In his early lecture note Versuch einiger Betrachtungen über den Optimismus (1759) a young supporter of metaphysical optimism called Immanuel Kant tested the Leibnizian optimism by posing some counter-arguments against it only to falsify them. His counter-arguments were very inventive and they feature often in modern scholarship on Leibniz. In this paper I will present Kant’s main arguments and evaluate them. I will argue that Kant’s understanding on Leibnizian optimism is little misguided and for this reason his own positive counter-argument (...) despite its ingeniousness is problematic. His second solution to the problem is comparable to the doctrine of metaphysical optimism, but fails also for the same reason as the first one. -/- . (shrink)

With this book we see a philosopher well steeped in the Western tradition thinking through ancient Eastern disciplines, meditating on what it means to learn to breathe, and urging us all at the dawn of a new century to rediscover indigenous Asian cultures. Yogic tradition, according to Irigaray, can provide an invaluable means for restoring the vital link between the present and eternity--and for re-envisioning the patriarchal traditions of the West. Western, logocentric rationality tends to abstract the teachings of yoga (...) from its everyday practice--most importantly, from the cultivation of breath. Lacking actual, personal experience with yoga or other Eastern spiritual practices, the Western philosophers who have tried to address Hindu and Buddhist teachings--particularly Schopenhauer--have frequently gone astray. Not so, Luce Irigaray. Incorporating her personal experience with yoga into her provocative philosophical thinking on sexual difference, Irigaray proposes a new way of understanding individuation and community in the contemporary world. She looks toward the indigenous, pre-Aryan cultures of India--which, she argues, have maintained an essentially creative ethic of sexual difference predicated on a respect for life, nature, and the feminine. Irigaray's focus on breath in this book is a natural outgrowth of the attention that she has given in previous books to the elements--air, water, and fire. By returning to fundamental human experiences--breathing and the fact of sexual difference--she finds a way out of the endless sociologizing abstractions of much contemporary thought to rethink questions of race, ethnicity, and globalization. (shrink)

This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world.

The focus of this paper will be on singular thoughts. In the first section I will present Jeshion’s cognitivism; a view that holds that one should characterize singular thoughts by their cognitive roles. In the second section I will argue that, contrary to Jeshion’s claims, results from studies of object tracking in cognitive psychology do not support cognitivism. In the third section I will discuss Jeshion’s easy transmission of singular thought and argue that it ignores a relevant distinction between general (...) and specific understanding of names. Finally, the last section will argue that conscious attention should replace Jeshion’s significance condition as a necessary condition for one to have a singular thought. The paper will show that we need to take seriously the acquaintance requirement for singular thoughts, as even the easy transmission of singular thoughts with the use of names will be called into question. (shrink)

A picture of the world as chiefly one of discrete objects, distributed in space and time, has sometimes seemed compelling. It is however one of the main targets of Henry Laycock's book; for it is seriously incomplete. The picture, he argues, leaves no space for "stuff" like air and water. With discrete objects, we may always ask "how many?," but with stuff the question has to be "how much?" Laycock's fascinating exploration also addresses key logical and linguistic questions about the (...) way we categorize the many and the much. (shrink)

French historian Mona Ozouf argues that French feminism lacks the rancor and resentment of its counterpart in America and explains why this placid brand of feminism is uniquely French. Ozouf portrays ten French women of letters whose lives span the period from the eve of the French Revolution to the resurgence of the feminist movement in the late 20th century.

Following Jacques Derrida’s reflections on witnessing and testimony, this article proposes a discontinuous economy between human witnessing and the nonhuman framing of any such instituted work...

This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics.

자신의 저술에서 민주주의를 옹호하거나 민주주의자를 자처한 적이 전혀 없음에도 불구하고 루소의 정치철학이 현대 민주주의의 정치원칙를 제공했다는데는 아무도 이의를 제기하지 않는다. 그렇다면 그 정치철학의 어떤 요인이 루소를 현대 민주주의 확립에 있어 가장 영향력 있는 사상가로 꼽히게 만드는가? 본고에서 연구자들은 루소 사상과 민주주의 연관성, 그리고 일반의지론에 대한 기존 연구들의 성과와 한계를 살펴본 후, 루소가 제시하는 “정치적 권리의 올바른 원칙”으로서의 “일반의지” 개념이 고전고대의 정치사상, 특히 아리스토텔레스의 『정치학』을 넘어 민주주의 정치철학의 현대적 전회에 어떤 기여를 하였는지 논한다.BR공화주의 관점에서 볼 때 아리스토텔레스와 루소는 연속성을 가졌다고 생각되어 (...) 왔다. 하지만 본 연구자들은 아리스토텔레스의 『정치학』과 루소의 『사회계약론』을 목차별로 비교·분석한 결과, “민주정(民主政)”에 관해 루소는 그 개념, 내용 및 역사적 평가를 아리스토텔레스와 거의 공유했음에도 불구하고, “일반의지”개념을 축으로 하여, 국가통치의 기조를 덕치주의에서 법치주의 또는 입헌주의로, 통치의 인적 기반을 ‘폴리스적 동물’에서, ‘자유롭고 평등한 인간으로서 주권자 시민’으로 혁명적으로 전형(轉形)하여, 태생적·지연적 인연이 아니라, 주권자 시민들이 이성적으로 동의한 정치적 권리에 근거하여 정립한 헌법적 원칙들에 의거하여 공화국 건국과 통치의 프로젝트를 제시했다는 특이점을 밝혀냈다. 바로 이 헌법기반의 공화국이야말로 현대적 국민국가의 정상적 통치모델로 간주되는 입헌민주주의에 다름 아니며, 결과적으로 루소는, ‘주민’ 또는 ‘인민’의 자연적 필요에 따라 자연발생적으로 성립되는 폴리스의 생태를 논한 현대 이전의 전형적 국가통치론으로서 아리스토텔레스적 개념의 정치학에서 벗어나, 자신의 이성적 국가능력을 자각하여 건국의 협약 당사자로 나선 ‘주권자 시민’이 국가 통치의 담당자라는 입론을 바탕으로 탈(脫)아리스토텔레스적 현대 정치학을 정립하였다. (shrink)

This paper explains why spacetime singularities do not constitute a breakdown of physical laws, and points out that the difference between the metrics at singularities and those outside of singularities is factual, rather than nomological.

In philosophy, “singular thought” refers to our capacity to represent entities as individuals, rather than as possessors of properties. Philosophers who defend singularism argue that perception allows us to mentally latch onto objects and persons directly, without conceptualizing them as being of a certain sort. Singularists assume that singular thought forms a unified psychological kind, regardless of the nature of the individuals represented. Empirical findings on the special psychological role of persons as opposed to inanimates threaten singularism. They raise the (...) possibility that tracking individuals specifically as persons might require conceptualizing them in certain ways, for example, as persons. In this paper, we take such a possibility seriously but ultimately reject it. Instead, we propose to revise a prominent singularist theory, the theory of mental files, in order to accommodate data on the psychological distinctiveness of persons: We advocate the postulation of perceptual person-files. Perceptual tracking via person-files is different from object-tracking but also from descriptive classification under the sortal concept PERSON. (shrink)

Linguistic ontologists and antilinguistic, ‘serious’ ontologists both accept the inference from ‘Fido is a dog’ to ‘Fido has the property of being a dog’ but disagree about its ontological consequences. In arguing that we are committed to properties on the basis of these transformations, linguistic ontologists employ a neo-Fregean meta-ontological principle, on which the function of singular terms is to refer. To reject this, serious ontologists must defend an alternative. This paper defends an alternative on which the function of singular (...) terms is not generally to refer and on which they are generally ontologically noncommittal. This is the best way to reject linguistic, ‘easy’ arguments for the existence of properties. The account recommends neutralism about quantification (drawing on Barcan Marcus and Meinongianism), coherently bringing together two important yet uncombined meta-ontological movements. Moreover, it employs Ramseyan insights about the transformations to provide a nonreductionist, non-error-theoretic redundancy approach to explicit talk about properties. (shrink)

ArgumentOne of the first high-altitude observatories was a hotel. Established in 1823, the chalet on Mount Faulhorn became a highpoint of nineteenth-century science. In this paper, I take this mountain as my entry point into the examination of the special attraction that mountains exerted on scientists. I argue that Mount Faulhorn stood for three different conceptions of the usefulness of the mountain in science: (1) in observation networks, stations were usually chosen for pragmatic rather than scientific reasons, but mountains representedsingularspots (...) in such networks, which deserved special attention; (2) the mountain also was amicrocosmwhere altitude differences were thought to capture essential features of latitude differences; (3) the mountain was sometimes no more than amacro-toolfor the pursuit of science, just a middle ground between the heaven and the earth. (shrink)

Aristotle’s categorical syllogistic is the first formal deductive system in the history of formal sciences. Most parts or elements of the system are validated by modern (first-order) mathematical logic, but the system is quite limited in scope, as it is incapable of analyzing inferences other than the ‘figure syllogisms’ consisting of a couple of_ a-e-i-o_ premises and an _a-e-i-o_ conclusion, containing three ‘moderately’ universal terms – terms that express neither a highest genus nor a lowest species – each of which (...) is common to a different couple of propositions out of the three. Logicians in the following ages dealt with various questions concerning the addition of various (novel) logical forms into this limited system, among which are singular predications, i.e. categorical propositions with a singular term as subject, and the most common choice has been interpreting singular predications as _universal _predications. This paper tries to take a strictly formal perspective on the system of categorical syllogisms, and argues in detail for a much simpler and fairly effective assimilation or translation scheme for singular predications. The key to the proposed scheme is the preservation of the supposed inferential relation between opposite singular predications, namely _contradiction_. It is argued that the resulting _singularized _syllogistic moods, which are also validated by first-order logic (under its standard renderings of _a-e-i-o_ and singular predications), promote in turn the mentioned type of treatment, since they call for the employment of two of the four subaltern moods of the system, disregarded by Aristotle, which are _formally _there. (shrink)

A singular thought about an object o is one that is directly about o in a characteristic way—grasp of that thought requires having some special epistemic relation to the object o, and the thought is ontologically dependent on o. One account of the nature of singular thought exploits a Russellian Structured Account of Propositions, according to which contents are represented by means of structured n-tuples of objects, properties, and functions. A proposition is singular, according to this framework, if and only (...) if it contains an object as a constituent. One advantage of the framework of Russellian Structured propositions is that it promises to provide a metaphysical basis for the notion of a singular thought about an object, grounding it in terms of constituency. In this paper, we argue that the attempt to ground the peculiar features of singular thoughts in terms of metaphysical constituency fails, and draw some consequences of our discussion for other debates. (shrink)

This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by our concepts of denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions 'denotes', 'extension' and 'true' are context-sensitive. The second, inspired by a brief, tantalizing remark of Godel's, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities (...) is presented and applied to a wide variety of versions of the definability paradoxes, Russell's paradox, and the Liar paradox. Keith Simmons argues that the singularity theory satisfies the following desiderata: it recognizes that the proper setting of the semantic paradoxes is natural language, not regimented formal languages; it minimizes any revision to our semantic concepts; it respects as far as possible Tarski's intuition that natural languages are universal; it responds adequately to the threat of revenge paradoxes; and it preserves classical logic and semantics. Simmons draws out the consequences of the singularity theory for deflationary views of our semantic concepts, and concludes that if we accept the singularity theory, we must reject deflationism. (shrink)

Is singular causation best understood within a dispositionalist framework? Although a positive answer has not yet been wholly developed, different philosophers have made some positive contributions suggesting that it is. Against these suggestions, I claim that any possible account of singular causation in terms of real, irreducible, dispositions conveys unsolvable flaws in its very metaphysical foundations.

In his posthumously published Broken Hegemonies, Reiner Schürmann shows how the ‘tragic denial’ of the differend – between the universal and the singular, natality and mortality, institution and destitution – gives rise to hegemonies. When ‘the sovereign fantasm’ that grounds and anchors the hegemony expires, the hegemony gets withered away. Taking Schürmann’s insights as point of departure, this paper attempts to think of singularisation to come in messianic sense, as truly anarchic thought worthy of our time, that is, to think (...) without hegemonies. Such a messianic/eschatological tragic-anarchic thought can’t be understood as the dialectical operation of the universal’s antagonism to the particular. Beyond the dialectical opposition of the universal and the particular, differend of the singularisation to come can only be understood as the unheard of an-arché, that is, living without ‘why’. (shrink)

Historians have thoroughly documented the development of mercury-based silver refining in Spanish America in the late sixteenth century, and its use for over 300 years on an industrial scale unknown in Europe. However, we currently lack any consensus about the significance of this technology in the global history of knowledge. This article critically reassesses the invention and improvement of this refining method with the aim of addressing two interrelated issues. Firstly, how experiential knowledge and practical skills in silver refining were (...) deliberately harnessed to solve a specific technical problem. Secondly, how economic incentives and patronage set the stage for empirical practices and a collaborative culture that facilitated the widespread use of this novel technique. In so doing, this article places silver refining within the theoretical constructs and historiography of useful knowledge, and bridges narratives that have remained largely isolated. (shrink)

This article is a critical notice of Bob Hale and Crispin Wright's *The Reason's Proper Study* (OUP). It focuses particularly on their attempts (crucial to their neo-logicist project) to say what a singular term is. I identify problems for their account but include some constructive suggestions about how it might be improved.

Recent work on emergence in physics has focused on the presence of singular limit relations between basal and upper-level theories as a criterion for emergence. However, over-emphasis on the role of singular limit relations has somewhat obscured what it means to say that a property or behaviour is emergent. This paper argues that singular limits are not central to emergence and develops an alternative account of emergence in terms of the failure of basal explainability. As a consequence, emergence and reduction, (...) long held to be two sides of the same coin in the emergentist tradition, are largely decoupled. (shrink)

What is required for an individual to entertain a singular thought about an object they have encountered before but that is currently no longer within their perceptual range? More specifically, does the individual have to think about the object as having been encountered in the past? I consider this question against the background of the assumption that non-human animals are cognitively ‘stuck in the present’. Does this mean that, for them, ‘out of sight is out of mind’, as, e.g., Schopenhauer (...) seems to have thought? I suggest an alternative answer, also drawing on some empirical work on animal cognition. (shrink)

It is widely supposed that if there is to be a plausible connection between the truth of a de re attitude report about a subject and that subject’s possession of a singular thought, then ‘acquaintance’-style requirements on singular thought must be rejected. I show that this belief rests on poorly motivated claims about how we talk about the attitudes. I offer a framework for propositional attitude reports which provides both attractive solutions to recalcitrant puzzle cases and the key to preserving (...) acquaintance constraints. The upshot is that there is an independently motivated response to the principal argument against acquaintance. (shrink)

Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore (...) invited prominent computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate. (shrink)

This paper contains two traditions of diagrammatic studies namely one, the Euler–Venn–Peirce diagram and the other, following tradition of Aristotle, the square of oppositions. We put together both the traditions to study representations of singular propositions, their negations and the inter relationship between the two. Along with classical negation we have incorporated negation of another kind viz. absence. We have also considered the changes that take place in the context of open universe.

A singular thought can be characterized as a thought which is directed at just one object. The term ‘thought’ can apply to episodes of thinking, or to the content of the episode (what is thought). This paper argues that episodes of thinking can be just as singular, in the above sense, when they are directed at things that do not exist as when they are directed at things that do exist. In this sense, then, singular thoughts are not object-dependent.

Neo-Fregeans take their argument for arithmetical realism to depend on the availability of certain, so-called broadly syntactic tests for whether a given expression functions as a singular term. The broadly syntactic tests proposed in the neo-Fregean tradition are the so-called inferential test and the Aristotelian test. If these tests are to subserve the neo-Fregean argument, they must be at least adequate, in the sense of correctly classifying paradigm cases of singular terms and non-singular terms. In this paper, I pursue two (...) main goals. On the one hand, I show that the tests’ current state-of-the-art formulations are inadequate and, hence, cannot subserve the neo-Fregean argument. On the other hand, I propose revisions that are adequate and, hence, can subserve this argument. (shrink)

Singular causal explanations cite explicitly, or may be paraphrased to cite explicitly, a particular factor as the cause of another particular factor. During recent years there has emerged a consensus account of the nature of an important feature of such explanations, the distinction between a factor regarded correctly in a given context of inquiry as ‘the cause’ of a given result and those other causally relevant factors, sometimes called ‘mere conditions’, which are not regarded correctly in that context of inquiry (...) as the cause of that result. In this paper that consensus account is characterized and developed. The developed version is then used to illuminate some recent discussions of singular causal explanations. (shrink)

One of the goals of a certain brand of philosopher has been to give an account of language and linguistic phenomena by means of showing how sentences are to be translated into a "logically perspicuous notation" (or an "ideal language"—to use passe terminology). The usual reason given by such philosophers for this activity is that such a notational system will somehow illustrate the "logical form" of these sentences. There are many candidates for this notational system: (almost) ordinary first-order predicate logic (...) (see Quine [1960]), higher-order predicate logic (see Parsons [1968, 1970]), intensional logic (see Montague [1969, 1970a, 1970b, 1971]), and transformational grammar (see Harrnan [1971]), to mention some of the more popular ones. I do not propose to discuss the general question of the correctness of this approach to the philosophy of language, nor do I wish to adjudicate among the notational systems mentioned here. Rather, I want to focus on one problem which must be faced by all such systems—a problem that must be discussed before one decides upon a notational system and tries to demontrate that it in fact can account for all linguistic phenomena. The general problem is to determine what we shall allow as linguistic data; in this paper I shall restrict my attention to this general problem as it appears when we try to account for certain words with non-singular reference, in particular, the words that are classified by the count/ mass and sortal/non-sortal distinctions. (shrink)

The radical evolutionary step that divides human decision-making from that of nonhumans is the ability to excite the reward process for its own sake, in imagination. Combined with hyperbolic over-valuation of the present, this ability is a potential threat to both the individual's long term survival and the natural selection of high intelligence. Human belief is intrinsically or under-founded, which may or may not be adaptive.

In this paper I challenge the widespread assumption that the conditions for singular reference are more or less the same as the conditions for singular thought. I claim that we refer singularly to things without thinking singularly about them more often than it is usually believed. I first argue that we should take the idea that singular thought is non-descriptive thought very seriously. If we do that, it seems that we cannot be so liberal about what counts as acquaintance; only (...) perception will do. I also briefly discuss and reject semantic instrumentalism. Finally, I argue that while singular reference is cheap, singular thought comes only at a price. (shrink)

In many people, caffeine causes slight muscle tremors, particularly in their hands. In general, the Caffeine → Muscle Tremors causal connection is a noisy one: someone can drink coffee and experience no hand shaking, and there are many other factors that can lead to muscle tremors. Now suppose that Jane drinks several cups of coffee and then notices that her hands are trembling; an obvious question is: did this instance of coffee drinking cause this instance of hand-trembling? Structurally similar questions (...) arise throughout everyday life: Did this pressing of the ‘k’ key cause this change in the pixels on the computer monitor? Did these episodes of smoking cause this lung cancer? Did this studying cause this test score? And so on. These questions all ask about singular causation in a particular situation, in contrast with general causation across multiple cases. They are thus particularly salient in situations in which we care about that specific case, as in many legal contexts, social interactions, physical explanations of anomalous events, and more. (shrink)

De re or singular thoughts are, intuitively, those essentially or constitutively about a particular object or objects; any thought about different objects would be a different thought. How should a philosophical articulation or thematization of their nature look like? In spite of extended discussion of the issue since it was brought to the attention of the philosophical community in the late fifties by Quine (1956), we are far from having a plausible response. This is glaringly revealed by the contrasting recent (...) takes on the issue by writers such as Soames (2005) – who adopts the view by Donnellan (1979) to be outlined presently – and Jeshion (2001), otherwise sharing a similar direct-reference approach to the prototypical expression of those contents. Discussing the matter in connection with the status of the Kripkean category of the contingent a priori in the just mentioned article, Donnellan (1979) argued that what can be properly classified as knowable a priori about utterances like those involving ‘one meter’ or ‘Neptune’ famously proposed by Kripke (1980) cannot be the very same singular content that is contingent; he distinguished to that end between knowing a true proposition expressed by an utterance, and knowing that an utterance expresses a true proposition. (Thus, for instance, if, while listening to an utterance in a language that I do not know, I am told by a reliable person who knows the language and whom I trust that the utterance is true, I come thereby to know that the sentence expresses a truth, without knowing the truth that it expresses.) Evans (1979) replied that, for a very specific sort of cases involving “descriptive names”, a related proto-two-dimensionalist account should be preferred, on which it is not the singular contingent content, but rather a general descriptive one which is knowable a priori. In a series of papers, Robin Jeshion (2000, 2001) has recently attacked Donnellan's proposal, arguing in favour of the most straightforward interpretation of Kripke's claim: in the relevant cases, the very same singular content can be both contingent and knowable a priori. In this paper, I will appeal to a generalized version of two-dimensional semantics to advance an account of the Kripkean cases along the lines of Evans's, and I will argue that Jeshion's compelling arguments against Donnellan's view do not apply to this version. (shrink)

This essay examines Italian philosopher Adriana Cavarero's ontology of uniqueness through a reading of Alex Haley's novel Roots, and the recent television adaptation of that book. If Cavarero has insisted throughout her work that we need to challenge the philosophical privileging of abstract universality and focus instead on the irreducibility of embodied singularity, and if such a move in her work has always relied on a feminist analysis of the role women play in such a drama, I argue that (...) attention to issues of race and the institution of slavery both supports and complicates her analysis in meaningful ways. (shrink)

The notion of singular (or de re) thought has become central in philosophy of mind and language, yet there is still little consensus concerning the best way to think about the nature of singular thought. Coinciding with recognition of the need for more clarity about the notion, there has been a surge of interest in the concept of a mental file as a way to understand what is distinctive about singular thought. What isn't always clear, however, is what mental files (...) are meant to be, and why we should believe that thoughts that employ them are singular as opposed to descriptive. This volume brings together original chapters by leading scholars which aim to examine and evaluate the viability of the mental files framework for theorizing about singular thought. (shrink)

What happens when machines become more intelligent than humans? One view is that this event will be followed by an explosion to ever-greater levels of intelligence, as each generation of machines creates more intelligent machines in turn. This intelligence explosion is now often known as the “singularity”. The basic argument here was set out by the statistician I.J. Good in his 1965 article “Speculations Concerning the First Ultraintelligent Machine”: Let an ultraintelligent machine be defined as a machine that can (...) far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an “intelligence explosion”, and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make. The key idea is that a machine that is more intelligent than humans will be better than humans at designing machines. So it will be capable of designing a machine more intelligent than the most intelligent machine that humans can design. So if it is itself designed by humans, it will be capable of designing a machine more intelligent than itself. By similar reasoning, this next machine will also be capable of designing a machine more intelligent than itself. If every machine in turn does what it is capable of, we should expect a sequence of ever more intelligent machines. This intelligence explosion is sometimes combined with another idea, which we might call the “speed explosion”. The argument for a speed explosion starts from the familiar observation that computer processing speed doubles at regular intervals. Suppose that speed doubles every two years and will do so indefinitely. Now suppose that we have human-level artificial intelligence 1 designing new processors. Then faster processing will lead to faster designers and an ever-faster design cycle, leading to a limit point soon afterwards. The argument for a speed explosion was set out by the artificial intelligence researcher Ray Solomonoff in his 1985 article “The Time Scale of Artificial Intelligence”.1 Eliezer Yudkowsky gives a succinct version of the argument in his 1996 article “Staring at the Singularity”: “Computing speed doubles every two subjective years of work.. (shrink)

The concept of a 'Singularity' is particularly intriguing as it is draws not just on philosophical but also neuroscientific issues. As a neuroscientist, perhaps my best contribution here therefore, would be to provide some reality checks against the elegant and challenging philosophical arguments set out by Chalmers. Aconvenient framework for addressing the points he raises will be to give my personal scientific take on the three basic questions summarised in the Conclusions section.

The singularity space consists of all germs , with X a Noetherian scheme and x a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a complete, separable space for the metric given by the order to which jets agree after base change. In the terminology of descriptive set-theory, the classification of singularities up to analytic extensions of scalars is a smooth problem. Over , the following two classification (...) problems up to isomorphism are then also smooth: analytic germs; and polarized schemes. (shrink)