We investigate connections between the syntactic and semantic distance of programs on an abstract, recursion theoretic level. For a certain rather restrictive notion of interdependency of the two kinds of distances, there remain only few and “unnatural” numberings allowing such close relationship. Weakening the requirements leads to the discovery of universal metrics such that for an arbitrary recursively enumerable family of functions a numbering compatible with such a metric can uniformly be constructed. We conclude our considerations with some implications on (...) learning theory. (shrink)

Adolf Menzel was one of the most important German artists of the 19th century, yet he is scarcely known outside his native land. In this study a leading art historian argues that Menzel deserves to be recognized not only as one of the greatest painters and draftsmen of his century but also as a master realist whose work engages profoundly with an extraordinary range of issues - artistic, scientific, philosophical and socio-political. Michael Fried explores Menzel's large and (...) fascinating oeuvre, and in so doing seeks to make the artist's achievement accessible to a wide audience. (shrink)

In Modal Logic as Metaphysics, Timothy Williamson claims that the possibilism-actualism (P-A) distinction is badly muddled. In its place, he introduces a necessitism-contingentism (N-C) distinction that he claims is free of the confusions that purportedly plague the P-A distinction. In this paper I argue first that the P-A distinction, properly understood, is historically well-grounded and entirely coherent. I then look at the two arguments Williamson levels at the P-A distinction and find them wanting and show, moreover, that, when the N-C (...) distinction is broadened (as per Williamson himself) so as to enable necessitists to fend off contingentist objections, the P-A distinction can be faithfully reconstructed in terms of the N-C distinction. However, Williamson’s critique does point to a genuine shortcoming in the common formulation of the P-A distinction. I propose a new definition of the distinction in terms of essential properties that avoids this shortcoming. (shrink)

Actualism is the doctrine that the only things there are, that have being in any sense, are the things that actually exist. In particular, actualism eschews possibilism, the doctrine that there are merely possible objects. It is widely held that one cannot both be an actualist and at the same time take possible world semantics seriously — that is, take it as the basis for a genuine theory of truth for modal languages, or look to it for insight into the (...) modal structure of reality. For possible world semantics, it is supposed, commits one to possibilism. In this paper I take issue with this view. To the contrary, I argue that one can take possible world semantics seriously without any commitment to possible worlds or possibilism and hence remain in full compliance with actualist scruples. Moreover, one can do so without without invoking either "ersatz" worlds or haecceities. (shrink)

In the United States, amid the fractious politics of attempting to achieve something close to universal access to basic health care, two impressions are likely to feed skepticism about the status of a right to universal access: the moral principles that underlie any right to universal access may seem incredibly "ideal," not well rooted in the society's actual fabric, and the necessary practical and political attempts to limit the scope of universally accessible care to make its achievement realistic may seem (...) marked less by moral rhyme and reason than by the pull of conflicting interests. I try to directly dispel the first of these impressions and to obliquely question the second. The immense political barriers to .. (shrink)

This paper traces the course of Prior’s struggles with the concepts and phenomena of modality, and the reasoning that led him to his own rather peculiar modal logic Q. I find myself in almost complete agreement with Prior’s intuitions and the arguments that rest upon them. However, I argue that those intuitions do not of themselves lead to Q, but that one must also accept a certain picture of what it is for a proposition to be possible. That picture. though, (...) is not inevitable. Rather, implicit in Prior’s own account is an alternative picture that has already appeared in various guises, most prominently in the work of Adams, Fine, Deutsch, and Almog. I, too, will opt for this alternative, though I will spell it out rather differently than these philosophers. I will then show that, starting with the alternative picture, Prior’s intuitions can lead instead to a much happier and more standard quantified modal logic than Q. The last section of the paper is devoted to the formal development of the logic and its metatheory. (shrink)

Actualism is a widely-held view in the metaphysics of modality that arises in response to the thesis of possibilism, the doctrine that, in addition to the things that actually exist — in particular, things that exist alongside us in the causal order — there are merely possible things as well, things that, in fact, fail to be actual but which could have been. The central motivation for possibilism is to explain what it is about reality that grounds such intuitively true (...) propositions as that Wittgenstein (who was childless) could have had children. In answer, possibilists argue that we must simply broaden our understanding of reality, of what there is in the broadest sense, beyond the actual, beyond what actually exists, so that it also includes the merely possible. In particular, says the possibilist, there are merely possible people, things that are not, in fact, people but which could have been. So, for the possibilist, the proposition that Wittgenstein could have had children is grounded in the fact that, among the possibilia, there are those that could have been his children. Actualism is (at the least) the denial of possibilism; to be an actualist is to deny that there are any possibilia. Put another way, for the actualist, there is no realm of reality, or being, beyond actual existence; to be is to exist, and to exist is to be actual. This article investigates the origins and nature of the debate between possibilists and actualists, with a particular focus on the implications of the debate for quantified modal logic. -/- . (shrink)

This book introduces generative grammar as an area of study and asks what it tells us about the human mind. Wolfram Hinzen lays the foundation for the unification of modern generative linguistics with the philosophies of mind and language. He introduces Chomsky's program of a 'minimalist' syntax as a novel explanatory vision of the human mind. He explains how the Minimalist Program originated in work in cognitive science, biology, linguistics, and philosophy, and examines its implications for work in these (...) fields. He considers the way the human mind is designed when seen as an arrangement of structural patterns in nature, and argues that its design is the product not so much of adaptive evolutionary history as of principles and processes that are ahistorical and internalist in character. Linguistic meaning, he suggests, arises in the mind as a consequence of structures emerging on formal rather than functional grounds. From this he substantiates an unexpected and deeply unfashionable notion of human nature. Clearly written in nontechnical language and assuming a limited knowledge of the fields it examines and links, Minimal Mind Design will appeal to a wide range of scholars in linguistics, philosophy, and cognitive science. It also provides an exceptionally clear insight into the nature and aims of Chomsky's Minimalist Program. (shrink)

The iterative conception of set is typically considered to provide the intuitive underpinnings for ZFCU (ZFC+Urelements). It is an easy theorem of ZFCU that all sets have a definite cardinality. But the iterative conception seems to be entirely consistent with the existence of “wide” sets, sets (of, in particular, urelements) that are larger than any cardinal. This paper diagnoses the source of the apparent disconnect here and proposes modifications of the Replacement and Powerset axioms so as to allow for the (...) existence of wide sets. Drawing upon Cantor’s notion of the absolute infinite, the paper argues that the modifications are warranted and preserve a robust iterative conception of set. The resulting theory is proved consistent relative to ZFC + “there exists an inaccessible cardinal number.”. (shrink)

Process modeling is ubiquitous in business and industry. While a great deal of effort has been devoted to the formal and philosophical investigation of processes, surprisingly little research connects this work to real world process modeling. The purpose of this paper is to begin making such a connection. To do so, we first develop a simple mathematical model of activities and their instances based upon the model theory for the NIST Process Specification Language (PSL), a simple language for describing these (...) entities, and a semantics for the latter in terms of the former, and a set of axioms for the semantics based upon the NIST Process Specification Language (PSL). On the basis of this foundation, we then develop a general notion of a process model, and an account of what it is for such a model to be realized by a collection of events. (shrink)

Life's Solution builds a persuasive case for the predictability of evolutionary outcomes. The case rests on a remarkable compilation of examples of convergent evolution, in which two or more lineages have independently evolved similar structures and functions. The examples range from the aerodynamics of hovering moths and hummingbirds to the use of silk by spiders and some insects to capture prey. Going against the grain of Darwinian orthodoxy, this book is a must read for anyone grappling with the meaning of (...) evolution and our place in the Universe. Simon Conway Morris is the Ad Hominen Professor in the Earth Science Department at the University of Cambridge and a Fellow of St. John's College and the Royal Society. His research focuses on the study of constraints on evolution, and the historical processes that lead to the emergence of complexity, especially with respect to the construction of the major animal body parts in the Cambrian explosion. Previous books include The Crucible of Creation (Getty Center for Education in the Arts, 1999) and co-author of Solnhofen (Cambridge, 1990). Hb ISBN (2003) 0-521-82704-3. (shrink)

Proposing a theory of the origins of human language ability and presenting an account of the early evolution of language, this text explains why humans are the only language-using animals and challenges the assumption that language is due to intelligence-- jacket cover.

Properly understood, Kant’s moral philosophy is incompatible with constitutivism. According to the constitutivist, being subject to the moral law cannot be a matter of free choice, and failure to c...

According to traditional theism, God alone exists a se, independent of all other things, and all other things exist ab alio, i.e., God both creates them and sustains them in existence. On the face of it, divine "aseity" is inconsistent with classical Platonism, i.e., the view that there are objectively existing, abstract objects. For according to the classical Platonist, at least some abstract entities are wholly uncreated, necessary beings and, hence, as such, they also exist a se. The thesis of (...) theistic activism purports to reconcile divine aseity with a robust Platonism. Specifically, the activist holds that God creates the abstract objects no less than the contingent concrete objects of the physical universe and hence that, like all created things, they exist ab alio after all, their necessity notwithstanding. But many philosophers believe a severe roadblock for activism remains — a problem known as the bootstrapping objection. Despite widespread faith in the deliverances of this argument, in this paper I show that the bootstrapping objection is open to significant objections on several fronts. (shrink)

By registering different health benefits on a common scale, CEA allows us to assess the relative social importance of different health care interventions and opens the way for the allocation decisions of health care policy. If it is really to be effective, however, CEA must be recalibrated so that it better reflects some of our widely held beliefs about the merits of different kinds of treatment.

First published in 1989. Routledge is an imprint of Taylor & Francis, an informa company.

There is resistance to policies that would reduce overall consumption levels to promote sustainability. In part, this resistance is aided by the economic concept of consumer sovereignty (CS) and its presumption that choice promotes wellbeing. We investigate the concept of consumer sovereignty in the context of deepening concerns about sustainability and scrutinise whether the two concepts are compatible. We draw on new findings in psychology on human decision-making traits; we take into account increasing awareness about human dependencies on ‘functioning’ ecosystems (...) and uncertainties on how ecosystems, human activities and human wellbeing are interlinked. We conclude that commitment to the concept of consumer sovereignty is incompatible with sustainability due to human characteristics, the difficult-to-predict behaviour of ecological systems and ignorance about the impact of human action on natural systems. We propose that the choice-set of available goods and services on markets should be constrained when consumption patterns can be linked to degradation of services provided by nature when those services are seen as crucial for human wellbeing. We advocate constraining the available choice-set through established governmental institutions aided by deliberative processes that engage members of the general public. Finally, we acknowledge that such processes are imperfect; nevertheless, we foresee that they will be essential for fostering wise decision-making and moving towards sustainability. (shrink)

This pioneering book lays new foundations for the study of reference and truth.

This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.

This chapter explores some fundamental consequences of the correspondence between physical process and computations. Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be considered formally undecidable. The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of calculation (...) that reproduce the outcome without tracing each step. Computational irreducibility is common among the systems investigated in mathematics and computation theory, but it may well be the exception rather than the rule, since most physical questions may be answerable only through irreducible amounts of computation. (shrink)

In this paper, an argument of Alvin Plantinga's for the existence of abstract possible worlds is shown to be unsound. The argument is based on a principle Plantinga calls "Quasicompactness", due to its structural similarity to the notion of compactness in first-order logic. The principle is shown to be false.

The year is 1919. Walter Benjamin flees his overbearing father to scrape a living as a jobbing critic. Ludwig Wittgenstein signs away his inheritance to teach schoolchildren in a provincial Austrian village, seeking spiritual clarity. Martin Heidegger renounces his faith and align his fortunes with the phenomenological school of Edmund Husserl. Ernst Cassirer sketches a new schema of human culture at the back of a cramped Berlin tram. The stage is set for a great intellectual drama, which will unfold over (...) the next decade. The lives and thought of this quartet will converge and intertwine as each gains world historical significance, between them remaking philosophy. Time of the Magicians tells the story of this revolution in Western thought through the remarkable and turbulent lives of its four protagonists, showing philosophy not gifted from on high but worked out in the mess of everyday life, and illuminating with rare clarity their ideas. (shrink)

This interdisciplinary book considers the relationship between language and thought from a philosophical perspective, drawing both on the philosophical study of language and the purely formal study of grammar, and arguing that the two should align. The claim is that grammar provides homo sapiens with the ability to think in certain grammatical ways and that this in turn explains the vast cognitive powers of human beings. Evidence is considered from biology, the evolution of language, language disorders, and linguistic phenomena.

In studying the early history of mathematical logic and set theory one typically reads that Georg Cantor discovered the so-called Burali-Forti (BF) paradox sometime in 1895, and that he offered his solution to it in his famous 1899 letter to Dedekind. This account, however, leaves it something of a mystery why Cantor never discussed the paradox in his writings. Far from regarding the foundations of set theory to be shaken, he showed no apparent concern over the paradox and its implications (...) whatever. Against this account, I will argue here that in fact Cantor never saw any paradox at all, but that his conception of set at that time, and already as far back as 1883, was one in which the paradoxes cannot arise. (shrink)

Epistemologists often offer theories of justification without paying much attention to the variety and diversity of locutions in which the notion of justification appears. For example, consider the following claims which contain some notion of justification: B is a justified belief, S's belief that p is justified, p is justified for S, S is justified in believing that p, S justifiably believes that p, S's believing p is justified, there is justification for S to believe that p, there is justification (...) for S's believing p, and S has a justification for believing that p. In addition to these passive uses of the notion of justification, there are active uses as well: S justified his belief in p, believing e justifies believing p, etc. The syntactic variety involves semantic difference as well. For example, the proposition S has a justification for believing that p does not entail that S believes p, whereas the proposition S justifiably believes that p does entail that S believes p. Our ultimate goal is to show that this diversity is only superficial by arguing that there is a basic kind of justification. On the way, however, we shall argue that there are three central uses of a notion of justifica- tion in the above list: propositional justification (as in p is justified for S), personal justification (as in S is justified in believing that p) and doxastic justification (as in S's believing p is justified). Our preliminary argument will be that the multiplicity above can be explained in terms of these three locutions, and the substance of our argument will be to show that one of these three is the basic kind of justification. Success in this task will thereby justify, at least in part, the practice of contem- porary epistemologists. Our conclusions, however, shall not be of much comfort to contemporary epistemology, for the way in which the apparent diversity in the uses of the notion of justification is eliminated undermines much of recent epistemology. (shrink)