The reconciliation of theories of concepts based on prototypes, exemplars, and theory-like structures is a longstanding problem in cognitive science. In response to this problem, researchers have recently tended to adopt either hybrid theories that combine various kinds of representational structure, or eliminative theories that replace concepts with a more finely grained taxonomy of mental representations. In this paper, we describe an alternative approach involving a single class of mental representations called “semantic pointers.” Semantic pointers are symbol-like representations (...) that result from the compression and recursive binding of perceptual, lexical, and motor representations, effectively integrating traditional connectionist and symbolic approaches. We present a computational model using semantic pointers that replicates experimental data from categorization studies involving each prior paradigm. We argue that a framework involving semantic pointers can provide a unified account of conceptual phenomena, and we compare our framework to existing alternatives in accounting for the scope, content, recursive combination, and neural implementation of concepts. (shrink)

We propose a unified theory of intentions as neural processes that integrate representations of states of affairs, actions, and emotional evaluation. We show how this theory provides answers to philosophical questions about the concept of intention, psychological questions about human behavior, computational questions about the relations between belief and action, and neuroscientific questions about how the brain produces actions. Our theory of intention ties together biologically plausible mechanisms for belief, planning, and motor control. The computational feasibility of these mechanisms is (...) shown by a model that simulates psychologically important cases of intention. (shrink)

We describe a fully abstract semantics for a simple functional language with locally declared names which may be used as pointers to names. It is based on a category of dialogue games acted upon by the group of natural number automorphisms. This allows a formal, semantic characterization of the key properties of names such as freshness and locality.We describe a model of the call-by-value λ-calculus based on these games, and show that it can be used to interpret the nu-calculus (...) of Pitts and Stark. We then construct a model of our pointer-language by extending our category of games with an explicit representation of the store, using a notion of semantic garbage-collection to erase inaccessible pointers. Using factorization and decomposition techniques, we show that the compact elements of our model are definable as terms, and hence it is fully abstract. (shrink)

What is the nature of semantic memory? Philosophers and cognitive scientists have long held that semantic memory stores invariant knowledge structures to be retrieved as such. In this paper, I argue that this conception of semantic memory is likely false. In particular, I argue that if episodic and semantic memory share causal mechanisms, and episodic memory is (re)constructive, then semantic memory is likely constructive too. I review evidence that suggests that episodic and semantic memory (...) are subserved by a domain-general system that supports representing and navigating relations among various kinds of stimuli, including space, time, events, and semantic relations. I then review the supposed hallmark properties of constructivism in episodic memory and show that they appear in semantic memory as well. To increase the inductive support for my proposal, I show how the view predicts some of the evidence others have marshaled in favor of a constructivist semantic memory system. Finally, I close by providing a proof of concept for the view on offer, the semantic pointer architecture. (shrink)

_ Source: _Volume 94, Issue 3, pp 381 - 390 Reference can fail in a way that intentionality cannot. Though the stream of phenomenal experience typically does not fail to target objects outside, it may do. How does the mind go about targeting objects beyond itself? The speculative conjecture of this paper is that it does so by a type of process which can be called _pointing_, and that the acts or act-aspects of pointing can be called _pointers_. The notion (...) of a pointer has several suggestive roots. One is the familiar physical gesture of pointing. Another is the existence of directional signs such as on roads. The third is the software data types making direct reference to memory locations in computers, also called ‘pointers’. A final source is demonstrative pronouns and other deictic expressions in language, of which Peter Geach wrote, “a demonstrative pronoun … works like a pointer, not like a label”. I suggest that there is in the mental cognitive repertoire a structurally and semantically analogous type of act which pierces the passivity of perception, directs us outside the machine, and prepares the way for drawing others’ minds to the same thing. (shrink)

The semantic paradoxes, whose paradigm is the Liar, played a crucial role at a crucial juncture in the development of modern logic. In his 1908 seminal paper, Russell outlined a system, soon to become that of the Principia Mathematicae, whose main goal was the solution of the logical paradoxes, both semantic and settheoretic. Russell did not distinguish between the two and his theory of types was designed to solve both kinds in the same uniform way. Set theoreticians, however, (...) were content to treat only the set-theoretic paradoxes, putting aside the semantic ones as a non-mathematical concern. This separation was explicitly proposed, eighteen years after Russell’s paper, by Ramsey, though he, like Russell, advocated a system that addresses both kinds. Since then, the semantic paradoxes have been viewed within the perspective of the theory of truth, where they have occupied a respectable niche, but one of rather specialized interest. (shrink)

A complete axiomatic system CTL$_{rp}$ is introduced for a temporal logic for finitely branching $\omega^+$-trees in a temporal language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL$^{*}$ into CTL$_{rp}$. In particular, that yields a complete axiomatization for the translations of all valid CTL$^{*}$-formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive medium for (...) reasoning about branching time. (shrink)

Background To produce and understand words, humans access the mental lexicon. From a functional perspective, the long-term memory component of the mental lexicon is comprised of three levels: the concept level, the lemma level, and the phonological level. At each level, different kinds of word information are stored. Semantic as well as phonological cues can help to facilitate word access during a naming task, especially when neural dysfunctions are present. The processing corresponding to word access occurs in specific parts (...) of working memory. Neural models for simulating speech processing help to uncover the complex relationships that exist between neural dysfunctions and corresponding behavioral patterns. Methods The Neural Engineering Framework (NEF) and the Semantic Pointer Architecture (SPA) are used to develop a quantitative neural model of the mental lexicon and its access during speech processing. By simulating a picture-naming task (WWT 6-10), the influence of cues is investigated by introducing neural dysfunctions within the neural model at different levels of the mental lexicon. Results First, the neural model is able to simulate the test behavior for normal children that exhibit no lexical dysfunction. Second, the model shows worse results in test performance as larger degrees of dysfunction are introduced. Third, if the severity of dysfunction is not too high, phonological and semantic cues are observed to lead to an increase in the number of correctly named words. Phonological cues are observed to be more effective than semantic cues. Conclusion Our simulation results are in line with human experimental data. Specifically, phonological cues seem not only to activate phonologically similar items within the phonological level. Moreover, phonological cues support higher-level processing during access of the mental lexicon. Thus, the neural model introduced in this paper offers a promising approach to modeling the mental lexicon, and to incorporating the mental lexicon into a complex model of language processing. (shrink)

We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, (...) Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (shrink)

This chapter provides a general overview of the issues surrounding so-called semantic monsters. In section 1, I outline the basics of Kaplan’s framework and spell out how and why the topic of “monsters” arises within that framework. In Section 2, I distinguish four notions of a monster that are discussed in the literature, and show why, although they can pull apart in different frameworks or with different assumptions, they all coincide within Kaplan’s framework. In Section 3, I discuss one (...) notion that has spun off into the linguistics literature, namely “indexical shift”. In Section 4, I emphasize the connection between monsters and the compositionality of asserted content in Kaplan’s original discussion. Section 5 discusses monsters and the more general idea of re-interpretation or meaning-shift. Section 6 closes with a brief survey of where monsters may dwell, and pointers to avenues for future research. (shrink)

In this article, I offer a provisional analysis of the philosophical semantics of "wisdom" in the thought of the New Confucian thinker Tang Junyi. I begin by providing some pointers concerning the concept of wisdom in general and situating the discourse on wisdom in comparative philosophy in the context of the later Foucault's and Pierre Hadot's historical investigations into ancient Graeco-Roman philosophy as a mode of spiritual self-cultivation and self-transformation. In the remainder of the paper, I try to describe and (...) think through what Foucault identifies as a "Cartesian moment," in which self-knowledge becomes the ultimate precondition for the ethico-spiritual project of "caring for the self," in Tang's approach of wisdom. In the course of my argument, I outline the complex relation between his vision of a renewed Confucian mode of religious practice on the one hand and his philosophical presuppositions concerning the transcendental status of subjectivity and the reflexivity of consciousness on the other. (shrink)

It is well known that humans represent the mental states of others and use these representations to successfully predict, understand, and manipulate their behaviour. This is an impressive ability. Many comparative psychologists believe that some non-human apes and monkeys attribute mental states to others. But is this ability unique to mammals? In this paper, I review findings from a range of behavioural studies on corvids, including food caching, food recaching and food sharing studies. In order to protect their caches from (...) being pilfered, corvids successfully keep track of observing conspecifics, employ a number of caching and recaching strategies, and exploit environmental factors to reduce the amount of visual and auditory information available to observing conspecifics. When giving food items as gifts, corvids give items for which conspecifics have developed a preference. I argue that the available evidence supports the hypothesis that corvids attribute mental states to conspecifics. I further hypothesize that corvids do so through process-driven simulation and the running of non-verbal multimodal rules accomplished by a class of mental representations called semantic pointers. (shrink)

IntroductionScientific pluralism is generally understood in the backdrop of scientific monism. So is mathematical pluralism. Though there are many culture-dependent mathematical practices, mathematical concepts and theories are generally taken to be culture invariant. We would like to explore in this paper whether mathematical pluralism is admissible or not.Materials and methodsMathematical pluralism may be approached at least from five different perspectives. 1. Foundational: The view would claim that different issues within mathematics need support of different foundations, apparently incompatible with one another. (...) 2. Ontological: The world itself is dappled—the mathematical counterpart of which can be traced to the admission of non-Euclidean spaces and also in simultaneous acceptance of set-theoretic and category theoretic entities in the ontology of mathematics. 3. The third route is epistemological. It follows from the view that the nature of reality is so complex that different aspects of it require alternative modes of representation and explanation sometimes severally, sometimes simultaneously, e.g., classical, constructivist, computer-aided and different finitist mathematics can be used depending on the knowledge situation. 4. The fourth route is semantic. Fuzzy mathematics, we know, gives up bivalence in theory of truth, and ascribes truth to mathematical propositions in degrees. 5. The last one is Programmatic: for some, mathematical pluralism is a stance, a programme. It provides a framework which strikes at the root of cultural hegemony and nourishes a climate of intellectual humility and tolerance. It is not my intention to hold the brief of any of these versions. I just want to present to the readers a more or less complete picture of the scenario, though not an exhaustive one. ConclusionUnlike monism, mathematical pluralism does not rule out any possibility—even the possibility of having a unitary over-arching framework of interpretation remains as an open option. This paper highlights the fact that motivations for upholding pluralism in mathematics have been many and one can be a pluralist just by subscribing to any of the views listed above. (shrink)

According to Thagard and Stewart :1–33, 2011), creativity results from the combination of neural representations, and combination results from convolution, an operation on vectors defined in the holographic reduced representation framework. They use these ideas to understand creativity as it occurs in many domains, and in particular in science. We argue that, because of its algebraic properties, convolution alone is ill-suited to the role proposed by Thagard and Stewart. The semantic pointer concept allows us to see how we (...) can apply the full range of HRR operations while keeping the modal representations so central to Thagard and Stewart’s theory. By adding another combination operation and using semantic pointers as the combinatorial basis, this modified version overcomes the limitations of the original theory and perhaps helps us explain aspects of creativity not covered by the original theory. While a priori reasons cast doubts on the use of HRR operations with modal representations :5039–5054, 1987) such as semantic pointers, recent models point in the other direction, allowing us to be optimistic about the success of the revised version. (shrink)

A standard philosophical approach to defining colour associates it with a ‘colour look‘ in standard circumstances. All extant plausible versions of this theory violate the condition that we should possess instinctive knowledge of colour. A more promising approach is a ‘semantic‘specification of the meaning of colour experiences, elaborated along the lines of Tarski=s semantic theory of truth: something is a particular colour if it really is the colour something looks to be when it presents the associated look. The (...) semantic theory is elaborated by means of an analogy between sensory systems and measuring instruments. The proposal is that sensory systems provide measurements in an ‘auto-calibrated‘ scale: in terms, that is, of something like a re-identifiable pointer position that is not specified by reference to an independently defined scale. (shrink)

Several approaches to implementing symbol-like representations in neurally plausible models have been proposed. These approaches include binding through synchrony, “mesh” binding, and conjunctive binding. Recent theoretical work has suggested that most of these methods will not scale well, that is, that they cannot encode structured representations using any of the tens of thousands of terms in the adult lexicon without making implausible resource assumptions. Here, we empirically demonstrate that the biologically plausible structured representations employed in the Semantic Pointer (...) Architecture approach to modeling cognition do scale appropriately. Specifically, we construct a spiking neural network of about 2.5 million neurons that employs semantic pointers to successfully encode and decode the main lexical relations in WordNet, which has over 100,000 terms. In addition, we show that the same representations can be employed to construct recursively structured sentences consisting of arbitrary WordNet concepts, while preserving the original lexical structure. We argue that these results suggest that semantic pointers are uniquely well-suited to providing a biologically plausible account of the structured representations that underwrite human cognition. (shrink)

The ability to improve in speed and accuracy as a result of repeating some task is an important hallmark of intelligent biological systems. Although gradual behavioral improvements from practice have been modeled in spiking neural networks, few such models have attempted to explain cognitive development of a task as complex as addition. In this work, we model the progression from a counting-based strategy for addition to a recall-based strategy. The model consists of two networks working in parallel: a slower basal (...) ganglia loop and a faster cortical network. The slow network methodically computes the count from one digit given another, corresponding to the addition of two digits, whereas the fast network gradually “memorizes” the output from the slow network. The faster network eventually learns how to add the same digits that initially drove the behavior of the slower network. Performance of this model is demonstrated by simulating a fully spiking neural network that includes basal ganglia, thalamus, and various cortical areas. Consequently, the model incorporates various neuroanatomical data, in terms of brain areas used for calculation and makes psychologically testable predictions related to frequency of rehearsal. Furthermore, the model replicates developmental progression through addition strategies in terms of reaction times and accuracy, and naturally explains observed symptoms of dyscalculia. (shrink)

This chapter presents the origin, history, and mathematics of the Yablo paradox. Careful formulations of the paradox within both arithmetic and a pointer semantics-based language are presented, as well as a number of formal results and philosophical observations that will be critical in the chapters to follow (e.g. the fact that the Yablo paradox, formulated in Peano arithmetic with a truth predicate, is not inconsistent, but merely ω -inconsistent). This chapter also provides a partial solution to the _Characterization Problem_ (...) (for the pointer semantics language) and shows how this problem is equivalent to an outstanding problem in the theory of directed graphs— that of determining whether a directed graph has a kernel. (shrink)

It has been suggested that Marr took the three levels he famously identifies to be independent. In this paper, we argue that Marr's view is more nuanced. Specifically, we show that the view explicitly articulated in his work attempts to integrate the levels, and in doing so results in Marr attacking both reductionism and vagueness. The result is a perspective in which both high-level information-processing constraints and low-level implementational constraints play mutually reinforcing and constraining roles. We discuss our recent work (...) on Spaun—currently the world's largest functional brain model—that demonstrates the positive impact of this kind of unifying integration of Marr's levels. We argue that this kind of integration avoids his concerns with both reductionism and vagueness. In short, we suggest that the methods behind Spaun can be used to satisfy Marr's explicit interest in combining high-level functional and detailed mechanistic explanations. (shrink)

For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated restricted variables called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time.We construct an axiomatic system for this (...) extended branching-time logic and prove its soundness and completeness with respect to bundle tree semantics. Finally, we show how our axiomatic system can be extended with a variety of important additional operators, such as Since and Until, a global difference operator, operators for undivided and divided histories, reference pointers, etc. (shrink)

Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic (...) of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities. (shrink)

Abstract In this paper I consider an easier-to-read and improved to a certain extent version of the causal chance-based analysis of counterfactuals that I proposed and argued for in my A Theory of Counterfactuals. Sections 2, 3 and 4 form Part I: In it, I survey the analysis of the core counterfactuals (in which, very roughly, the antecedent is compatible with history prior to it). In section 2 I go through the three main aspects of this analysis, which are the (...) following. First, it is a causal analysis, in that it requires that intermediate events to which the antecedent event is not a cause be preserved in the main truth-condition schema. Second, it highlights the central notion to the semantics of counterfactuals on the account presented here -- the notion of the counterfactual probability of a given counterfactual, which is the probability of the consequent given the following: the antecedent, the prior history, and the preserved intermediate events. Third, it considers the truth conditions for counterfactuals of this sort as consisting in this counterfactual probability being higher than a threshold. In section 3, I re-formulate the analysis of preservational counterfactuals in terms of the notion of being a cause, which ends up being quite compact. In section 4 I illustrate this analysis by showing how it handles two examples that have been considered puzzling – Morgenbesser's counterfactual and Edgington's counterfactual. Sections 5 and on constitute Part II: Its main initial thrust is provided in section 5, where I present the main lines of the extension of the theory from the core counterfactuals (analyzed in part I) to counterfactuals (roughly) whose antecedents are not compatible with their prior history. In this part II, I elaborate on counterfactuals that don't belong to the core, and more specifically on so-called reconstructional counterfactuals (as opposed to the preservational counterfactuals, which constitute the core counterfactual-type). The heart of the analysis is formulated in terms of processes leading to the antecedent (event/state), and more specifically in terms of processes likely to have led to the antecedent, a notion which is analyzed entirely in terms of chance. It covers so-called reconstructional counterfactuals as opposed to the core, so-called preservational counterfactuals, which are analyzed in sections 2 and 3 of part I. The counterfactual probability of such reconstructional counterfactuals is determined via the probability of possible processes leading to the antecedent weighed, primarily and roughly, by the conditional probability of the antecedent given such process: The counterfactual probability is thus, very roughly, a weighted sum for all processes most likely to have led to the antecedent, diverging at a fixed time. In section 6 I explain and elaborate further on the main points in section 5. In section 7 I illustrate the reconstructional analysis. I specify counterfactuals which are so-called process-pointers, since their consequent specifies stages in processes likely to have led to their antecedent. I argue that so-called backtracking counterfactuals are process-pointers counterfactuals, which fit into the reconstructional analysis, and do not call for a separate reading. I then illustrate cases where a speaker unwittingly employs a certain counterfactual while charitably construable as intending to assert (or ‘having in mind’) another. Here I also cover the issue of how to construe what one can take as back-tracking counterfactuals, or counterfactuals of the reconstructional sort, and more specifically, which divergence point they should be taken as alluding to (prior to which the history is held fixed). Some such cases also give rise to what one can take as a dual reading of a counterfactual between preservational and reconstructional readings. Such cases may yield an ambiguity, where in many cases one construal is dominant. In section 8 I illustrate the analysis by applying it to the famous Bizet-Verdi counterfactuals. This detailed analysis of counterfactuals (designed for the indeterministic case) has three main distinctive elements: its being chance-based, its causal aspect, and the use it makes of processes most likely to have led to the antecedent-event. This analysis is couched in a very different conceptual base from, and is an alternative account to, analyses in terms of the standard notion of closeness or distance of possible worlds, which is the main feature of the Stalnaker-Lewis-type analyses of counterfactuals. This notion of closeness or distance plays no role whatsoever in the analysis presented here. (This notion of closeness has been left open by Stalnaker, and to significant extent also by Lewis's second account.) . (shrink)

The ethics of Kant and the ethics of Crusius are strikingly similar. This is manifested in a whole range of principles and concepts. Crusius’ moral teaching hinges on the rigorous moral law which has to be obeyed absolutely, and which makes it different from other prescriptions that are binding only to a relative degree. This is very close to the Kantian distinction between hypothetical and categorical imperatives. Another salient feature of Crusius’ moral teaching is the stress laid on the sphere (...) of internal motives. It is the inner motive that determines the morality of an act, rather than the external form of the act. These and some other features of Crusius’ ethics suggest a possible influence of Crusius on Kant. The possibility of such influence has repeatedly come under close scrutiny. The first works devoted to this problem date to the turn of the nineteenth and twentieth centuries. Pointers to the possibility of such influence are semantic and structural similarities of the two thinkers’ systems. Besides, it is an unchallengeable fact that Kant was fairly familiar with the main theses of Crusian philosophy. Some scholars proceed from the study of Kantian vocabulary. Some of the terms Kant uses, especially in his early works which later formed the basis of his ethical teaching in the critical period, can be traced to the terms of Crusian philosophy. However, an alternative view is that Kant was primarily influenced by Wolffian philosophy (mainly through Baumgarten), while the direct influence of Crusius remains unproven. I examine both points of view and propose my own solution to the problem. (shrink)

This dissertation is a study of some recent theories of truth. The theories fall into three groups: The Revision Theories, the context-sensitive theories, and the "Chrysippian theories". ;The "Chrysippian theories" are based on the intuition that pathologicalities arising from the concept of truth can be recognized and acknowledged with the concept of truth itself. Thus, from the pathologicality of the Liar, for example, we can conclude that the Liar is not true. This leads to immediate difficulties since the Liar claims (...) just that--that it is not true--and it would thus seem to be true. The Chrysippian theories are designed to avoid these difficulties while preserving the motivating intuition. Haim Gaifman's Pointer Semantics, and Brian Skyrms' Intensional Fixed-Point Theory of Truth are examples of such theories. They are exposited and criticized. ;The context-sensitive theories dealt with are Tyler Burge's Indexical Theory of Truth and the theory of Jon Barwise and John Etchemendy. These theories claim that an ambiguity due to a contextual parameter is the reason for the difficulties we encounter. Burge offers a theory of Tarskian levels coupled with a pragmatic theory that explains the assignment of levels to occurrences of 'true'. Barwise and Etchemendy make explicit a situational parameter in their account of propositions. They consider the ambiguity with respect to the situation a propositions is about a main source of the paradoxes. ;Finally, the Revision Theories of Truth of Anil Gupta and Nuel Belnap and two variations of this theory are considered. One is due to Aladdin Yaqub, the other, the "fully-varied theory", is due to Gupta and Belnap but remains largely unexplored. Revision theories are put forward as the most promising account of the difficulties. They are based on a definitional reading of all Tarski biconditionals. The circularity implied by such a reading is handled by Gupta's and Belnap's general theory of definitions. ;Yaqub's objections raised against the standard theory are examined, and his proposed solution is shown to be inadequate. The fully-varied Revision Theory is shown to provide a better solution. (shrink)

Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the modal logic T. We give a semantics, a proof theory, and prove a completeness theorem. In addition, we prove a Realization Theorem, something that plays a central role for justification logics generally. Since (...) justification logics are newer and less well-known than hybrid logics, we sketch their background, and give pointers to their range of applicability. We conclude with suggestions for future research. Indeed, the main goal of this paper is to encourage others to continue the investigation begun here. (shrink)

We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion (...) operator and give its complete axiomatization. This logic is a sub-logic of statements in which the semantic predicates become internalized (for instance, counterparts of Tarski’s definitions and T-schemata become tautologies). Examples of analysis of self-referential paradoxes are given and the approach is compared to the alternative ones. (shrink)

I am quite prepared to admit that modern western thought is shot through with contradictions. For example, it is not coherent to think both that the idea of human nature is an illusion and that eugenics is an out-and-out evil; or to claim to be a democrat and exclude a priori the topic of eugenics from political debate. However, I personally very much doubt that the notions of nature and democracy are themselves in crisis. In my view they simply give (...) rise to semantic confusion and false problems that certain basic twentieth-century discoveries - in the field of physics, anthropology and political science - ought to be able to clear up, if they were better known. We shall just touch on a few thinkers whose work may give us some pointers to a clearer, calmer view of things. First a philosopher, Raymond Ruyer (1902-1987), and an economist, Joseph Schumpeter (1883-1950), two of whose key ideas this paper will combine: a neo-Aristotelian conception of nature, implying the existence of regulating principles and norms, to which humans and their societies, like everything else, are subject; a procedural conception of democracy that says it is not an end in itself but, under certain conditions, an appropriate means of making political decisions and settling disputes. And in addition some anthropologists, who helped either to put human beings back into a neo-Aristotelian world, or to define more accurately the essence of the political: Claude Lévi-Strauss, whose structuralism gave back its full importance to the notion of formal cause and even to the idea of final cause, and André Leroi-Gourhan, who confirmed that ‘art imitates nature’ by demonstrating that technical skill is a natural extension of life, whose processes and results it mimics; Arthur Maurice Hocart, who demonstrated the ritual origin of all institutions, particularly political ones. (shrink)

We tackle the problem of preservation of totality by composition in arena games. We first explain how this problem reduces to a finiteness theorem on what we call pointer structures, similar to the parity pointer functions of Harmer, Hyland and Mélliès and the interaction sequences of Coquand. We discuss how this theorem relates to normalization of linear head reduction in simply-typed lambda-calculus, leading us to a semantic realizability proof à la Kleene of our theorem. We then present (...) another proof of a more combinatorial nature. Finally, we discuss the exact class of strategies to which our theorems apply. (shrink)

There is a dilemma for all God-talk: either the predicates retain their familiar connotation, but then they are unsuitable for God; or they measure up to God, but then we no longer know what they mean. As a way out of the dilemma tradition has appealed to analogy. For Aristotle analogy is what is later called proportionality, i.e. a similarity between relations. It is shown that this analogy, by itself, cannot solve the problem. Aristotle, however, has another ontologico-semantic device, (...) namely 'to be or to be named from one or towards one', which looks more promising. This is the later so called analogy of proportion or of attribution. Thus an accident, f.i. a quality, is called 'being' from the substance, the primary being, because it is directed towards the substance and depends on it. For Thomas this is the kind of analogy that makes God-talk possible. It implies a twofold dynamic: the three ways of Dionysius and the strategy of seeing creatures as traces of or pointers towards God. I.T. Ramsey's theory of qualified models leading to a disclosure makes this dynamic more explicit. Far from being old-fashioned, the theories of analogy and of qualified models have everything to do with what J.-F. Lyotard sees as the concern of both avant-garde art and postmodern philosophy: to make allusions to the Sublime, to point towards the Transcendent, which as transcending the observable cannot be represented. (shrink)

Rough set theory models uncertainty by approximating target concepts via lower and upper sets induced by indiscernibility (or more general granulation) relations in data tables. This perspective captures vagueness caused by limited observational resolution and supports settheoretic reasoning about what can be determined with certainty versus what remains only possible. The present book is written as a model map: rather than developing a single algorithmic pipeline in depth, we provide a systematic survey of the main rough-set paradigms and their extension (...) routes. Concretely, we organize representative variants according to (i) the underlying granulation mechanism (e.g., equivalence-, tolerance-, covering-, neighborhood-, and probabilistic-based approximations) and (ii) the uncertainty semantics attached to data and relations (e.g., crisp, fuzzy, intuitionistic fuzzy, neutrosophic, and plithogenic settings), and we explain how each choice changes the form of approximations and the interpretation of boundary regions. Throughout, small illustrative examples are used to clarify modeling intent and typical use-cases in classification and decision support. Finally, we note an important scope clarification: if the purpose of this book is limited to a model map, then the Abstract/Introduction should not lead readers to expect that feature reduction and rule induction are primary goals. Those topics are central in the rough-set literature, but here they are discussed mainly as motivating applications and as pointers to the broader ecosystem; the main objective is to align the book’s stated aim with its actual focus on surveying and positioning rough-set models and extensions. (shrink)

When restorative justice was translated from the criminal justice context to schools and universities, there was an increased focus on proactively building positive relational ecologies in addition to responding restoratively to incidents of harm. Still, restorative justice often falls short of providing a method for addressing structural and institutional inequities that cause harm within communities. The Sustained Restorative Dialogue process was designed and first piloted at Victoria University of Wellington in New Zealand as a restorative approach to understanding and addressing (...) those broader structural sources of harm. The first iteration was focused on understanding and addressing the prevalence of sexual harm. The process was later piloted at Roberts Wesleyan University to address issues involving multicultural inequity. The design of the Sustained Restorative Dialogue will be discussed as well as the outcomes of both pilots, including examples of speech data from participants of the dialogues, and resulting institutional changes. (shrink)

Background Clinical ethics consultants are expected to “reduce disparities, discrimination, and inequities when providing consultations,” but few studies about inequities in ethics consultation exist.1 The objectives of this study were (1) to determine if there were racial or gender differences in the timing of requests for ethics consultations related to limiting treatment, and (2) if such differences were found, to identify factors associated with that difference and the role, if any, of ethics consultants in mitigating them. Methods The study was (...) a mixed methods retrospective study of consultation summaries and hospital and ethics center data on 56 age-and gender-matched Caucasian and African American Medicare patients who received ethics consultations related to issues around limiting medical treatment in the period 2011 to 2014. The average age of patients was 70.9. Results Consultation requests for females were made significantly earlier in their stays in the hospital (6.57 days) than were consultation requests made for males (16.07 days). For African American patients, the differences in admission-to-request intervals for female patients (5.93 days) and male patients (18.64 days) were greater than for Caucasian male and female patients. Differences in the timing of a consultation were not significantly correlated with the presence of an advance directive, the specialty of the attending physician, or the reasons for the consult request. Ethics consultants may have mitigated problems that developed during the lag in request times for African American males by spending more time, on average, on those consultations (316 minutes), especially more time, on average, than on consultations with Caucasian females (195 minutes). Most consultations (40 of 56) did result in movement toward limiting treatment, but no statistically significant differences were found among the groups studied in the movement toward limiting treatment. The average number of days from consult to discharge or death were strongly correlated with the intervals between admission to the hospital and request for an ethics consultation. Conclusion Our findings suggest race and gender disparities in the timing of ethics consultations that consultants may have partially mitigated. (shrink)