We discuss several possible extensions of the classical Löwenheim-Skolem Theorem to finite structures and give a counterexample refuting almost all of them.

Many logics considered in finite model theory have a natural notion of an arity. The purpose of this article is to study the hierarchies which are formed by the fragments of such logics whose formulae are of bounded arity.Based on a construction of finite graphs with a certain property of homogeneity, we develop a method that allows us to prove that the arity hierarchies are strict for several logics, including fixed-point logics, transitive closure logic and its deterministic version, variants of (...) the database language Datalog, and extensions of first-order logic by implicit definitions.Furthermore, we show that all our results already hold on the class of finite graphs. (shrink)

In this paper we prove that thek-ary fragment of transitive closure logic is not contained in the extension of the (k−1)-ary fragment of partial fixed point logic by all (2k−1)-ary generalized quantifiers. As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are strict simultaneously with respect to the arity of the induction predicates and the arity of generalized quantifiers.Although it is known that our theorem cannot be extended to the sublogic deterministic transitive closure logic, (...) we show that an extension is possible when we close this logic under congruence. (shrink)

We prove an existential version of Gaifman's locality theorem and show how it can be applied algorithmically to evaluate existential first-order sentences in finite structures.

Throughout the development of finite model theory, the fragments of first-order logic with only finitely many variables have played a central role. This survey gives an introduction to the theory of finite variable logics and reports on recent progress in the area.For each k ≥ 1 we let Lk be the fragment of first-order logic consisting of all formulas with at most k variables. The logics Lk are the simplest finite-variable logics. Later, we are going to consider infinitary variants and (...) extensions by so-called counting quantifiers.Finite variable logics have mostly been studied on finite structures. Like the whole area of finite model theory, they have interesting model theoretic, complexity theoretic, and combinatorial aspects. For finite structures, first-order logic is often too expressive, since each finite structure can be characterized up to isomorphism by a single first-order sentence, and each class of finite structures that is closed under isomorphism can be characterized by a first-order theory. The finite variable fragments seem to be promising candidates with the right balance between expressive power and weakness for a model theory of finite structures. This may have motivated Poizat [67] to collect some basic model theoretic properties of the Lk. Around the same time Immerman [45] showed that important complexity classes such as polynomial time or polynomial space can be characterized as collections of all classes of finite structures definable by uniform sequences of first-order formulas with a fixed number of variables and varying quantifier-depth. (shrink)

The model-checking problem for a logic L on a class C of structures asks whether a given L-sentence holds in a given structure in C. In this paper, we give super-exponential lower bounds for fixed-parameter tractable model-checking problems for first-order and monadic second-order logic. We show that unless PTIME=NP, the model-checking problem for monadic second-order logic on finite words is not solvable in time f·p, for any elementary function f and any polynomial p. Here k denotes the size of the (...) input sentence and n the size of the input word. We establish a number of similar lower bounds for the model-checking problem for first-order logic, for example, on the class of all trees. (shrink)

We observe that the W*-hierarchy, a variant (introduced by Downey, Fellows, and Taylor [7]) of the better known W-hierarchy, coincides with the W-hierarchy, though not level wise, but just as a whole hierarchy. More precisely, we prove that W[t] ⊆ W*[t] ⊆ W[2t − 2] for each t ≥ 2. It was known before that W[1] = W*[1] and W[2] = W*[2]. Our second main result is a new logical characterization of the W*-hierarchy in terms of "Fagin-definable problems." As a (...) by-product, we also obtain an improvement of our earlier characterization of the hierarchy in terms of model-checking problems. Furthermore, we obtain new complete problems for the classes W[3] and W*[3]. (shrink)

We study a refined framework of parameterized complexity theory where the parameter dependence of fixed-parameter tractable algorithms is not arbitrary, but restricted by a function in some family . For every family of functions, this yields a notion of -fixed-parameter tractability. If is the class of all polynomially bounded functions, then -fixed-parameter tractability coincides with polynomial time decidability and if is the class of all computable functions, -fixed-parameter tractability coincides with the standard notion of fixed-parameter tractability. There are interesting choices (...) of between these two extremes, for example the class of all singly exponential functions. In this article, we study the general theory of -fixed-parameter tractability. We introduce a generic notion of reduction and two classes -W[P] and -XP, which may be viewed as analogues of NP and EXPTIME, respectively, in the world of -fixed-parameter tractability. (shrink)

A long-standing theme in discussion of perception and thought has been that our primary cognitive contact with individual objects and events in the world derives from our perceptual contact with them. When I look at a duck in front of me, I am not merely presented with the fact that there is at least one duck in the area, rather I seem to be presented withthisthing (as one might put it from my perspective) in front of me, which looks to (...) me to be a duck. Furthermore, such a perception would seem to put me in a position not merely to make the existential judgment that there is some duck or other present, but rather to make a singular, demonstrative judgment, that that is a duck. My grounds for an existential judgment in this case derives from my apprehension of the demonstrative thought and not vice versa. (shrink)

On Inception is a translation of Martin Heidegger's Gesamtausgabe 70. This work belongs to the crucial period, before and during WWII, when Heidegger was at work on a series of treatises that begins with "Contributions to Philosophy" and includes "The Event" and "The History of Beyng." These works are difficult, even hermetic, but represent a crucial development in Heidegger's thinking. On Inception deepens the investigation underway in the other volumes of the series and provides a unique perspective on Heidegger's (...) thinking of Being and of Event. Here, Heidegger asks, with a greater insistence than anywhere else in his work, what it might mean to think of being as event, and not as presence. Event cannot be thought without the sense of a beginning - an inception - and so, Heidegger insists, we must try to think of being as inception, as fundamentally inceptive. On Inception pursues rigorously the difficult and puzzling implications of this speculation. It does not merely extend work already undertaken but also opens doors onto wholly other pathways. (shrink)

Is it OK to lie to Siri? Is it bad to mistreat a robot for our own pleasure? Under what condition should we grant a moral status to an artificial intelligence (AI) system? This paper looks at different arguments for granting moral status to an AI system: the idea of indirect duties, the relational argument, the argument from intelligence, the arguments from life and information, and the argument from sentience. In each but the last case, we find unresolved issues with (...) the particular argument, which leads us to move to a different one. We leave the idea of indirect duties aside since these duties do not imply considering an AI system for its own sake. The paper rejects the relational argument and the argument from intelligence. The argument from life may lead us to grant a moral status to an AI system, but only in a weak sense. Sentience, by contrast, is a strong argument for the moral status of an AI system—based, among other things, on the Aristotelian principle of equality: that same cases should be treated in the same way. The paper points out, however, that no AI system is sentient given the current level of technological development. (shrink)

Over the past three decades, the philosophy of biology has emerged from the shadow of the philosophy of physics to become a respectable and thriving philosophical subdiscipline. The authors take a fresh look at the life sciences and the philosophy of biology from a strictly realist and emergentist-naturalist perspective. They outline a unified and science-oriented philosophical framework that enables the clarification of many foundational and philosophical issues in biology. This book will be of interest both to life scientists and philosophers.

We provide a battery of examples of delusions against which theoretical accounts can be tested. Then, we identify neuropsychological anomalies that could produce the unusual experiences that may lead, in turn, to the delusions in our battery. However, we argue against Maher’s view that delusions are false beliefs that arise as normal responses to anomalous experiences. We propose, instead, that a second factor is required to account for the transition from unusual experience to delusional belief. The second factor in the (...) aetiology of delusions can be described superficially as a loss of the ability to reject a candidate for belief on the grounds of its implausibility and its inconsistency with everything else that the patient knows. But we point out some problems that confront any attempt to say more about the nature of this second factor. (shrink)

Martin Heidegger's Contributions to Philosophy reflects his famous philosophical "turning." In this work, Heidegger returns to the question of being from its inception in Being and Time to a new questioning of being as event.

What exactly is hope and how does it influence our decisions? In How We Hope, Adrienne Martin presents a novel account of hope, the motivational resources it presupposes, and its function in our practical lives. She contends that hoping for an outcome means treating certain feelings, plans, and imaginings as justified, and that hope thereby involves sophisticated reflective and conceptual capacities. Martin develops this original perspective on hope--what she calls the "incorporation analysis"--in contrast to the two dominant philosophical (...) conceptions of hope: the orthodox definition, where hoping for an outcome is simply desiring it while thinking it possible, and agent-centered views, where hoping for an outcome is setting oneself to pursue it. In exploring how hope influences our decisions, she establishes that it is not always a positive motivational force and can render us complacent. She also examines the relationship between hope and faith, both religious and secular, and identifies a previously unnoted form of hope: normative or interpersonal hope. When we place normative hope in people, we relate to them as responsible agents and aspire for them to overcome challenges arising from situation or character. Demonstrating that hope merits rigorous philosophical investigation, both in its own right and in virtue of what it reveals about the nature of human emotion and motivation, How We Hope offers an original, sustained look at a largely neglected topic in philosophy. (shrink)

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an argument against the (...) second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)

Martin Heidegger is one of the most important and influential philosophers of the 20th Century. A major figure in the development of phenomenology, his work also profoundly influenced many of the intellectual movements that followed in his wake, from Sartre's Existentialism to Derrida's deconstructionism. Towards the Definition of Philosophy brings together two seminal lectures that mark a breakthrough moment in Heidegger's thought and introduces the major themes that he would develop in his opus Being and Time.

A landmark discussion between two great thinkers, vital to an understanding of twentieth-century philosophy and intellectual history.

This paper proposes a view of time that takes passage to be the most basic temporal notion, instead of the usual A-theoretic and B-theoretic notions, and explores how we should think of a world that exhibits such a genuine temporal passage. It will be argued that an objective passage of time can only be made sense of from an atemporal point of view and only when it is able to constitute a genuine change of objects across time. This requires that (...) passage can flip one fact into a contrary fact, even though neither side of the temporal passage is privileged over the other. We can make sense of this if the world is inherently perspectival. Such an inherently perspectival world is characterized by fragmentalism, a view that has been introduced by Fine in his ‘Tense and Reality’ (2005). Unlike Fine's tense-theoretic fragmentalism though, the proposed view will be a fragmentalist view based in a primitive notion of passage. (shrink)

Martin Heidegger's Nietzsche's Second Untimely Meditation presents crucial elements for understanding Heidegger's thinking from 1936 to 1940. Heidegger offers a radically different reading of a text that he had read decades earlier, showing how his relationship with Nietzche's has changed, as well as how his understandings of the differences between animals and humans, temporality and history, and the Western philosophical tradition developed. With his new reading, Heidegger delineates three Nietzschean modes of history, which should be understood as grounded in (...) the structure of temporality or historicity and also offers a metaphysical determination of life and the essence of humankind. Ullrich Hasse and Mark Sinclair offer a clear and accessible translation despite the fragmentary and disjointed quality of the original lecture notes that comprise this text. (shrink)

This book provides the first systematic presentation of anthropology's 'ontological turn', placing it in the landscape of contemporary social theory.

The Liar paradox arises when we consider a sentence that says of itself that it is not true. If such self-referential sentences exist? and examples like?This sentence is not true? certainly suggest this?, then our logic and standard notion of truth allow to infer a contradiction: The Liar sentence is true and not true. What has gone wrong? Must we revise our notion of truth and our logic? Or can we dispel the common conviction that there are such self-referential sentences? (...) The present study explores the second path.0After comparing the Liar reasoning in formal and informal logic and showing that there are no Gödelian Liar sentences, the study moves on from the semantics of self-reference to the metaphysics of expressions and proposes a novel solution to the Liar paradox: Meaningful expressions are distinct from their syntactic bases and exist only relative to contexts. Detailed semantico-metaphysical arguments show that in this dynamic setting, an object can be referred to only after it has started to exist. Hence the circular reference needed in the Liar paradox cannot occur, after all. As this solution is contextualist, it evades the expressibility problems of other proposals. (shrink)

Richard Rorty (1931 - 2007) ist einer der wichtigsten amerikanischen Philosophen der Gegenwart, der die analytische Philosophie sowohl geprägt als auch maßgeblich zu ihrer Kritik beigetragen und damit die Wiederentdeckung des Pragmatismus vorangetrieben hat. In diesem Handbuch werden alle wichtigen Aspekte seines Lebens und seiner philosophischen Arbeit dargestellt und einer wissenschaftlichen Diskussion unterzogen.

The Routledge International Handbook of Neuroaesthetics is an authoritative reference work that provides the reader with a wide-ranging introduction to this exciting new scientific discipline. The book brings together leading international academics to offer a well-balanced overview of this burgeoning field while addressing two questions central to the field; how the brain computes aesthetic appreciation for sensory objects, and how is art created and experienced.

Humanity has reached a critical moment. Our world is unsettled and rapidly changing, and we face existential risks over the next century. Various outcomes--good and bad--are possible. Yet our approach to the future is characterized by short-term thinking, polarizing debates, alarmist rhetoric, and pessimism. In this short, exhilarating book, renowned scientist and bestselling author Martin Rees argues that humanity's prospects depend on our taking a very different approach to planning for tomorrow. The future of humanity is bound to the (...) future of science and hinges on how successfully we harness technological advances to address our challenges. If we are to use science to solve our problems while avoiding its dystopian risks, we must think rationally, globally, collectively, and optimistically about the long term. Advances in biotechnology, cybertechnology, robotics, and artificial intelligence--if pursued and applied wisely--could empower us to boost the developing and developed world and overcome the threats humanity faces on Earth, from climate change to nuclear war. At the same time, further advances in space science will allow humans to explore the solar system and beyond with robots and AI. But there is no "Plan B" for Earth--no viable alternative within reach if we do not care for our home planet. Rich with fascinating insights into cutting-edge science and technology, this accessible book will captivate anyone who wants to understand the critical issues that will define the future of humanity on Earth and beyond."-- Provided by publisher. (shrink)

Material from this paper appears in Chap. 7 of my book Reason and Being, but there is also stuff here that isn't in the book. In particular, it discusses the claims that, for Spinoza, conceiving implies explaining and that existence is identical to or reducible to conceivability. So, if you're interested in those issues, this paper might be worth a read.

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data will (...) run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data. (shrink)

My concern in this paper is with the claim that knowledge is a mental state – a claim that Williamson places front and centre in Knowledge and Its Limits. While I am not by any means convinced that the claim is false, I do think it carries certain costs that have not been widely appreciated. One source of resistance to this claim derives from internalism about the mental – the view, roughly speaking, that one’s mental states are determined by one’s (...) internal physical state. In order to know that something is the case it is not, in general, enough for one’s internal physical state to be a certain way – the wider world must also be a certain way. If we accept that knowledge is a mental state, we must give up internalism. One might think that this is no cost, since much recent work in the philosophy of mind has, in any case, converged on the view that internalism is false. This thought, though, is too quick. As I will argue here, the claim that knowledge is a mental state would take us to a view much further from internalism than anything philosophers of mind have converged upon. (shrink)

Objects often manifest themselves in incompatible ways across perspectives that are epistemically on a par. The standard response to such cases is to deny that the properties that things appear to have from different perspectives are properties that things really have out there. This type of response seems worrying: too many properties admit of perspectival variance and there are good theoretical reasons to think that such properties are genuinely instantiated. So, we have reason to explore views on which things can (...) have the incompatible properties they appear to have across perspectives. This paper explores the view that things can have incompatible properties if the world is not a metaphysically unified place but is instead fragmented. There is a sensible notion of co-obtainment, on which two facts can each obtain without co-obtaining. Using this notion, we can step back from our embedded perspectives on the world without deeming the contents of those perspectives to be mere appearances. This renders th.. (shrink)

Anosognosia is literally ‘unawareness of or failure to acknowledge one’s hemi- plegia or other disability’ (OED). Etymology would suggest the meaning ‘lack of knowledge of disease’ so that anosognosia would include any denial of impairment, such as denial of blindness (Anton’s syndrome). But Babinski, who introduced the term in 1914, applied it only to patients with hemiplegia who fail to acknowledge their paralysis. Most commonly, this is failure to acknowledge paralysis of the left side of the body following damage to (...) the right hemisphere of the brain. In this paper, we shall mainly be concerned with anosognosia for hemiplegia. But we shall also use the term ‘anosognosia’ in an inclusive way to encompass lack of knowledge or acknowledgement of any impairment. Indeed, in the construction ‘anosognosia for X’, X might even be anosognosia for some Y. (shrink)

Increasingly, medical educators integrate art-viewing into curricular interventions that teach clinical observation—often with local art museum educators. How can cross-disciplinary collaborators explicitly connect the skills learned in the art museum with those used at the bedside? One approach is for educators to align their pedagogical approach using similar teaching methods in the separate contexts of the galleries and the clinic. We describe two linked pedagogical exercises—Visual Thinking Strategies (VTS) in the museum galleries and observation at the bedside—from “Training the Eye: (...) Improving the Art of Physical Diagnosis,” an elective museum-based course at Harvard Medical School. It is our opinion that while strategic interactions with the visual arts can improve skills, it is essential for students to apply them in a clinical context with faculty support—requiring educators across disciplines to learn from one another. (shrink)

Cognitive approaches contribute to our understanding of delusions by providing an explanatory framework that extends beyond the personal level to the sub personal level of information-processing systems. According to one influential cognitive approach, two factors are required to account for the content of a delusion, its initial adoption as a belief, and its persistence. This chapter reviews Bayesian developments of the two-factor framework.