_Anthropic Bias_ explores how to reason when you suspect that your evidence is biased by "observation selection effects"--that is, evidence that has been filtered by the precondition that there be some suitably positioned observer to "have" the evidence. This conundrum--sometimes alluded to as "the anthropic principle," "self-locating belief," or "indexical information"--turns out to be a surprisingly perplexing and intellectually stimulating challenge, one abounding with important implications for many areas in science and philosophy. There are the philosophical thought experiments and paradoxes: (...) the Doomsday Argument; Sleeping Beauty; the Presumptuous Philosopher; Adam & Eve; the Absent-Minded Driver; the Shooting Room. And there are the applications in contemporary science: cosmology ; evolutionary theory ; the problem of time's arrow ; quantum physics ; game-theory problems with imperfect recall ; even traffic analysis. _Anthropic Bias_ argues that the same principles are at work across all these domains. And it offers a synthesis: a mathematically explicit theory of observation selection effects that attempts to meet scientific needs while steering clear of philosophical paradox. (shrink)

Philosophers often characterize discourse in general as aiming at some sort of convergence (in beliefs, plans, dispositions, feelings, etc.), and many views about aesthetic discourse in particular affirm this thought. I argue that a convergence norm does not govern aesthetic discourse. The conversational dynamics of aesthetic discourse suggest that typical aesthetic claims have directive force. I distinguish between dynamic and illocutionary force and develop related theories of each for aesthetic discourse. I argue that the illocutionary force of aesthetic utterances is (...) typically invitational because its dynamic force is influenced by a ‘communal’ norm. I draw on dynamic pragmatics to develop a formal account of this dynamic force that explains why invitation has pride of place in aesthetic conversation. It turns out that the end of aesthetic discourse is not convergence but a distinctive form of community, a kind of harmony of individuality, that is compatible with aesthetic disagreement. If this is right, then convergence theories of aesthetic and normative discourse, and of conversation in general, need to be revised. (shrink)

This paper investigates the significance of T-duality in string theory: the indistinguisha- bility with respect to all observables, of models attributing radically different radii to space – larger than the observable universe, or far smaller than the Planck length, say. Two interpretational branch points are identified and discussed. First, whether duals are physically equivalent or not: by considering a duality of the familiar simple harmonic oscillator, I argue that they are. Unlike the oscillator, there are no measurements ‘outside’ string theory (...) that could distinguish the duals. Second, whether duals agree or disagree on the radius of ‘target space’, the space in which strings evolve according to string theory. I argue for the latter position, because the alternative leaves it unknown what the radius is. Since duals are physically equivalent yet disagree on the radius of target space, it follows that the radius is indeterminate between them. Using an analysis of Brandenberger and Vafa (1989), I explain why – even so – space is observed to have a determinate, large radius. The conclusion is that observed, ‘phenomenal’ space is not target space, since a space cannot have both a determinate and indeterminate radius: instead phenomenal space must be a higher-level phenomenon, not fundamental. (shrink)

How should we pursue aesthetic value, or incorporate it into our lives, if we want to? Is there an ideal of aesthetic life? Philosophers have proposed numerous answers to the analogous question in moral philosophy, but the aesthetic question has received relatively little attention. There is, in essence, a single view, which is that one should develop a sensibility that would give one sweeping access to aesthetic value. I challenge this view on two grounds. First, it threatens to undermine our (...) "aesthetic love", or the meaningful attachments we form with aesthetic items, e.g., poems, paintings, songs, or items of design and dress. Second, it fails to accommodate the motivational character of our encounter with beauty, which can diminish our desire to pursue the wider world of aesthetic value. I conclude that whatever the aesthetic ideal is, it must reconcile our desire to broaden our access to aesthetic value with our desire to maintain and cultivate our meaningful aesthetic attachments. I motivate the alternative thought that having style is the aesthetic ideal. (shrink)

Weyl symmetry of the classical bosonic string Lagrangian is broken by quantization, with profound consequences described here. Reimposing symmetry requires that the background space-time satisfy the equations of general relativity: general relativity, hence classical space-time as we know it, arises from string theory. We investigate the logical role of Weyl symmetry in this explanation of general relativity: it is not an independent physical postulate but required in quantum string theory, so from a certain point of view it plays only a (...) formal role in the explanation. (shrink)

The Sleeping Beauty problem is test stone for theories about self-locating belief, i.e. theories about how we should reasons when data or theories contain indexical information. Opinion on this problem is split between two camps, those who defend the "1/2 view" and those who advocate the "1/3 view". I argue that both these positions are mistaken. Instead, I propose a new "hybrid" model, which avoids the faults of the standard views while retaining their attractive properties. This model _appears_ to violate (...) Bayesian conditionalization, but I argue that this is not the case. By paying close attention to the details of conditionalization in contexts where indexical information is relevant, we discover that the hybrid model is in fact consistent with Bayesian kinematics. If the proposed model is correct, there are important lessons for the study of self-location, observation selection theory, and anthropic reasoning. (shrink)

People are unable to report how they decide whether to move backwards or forwards to catch a ball. When asked to imagine how their angle of elevation of gaze would change when they caught a ball, most people are unable to describe what happens although their interception strategy is based on controlling changes in this angle. Just after catching a ball, many people are unable to recognise a description of how their angle of gaze changed during the catch. Some people (...) confidently choose incorrect descriptions that would guarantee failure of interception demonstrating unconscious knowledge co-existing with systematically different conscious beliefs. Where simple solutions to important evolutionary problems exist, unconscious perception needs to be impervious to conscious beliefs. (shrink)

This article considers a series of ideas disturbing the conventional wisdom that decrees education an essential force in saving the world. Taking Morton's descriptions of hyperobjects seriously, we consider his radical idea that the world has ended amidst the eco-political depredations of the Anthropocene. Accordingly, we claim that education in modernity most properly belongs - materially and ideologically - with technological enframing and the rise of biopower. In other words, what is taken almost universally as the sacred realm of education (...) is, in fact, a contributory factor in the global eco-ontological crisis. Morton describes global warming, plastics and nuclear arsenals as hyperobjects: viscous, nonlocal entities that exist in temporal and spatial planes vastly different from our own immediate worlds. They are the threatening, difficult to access entities that express the Anthropocene. While most will propose that education will be vital in combating looming ecological apocalypse, we consider that education is a hyperobject itself. Education, we opine, is aligned with the forces and conditions that have generated the present crisis. This is because education embodies the same qualities as the hyperobjects of modernity; according to any rigorous historical ontology, education as we know it must be seen as the most extensive expression of a dangerous biopower that is beyond control. If this position is to be taken seriously, education is not merely impotent in combatting ecological catastrophe, but is a key apparatus supporting the Anthropocene. Education is thus another element of the end of the world. (shrink)

Quantum gravity--the marriage of quantum physics with general relativity--is bound to contain deep and important lessons for the nature of physical time. Some of these lessons shall be canvassed here, particularly as they arise from quantum general relativity and string theory and related approaches. Of particular interest is the question of which of the intuitive aspects of time will turn out to be fundamental, and which 'emergent' in some sense.

This paper argues that the dirty hands literature has overlooked a crucial distinction in neglecting to discuss explicitly the issue of, what I call, symmetry. This is the question of whether, once we are confronted with a dirty hands situation, we could emerge with our hands clean depending on the action we choose. A position that argues that we can keep our hands clean I call “asymmetrical” and one that says that we will get our hands dirty no matter what (...) we do I call “symmetrical”. Not acknowledging this distinction is a problem because, firstly, it adds to the existing confusions about how best to define what dirty hands are. Secondly, it prevents the concept of dirty hands from being applied properly to other contexts such as, for example, the responsibility and accountability of politicians. I argue that we have good reason to favour a symmetrical understanding because it gives a more convincing account of what makes an action dirty and because it more accurately captures our complex moral decision-making when faced with dirty hands situations. The paper concludes by outlining possible implications that the distinction between the symmetry view and the asymmetry view has on wider debates surrounding the problem of dirty hands. (shrink)

The Doomsday argument purports to show that the risk of the human species going extinct soon has been systematically underestimated. This argument has something in common with controversial forms of reasoning in other areas, including: game theoretic problems with imperfect recall, the methodology of cosmology, the epistemology of indexical belief, and the debate over so-called fine-tuning arguments for the design hypothesis. The common denominator is a certain premiss: the Self-Sampling Assumption. We present two strands of argument in favor of this (...) assumption. Through a series of thought experiments we then investigate some bizarre prima facie consequences – backward causation, psychic powers, and an apparent conflict with the Principal Principle. (shrink)

This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal proper- ties represent properties of time: these are surveyed. The central question of the paper is whether the existing representation of time is adequate, or whether it can or should be supplemented: especially, do we need a physics incorporating some kind of ‘dynamical passage’ of time? The paper argues that the existing mathematical framework is resistant to such (...) changes, and might have to be rejected by anyone seeking a physics of passage. Then it rebuts two common arguments for incorporating passage into physics, especially the claim that it is an element of experience. Finally the paper investigates whether, as has been claimed, ‘causal set theory’ provides a physics of passage. (shrink)

Three experiments investigated the contrasting predictions of the evolutionary and decision-theoretic approaches to deontic reasoning. Two experiments embedded a hazard management (HM) rule in a social contract scenario that should lead to competition between innate modules. A 3rd experiment used a pure HM task. Threatening material was also introduced into the antecedent, p, of a deontic rule, if p then must q. According to the evolutionary approach, more HM responses (Cosmides & Tooby, 2000) are predicted when p is threatening, whereas (...) decision theory predicts fewer. All 3 experiments were consistent with decision theory. Other theories are discussed, and it is concluded that they cannot account for the behavior observed in these experiments. (shrink)

Current cosmological theories say that the world is so big that all possible observations are in fact made. But then, how can such theories be tested? What could count as negative evidence? To answer that, we need to consider observation selection effects.

Contemporary education now appears to be dominated by the continual drive for improvement measured against the assessment of what students have learned. It is our contention that a foundational relation with assessment organises contemporary education. Here we draw on a 'way of thinking' that is deconstructive in its intent. Such thinking makes clear the vicious circularity of the argument for improvement, wherein assessment valorised in discourses of improvement provides not only a rationalisation for improvement via assessment, but also the very (...) means of achieving such possibilities via targets grounded in limited specifications of assessment. On reading Heidegger's 'question concerning technology' we sought to reconsider the vicious circle of improvement in relation to Being. We claim that the means-ends driven technology of assessment, rather than being at our disposal and under our control, only serves to reveals the Real to us in accordance with the restricting principle of reason. The principle of reason, we argue, grounds 'Enframing' that ranks and orders the very beings of education as objects to produce an objective 'world as picture', rather than opening the possibility of their identity as belongings with a movement of difference. So, 'improvement' becomes normative and binding for institutions and practices on grounds of the principle of assessment, and renders agents of education as functionaries of 'Enframing'. (shrink)

I defend logical realism. I begin by motivating the realist approach by underlining the difficulties for its main rival: inferentialism. I then focus on AND and OR, and delineate a realist view of these two logical constants. The realist view is developed in terms of Alexander’s Principleshowing that AND and OR have distinctive determining roles. After that, I say what logic is not. We should not take logic to be essentially about the mind, or language, or exclusively about an abstract (...) realm, or about reasoning, truth, truth-tables, truth-functions, topic-neutrality or form. Lastly, I turn to consider NEGATION and argue that we cannot escape negative facts, and facts conjoining and disjoining negative facts with positive facts. I then give NEGATION a distinctive role, one that contrasts with AND and OR. I reflect on the notion of logic in the coda. (shrink)

This paper defends the right of historians to make use of their knowledge of the remote consequences of past actions. In particular, it is argued that the disciplinary cohesion of the history of science relies crucially upon our ability to target, for further investigation, those past activities ancestral to modern science. The history of science is not limited to the study of those activities but it is structured around them. In this sense, the discipline is inherently ‘present-centred’: its boundaries are (...) determined, in part, by judgements inaccessible to the historical actors. Present-centredness of this sort, it is urged, should not be regarded as a problem; its methodological consequences are minimal.Author Keywords: Anachronism; Diachronic history; Present-centred history; Actors’ categories; Historical causation; Retrospective explanation. (shrink)

Beginning with a reconsideration of what the school is and has been, this paper explores the idea of the school to come. Emphasizing the governmental role of education in modernity, I offer a line of thinking that calls into question the assumption of both the school and education as possible conduits for either democracy or social justice. Drawing on Derrida’s spectral ontology I argue that any automatic correlation of education with democracy is misguided: especially within redemptive discourses that seek to (...) liberate education from its present enclosure. This rereading of the field of education in the light of an account of the fundamental ontology of its key institution problematizes all rhetorics of education as social salvation. Education, it proposes, cannot be conceived as the ideal soul of a corrupted or as yet defective body, the school. Education—having taken on the character of an ontotheological principle—has become a governmental instrument as much as its specific institutions. This ontological condition can be understood within various accounts of the nature of contemporaneity. This paper considers the monstrous proposal that education be abandoned as the grounds for social, ethical and cultural redemption. The good news is that this abandonment opens the possibility for thinking beyond education, a beyond that is also beyond the strictures of instrumental rationality. (shrink)

In some situations a number of agents each have the ability to undertake an initiative that would have significant effects on the others. Suppose that each of these agents is purely motivated by an altruistic concern for the common good. We show that if each agent acts on her own personal judgment as to whether the initiative should be undertaken, then the initiative will be undertaken more often than is optimal. We suggest that this phenomenon, which we call the unilateralist’s (...) curse, arises in many contexts, including some that are important for public policy. To lift the curse, we propose a principle of conformity, which would discourage unilateralist action. We consider three different models for how this principle could be implemented, and respond to an objection that could be raised against it. (shrink)

This is the introduction to the special issue of Studies in the History and Philosophy of Modern Physics on the emergence of spacetime in quantum theories of spacetime.

It is intuitively plausible that art and imagination are intimately connected. This chapter explores attempts to explain that connection. We focus on three areas in which art and imagination might be linked: production, ontology, and appreciation. We examine views which treat imagination as a fundamental human faculty, and aim for comprehensive accounts of art and artistic practice: for example, those of Kant and Collingwood. We also discuss philosophers who argue that a specific kind of imagining may explain some particular element (...) of the artistic domain: for example, Walton's ideas about representational art, and Kivy’s about reading. (shrink)

In this article, we explore the institutional negotiation of public engagement in matters of science and technology. We take the example of the Science in Society dialogue program initiated by the UK’s Royal Society, but set this case within the wider experience of the public engagement activities of a range of charities, corporations, governmental departments, and scientific institutions. The novelty of the analysis lies in the linking of an account of the dialogue event and its outcomes to the values, practices, (...) and imperatives—the institutional rationality—of the commissioning organization. We argue that the often tacit institutional construction of scientific citizenship is a critical, and relatively undeveloped, element of analysis—one that offers considerable insight into the practice and democratic implications of engaging publics in science and science policy. We also present evidence indicating that over time the expanding ‘‘capacities’’ associated with dialogue can act in subtle ways to enroll other elements of institutional architectures into more reflexive modes of thinking and acting. In the concluding section of the article, we consider the ways in which research and practice could engage more squarely with facets of institutional context and culture. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 9.3 (2002) 237-241 [Access article in PDF] Practical, Functional, and Natural Kinds Nick Haslam Keywords: Classification, essentialism, natural kinds, practical kinds. I am grateful to the two commentators for giving my paper their serious attention, and for writing such stimulating, clarifying, and challenging responses. In a brief response I can only begin to discuss a select few issues, although both commentaries could generate a (...) great deal of profitable exchange.Zachar's commentary elaborates his practical kinds model, discusses several of the graded series of kinds proposed in my taxonomy of psychiatric categories, and disputes some aspects of my treatment of natural kinds. Zachar and I have no quarrel on his first point. I recognize his practical kinds model as a general theory of psychiatric classification rather than simply as a description of one type of category, the "practical kind." It was perhaps bad form to pilfer a term from Zachar's model and give it a more circumscribed role in my own, although by doing so I intended both to acknowledge the importance of the concept and to situate it among some of its alternatives.All the same, I stand by the account of practical kinds developed in my paper, even if it reflects a narrower sense than Zachar's. In my sense, practical kinds are pragmatically drawn distinctions imposed on continuous dimensions, whereas to Zachar all psychiatric categories are at least to some degree practical. He therefore proposes a broad "continuum" of practical kinds. The difficulty that I have with this proposal is that such a continuum implies a fundamental unity among psychiatric categories: categories are all to be understood first and foremost in pragmatic terms and differences in kind between them in internal structure are to be neglected. In my view, although the pragmatic bases of psychiatric classification are vitally important, and perhaps inadequately formulated in my paper, the neglect of internal structure and of possible breaks in the continuum of kinds are real limitations of the practical kinds model. Although Zachar is partially justified in claiming that his view is pluralistic, allowing as it does for variability in degrees of practicality, by failing to acknowledge distinctly different kinds of categories in the psychiatric domain, his view is less pluralistic than I believe it should be.One example of what I take to be this neglect of structural differences is a conflation of two sorts of practicality in Zachar's work. On the one hand, certain categories such as hypertension or obesity are defined on pragmatic grounds, a binary distinction being drawn in the absence of an internal discontinuity, because individuals identified as category members are adjudged to [End Page 237] be at significantly elevated risk. On the other hand, some categories just happen to have high practical utility. Zachar argues that schizotaxia, for example, is practical because it affords a variety of scientific and clinical inferences.It seems to me that these sorts of practicality—or perhaps these sorts of relations to practicality—are importantly different. Hypertension is defined as a category because of its practical utility—because a certain blood pressure threshold marks an inflection in actuarial risk of other illnesses—and might therefore be said to have "front-end" or constitutive practicality. Schizotaxia, which taxometric research shows to be a discrete kind (Haslam, 2003), is not defined and identified primarily on the basis of its relation to an external criterion, but on the basis of its internal structure. Its features cohere in a way that indicates a category with a determinate prevalence. It has "back-end" or consequential practicality to the degree that this category enables useful predictions. These two proposed forms of practicality are equally important: both mean that categories will be pragmatically valuable. However, they are also different, being characteristic of different kinds of categories and perhaps even negatively related. Kinds with front-end practicality, that is, may tend to have a more restricted range of practical implications, defined as they are in relation to specific external criteria. Kinds with back-end practicality, in contrast, may enable a wider array of predictions to the extent that... (shrink)

Despite his longstanding silence regarding Marx’s Capital, I wish here to argue that Badiou has in fact, in the three volumes of Being and Event, produced the materials for a contemporary logic of the capitalist social form. He has done so, however, in the form of an arsenal of abstract concepts that have yet to be precisely measured against Marx’s critical and formal reproduction of capitalism, the systematic exposition of which consumes the three volumes of Capital. I first argue that (...) Badiou’s general disinterest in the logic of capitalism and Marx’s Capital specifically takes on a strongly symptomatic, spectral presence in the 1994-1995 seminar Lacan: Anti-philosophy 3. Secondly, while it is true that Badiou’s Logics of Worlds never discusses the logic of appearance that governs all capitalist things, it is possible nonetheless to read Logics as an abstract translation and formalisation of Marx’s Capital. In this view, Capital should quite simply be read as a systematic demonstration of the logic of what Marx calls the capitalist social form, which is to say, in Badiou’s jargon, the logic or science of the appearance of things in the capitalist world. In a sense, then, this means nothing more, though nothing less, than subjecting the Logics of Worlds to a Marxian torsion: in order to demonstrate that which Badiou has neglected, Marx has in fact already accomplished, i.e. the systematic, synthetic demonstration of the necessary forms of the appearance of commodities in the capitalist social form. (shrink)

Journal of Social Philosophy, EarlyView.

This paper investigates the historiographical utility of psychoanalysis, focussing in particular on retrospective explanations of demonic possession and exorcism. It is argued that while 'full-blown' psychoanalytic explanations-those that impose Oedipus complexes, anal eroticism or other sophisticated theoretical structures on the historical actors-may be vulnerable to the charge of anachronism, a weaker form of retrospective psychoanalysis can be defended as a legitimate historical lens. The paper concludes, however, by urging historians to look at psychoanalysis as well as trying to look through (...) it. Full-blown psychoanalysis is a bad historical lens but it may, in some cases, be an excellent explanatory template: a thorough understanding of how psychoanalytic therapy functions in the modern world is, for example, a good theoretical preparation for historians seeking to understand the sixteenth-century's demonological universe. (shrink)

The latter part of the twentieth century saw the Chinese economy moving towards a socialist market economy rather than a planned system. Despite growing interest in Chinese business ethics, little work has examined ethical issues concerning the Chinese sales force. This study draws from existing work on Chinese and Western business and sales ethics to develop hypotheses regarding the perceptions of unethical selling behaviour of modern Chinese salespeople. A survey of Chinese sales executives is conducted and statistically analysed. Results are (...) compared with those reported in previous US-based research with regard to differences in perceptions of unethical selling behaviour. The results indicate that contemporary Chinese salespeople were more favourably disposed than expected towards unethical selling behaviour, and also more favourably disposed than previously studied US salespeople. Younger Chinese salespeople evaluated unethical behaviours more favourably than older ones. The results are discussed, along with implications for theory, practice and future work. (shrink)

In this paper, I assess Dickie's institutional theory of art. I compare the earlier and later forms of the theory, and I point to various problems of detail with these accounts. I then proceed by arguing that Dickie's definition excludes Krispy Kreme doughnut boxes from possessing the status of being works of art, and it excludes those who made them from possessing the status of being artists. The intention is not to offer a counter example to Dickie's account. Rather, the (...) complaint is that there could be no philosophical point or interest in a concept of art which excludes these doughnut boxes. The best way to see this is by contrast with a concept of art that includes them. Thus I outline what I call a ‘creative’ account. What we want is a concept of art which helps us understand a certain phenomenon in the world – the phenomenon that we call ‘art’. In this light, I argue that Dickie's institutional theory tells us nothing about why people want to make art and nothing about why they want to experience it. By contrast, the creative theory, which embraces both doughnut boxes and things in galleries, is more explanatory. (shrink)

Cummins (this issue) puts the case for an innate module for deontic reasoning. We argue that this case is not persuasive. First, we claim that Cummins’evolutionary arguments are neutral regarding whether deontic reasoning is learned or innate. Second, we argue that task differences between deontic and indicative reasoning explain many of the phenomena that Cummins takes as evidence for a deontic module. Third, we argue against the suggestion that deontic reasoning is superior to indicative reasoning, either in adults or children. (...) Finally, we re‐evaluate Cummins’interpretation of differences in children's performance on deontic and indicative versions of Wason's selection task. (shrink)

In a recent paper in this journal, Ken Olum attempts to refute the doomsday argument by appealing to the self–indication assumption (SIA) that your very existence gives you reason to think that there are many observers. Unlike earlier users of this strategy, Olum tries to counter objections that have been made against (SIA). We argue that his defence of (SIA) is unsuccessful. This does not, however, mean that one has to accept the doomsday argument (or the other counter–intuitive results that (...) flow from related thought–experiments). A developed theory of observation selection effects shows why the doomsday argument is inconclusive, and how one can consistently reject both it and (SIA). (shrink)

In two experiments, we examined whether POWER is embodied in terms of horizontal forward and backward movement using an action compatibility task. Participants were asked to categorize power-relate...

Must mental properties figure in psychological causal laws if they are causally efficacious? And do those psychological causal laws give the essence of mental properties? Contrary to the prevailing consensus, I argue that, on the usual conception of laws that is in play in these debates, there are in fact lawless causally efficacious properties both in and out of the philosophy of mind. I argue that this makes a great difference to the philosophical relevance of empirical psychology. 1 begin by (...) making the case that revolutions and hurricanes are lawless phenomena, before arguing for a similar thesis about creativity, love, courage, dreams, daydreams, and musings. Furthermore, the empirical research on these phenomena suggests that the philosophical issues may be independent of what empirical psychology can tell us. (shrink)

There are two boxes in front of you and you are asked to choose between taking only box B or taking both box A and box B. Box A contains $ 1,000. Box B will contain either nothing or $ 1,000,000. What B will contain is (or will be) determined by Predictor, who has an excellent track record of predicting your choices. There are two possibilities. Either Predictor has already made his move by predicting your choice and putting a million (...) dollars in B iff he predicted that you will take only B (like in the standard Newcomb problem); or else Predictor has not yet made his move but will wait and observe what box you choose and then put a million dollars in B iff you take only B. In cases like this, Predictor makes his move before the subject roughly half of the time. However, there is a Metapredictor, who has an excellent track record of predicting Predictor’s choices as well as your own. You know all this. Metapredictor informs you of the following truth functional: Either you choose A and B, and Predictor will make his move after you make your choice; or else you choose only B, and Predictor has already made his choice. Now, what do you choose? (shrink)

A set of axioms is presented defining an ‘analytic Zariski structure’, as a generalisation of Hrushovski and Zilber’s Zariski structures. Some consequences of the axioms are explored. A simple example of a structure constructed using Hrushovski’s method of free amalgamation is shown to be a non-trivial example of an analytic Zariski structure. A number of ‘quasi-analytic’ results are derived for this example e.g. analogues of Chow’s theorem and the proper mapping theorem.

The filtration method for proving decidability in a focused minimal manner is a highlight of modal logic, widely used, but also posing a bit of a challenge as to its scope and what makes it tick. In this paper, we bring together a number of modern perspectives on filtration, including model-theoretic and proof-theoretic ones. We also include a few more unusual recent connections with dynamic logics of model change and logics of questions and issues. Finally, we analyze where the filtration (...) method fails in full first-order logic, and what it still has to say there. (shrink)