The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements ("if P then Q") as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems can (...) be represented in it. This includes decision problems expressed in languages of classical propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems. (shrink)

We shall consider a formulation of generalised quantifiers using type theory with records (TTR). TTR follows closely the development of record types in Martin-L¨of or constructive type theory but differs in that the type theory is defined on a classical set theoretic basis. This means that the classical set-theoretic approach to generalised quantifiers can be imported into the type theoretic framework. The result is, I believe, equivalent to the proposal for dynamic generalised quantifiers in Chierchia (1995). The use of dependent (...) types provides us with an elegant approach to the formulation of dynamic quantifiers. We use a notion of hypothetical context which we have used elsewhere to give accounts of intentional identity, answers to questions and information state updates in dialogue management. We suggest that this points towards a general theory of hypothetical context in natural language. We suspect also that our analysis using records will support analyses of common noun phrase and verb-phrase anaphora and also facilitate representations which are underspecified with respect to quantifier scope, though we leave the investigation of this to future research. (shrink)

Fear generalisation is a psychological phenomenon that occurs when fear that is elicited in response to a frightening stimulus spreads to similar or related stimuli. The practical harms of pathological fear generalisation related to trauma are well-documented, but little or no attention has been given so far to its epistemic harms. This paper fills this gap in the literature. It shows how the psychological phenomenon, when it becomes pathological, substantially curbs the epistemic agency of those who experience the (...) fear that generalizes, limiting their ability to respond to evidence, and substantially limiting their epistemic horizons. It is argued that when these epistemic harms are caused by wrongful actions and decisions of individuals or institutions, because the fear is elicited in response to a traumatic experience inflicted by them, the harms should be considered epistemic wrongs. The epistemic wrongs are closely akin to agential epistemic injustice, a variety of distributive epistemic injustice, and sometimes also involve epistemic exclusion. The paper thereby identifies a previously underexplored psychological mechanism that can be a vehicle through which both individuals and institutions can epistemically wrong others. The argument has implications for how both epistemic wrongs and epistemic injustice should be conceived, suggesting that both can occur without being caused by primarily epistemic flaws or errors, or a bad epistemic character. Finally, it highlights the advantage of taking a victim-centred approach to understanding epistemic harm. (shrink)

In what sense are the special sciences autonomous of fundamental physics? Autonomy is an enduring theme in discussions of the relationship between the special sciences and fundamental physics or, more generally, between higher and lower-level facts. Discussion of ‘autonomy’ often fails to recognise that autonomy admits of degrees; consequently, autonomy is either taken to require full independence, or risk relegation to mere apparent autonomy. In addition, the definition of autonomy used by Fodor, the most famous proponent of the autonomy of (...) the special sciences, has been robustly criticised by Loewer. In this paper I develop a new account of autonomy following Woodward which I dub ‘generalised autonomy’ since it unifies dynamical, causal and nomic autonomy. Autonomy, on this account, can be partial: some lower-level details matter while others do not. To summarise: whilst the detailed lower level is unconditionally relevant, conditionalising on the higher-level facts renders some lower-level details irrelevant. The macrodependencies that the higher-level facts enter into — be they dynamical, causal or nomic — screen off the underlying microdetails. This account helps resolve an explanatory puzzle: if the lower-level facts in some way underpin the higher-level facts, why don’t the lower-level details matter more for the day-to-day practice of the special sciences? The answer will be: the facts uncovered by the special sciences are autonomous in my sense, and so practitioners of these special sciences need not study more fundamental sciences, since these underlying facts are genuinely irrelevant. (shrink)

Generalises the concept of a relational model for modal logic, due to Kripke, so as to obtain a closer correspondence between relational and algebraic models. The generalisation obtained is essentially equivalent to the notion of a "first-order" model that was defined independently by S.K.Thomason.

Conceptual generalisation occurs when conditional responses generalise to novel stimuli from the same category. Past research demonstrates that physiological fear responses generalise across categories, however, conceptual generalisation of stimulus valence evaluations during fear conditioning has not been examined. We investigated whether conceptual generalisation, as indexed by electrodermal responses and stimulus evaluations, would occur, and differ after training with single or multiple conditional stimuli (CSs). Stimuli from two of four categories (vegetables, farm animals, clothing, and office supplies) were (...) used as the CS+ (followed by an electric stimulus) or CS- (presented alone). Generalisation was assessed by presenting novel stimuli from the CS categories after acquisition, extinction, and reinstatement. One category exemplar was used as the CS+ and CS- in the single group, whereas three exemplars were used as the CS+ and CS- in the multiple group. Electrodermal responses generalised in acquisition and extinction but did not differ between groups. In the multiple group, CS evaluations generalised in acquisition and extinction, whereas generalisation was not evident in the single group. Training with multiple CSs also resulted in the extinction of stimulus valence. The current findings have implications for future research examining the generalisation of valence and for exposure-based treatments of anxiety. (shrink)

We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation. The generalisation involves replacing Martin-Löf type theory with a new type theory in which logic is treated as primitive. The primitive treatment of logic in type theories allows us to study reinterpretations of logic, such as the double-negation translation.

Misreadings of Derrida's Of Grammatology were prevalent from the time of its debut, up to the present day. For fifty years, Derrida's generalised textuality has been misread as though he meant there was nothing outside text in the traditional sense. This misreading always serves to re-institute notions of linear temporal progress, either among self-styled avant-garde authors who would like to break with past traditions, or among self-styled conservatives who hope to repeat them. If the binaries that divide these works from (...) past texts are undecidable, the ground for such temporal progress disappears, along with the divisions by which we create linear narratives of history. The misreading of Derrida is an attempt to exorcise this undecidability and regain the intellectual and market value of novelty or repetition. (shrink)

While the biomedical model is still theleading paradigm within modern medicine and healthcare, and people with generalised chronicmusculoskeletal pain are frequent users of health careservices, their diagnoses are rated as having thelowest prestige among health care personnel. Anepistemological framework for understanding relationsbetween body, emotions, mind and meaning is presented.An approach based on a phenomenological epistemologyis discussed as a supplement to actions based on thebiomedical model.Within the phenomenological frame of understanding,the body is viewed as a subject and carrier ofmeaning, and therefore (...) chronic pain can be interpretedas a rational reaction to the totality of a person'slife situation. Search for possible hidden individualmeanings in painful muscles presupposes meeting healthpersonnel who view the person within a holistic frameof reference. (shrink)

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. In (...) this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces. (shrink)

Canonical extension has proven to be a powerful tool in algebraic study of propositional logics. In this paper we describe a generalisation of the theory of canonical extension to the setting of first order logic. We define a notion of canonical extension for coherent categories. These are the categorical analogues of distributive lattices and they provide categorical semantics for coherent logic, the fragment of first order logic in the connectives ∧, ∨, 0, 1 and ∃. We describe a universal (...) property of our construction and show that it generalises the existing notion of canonical extension for distributive lattices. Our new construction for coherent categories has led us to an alternative description of the topos of types, introduced by Makkai in [22]. This allows us to give new and transparent proofs of some properties of the action of the topos of types construction on morphisms. Furthermore, we prove a new result relating, for a coherent category C, its topos of types to its category of models. (shrink)

We study the Iterated Bilateral Reciprocity game in which the need for help arises randomly. Players are heterogeneous with respect to ‘neediness’ i.e. probability of needing help. We find bounds on the amount of heterogeneity which can be tolerated for cooperation (all players help when asked to help) to be sustainable in a collectivity. We introduce the notion of Generalised Reciprocity. Individuals make a costly first move to benefit another under the reasonable expectation that either the other or somebody else (...) will reciprocate. We hope that these tentative attempts at extending Axelrod’s seminal work on cooperation will inspire future efforts in the field of organisational culture and social theory more generally. (shrink)

This chapter suggests that evidence should be viewed as a field of study, one to which most disciplines could contribute and from which most could benefit, and that generalisations should be viewed as part of that field. Every argument must be based upon a generalisation that can be stated as a major premise. The relationship between a supporting proposition or propositions and an inferred proposition can be restated in a quasi-deductive form by identifying the generalisation upon which the (...) inference depends. A datum or a proposition can be evidence if and only if it alters the probability, positively or negatively, of a proposition to be inferred. In order to demonstrate that an evidential proposition is relevant, an analyst must be able to identify and articulate a generalisation that justifies the claim that the evidential proposition alters the probability of an inferred proposition. This chapter develops these ideas and presents a method of generalisation-analysis. It also argues that generalisation-analysis is a tool in the field of evidence that could be useful in analysing and critiquing arguments in many disciplines. (shrink)

The aim of this paper is to explore the conditions under which generalisation from single case studies, in the sense of making inferences concerning a wider class of phenomena beyond a case, is reasonable. Two sets of conditions, in particular, provide the basis for our consideration of this issue. The first is an exploration of the impressive amount of empirical knowledge that is contained within the theories that are used to make observations, to classify phenomena, and to understand and (...) interpret cases. The second is recognition of the role of a pattern of inference known as abduction, or inference to the best explanation, in drawing conclusions from case studies. It is argued that these two conditions, when applied to the procedures for conducting case studies, can be used to defend, as reasonable, the making of certain provisional generalisations from single cases. An epistemological procedure for testing and further justifying these generalisations, with a particular emphasis on dealing with the problem of confirmation bias, is then discussed and recommended. (shrink)

The aim of this paper is to explore the conditions under which generalisation from single case studies, in the sense of making inferences concerning a wider class of phenomena beyond a case, is reasonable. Two sets of conditions, in particular, provide the basis for our consideration of this issue. The first is an exploration of the impressive amount of empirical knowledge that is contained within the theories that are used to make observations, to classify phenomena, and to understand and (...) interpret cases. The second is recognition of the role of a pattern of inference known as abduction, or inference to the best explanation, in drawing conclusions from case studies. It is argued that these two conditions, when applied to the procedures for conducting case studies, can be used to defend, as reasonable, the making of certain provisional generalisations from single cases. An epistemological procedure for testing and further justifying these generalisations, with a particular emphasis on dealing with the problem of confirmation bias, is then discussed and recommended. (shrink)

The most common way of analysing the meaning of causal generalisations relies on referentialist semantics. In this article, we instead develop an analysis based on inferentialist semantics. According to this approach, the meaning of a causal generalisation is constituted by the web of inferential connections in which the generalisation participates. We distinguish and discuss five classes of inferential connections that constitute the meaning of causal generalisations produced in policy-oriented economic research. The usefulness of our account is illustrated with (...) the analysis of generalisations about unemployment put forward by the Organisation for Economic Co-operation and Development in its highly influential 1994 OECD Jobs Study. The article ends with a discussion of some crucial philosophical questions about the use of inferentialism in the analysis of causal generalisations. (shrink)

Fear generalisation, a process by which conditioned fear spreads to similar but innocuous stimuli, is key in understanding why some individuals feel unsafe in objectively non-threatening situations. Both trait neuroticism and lack of predictability about the likelihood of feared consequences are associated with negative affect in the face of ambiguity and may increase the degree to which fear generalises. Undergraduates with varying degrees of neuroticism were randomised to either high- or low-instructional predictability conditions prior to fear acquisition. A fear (...) generalisation test measured risk ratings and attentional bias on a modified dot-probe paradigm. Among individuals with higher neuroticism, providing instructional predictability did not reduce fear; these individuals reported higher risk and increased attentional bias toward ambiguous stimuli. Overall, for individuals with higher neuroticism, predictability information hurt rather than helped interpretation of ambiguous stimuli, challenging a common conceptualisation of predictability as a factor that reduces fear. (shrink)

Excessive fear generalisation is a feature characteristic of clinical anxiety and has been linked to its aetiology. Previous animal studies have shown that the mere passage of time increases fear generalisation and that brief exposure to training cues prior to long-term testing reverses this effect. The current study examined these phenomena in humans. Healthy participants learned the relationship between the presentation of a picture of a neutral male face and the delivery of a mild shock. One group was (...) immediately tested with a novel picture of a somewhat different male face (generalisation test). Another group was tested one week later. A third group was also tested one week later and was additionally exposed to the training picture prior to testing. During picture presentations, shock-expectancy ratings were obtained as a measure of fear. Fear generalisation increased from the immediate test to the 1-week follow-up test. This result could not be attributed to level of neuroticism or a general increase in fear (incubation). Furthermore, the time-dependent increase in fear generalisation vanished following brief exposure to the training picture. Results indicate that human fear generalisation is a temporally dynamic process and that memory for stimulus details can be re-established following a reminder treatment. (shrink)

A physiological function can be described as a cycle based on a cusp bifurcation set in catastrophe theory. This cycle involves four phases that are successively developed along a functional potential, which is used to perform a given physiological act. The work we present is firstly based on a detailed study of the global function of vision, which covers a vast field extending from the molecular to cerebral scale. We then present other examples of generalised functions by expanding the frame (...) of reference, from the scale of an organ to the scale of a whole organism with predation function, and to the scale of a social group with crisis management. We observed that the criteria remain the same, whether the function is considered on the scale of a cell membrane or a group of individuals organised into a cohort. Moreover, a so-called generalised function can be broken down into simpler sub-functions, each phase of the initial function containing the physiological act of each sub-function. It seems thus that a fractal extension may characterise the four-cusp spiral. This spiral is increasingly large as the types of sub-functions are multiplied. In functions relative to sociological science, such as crisis management, which are not natural but built and designed by humans, close attention must be paid to following the rules of these generalised biological functions. (shrink)

1. Generalising a given set of examples is essential in many machine learning techniques. In principle, a machine learning algorithm builds an abstract model that represents a set of examples. But...

We study ultraproducts of finite residue rings \ where \ is a non-principal ultrafilter. We find sufficient conditions of the ultrafilter \ to determine if the resulting ultraproduct \ has simple, NIP, \ but not simple nor NIP, or \ theory, noting that all these four cases occur.

Science is always presupposing some basic concepts that are held to be useful. These absolute presuppositions (Collingwood) are rarely debated and form the framework for what has been termed paradigm by Kuhn. Our currently accepted scientific model is predicated on a set of presuppositions that have difficulty accommodating holistic structures and relationships and are not geared towards incorporating non-local correlations. Since the theoretical models we hold also determine what we perceive and take as scientifically viable, it is important to look (...) for an alternative model that can deal with holistic relationships. One approach is to generalise algebraic quantum theory, which is an inherently holistic framework, into a generic model. Relaxing some restrictions and definitions from quantum theory proper yields an axiomatic framework that can be applied to any type of system. Most importantly, it keeps the core of the quantum theoretical formalism. It is capable of handling complementary observables, i.e. descriptors which are non-commuting, incompatible and yet collectively required to fully describe certain situations. It also predicts a generalised form of non-local correlations that in quantum theory are known as entanglement. This generalised version is not quantum entanglement but an analogue form of holistic, non-local connectedness of elements within systems, predicted to occur whenever elements within systems are described by observables which are complementary to the description of the whole system. While a considerable body of circumstantial evidence supports the plausibility of the model, we are not yet in a position to use it for clear cut predictions that could be experimentally falsified. The series of papers offered in this special issue are the beginning of what we hope will become a rich scientific debate. (shrink)

The paper contains an exposition of some non standard approach to gentzenization of modal logics. The first section is devoted to short discussion of desirable properties of Gentzen systems and the short review of various sequential systems for modal logics. Two non standard, cut-free sequent systems are then presented, both based on the idea of using special modal sequents, in addition to usual ones. First of them, GSC I is well suited for nonsymmetric modal logics The second one, GSC II (...) is devised specially for symmetric, i.e. Blogics. GSC I and GSC II are not different formalizations, from the theoretical point of view GSC I may be seen as a simplification of the more general approach present in GSC II. They are considered separately, mainly because Blogics demand different, and more complicated, strategy in completeness proof, whereas non symmetric logics are easily and uniformly characterised by means of Fitting's Consistency Properties. The weakest modal logic captured by this formalization is minimal regular logic C, but many stronger logics are obtainable by addition of suitable structural rules, which conforms to Do en's methodology. Both variants of GSC satisfy also other, besides cut-freedom, desirable properties. (shrink)

In this paper non-Hausdorff manifolds as potential basic objects of General Relativity are investigated. One can distinguish four stages of identifying an appropriate mathematical structure to describe physical systems: kinematic, dynamical, physical reasonability, and empirical. The thesis of this paper is that in the context of General Relativity, non-Hausdorff manifolds pass the first two stages, as they enable one to define the basic notions of differential geometry needed to pose the problem of the evolution-distribution of matter and are not in (...) conflict with the Einstein equations. With regard to the third stage, various potential conflicts with physical reasonability conditions are considered with a tentative conclusion that non-Hausdorff manifolds are more likely to pass this stage than is typically assumed. When dealing with some of these problems, the modal interpretation of non-Hausdorff manifolds is invoked, according to which they represent bundles of alternative possible spacetimes rather than single spacetimes. (shrink)

Recent work on compositional distributional models shows that bialgebras over finite dimensional vector spaces can be applied to treat generalised quantifiersGeneralised quantifiers for natural language. That technique requires one to construct the vector space over powersets, and therefore is computationally costly. In this paper, we overcome this problem by considering fuzzy versions of quantifiers along the lines of ZadehZadeh, L. A., within the category of many valued relationsMany valued relations. We show that this category is a concrete instantiation of the (...) compositional distributional model. We show that the semantics obtained in this model is equivalent to the semantics of the fuzzy quantifiers of ZadehZadeh, L. A.. As a result, we are now able to treat fuzzy quantification without requiring a powerset construction. (shrink)

The principle of the common cause claims that if an improbable coincidence has occurred, there must exist a common cause. This is generally taken to mean that positive correlations between non-causally related events should disappear when conditioning on the action of some underlying common cause. The extended interpretation of the principle, by contrast, urges that common causes should be called for in order to explain positive deviations between the estimated correlation of two events and the expected value of their correlation. (...) The aim of this paper is to provide the extended reading of the principle with a general probabilistic model, capturing the simultaneous action of a system of multiple common causes. To this end, two distinct models are elaborated, and the necessary and sufficient conditions for their existence are determined. (shrink)

In the United States there is an increasing tendency to view the only educational research worthy of federal funding as that which is designed as an experiment using randomised controls. One of the foundational assumptions underlying this research design is that the results of such research are meant to be generalisable beyond any particular research study. The purpose of this paper is to historicise the assumption of generalisability by explaining the ways in which it is a particularly modern research project. (...) By historicising generalisability, I show the ways in which the current research standards are products of culturally specific historical circumstances. In other words, generalisability is a local phenomenon and not generalisable to other times and places. (shrink)

The present paper proposes a generalisation of the notion of disjunctive sequence, that is, of an infinite sequence of letters having each finite sequence as a subword. Our aim is to give a reasonable notion of disjunctiveness relative to a given set of sequences F. We show that a definition like “every subword which occurs at infinitely many different positions in sequences in F has to occur infinitely often in the sequence” fulfils properties similar to the original unrelativised notion (...) of disjunctiveness. Finally, we investigate our concept of generalised disjunctiveness in spaces of Cantor expansions of reals. (shrink)

Generic generalisations like ‘Opioids are highly addictive’ are very useful in scientific communication, but they can often be interpreted in many different ways. Although this is not a problem when all interpretations provide the same answer to the question under discussion, a problem arises when a generic generalisation is used to answer a question other than that originally intended. In such cases, some interpretations of the generalisation might answer the question in a way that the original speaker would (...) not endorse. Rather than excising generic generalisations from scientific communication, I recommend that scientific communicators carefully consider the kinds of questions their words might be taken to answer and try to avoid phrasing that might be taken to provide unintended answers. (shrink)

The objective of this article is to characterise elimination of finite generalised imaginaries as defined in [9] in terms of group cohomology. As an application, I consider series of Zariski geometries constructed [10, 23, 24] by Hrushovski and Zilber and indicate how their nondefinability in algebraically closed fields is connected to eliminability of certain generalised imaginaries.

This paper is a compilation of results originating in the author's master thesis. We give a useful characterization of the generalized bounding and dominating numbers, and. We show that when. And we prove a higher analogue of Bell's theorem stating that is equivalent to ‐centered).

Working within the framework of Bishop's constructive mathematics, we will show that it is possible to define compactness in a more general setting than that of uniform spaces. It is also shown that it is not possible to do this in a topological space.

ABSTRACTIn this paper, we present a generalisation of proof simulation procedures for Frege systems by Bonet and Buss to some logics for which the deduction theorem does not hold. In particular, we study the case of finite-valued Łukasiewicz logics. To this end, we provide proof systems and which augment Avron's Frege system HŁuk with nested and general versions of the disjunction elimination rule, respectively. For these systems, we provide upper bounds on speed-ups w.r.t. both the number of steps in (...) proofs and the length of proofs. We also consider Tamminga's natural deduction and Avron's hypersequent calculus GŁuk for 3-valued Łukasiewicz logic and generalise our results considering the disjunction elimination rule to all finite-valued Łukasiewicz logics. (shrink)

Disquotational theories of truth are often criticised for being too weak to prove interesting generalisations about truth. In this paper we will propose a certain formal theory to serve as a framework for a solution of the generalisation problem. In contrast with Horwich’s original proposal, our framework will eschew psychological notions altogether, replacing them with the epistemic notion of believability. The aim will be to explain why someone who accepts a given disquotational truth theory Th, should also accept various (...) generalisations not provable in Th. The strategy will consist of the development of an axiomatic theory of believability, one permitting us to show how to derive the believability of generalisations from basic axioms that characterise the believability predicate, together with the information that Th is a theory of truth that we accept. (shrink)