and irreducible. These options range from a full-blooded form of actualism at one extreme to a full-blooded form of possibilism at the other. The two intermediate positions are possibilist in that they accept the intelligibility of possibilist discourse but actualist in that they attempt to dispense with its prima facie commitment to possibilia. All four positions have found advocates in the literature. Quine, in his less irenic moments, favours option (i); Forbes advocates option (ii), at least for certain parts of possibilist discourse; many philosophers, including Adams and myself, opt for (iii); while Lewis and Stalnaker have endorsed versions of (iv), that differ in how full-blooded they take the possible objects to be.. (shrink)

The theory of embodiment is used in providing an account of the identity of acts and in providing solutions to various puzzles concerning acts.

A number of philosophers have recently become receptive to the idea that, in addition to scientific or causal explanation, there may be a distinctive kind of metaphysical explanation, in which explanans and explanandum are connected, not through some sort of causal mechanism, but through some constitutive form of determination. I myself have long been sympathetic to this idea of constitutive determination or ‘ontological ground’; and it is the aim of the present paper to help put the idea on a firmer (...) footing - to explain how it is to be understood, how it relates to other ideas, and how it might be of use in philosophy. (shrink)

Selections seeks to provide an accurate and readable translation that will allow the reader to follow Aristotle's use of crucial technical terms and to grasp the details of his argument. Unlike anthologies that combine translations by many hands, this volume includes a fully integrated set of translations by a two-person team. The glossary--the most detailed in any edition--explains Aristotle's vocabulary and indicates the correspondences between Greek and English words. Brief notes supply alternative translations and elucidate difficult passages.

This article compares two philosophers who have a different theoretical origin: respectively, Arthur C. Danto and Jean-François Lyotard. Both of them are interested in the revolutionary character of Andy Warhol’s art. Danto as well as Lyotard argues that Warhol conceives the work of art as a machine: according to the former, it is a philosophical machine; according to the latter, it is a consumerist machine. Nonetheless, the two hypotheses converge on judging Warhol’s art as a turn in the history of (...) art and its relationship to the world. According to Danto, who follows Hegel here, Warhol at the same time interprets and transcends the 1960s and their Zeitgeist. But paradoxically, Warhol’s historical gesture, epitomized by his work Brillo Box, initiates the age of the “end of art”. According to Lyotard, on the contrary, Warhol represents the end of the critical power of modern art, to which the sublime alone can remediate. The two perspectives converge in the idea that the investigation of repetition is the very center of Warhol’s art. Art has now become the pivot of the Western capitalism and consumerist society. Warhol actually explores the different forms and modes of repetition (commodities, icons, symbols) and, in this way, anticipates the confrontation of contemporary art with the “finite infinite” represented by the media world. (shrink)

I provide a brief history and some philosophical reflections on the development of the method of abstraction in mathematics during the late nineteenth and early twentieth century.

I lay down a system of structural rules for various notions of ground and establish soundness and completeness.

Kit Fine develops a Fregean theory of abstraction, and suggests that it may yield a new philosophical foundation for mathematics, one that can account for both our reference to various mathematical objects and our knowledge of various mathematical truths. The Limits ofion breaks new ground both technically and philosophically.

I present a novel account of unconditional obligation and of its relationship to conditional obligation and bring this account to bear upon Chisholm's puzzle concerning contrary-to duty obligation.

I propose formulating identity criteria as generic statements of ground, thereby avoiding objections that have been made to the more usual formulations.

Plato on Knowledge and Forms brings together a set of connected essays by Gail Fine, in her main area of research since the late 1970s: Plato's metaphysics and epistemology. She discusses central issues in Plato's metaphysics and epistemology, issues concerning the nature and extent of knowledge, and its relation to perception, sensibles, and forms; and issues concerning the nature of forms, such as whether they are universals or particulars, separate or immanent, and whether they are causes. A specially written (...) introduction draws together the themes of the volume, which will reward the attention of anyone interested in Plato or in ancient metaphysics and epistemology. (shrink)

In recent years, a growing discussion about how we should design our cities has emerged, particularly for the more controversial modes of design such as “defensive,” “hostile,” or “disciplinary” architecture (i.e., benches on which one cannot sleep, or metal studs on which one cannot skate). Although this debate is relatively mature, many studies have argued that these design notions are undertheorized and are, thus, challenging to study from an empirical and normative perspective. In this paper, I will defne the most (...) common terms used in the literature and show how they are interconnected by utilizing a set of “conditions of adequacy” from philosophy to facilitate a more transparent and well-grounded discussion of them. Terms such as “hostile” and “defensive” design are underlined by several diferent phenomena, not just one as is sometimes commonly assumed. I will also show that these phenomena and their conceptualizations require—and sometimes force us to use—diferent moral reasons when justifying the utilization of diferent designs. (shrink)

Trust is often perceived as having great value. For example, there is a strong belief that trust will bring different sorts of public goods and help us preserve common resources. A related concept which is just as important, but perhaps not explicitly discussed to the same extent as “trust”, is “reliance” or “confidence”. To be able to rely on some agent is often seen as a prerequisite for being able to trust this agent. Up to now, the conceptual discussion about (...) the definition of trust and reliance has been rational in the sense that most people involved have offered arguments for their respective views, or against competing views. While these arguments rely on some criterion or other, these criteria are rarely explicitly stated, and to our knowledge, no systematic account of such criteria has been offered. In this paper we give an account of what criteria we should use to assess tentative definitions of “trust” and “reliance”. We will also offer our own well-founded definitions of “trust” and “reliance”. Trust should be regarded as a kind of reliance and we defend what we call “the accountability view” of trust, by appealing to the desiderata we identify in the first parts of the paper. (shrink)

The interest in "social sustainability" has recently increased in the field of urban development. We want societies, cities, and neighborhoods to be economically and environmentally sustainable, but we also want urban areas that are safe, diverse, walkable, and relaxing, just to mention a few examples. Strikingly, however, there is no consensus regarding what definition of "social sustainability" should be employed. Additionally, some people are skeptical about the prospect of finding a useful definition at all and claim it is impossible to (...) satisfactorily define the concept for various reasons, such as its complexity. A potential first step towards navigating this conceptual maze is to provide desiderata for a definition of social sustainability. We defend a list of nine desiderata and thereby create a theoretical framework for analyzing and constructing a definition of "social sustainability". We also examine the skeptical arguments and find that it is premature to conclude that the goal of finding a useful definition is hopeless. With the criteria in place, the future debate can proceed by assessing definitions of "social sustainability" in a more structured and transparent manner. This activity is of upmost importance if we want to create just cities. Keywords: Social Sustainability, Definition, Purposes and Aims, Conditions of Adequacy. (shrink)

For many years, some urban architecture has aimed to exclude unwanted groups of people from some locations. This type of architecture is called “defensive” or “hostile” architecture and includes benches that cannot be slept on, spikes in the ground that cannot be stood on, and pieces of metal that hinder one’s ability to skateboard. These defensive measures have sparked public outrage, with many thinking such measures lead to suffering, are disrespectful, and violate people’s rights. In this paper, it is argued (...) that these views are difficult to defend and that much more empirical research on the topic is needed. (shrink)

The core argument in this paper is that, to reconstruct the last unwritten section on Judging in Hannah Arendt's Life of the Mind , it is necessary to address what Arendt was doing with the book as a whole and how the different parts relate internally to one another. This is no easy matter, especially as the existing sections on Thinking and Willing are quite different in tone from one another. My proposition is that the work should be read as (...) a critique of the life of the `modern' mind, and especially of the differentiation of the modern mind into distinct and reified faculties. The work as a whole is an attempt to understand the distorted forms of modernization that result from the division of the life of the mind into opposing faculties. It is, so to speak, a critique of the combined and uneven development of the life of the modern mind. While Arendt famously argues that the activity of thinking itself conditions people against evildoing, the spectre that informs her analysis of both thinking and willing is the danger of nihilism inherent in these mental activities. The work raises vital questions concerning the conditions under which this danger is actualized and the means by which it might be averted. What this entails for our reconstruction of the missing section on judgment is that, rather than see it as the core of Arendt's contribution to political thought or as the promised solution to an impasse, we should explore the equivocations of judging. This aporetic reading of the text helps clarify Arendt's concerns over the separation of the life of the mind from the world and the role of both judging and understanding in renewing its connections to the world. (shrink)