A common objection to Russell's theory of descriptions concerns incomplete definite descriptions: uses of (for example) ‘the book is overdue’ in contexts where there is clearly more than one book. Many contemporary Russellians hold that such utterances will invariably convey a contextually determined complete proposition, for example, that the book in your briefcase is overdue. But according to the objection this gets things wrong: typically, when a speaker utters such a sentence, no facts about the context or the speaker's communicative (...) intentions single out a particular description-theoretic proposition as the proposition expressed. However, this is an objection only if it is assumed that successful linguistic communication requires the hearer to identify a proposition uniquely intended by the speaker. We argue that this assumption is mistaken. On our view, no proposition, descriptive or referential, is uniquely intended in such a context; thus, no proposition can nor need be identified as the proposition expressed. One significant upshot is that, once the aforementioned assumption is rejected, incompleteness no longer poses a threat to Russell's theory of descriptions. (shrink)

The frame problem is a fundamental challenge in AI, and the Lucas-Penrose argument is supposed to show a limitation of AI if it is successful at all. Here we discuss both of them from a unified Gödelian point of view. We give an informational reformulation of the frame problem, which turns out to be tightly intertwined with the nature of Gödelian incompleteness in the sense that they both hinge upon the finitarity condition of agents or systems, without (...) which their alleged limitations can readily be overcome, and that they can both be seen as instances of the fundamental discrepancy between finitary beings and infinitary reality. We then revisit the Lucas-Penrose argument, elaborating a version of it which indicates the impossibility of information physics or the computational theory of the universe. It turns out through a finer analysis that if the Lucas-Penrose argument is accepted then information physics is impossible too; the possibility of AI or the computational theory of the mind is thus linked with the possibility of information physics or the computational theory of the universe. We finally reconsider the Penrose’s Quantum Mind Thesis in light of recent advances in quantum modelling of cognition, giving a structural reformulation of it and thereby shedding new light on what is problematic in the Quantum Mind Thesis. Overall, we consider it promising to link the computational theory of the mind with the computational theory of the universe; their integration would allow us to go beyond the Cartesian dualism, giving, in particular, an incarnation of Chalmers’ double-aspect theory of information. (shrink)

Sober (1984) has considered the problem of determining the evidential support, in terms of likelihood, for a hypothesis that is incomplete in the sense of not providing a unique probability function over the event space in its domain. Causal hypotheses are typically like this because they do not specify the probability of their initial conditions. Sober's (1984) solution to this problem does not work, as will be shown by examining his own biological examples of common cause explanation. The (...) proposed solution will lead to the conclusion, contra Sober, that common cause hypotheses explain statistical correlations and not matchings between event tokens. (shrink)

Frege seems committed to the thesis that the senses of the fundamental notions of arithmetic remain stable and are stably grasped by thinkers throughout history. Fully competent practitioners grasp those senses clearly and distinctly, while uncertain practitioners see them, the very same senses, “as if through a mist”. There is thus a common object of the understanding apprehended to a greater or lesser degree by thinkers of diverging conceptual competence. Frege takes the thesis to be a condition for the possibility (...) of the rational intelligibility of mathematical practice. I argue however that the idea that senses could be grasped as a matter of degree is in tension with the constitutive theses that Frege held with regard to sense. Given those theses, there can in fact be no such thing as misty grasp of sense, since any uncertainty as to the logical features of a given sense will entail that one is getting hold of a different sense or of no sense at all. I consider various ways of resolving the tension and conclude that Frege’s thesis cannot be defended if we take it to be a thesis about our competence with concepts. This leaves unresolved what I call the problem of normative guidance, that is, the problem of explaining how the fundamental notions of logic and arithmetic can provide inferential guidance to thinkers. (shrink)

Although there has been little written to date that speaks directly to problems of religious luck, described in other terms these problems have a long history. Contemporary contributors to the literature have referred to “soteriological luck” (Anderson 2011) “salvific luck” (Davidson 1999) and “religious luck” (Zagzebski 1994). Using “religious” as the unifying term, Part I of this monograph begins with the need a more comprehensive taxonomy. Serious philosophic interest in moral and epistemic luck took hold only after comprehensive taxonomies for (...) those kinds of luck were introduced, but this has not yet been done for religious luck. Even if incomplete, the more comprehensive taxonomy, as introduced in Chapter One enables better diagnostic questions to be raised for researchers. Emerging questions about potentially ‘luck leaning’ attributions of good/bad religious luck, and of the possibility and desirability of “luck free theologies,” are questions which I hope to motivate as of central interest to researchers in philosophy of religion, both secular and religious. The taxonomy highlights why we should take two concerns — with the concept of religious luck and with asymmetric or sharply differential ascriptions of religious value — to be inextricably connected. The connection between attributing good/bad luck and violating inductive norms is easy to see upon reflection. One related distinction common in recent work on epistemic luck is that between benign evidential luck (‘benign’ because consistent with justified belief and knowledge), and malign (positive epistemic status undercutting) veritic luck. How, philosophically, this distinction should be understood is an especially acute problem when it comes to testimonial trust, and to intellectually virtuous or vicious ways of assessing testimonial claims, and sources of claims. So the chapter concludes with development of the case of Tess, as an example of testimonial environmental veritic luck. The Tess case is constructed to be formally analogous to the environmental veritic luck operating in fake barn cases (where visual perception rather than reception of testimony is the source of the agent’s belief). There does seem to be an intrinsic connection between epistemic assessment of the agent’s beliefs and the inductive context in which their own and their religious community’s inquiry takes place. This will allow for some potentially powerful thought experiments in successive chapters, about luck, risk, and questions of epistemic in/justice as they pertain to religious faith ventures. (shrink)

이 글은 『지성 교정론』의 미완의 이유로 제기된 다양한 가설들 가운데 방법이라는 기획 자체의 문제를 다룬다. 스피노자는 가상의 반박자의 입을 빌려 방법의 기획에 다음과 같은 치명적 문제를 제기한다. 첫째, 올바른 방법을 마련하려면 그것을 마련할 올바른 방법이, 또 이를 발견할 올바른 방법 등등이 필요하지 않은가? (무한퇴행의 문제) 둘째, 방법의 출발점인 주어진 참된 관념의 참됨은 어떻게 보증하는가? (진리의 보증 문제) 셋째, 진리는 스스로 참됨을 드러내는데 인식 과정과 별도로 방법이 왜 필요한가? (방법의 필요 문제) 스피노자는 인식에 대한 방법의 내재성과 진리의 자기현시를 통해 앞의 두 (...) 물음에 답함과 동시에, 스스로를 베이컨 및 데카르트의 입장과 차별화한다. 단 마지막 문제는 내가 보기에 충분히 답변되지 않았으며, 나는 여기에 논고가 미완으로 남은 이유가 함축되어 있다고 본다. 곧 방법 논의는 한편으로는 관념들의 발생적 원인에 대한 논의로 대체되어야 했고, 다른 한편으로는 진리의 자기현시를 가로막는 편견이나 정념의 치유에 대한 논의로 대체되어야 했다. (shrink)

Recently we proposed the linguistic Copenhagen interpretation of quantum mechanics, which is called quantum language or measurement theory. This theory is valid for both quantum and classical systems. Thus, we think that quantum language is one of the most powerful scientific theories, like statistics, and thus, it is the scientific completion (i.e., the destination) of dualistic idealism. If so, we can introduce the concept “progress” in the dualistic idealism. For example, we can assert that [Plato → Descartes → Kant → (...) Wittgenstein → quantum language], where [“X” → “Y”] means that “Y” is more like quantum language than “X”. In this paper, we will study the problem of universals from the perspective of quantum language (i.e., from the scientific perspective of ignoring any religious perspective). And we can be confident of the progress of both of the two time series [Plato → Anselmus → Thomas Aquinas → quantum language] and [Descartes → Thomas Aquinas → quantum language] in dualistic idealism. The reader may find it surprising that Scholastic philosophy is more scientific than Cartesian-Kantian philosophy. However, this is because Descartes gave up the pursuit of “universals” and presented dualism as a visible “mind-matter dualism” so that it could be familiar to the general public. This made the Cartesian-Kantian philosophy socially successful, but unscientific. The problem of universals has not always been clear in the long history of philosophy. The reader should be convinced that the reason is that the problem of universals has been discussed in an incomplete non-scientific dualism to this day. (shrink)

This article revisits the standard results of demand theory when the preference relation is a continuous preorder that admits an equicontinuous multi-utility representation. We study the consumer problem as the constrained maximization of a continuous vector-valued utility mapping, and show how to rederive those results. In particular, we provide a link between the literature on vector optimization and the analysis of the consumer problem under incomplete preferences.

This paper examines four arguments in support of Frege's theory of incomplete entities, the heart of his semantics and ontology. Two of these arguments are based upon Frege's contributions to the foundations of mathematics. These are shown to be question-begging. Two are based upon Frege's solution to the problem of the relation of language to thought and reality. They are metaphysical in nature and they force Frege to maintain a theory of types. The latter puts his theory of incomplete (...) entities in the paradoxical position of maintaining that it is no theory at all. Moreover, his metaphysics rules out well-known suggestions for avoiding this difficulty. (shrink)

The problem of demarcating science from nonscience remains unsolved. This article executes an analytical process of elimination of different demarcation proposals put forward since the professionalization of the philosophy of science, explaining why each of those proposals is unsatisfactory or incomplete. Then, it elaborates on how to execute an alternative multicriterial scientific demarcation project put forward by Mahner. This project allows for the demarcation not only of science from non-science and from pseudoscience, but also of different types of sciences (...) and of scientific fields from each other. This article also offers arguments in favor of accepting two types of scientific demarcations, namely epistemic-warrant scientific demarcations and territorial scientific demarcations, and argues in favor of accepting a territorially broad scientific demarcation. (shrink)

Organisms' environments are thought to play a fundamental role in determining their fitness and hence in natural selection. Existing intuitive conceptions of environment are sufficient for biological practice. I argue, however, that attempts to produce a general characterization of fitness and natural selection are incomplete without the help of general conceptions of what conditions are included in the environment. Thus there is a "problem of the reference environment"—more particularly, problems of specifying principles which pick out those environmental conditions which (...) determine fitness. I distinguish various reference environment problems and propose solutions to some of them. While there has been a limited amount of work on problems concerning what I call "subenvironments", there appears to be no earlier work on problems of what I call the "whole environment". The first solution I propose for a whole environment problem specifies the overall environment for natural selection on a set of biological types present in a population over a specified period of time. The second specifies an environment relevant to extinction of types in a population; this kind of environment is especially relevant to certain kinds of long-term evolution. (shrink)

The incompleteness problem for virtue ethics is inherited by a virtue-based theory of argumentation as developed by Daniel Cohen. A complete normative theory of argumentation should be able to provide reasons for why argumentative virtues such as open-mindedness are worthwhile, along with being able to resolve conflicts of such virtues. Adumbrating virtue-based argumentation theory with a pragmatic utilitarian approach constitutes a more complete theory that can account for why argumentative virtues are worthwhile.

In lieu of an abstract, here is a brief excerpt of the content:Ethics & the Environment 7.1 (2002) 109-123 [Access article in PDF] The Problem of Finding a Positive Role for Humans in the Natural World Ned Hettinger As necessary as it obviously is, the effort of "wilderness preservation" has too often implied that it is enough to save a series of islands of pristine and uninhabited wilderness in an otherwise exploited, damaged, and polluted land. And, further, that the (...) pristine wilderness is the only alternative to exploitation and abuse. So far, the moral landscape of the conservation movement has tended to be a landscape of extremes.... On the one hand we have the unspoiled wilderness, and on the other hand we have scenes of utter devastation—strip mines, clear-cuts, industrially polluted wastelands, and so on. We wish, say the conservationists, to have more of the one, and less of the other. To which, of course, one must say amen. But it must be a qualified amen, for the conservationist's program has been embarrassingly incomplete. Its picture of the world as either deserted landscape or desertified landscape has misrepresented both the world and humanity. If we are to have an accurate picture of the world, even in its present diseased condition, we must interpose between the unused landscape and the misused landscape a landscape that humans have used well. Wendell Berry (1995, 64) [End Page 109] Introduction If one wants to identify what has gone wrong with humans' relationship to the natural world, there is probably no better place to look than in Eric Katz's (1997) fine collection of essays, Nature as Subject: Human Obligation and Natural Community. 1 Many key insights for understanding our disastrous attitudes toward nature can be found in this compilation of twenty years of merciless criticism of anthropocentrism. Katz's articulation of the source of our moral obligations to nature is deeply on target: Nature is a subject owed moral concern fundamentally because of its independence from humanity and its autonomy from human domination and control.What cannot be found in Nature as Subject is a vision of a positive role for humanity in the natural world. My worry is that Katz's views about the value of nature and our obligations to it leave no room for such an account. I fear that Katz's conceptualization of how humans have wronged nature may entail that all human activity toward nature wrongs nature. This would undermine the possibility of envisioning an environmentally just future in which humans live in the natural world in a morally appropriate way. This is a serious problem, because environmental philosophy needs an ethic for the use of nature, as well as for its nonuse. We need a vision of a constructive human relationship with nature, in addition to a characterization of our past failures of relationship. The question I pose is whether Katz's ideas allow for an account of how humans can be flourishing members who contribute to natural community.This is a problem not just for Eric Katz, but for all of us who accept a broadly preservationist environmental philosophy. If one believes that natural value is fundamentally a function of nature's autonomy from humanity and that a major goal of environmentalism should be to preserve nature relatively uninfluenced by humans, one will have to work hard to explain what positive role humans might have in nature. The alternatives of either minimizing human influence on nature, or sacrificing natural value for human goods, fail to provide for such a positive role. Katz's conceptualization of these matters brings out this problem poignantly. After a brief characterization of the wealth of ideas in Nature as Subject, I will explore this difficulty in some detail. In explaining why this is a problem for Katz and in exploring ways he can avoid it, I hope to set a path that preservationist environmental philosophers can follow if they are to develop a positive vision of humans' place in nature. [End Page 110] A Sketch of Katz's Position Katz defends a nonanthropocentric, holist, and communal environmental philosophy that treats... (shrink)

In considering this problem a distinction should first be made between its scientific and it philosophical aspects. The scientific problem is that of defining in exact understandable terms those conditions and factors which make possible the synthesis of the living organism from the simpler elements of the non-living environment, and also its maintenance in the adult state as a fully developed and autonomous organic individual. The problem as thus stated is one to be approached by methods of (...) observation and experiment, leading to verifiable results which are then expressed in systematic and intelligible form. The final statements or representations thus reached, the accepted scientific generalizations, inevitably take on a theoretical form, and as such are necessarily partial and abstract. Many of them, in fact, are to be regarded primarily as simplifications or models devised in the interest of clear representation or understanding. Their relation to concrete reality may range from attempts at exact portraiture to formulæ or diagrams having little more than heuristic significance. Any realistic philosophy of nature must always remember how incomplete and provisional are the theoretical conceptions of any natural science. (shrink)

One big question in biology is what life is, but another is how life divides into living things. This is the problem of biological individuality. Proposed statements of the problem have been vague and incomplete. And proposed theories of biological individuality are not detailed enough to solve the problem even if they are correct. The root of these troubles is that their authors have not recognized the metaphysical claims presupposed in their statement of the problem. Making (...) these claims explicit will enable us to see better what the problem is and what form a solution to it would need to have. (shrink)

This essay discusses implications of incommensurability of values for justified decision-making, ethics and justice. Under particular conditions incommensurability of values causes what might be called ‘incomplete comparability’ of options. Some leading theorists interpret this in terms of ‘imprecise equality’ and ‘imprecise comparability.’ This interpretation is mistaken and conceals the implications of incommensurability for practical and ethical reasoning. The aim of this essay is to show that, in many cases, incommensurability prevents the assignment of determinate weights to competing values. This may (...) have problematic consequences for a complete and impartial justification of decisions concerning conflicting values to the extent that they depend on the need of weighing them. (shrink)

According to an influential family of views, agents are virtuous when and because they possess the correct attitudes towards the actual good and bad. But there are multiple ways of conceptualizing the actual good and bad, and attitudes towards some conceptualizations of the good and bad seem to be irrelevant to moral character. It is deceptively difficult to provide a theoretical rationale for distinguishing between those conceptualizations of the good and bad that seem to be relevant and those that do (...) not: I argue that a previous attempt to provide such a rationale fails, as do a number of seemingly promising alternatives. This problem merits further attention not only because it shows that certain theoretical accounts of character are incomplete, but because it is likely to interfere with our ability to evaluate certain real-world agents, who care about the actual good conceptualized in certain ways but not in others. Since a generalized version of the problem of conceptualization also affects other “intrinsic” accounts of virtue and vice, I argue that we must either solve this problem or abandon such accounts. (shrink)

Metanormativists hold that moral uncertainty can affect how we ought, in some morally authoritative sense, to act. Many metanormativists aim to generalize expected utility theory for normative uncertainty. Such accounts face the “easy problem of intertheoretic comparisons”: the worry that distinct theories’ assessments of choiceworthiness are incomparable. The easy problem may well be resolvable, but another problem looms: while some moral theories assign cardinal degrees of choiceworthiness, other theories’ choiceworthiness assignments are merely ordinal. Expected choiceworthiness over such (...) theories is undefined. Call this the “hard problem of intertheoretic comparisons.” This paper argues that to solve the hard problem, we should model moral theories with imprecise choiceworthiness. Imprecise choiceworthiness assignments can model incomplete cardinal information about choiceworthiness, with precise cardinal choiceworthiness and merely ordinal choiceworthiness as limiting cases. Generalizing familiar decision theories for imprecise choiceworthiness to the case of moral uncertainty generates puzzles, however: natural generalizations seem to require reifying parts of the model that don’t correspond to anything in normative reality. I discuss three ways of addressing this problem: by demystifying the reified elements by using them as promiscuously as possible; by constructing alternative decision theories that don’t require the troublesome elements; and by employing an alternative model of metanormative decision problems, and of moral uncertainty generally. (shrink)

I explain and motivate the shutdown problem: the problem of creating artificial agents that (1) shut down when a shutdown button is pressed, (2) don’t try to prevent or cause the pressing of the shutdown button, and (3) otherwise pursue goals competently. I then propose a solution: train agents to have incomplete preferences. Specifically, I propose that we train agents to lack a preference between every pair of different-length trajectories. I suggest a way to train such agents using (...) reinforcement learning: we give the agent lower reward for repeatedly choosing same-length trajectories. (shrink)

Many years the academic community has been discussing issues of a universal metalanguage as the general conceptual framework of modern social and humanitarian research, especially of philosophy. The article questions the claim that the language of Western philosophy was already accepted as a unified tool in the 20th century. The peculiarities of perception and further application of Western philosophical terminology in Japan in late 19th – first half of the 20th centuries are investigated here as a factual evidence base of (...) argumentation. Special attention is given to examples of translation and interpretation of some concepts of Western origin, such as metaphysics, ethics, logic, substance, subject, etc., as observed in the works of eminent thinkers Nishi Amane, Inoue Tetsujiro, Nishida Kitaro, and Watsuji Tetsuro. The paper provides examples of new original concepts developed by modern Japanese philosophers, such as Kimura Bin, Hiromatsu Wataru et al. The author concludes that the general conceptual framework that modern philosophy operates with is a very dynamic and open system, capable of transforming in different cultural contexts and in keeping with newly emerging issues that require analysis. The article identifies factors that provide philosophical communication between different cultures at the conceptual level, that is, the presence of a common circle of problems and presence of partial overlap between the key concepts. The author poses the problem of the emergence of new approaches and ideas in a situation of “conflicting interpretations,” or incomplete equivalence of similar notions when used by the parties in a dialogue, casting doubt on possibility, necessity and reasonability of exact reproduction of meanings and “complete domestication” in other cultures. (shrink)

The purpose of this paper is to discuss two phenomena related to the semantics of definite descriptions: that of incomplete uses of descriptions, and that of the underdetermination of referential uses of descriptions. The Russellian theorist has a way of accounting for incomplete uses of descriptions by appealing to an account of quantifier domain restriction, such as the one proposed in Stanley and Szabó (2000a). But, I argue, the Russellian is not the only one in a position to appeal to (...) such an account of incomplete uses of descriptions. Proponents of other theories, such as the Fregean, which does not treat descriptions as quantifiers, might benefit from this account of domain restriction. In the second part of the paper I discuss referential uses of incomplete definite descriptions. Relative to such uses, Wettstein (1981) and others have argued that the Russellian theory faces a problem of underdetermination of semantic content. Neale (2004) has replied to this objection showing why it does not pose a threat to the Russellian theory. Again, I argue that not only the Russellian, but also the Fregean can subscribe to Neale’s (2004) suggestion. (shrink)

This book concentrates on research done during the last twenty years on the philosophy of quantum mechanics. In particular, the author focuses on three major issues: whether quantum mechanics is an incomplete theory, whether it is non-local, and whether it can be interpreted realistically. Much of the book is concerned with distinguishing various senses in which these questions can be taken, and assessing the bewildering variety of answers philosophers and physicists have given up to now. The book is self-contained in (...) that it presents the necessary parts of the mathematical formalism of quantum mechanics and also covers other interpretative topics, such as the problem of measurement and the uncertainty relations. A considerable portion of the book is based on original arguments presented by the author in lectures and research papers over the past ten years. However, this material is integrated with a broad coverage of most of the recent research in the field, so as to provide a balanced introduction to the whole subject. (shrink)

Proponents of evidence-based medicine and some philosophers of science seem to agree that knowledge of mechanisms can help solve the problem of applying results of controlled studies to target populations (‘the problem of extrapolation’). We describe the problem of extrapolation, characterize mechanisms, and outline how mechanistic knowledge might be used to solve the problem. Our main thesis is that there are four often overlooked problems with using mechanistic knowledge to solve the problem of extrapolation. First, (...) our understanding of mechanisms is often (and arguably, likely to remain) incomplete. Secondly, knowledge of mechanisms is not always applicable outside the tightly controlled laboratory conditions in which it is gained. Thirdly, mechanisms can behave paradoxically. Fourthly, as Daniel Steel points out, using mechanistic knowledge faces the problem of the ‘extrapolator’s circle’. At the same time, when the problems with mechanistic knowledge have been addressed, such knowledge can and should be used to mitigate (nothing can entirely solve) the problem of extrapolation. (shrink)

Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. We show that representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something (...) real, the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein’s preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein’s attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927. (shrink)

Recently, Dollimore criticized our claim that Organizational Ecology is not a Darwinian research program. She argued that Organizational Ecology is merely an incomplete Darwinian program and provided a suggestion as to how this incompleteness could be remedied. Here, we argue that Dollimore’s suggestion fails to remedy the principal problem that Organizational Ecology faces and that there are good reasons to think of the program as deeply incompatible with Darwinian thinking.

The figure of form-of-life is a life lived as a ‘how’ or a mode of living, beyond every relation. Form-of-life is a form of impotent, destituent power that seeks to deactivate the biopolitics that continuously divides and separates life itself. Agamben’s work is remarkably silent on the question of reproductive rights. The pregnant woman’s life is regulated continuously by biopolitics, yet Agamben does not discuss this regulation. The woman’s relationship with her foetus is difficult to reconcile with Agamben’s philosophy that (...) seeks to think beyond every relation. In addition, the right to abortion is difficult to reconcile with form-of-life. It is not clear how a woman seeking an abortion is not exercising a sovereign decision to create bare life. I use the UK’s abortion laws as a way to interrogate Agamben’s figure of form-of-life, and to illustrate how, by not accounting for reproductive rights, Agamben’s thought remains incomplete. (shrink)

This paper offers a unified, quantificational treatment of incomplete descriptions like ‘the table’. An incomplete quantified expression like ‘every bottle’ (as in “Every bottle is empty”) can feature in true utterances despite the fact that the world contains nonempty bottles. Positing a contextual restriction on the bottles being talked about is a straightforward solution. It is argued that the same strategy can be extended to incomplete definite descriptions across the board. ncorporating the contextual restrictions into semantics involves meeting a complex (...) array of desiderata, yet the apparently simpler pragmatic alternative faces severe problems and is therefore a nonstarter. (shrink)

It has been suggested that the Modal Interpretation of Quantum Mechanics (QM) is "incomplete" if it lacks a dynamics for possessed values. I argue that this is only one of two possible attitudes one might adopt toward a Modal Interpretation without dynamics. According to the other attitude, such an interpretation is a complete interpretation of QM as standardly formulated, an interpretation whose innovation is to attempt to make sense of the quantum realm without the expedient of novel physics. Then I (...) explain why this attitude, though available, is unattractive. Without dynamics, the Modal Interpretation vanquishes the measurement problem only, it seems, to succumb to the problem of state preparation. On this view, the Modal Interpretation needs dynamics not to be an interpretation at all, but to be an adequate one. I review reasons to suspect that the dynamics which would best suit the Modal Interpretation--a dynamics equivalent to a set of two time transition probabilities of the sort used to solve the preparation problem--is not a dynamics the interpretation can have. I close with a brief discussion of versions of the Modal Interpretation that may not succumb to the considerations presented here. (shrink)

The book is intended as a critical history of the growth of the ideal of knowledge in science, philosophy and history since Hegel. In order to give some conception of its encyclopædic scope, one need only mention an incomplete list of the topics which are considered in it: the development of non-Euclidean geometries, the logical foundation of the concept of number, the effect of the quantum theory on the concept of physical knowledge, the development of classification and systematization of natural (...) forms in biology, the effects of Darwinism and of the mechanism-vitalism controversy on biological thought, the development of such modes of historiography as the romantic, positivistic and political, as well as of the history of civilization and the history of religion. (shrink)

The law of excluded middle is usually considered as intrinsically connected with the realistic standpoint and incompatible with the idealistic position. This is just what Ajdukiewicz claims in his critique of transcendental idealism. The analysis of Ajdukiewicz's argumentation raises the problem of validity of the law of excluded middle for vague (or incomplete) languages. The problem is being solved by differentiating between the logical (or ontological) and the metalogical (or semantical) law of excluded middle: in contrast to the (...) former, the latter is claimed to be invalid for the languages in question, without thereby embracing the idealist position. (shrink)

The law of excluded middle is usually considered as intrinsically connected with the realistic standpoint and incompatible with the idealistic position. This is just what Ajdukiewicz claims in his critique of transcendental idealism. The analysis of Ajdukiewicz's argumentation raises the problem of validity of the law of excluded middle for vague (or incomplete) languages. The problem is being solved by differentiating between the logical (or ontological) and the metalogical (or semantical) law of excluded middle: in contrast to the (...) former, the latter is claimed to be invalid for the languages in question, without thereby embracing the idealist position. (shrink)

This paper argues that existing accounts of shame are incomplete in so far as they don’t take account of the problem of shame. This is the problem concerning the possibility of a primary experience...

The phrase τά ένί διαστηματι γ ραφόμενα occurs in that part of Pappus' Collection Book VIII which deals with instrumental solutions to problems more practical than purely geometrical. In the preceding section an instrumental solution for the problem of doubling the cube has been propounded, which is dependent on the use of a ruler passing through a point about which it is turned in the generation of the locus of points known as the cissoid, and in the subsequent section (...) a solution is propounded for the problem of finding the diameter of a cylinder of which only an incomplete portion of the side remains, leaving neither base intact. (shrink)

This book concentrates on research done during the last twenty years on the philosophy of quantum mechanics. In particular, the author focuses on three major issues: whether quantum mechanics is an incomplete theory, whether it is non-local, and whether it can be interpreted realistically. Much of the book is concerned with distinguishing various senses in which these questions can be taken, and assessing the bewildering variety of answers philosophers and physicists have given up to now. The book is self-contained in (...) that it presents the necessary parts of the mathematical formalism of quantum mechanics and also covers other interpretative topics, such as the problem of measurement and the uncertainty relations. A considerable portion of the book is based on original arguments presented by the author in lectures and research papers over the past ten years. However, this material is integrated with a broad coverage of most of the recent research in the field, so as to provide a balanced introduction to the whole subject. (shrink)

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...) mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

The foundational conviction of contemporary liberal thought is that all persons possess equal moral worth and are entitled to equal concern and respect by others. At the same time, nation states, as the primary organs of our collective self-governance, frequently pursue policies that are strikingly partial towards the interests of compatriots over those of foreigners. A common strategy for justifying this national partiality is to view it as grounded in associative obligations that we incur by standing in special relationships with (...) our fellow citizens. For instance, according to familiar arguments from ‘fair play’, voluntarily partaking in and benefiting from cooperative relationships with our fellow citizens gives us reciprocal obligations to maintain these social institutions and care for needy compatriots. By contrast, we do not have corresponding associative obligations towards foreigners. I maintain that such arguments from associative obligations face an important stumbling block. I argue for the following “Boundary Principle”, according to which we cannot appeal to special relationships amongst members of a group to justify an attitude of partiality towards them unless the boundaries of this group, and the fact that they exclude other persons from membership, can also be justified. If this is right, arguments from associative obligations, by themselves, are necessarily incomplete. Most modern states severely limit the scope of economic migration, and thereby prevent many would-be contributors to the collective enterprises of affluent societies from entering into those special relationships with us that would give rise to associative obligations on our part. Not only are would-be immigrants excluded from the benefits that participation in the cooperative schemes of affluent nation-states would itself confer; in addition, the fact that they do not stand in such cooperative relationships with us is then appealed to in order to justify the fact that we assign significantly less weight to their interests in the formulation of state policy. The upshot of my discussion is not that a defense of national partiality in terms of associative obligations cannot succeed. It is rather that a successful defense of national partiality in these terms is more closely tied to the question whether principled restrictions can be placed on immigration than most political philosophers have hitherto assumed. (shrink)

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond NP ≠ coNP. These conjectures formally connect computational complexity with the difficulty of proving some sentences, which means that high computational complexity of a problem associated with a sentence implies that the sentence is not provable in a weak theory, or requires a long proof. Another reason for putting forward these conjectures is that some results in proof complexity (...) seem to be special cases of such general statements and we want to formalize and fully understand these statements. Roughly speaking, we are trying to connect syntactic complexity, by which we mean the complexity of sentences and strengths of the theories in which they are provable, with the semantic concept of complexity of the computational problems represented by these sentences. -/- We have introduced the most fundamental conjectures in our earlier works. Our aim in this article is to present them in a more systematic way, along with several new conjectures, and prove new connections between them and some other statements studied before. (shrink)

Objective: To determine if the medical record might overestimate the quality of care through false, and potentially unethical, documentation by physicians.Design: Prospective trial comparing two methods for measuring the quality of care for four common outpatient conditions: structured reports by standardised patients who presented unannounced to the physicians’ clinics, and abstraction of the medical records generated during these visits.Setting: The general medicine clinics of two veterans affairs medical centres.Participants: Twenty randomly selected physicians from among eligible second and third year internal (...) medicine residents and attending physicians.Main measurements: Explicit criteria were used to score the medical records of physicians and the reports of SPs generated during 160 visits . Individual scoring items were categorised into four domains of clinical performance: history, physical examination, treatment, and diagnosis. To determine the false positive rate, physician entries were classified as false positive , false negative, true positive, and true negative.Results: False positives were identified in the medical record for 6.4% of measured items. The false positive rate was higher for physical examination and diagnosis than for history and treatment . For individual physician subjects, the false positive rate ranged from 0.098 to 0.397.Conclusions: These data indicate that the medical record falsely overestimates the quality of important dimensions of care such as the physical examination. Though it is doubtful that most subjects in our study participated in regular, intentional falsification, we cannot exclude the possibility that false positives were in some instances intentional, and therefore fraudulent, misrepresentations. Further research is needed to explore the questions raised but incompletely answered by this research. (shrink)

whole numbers that manages to assert that it itself is unprovable (from a given finite set F of axioms using formal logic). (Gödel's paper is included in the well-known anthology [1].) GF : ``GF cannot be proved from the finite set of axioms F.'' This assertion GF is therefore true if and only if it is unprovable, and the formal axiomatic system F in question either proves falsehoods (because it enables us to prove GF) or fails to prove a true (...) assertion (because it does not enable us to prove GF). If we assume that the former situation is impossible, we conclude that F is necessarily incomplete since it does not permit us to establish the true statement GF. (shrink)

This article examines some aspects of the natural philosophy of Juan Gallego de la Serna, royal physician to the Spanish kings Philip III and Philip IV. In his account of animal generation, Gallego criticizes widely accepted views: (1) the view that animal seeds are animated, and (2) the alternative view that animal seeds, even if not animated, possess active potencies sufficient for the development of animal souls. According to his view, animal seeds are purely material beings. This, of course, raises (...) the question of how living beings can arise from inanimate matter. Gallego is aware that two other thinkers who understood animal seeds as purely material beings, Duns Scotus and the Louvain-based physician Thomas Feyens, did not solve this problem. Gallego’s solution makes use of the notion of incomplete entities developed by the Spanish Jesuit Francisco Suarez. While Suarez applies this notion to soul and body in order to explain why souls have a natural tendency towards organic bodies and organic bodies have a natural tendency towards souls, Gallego applies this notion to the natural tendency of animal seeds towards each other and towards further substances in their respective environment. In his view, this natural tendency of animal seeds to incorporate further substances explains that origin of material structures complex enough to constitute an animal soul. (shrink)

In "Virtue and Right" Robert Johnson argues that virtue ethics that accept standards such as Virtuous Agent (A's x-ing is right in circumstances c iff a fully virtuous agent would x in c) are incomplete, since they cannot account for duties of moral self-improvement. This paper offers four solutions to the problem of incompleteness: the first discards Virtuous Agent and counts actions as wrong iff a vicious person would perform them; the second retains Virtuous Agent but counts self-improving (...) actions as countererogatory: wrong but nonetheless good to do; the third replaces Virtuous Agent with a standard appealing to the Mengzian virtue of righteousness, understood as situational appropriateness; the fourth replaces Virtuous Agent with a standard that holds an action right if it promotes the agent's virtue. Each solution accommodates duties of moral self-improvement, so a virtue ethics embracing any of them would not be incomplete. (shrink)

Wittgenstein’s philosophy of mathematics is often devalued due to its peculiar features, especially its radical departure from any of standard positions in foundations of mathematics, such as logicism, intuitionism, and formalism. We first contrast Wittgenstein’s finitism with Hilbert’s finitism, arguing that Wittgenstein’s is perspicuous or surveyable finitism whereas Hilbert’s is transcendental finitism. We then further elucidate Wittgenstein’s philosophy by explicating his natural history view of logic and mathematics, which is tightly linked with the so-called rule-following problem and Kripkenstein’s paradox, (...) yielding vital implications to the nature of mathematical understanding, and to the nature of the certainty and objectivity of mathematical truth. Since the incompleteness theorems, foundations of mathematics have mostly lost their philosophical driving force, and anti-foundationalism has become prevalent and pervasive. Yet new foundations have nevertheless emerged and come into the scene, namely categorical foundations. We articulate the foundational significance of category theory by explicating three forms of foundations, i.e., global foundations, local foundations, and conceptual foundations. And we explore the possibility of categorical unified science qua pluralistic unified science, arguing for the categorical unity of science on both mathematical and philosophical grounds. We then turn to an issue in conceptual foundations of mathematics, namely the nature of the concept of space. We elucidate Wittgenstein’s intensional conception of space in relation to Brouwer’s theory of space continua and to the modern conception of space as point-free structure in category theory and algebraic geometry. We finally give a bird’s-eye view of mathematical philosophy from a Wittgensteinian perspective, and further sheds new light on Wittgenstein’s constructive structuralism and his view of incompleteness and contradictions in mathematics. (shrink)