It is frequently claimed that the human mind is organized in a modular fashion, a hypothesis linked historically, though not inevitably, to the claim that many aspects of the human mind are innately specified. A specific instance of this line of thought is the proposal of an innately specified geometric module for human reorientation. From a massive modularity position, the reorientation module would be one of a large number that organized the mind. From the core knowledge position, (...) the reorientation module is one of five innate and encapsulated modules that can later be supplemented by use of human language. In this paper, we marshall five lines of evidence that cast doubt on the geometric module hypothesis, unfolded in a series of reasons: (1) Language does not play a necessary role in the integration of feature and geometric cues, although it can be helpful. (2) A model of reorientation requires flexibility to explain variable phenomena. (3) Experience matters over short and long periods. (4) Features are used for true reorientation. (5) The nature of geometric information is not as yet clearly specified. In the final section, we review recent theoretical approaches to the known reorientation phenomena. (shrink)

Many species rely on the three-dimensional surface layout of an environment to find a desired goal following disorientation. They generally do so to the exclusion of other important spatial cues. Two influential frameworks for explaining that phenomenon are provided by geometric-module theories and view-matching theories of reorientation respectively. The former posit a module that operates only on representations of the global geo- metry of three-dimensional surfaces to guide behavior. The latter place snapshots, stored representations of the subject’s (...) two-dimensional retinal stimulation at specific locations, at the heart of their accounts. In this paper, I take a fresh look at the debate between them. I begin by making a case that the empirical evidence we currently have does not clearly favor one framework over the other, and that the debate has reached something of an impasse. Then, I present a new explanatory problem—the representation selection problem—that offers the pro- spect of breaking the impasse by introducing a new type of explanatory consideration that both frameworks must address. The representation selection problem requires explaining how subjects can reliably select the relevant representation with which they initiate the reorientation process. I argue that the view-matching framework does not have the resources to address this problem, while a certain type of theory within the geometric-module framework can provide a natural response to it. In showing this, I develop a new geometric-module theory. (shrink)

The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Töne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Töne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory of (...) musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples. (shrink)

Let R be a real closed field, and X⊆Rm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq R^m}$$\end{document} semi-algebraic and 1-dimensional. We consider complete first-order theories of modules over the ring of continuous semi-algebraic functions X→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\to R}$$\end{document} definable with parameters in R. As a tool we introduce -piecewise vector bundles on X and show that the category of piecewise vector bundles on X is equivalent to the category of syzygies of (...) finitely generated submodules of free modules. We give an explicit method to determine the Baur–Monk invariants of free modules in terms of pre-piecewise vector bundles. When R is a recursive real closed field this yields the decidability of the theory of free modules. Where it makes sense, we address the same questions for continuous definable functions in o-minimal expansions of a real closed field. From the free module case we are able to deduce generalisations of some results to arbitrary modules over the ring. We present a geometrically motivated quantifier elimination result down to the level of positive primitive formulae with a certain block decomposition of the matrix of coefficients. (shrink)

Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological relations between points, lines, and circles in geometric diagrams. We hypothesized in particular that a counterexample search generally underlies this type of reasoning. We first verified that educated adults without specific math training were able to produce correct diagrammatic representations contained in the premisses of an inference. Our first experiment then revealed that subjects who correctly judged (...) an inference as invalid almost always produced a counterexample to support their answer. Noticeably, even if the counterexample always bore a certain level of similarity to the initial diagram, we observed that an object was more likely to be varied between the two drawings if it was present in the conclusion of the inference. Experiments 2 and 3 then directly probed counterexample search. While participants were asked to evaluate a conclusion on the basis of a given diagram and some premisses, we modulated the difficulty of reaching a counterexample from the diagram. Our results indicate that both decreasing the counterexample density and increasing the counterexample distance impaired reasoning performance. Taken together, our results suggest that a search procedure for counterexamples, which proceeds object‐wise, could underlie diagram‐based geometric reasoning. Transposing points, lines, and circles to our spatial environment, the present study may ultimately provide insights on how humans reason about topological relations between positions, paths, and regions. (shrink)

The hypothesis that nonhuman species, lacking verbal language, do not really integrate information from different modules, but use instead information sequentially, appears difficult to put under empirical scrutiny. Evidence is discussed showing that in nonhuman species storing of geometric information occurs spontaneously even when landmark information suffices for spatial reorientation, suggesting simultaneous encoding, if not use, of information from different modules.

Our model of haptic object recognition points to the importance of material, as well as geometric properties of objects. Collectively, these can elicit a recognition response after an initial contact, without sequential exploration. This model suggests a revision of the authors' proposals, which takes into account an individual's intention and the extent of exploratory movement.

There are several models of the use of geometric and feature cues in reorientation. The adaptive combination approach posits that people integrate cues with weights that depend on cue salience and learning, or, when discrepancies are large, they choose between cues based on these variables. In a new paradigm designed to evaluate integration and choice, disoriented participants attempted to return to a heading direction, in a trapezoidal enclosure in which feature and geometric cues both unambiguously specified a heading, (...) but later the feature was moved. With discrepancies greater than 90 degrees, participants choose geometry. With smaller discrepancies, integration appeared in three of five situations; otherwise, participants used geometry alone. Variation depended on direction of feature movement and whether the nearest corner was acute or obtuse. The results have implications for contrasting adaptive combination and modularity theory, and for future research, offering a new paradigm for reorientation research, and for testing cue integration more broadly. (shrink)

A geometric constraint solver for finding legal configurations for an under-constrained set of geometric components is proposed. While making drawings interactively, the user usually specifies few geometric constraints explicitly because some constraints are not clear to him- or her-self, or it is not practical to specify all constraints at any early design stage. Theoretically, the full geometric constraints are necessary to define a unique layout of every geometric components, but it is naturally not given throughout (...) the process. Therefore, in such an under-constrained situation, the lack of constraints must be supplemented properly to determine the final layout of components remaining undefined. For this purpose, we propose a geometric constraint solver that works in two phases: the former is to satisfy all the explicit constraints imposed by the user, and the latter is to choose appropriate value instances for every geometric component whose layout is not yet determined. We implemented a constraint-based interactive system for designing line drawings which is composed of the solver and the interactive module to let the user input geometric modi.cation commands incrementally, and proved its effectiveness by some experiments. (shrink)

Gjirokastra’s buildings occupy a special place in the housing typology of Albanian popular dwellings in the feudal period. The “popular tower" is linked with its defensive character, therefore in many cases, it takes the name of a castle or defensive tower. This paper takes into consideration a typical example of the historical fortified dwelling in a well-known city of Albania, Gjirokastra. The methodology used in order to improve the way of thinking, the way of implementing, and the way of designing (...) future dwellings is very related to the historical attitude of the dwelling. Based on the historical documentation, of the fortified dwelling a real analysis is performed according to the logic of modulations. The purpose of this paper is to create a methodology for future generations of architects in order to better engage in the design process, respecting the valuable architectural history. The modern dwellings of Gjirokastra historical-urban context must adopt the historical architectural elements, the historical manners of construction, the typical construction materials, the operational mode, and people’s lifestyle, in order to preserve the city's historical values via a modern touch. KEYWORDS: Architectural elements, historical preservation values, geometric ratios, modular. (shrink)

When we cut a multiplicative proof-net of linear logic in two parts we get two modules with a certain border. We call pretype of a module the set of partitions over its border induced by Danos-Regnier switchings. The type of a module is then defined as the double orthogonal of its pretype. This is an optimal notion describing the behaviour of a module: two modules behave in the same way precisely if they have the same type.In this (...) paper we define a procedure which allows to characterize (and calculate) the type of a module only exploiting its intrinsic geometrical properties and without any explicit mention to the notion of orthogonality. This procedure is simply based on elementary graph rewriting steps, corresponding to the associativity, commutativity and weak-distributivity of the multiplicative connectives of linear logic. (shrink)

Graphical displays of simple moving geometrical figures have been repeatedly used to study the attribution of animacy in human observers. Yet little is known about the relevant movement characteristics responsible for this experience. The present study introduces a novel parametric research paradigm, which allows for the experimental control of specific motion parameters and a predictable influence on the attribution of animacy. Two experiments were conducted using 3D computer animations of one or two objects systematically introducing variations in the following aspects (...) of motion: directionality, discontinuity and responsiveness. Both experiments further varied temporal kinematics. Results showed that animacy experience increased with the time a moving object paused in the vicinity of a second object and with increasing complexity of interaction between the objects . The experience of animacy could be successfully modulated in a parametric fashion by the systematic variation of comparably simple differential movement characteristics. (shrink)

According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that nevertheless (...) intuition comes into play in a fundamentally different way to that which Kant had foreseen: in the form of a formal or “categorical” yet not sensible intuition. We show further that the statement that our space is mathematically three-dimensional and locally Euclidean by no means follows from a supposed a priori nature of the sensible or subjective space as Kant claimed. In fact, the three-dimensional space can bear many different geometrical and topological structures, as particularly the mathematical results of Milnor, Smale, Thurston and Donaldson demonstrated. On the other hand, it has been stressed that even the phenomenological or perceptual space, and especially the visual system, carries a very rich geometrical organization whose structure is essentially non-Euclidean. Finally, we argue that in order to grasp the meaning of abstract geometric objects, as n-dimensional spaces, connections on a manifold, fiber spaces, module spaces, knotted spaces and so forth, where sensible intuition is essentially lacking and where therefore another type of mathematical idealization intervenes, we need to develop a new form of intuition. (shrink)

Dual process accounts of affective learning state that the learning of likes and dislikes reflects a learning mechanism that is distinct from the one reflected in expectancy learning, the learning of signal relationships, and has different empirical characteristics. Affective learning, for example, is said not to be affected by: (a) extinction training; (b) occasion setting; (c) cue competition; and (d) awareness of the CS-US contingencies. These predictions were tested in a series of experiments that employed simple Pavlovian conditioning procedures. Neutral (...) visual pictures of geometric shapes, or tactile conditional stimuli (CS) were paired with aversive electrotactile unconditional stimuli (US). Dependent measures were physiological (skin conductance, blink startle modulation) or verbal (US expectancy, on-line and off-line ratings of CS pleasantness). Different combinations of these dependent measures were employed across different experiments in an attempt to assess affective and expectancy learning simultaneously. Changes in CS pleasantness as indexed by ratings or blink startle modulation were readily observed. However, contrary to the predictions from dual-process accounts, results indicated that acquired CS unpleasantness is subject to extinction, occasion setting, cue competition, and not found in absence of CS-US contingency awareness. (shrink)

We use the Tolman–Oppenheimer–Volkoff equations for a Chaplygin type fluid to study, analytically and numerically, the global behavior of static solutions of spherically symmetric objects. Two possible regimes are especially investigated. The first one is the phantom regime in which the pressure module exceeds the energy density. In this case the equator is absent and all the solutions have the geometry of a truncated spheroid with the same kind of singularity. The second case is the normal regime for which (...) we determine all the solutions, excluding the de Sitter one, corresponding to a tri-dimensional spheroidal geometry. Beyond the equator, three possible cases are considered; the first case has a closed spheroid characterized by a Schwarzschild-kind singularity with an infinite blue-shift at the south pole, the second case configuration has a regular spheroid and the third case has configuration of a truncated spheroid having a scalar curvature singularity to a finite value of the radial distance. We also compare all the geometric configurations with ones obtained in the special case of Chaplygin gas. (shrink)

Three experiments investigated the role of target-target perceptual similarity within the attentional blink. Various geometric shapes were presented in a rapid serial visual presentation task. Targets could have 2, 1, or 0 shared features. Features included shape and size. The second target was presented after five or six different lags after the first target. The task was to detect both targets on each trial. Second-target report accuracy was increased by target-target similarity. This modulation was observed more for mixed-trial design (...) as compared with blocked design. Results are discussed in terms of increased stability of working memory representations and reduced interference for second-target processing. (shrink)

Some simulationists have argued that the information obtained during the perceptual process of facial expression (the geometric features) is sufficient for recognition of the emotion intended by that expression. Drawing on evidence from cross-cultural studies, with particular attention to conceptual act theories, I show that both emotion expression and recognition are top-down modulated by expressivity norms, observer-specific internal representations, and expectations. I thus conclude that direct simulation, or a purely bottom-up approach, is not sufficient for emotion recognition. Next, I (...) will consider the generate and test strategy as an alternative to direct simulation. This is a highly promising approach in that top-down and bottom-up processes work in parallel, according to the presence, or not, of additional information. For this reason, it avoids the difficulties of direct simulation. I will argue, however, that it is based on a misconception of emotions, specifically on how emotions are represented in the brain. To improve the model, I distinguish between two different categorical approaches to emotions, then argue that only one of which is viable in a simulational account of emotion recognition. (shrink)

In this article we review the discussion over the thesis that language serves as an integrator of contents coming from different cognitive modules. After presenting the theoretical considerations, we examine two strands of empirical research that tested the hypothesis — spatial cognition and mathematical cognition. The idea shared by both of them is that each is composed of two separate modules processing information of a specific kind. For spatial thinking these are geometric information about the location of the object (...) and the information about the object’s properties such as color or size. For mathematical thinking, they are the absolute representation of small numbers and the approximate representation of numerosities. Language is said to integrate the two kinds of information within each of these domains, which the reviewed data demonstrates. In the final part of the paper, we offer some comments on the theoretical side of the discussion. (shrink)

To what extent are cognitive capacities, especially perceptual capacities, informationally encapsulated and to what extent are they cognitively penetrable? And why does this matter? Two reasons we care about encapsulation/penetrability are: (a) encapsulation is sometimes held to be definitional of modularity, and (b) penetrability has epistemological implications independent of modularity. I argue that modularity does not require encapsulation; that modularity may have epistemological implications independently of encapsulation; and that the epistemological implications of the cognitive penetrability of perception are messier than (...) is sometimes thought. (shrink)

When faced with uncertainty, consequentialists often advocate choosing the option with the largest expected utility, as calculated using the arithmetic average. I provide some arguments to suggest that instead, one should consider choosing the option with the largest geometric average of utility. I explore the difference between these two approaches in a variety of ethical dilemmas and argue that geometric averaging has some appealing properties as a normative decision-making tool.

Aggressive behavior is instinctively driven behavior that helps animals to survive and reproduce and is closely related to multiple behavioral and physiological processes. The dorsal raphe nucleus (DRN) is an evolutionarily conserved midbrain structure that regulates aggressive behavior by integrating diverse brain inputs. The DRN consists predominantly of serotonergic (5‐HT:5‐hydroxytryptamine) neurons and decreased 5‐HT activity was classically thought to increase aggression. However, recent studies challenge this 5‐HT deficiency model, revealing a more complex role for the DRN 5‐HT system in aggression. (...) Furthermore, emerging evidence has shown that non‐5‐HT populations in the DRN and specific neural circuits contribute to the escalation of aggressive behavior. This review argues that the DRN serves as a multifaceted modulator of aggression, acting not only via 5‐HT but also via other neurotransmitters and neural pathways, as well as different subsets of 5‐HT neurons. In addition, we discuss the contribution of DRN neurons in the behavioral and physiological aspects implicated in aggressive behavior, such as arousal, reward, and impulsivity, to further our understanding of DRN‐mediated aggression modulation. (shrink)

In this paper, considering \(L\)-algebras, which include a significant number of other algebraic structures, we present a definition of modules on \(L\)-algebras (\(L\)-modules). Then we provide some examples and obtain some results on \(L\)-modules. Also, we present definitions of prime ideals of \(L\)-algebras and \(L\)-submodules (prime \(L\)-submodules) of \(L\)-modules, and investigate the relationship between them. Finally, by proving a number of theorems, we provide some conditions for having prime \(L\)-submodules.

Gordon Belot investigates the distinctive notion of geometric possibility that relationalists rely upon. He examines the prospects for adapting to the geometric case the standard philosophical accounts of the related notion of physical possibility, with particular emphasis on Humean, primitivist, and necessitarian accounts of physical and geometric possibility. This contribution to the debate concerning the nature of space will be of interest not only to philosophers and metaphysicians concerned with space and time, but also to those interested (...) in laws of nature, modal notions, or more general issues in ontology. (shrink)

Evans’ 1968 ANALOGY system was the first computer model of analogy. This paper demonstrates that the structure mapping model of analogy, when combined with high‐level visual processing and qualitative representations, can solve the same kinds of geometric analogy problems as were solved by ANALOGY. Importantly, the bulk of the computations are not particular to the model of this task but are general purpose: We use our existing sketch understanding system, CogSketch, to compute visual structure that is used by our (...) existing analogical matcher, Structure Mapping Engine (SME). We show how SME can be used to facilitate high‐level visual matching, proposing a role for structural alignment in mental rotation. We show how second‐order analogies over differences computed via analogies between pictures provide a more elegant model of the geometric analogy task. We compare our model against human data on a set of problems, showing that the model aligns well with both the answers chosen by people and the reaction times required to choose the answers. (shrink)

Fodor claims that cognitive modules can be thought of as constituting a psychological natural kind in virtue of their possession of most or all of nine specified properties. The challenge to this considered here comes from synaesthesia. Synaesthesia is a type of cross-modal association: input to one sensory modality reliably generates an additional sensory output that is usually generated by the input to a distinct sensory modality. The most common form of synaesthesia manifests Fodor's nine specified properties of modularity, and (...) hence, according to Segal (1997), it should be understood as involving an extra module. Many psychologists believe that synaesthesia involves a breakdown in modularity. After outlining how both theories can explain the manifestation of the nine alleged properties of modularity in synaesthesia, I discuss the two concepts of function which initially motivate the respective theories. I argue that only a teleological concept of function is properly able to adjudicate between the two theories. The upshot is a further application of so-called externalist considerations to mental phenomena. (shrink)

Public “upstream engagement” and other approaches to the social control of technology are currently receiving international attention in policy discourses around emerging technologies such as nanotechnology. To the extent that such approaches hold implications for research and development (R&D) activities, the distinct participation of scientists and engineers is required. The capacity of technoscientists to broaden the influences on R&D activities, however, implies that they conduct R&D differently. This article discusses the possibility for more reflexive participation by scientists and engineers in (...) the internal governance of technology development. It reviews various historical attempts to govern technoscience and introduces the concept of midstream modulation, through which scientists and engineers, ideally in concert with others, bring societal considerations to bear on their work. (shrink)

There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and (...) continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous. (shrink)

The meaning that expressions take on particular occasions often depends on the context in ways which seem to transcend its direct effect on context-sensitive parameters. ‘Truth-conditional pragmatics’ is the project of trying to model such semantic flexibility within a compositional truth-conditional framework. Most proposals proceed by radically ‘freeing up’ the compositional operations of language. I argue, however, that the resulting theories are too unconstrained, and predict flexibility in cases where it is not observed. These accounts fall into this position because (...) they rarely, if ever, take advantage of the rich information made available by lexical items. I hold, instead, that lexical items encode both extension and non-extension determining information. Under certain conditions, the non-extension determining information of an expression e can enter into the compositional processes that determine the meaning of more complex expressions which contain e. This paper presents and motivates a set of type-driven compositional operations that can access non-extension determining information and introduce bits of it into the meaning of complex expressions. The resulting multidimensional semantics has the tools to deal with key cases of semantic flexibility in appropriately constrained ways, making it a promising framework to pursue the project of truth-conditional pragmatics. (shrink)

We investigate the processes underlying the feeling of control over one’s actions . Sense of agency may depend on internal motoric signals, and general inferences about external events. We used priming to modulate the sense of agency for voluntary and involuntary movements, by modifying the content of conscious thought prior to moving. Trials began with the presentation of one of two supraliminal primes, which corresponded to the effect of a voluntary action participants subsequently made. The perceived interval between movement and (...) effect was used as an implicit measure of sense of agency. Primes modulated perceived intervals for both voluntary and involuntary movements, but the modulation was greatest for involuntary movements. A second experiment showed that this modulation depended on prime–movement contiguity. We propose that sense of agency is based on a combination of internal motoric signals and external sensory evidence about the source of actions and effects. (shrink)

We study Martsinkovsky–Russell torsion modules with pure embeddings as an abstract elementary class. We give a model-theoretic characterization of the pure-injective and the Σ-pure-injective modules relative to the class of torsion modules assuming that the torsion submodule is a pure submodule. Our characterization of relative Σ-pure-injective modules extends the classical characterization of Gruson and Jenson as well as Zimmermann. We study the limit models of the class and determine when the class is superstable assuming that the torsion submodule is a (...) pure submodule. As a corollary, we show that the class of torsion abelian groups with pure embeddings is strictly stable (i.e., stable not superstable). (shrink)

At some point in the Incessu Animalium, Aristotle appeals to some geometrical claims in order to explain why animal progression necessarily involves the bending (of the limbs), and this appeal to geometrical claims might be taking as violating the recommendation to avoid “kind-crossing” (as found in the Posterior Analytic). But a very unclear notion of kind-crossing has been assumed in most debates. I will argue that kind-crossing in the Posterior Analytics does not mean any employment of premises from a discipline (...) other than that to which the explanandum belongs. Kind-crossing was meant to cover a specific sort of employment of premises from a different discipline, namely, the case in which premises from a discipline X are taken as the most important explanatory factor that delivers the fullest appropriate explanation of an explanandum within discipline Y. If this is so, the employment of geometrical premises in the Incessu Animalium is not an instance of the prohibited kind-crossing, but something that is in line with the theory of the Posterior Analytics. (shrink)

The purpose of this work is to address what notion of geometrical object and geometrical figure we have in different kinds of geometry: practical, pure, and applied. Also, we address the relation between geometrical objects and figures when this is possible, which is the case of pure and applied geometry. In practical geometry it turns out that there is no conception of geometrical object.

I draw together some recent literature on the debate between dynamical versus geometrical approaches to spacetime theories, in order to argue that there exist defensible versions of the geometr...

We analyze the geometric foundations of classical Yang-Mills theory by studying the relationships between internal relativity, locality, global/local invariance, and background independence. We argue that internal relativity and background independence are the two independent defining principles of Yang-Mills theory. We show that local gauge invariance -heuristically implemented by means of the gauge argument- is a direct consequence of internal relativity. Finally, we analyze the conceptual meaning of BRST symmetry in terms of the invariance of the gauge fixed theory under (...) general local gauge transformations. (shrink)

The object of this paper is to show the predominance of the influence of geometrical ideas in Aristotle's account of first principles in the Posterior Analytics— to show that his analysis of first principles is in its essentials an analysis of the first principles of geometry as he conceived them. My proof of this falls into two parts. I. A consideration of the parallel between Aristotle's and Euclid's account of first principles. II. A comparison between the general movement of thought (...) in the Aristotelian παγωγ and πδειξις and in the δινοια and νησις of the Platonic dialectic. (shrink)

This book offers solutions to two persistent and I believe closely related problems in epistemology. The first problem is that of drawing a principled distinction between perception and inference: what is the difference between seeing that something is the case and merely believing it on the basis of what we do see? The second problem is that of specifying which beliefs are epistemologically basic (i.e., directly, or noninferentially, justified) and which are not. I argue that what makes a belief a (...) perceptual belief, or a basic belief, is not any introspectible feature of the belief but rather the nature of the cognitive system, or "module", that is causally responsible for the belief. Thus, even zombies, who in the philosophical literature lack conscious experiences altogether, can have basic, justified, perceptual beliefs. -/- The theories of perceptual and basic beliefs developed in the monograph are embedded in a larger reliabilist epistemology. I use this theory of basic beliefs to develop a detailed reliabilist theory: Inferentialist Reliabilism, which offers a reliabilist theory of inferential justification and which solves some longstanding problems for other reliabilist views by demanding inferential support for some—but not all—beliefs. The book is an instance of a thoroughgoingly naturalistic approach to epistemology. Many of my arguments have an empirical basis, and the view that I endorse reserves a central role for the cognitive sciences—in particular, cognitive neuroscience—in filling in the details of an applied epistemological theory. (shrink)

Large portions of mathematics such as algebra and geometry can be formalized using first-order axiomatizations. In many cases it is even possible to use a very well-behaved class of first-order axioms, namely, what are called coherent or geometric implications. Such class of axioms can be translated to inference rules that can be added to a sequent calculus while preserving its structural properties. In this work, this fundamental result is extended to their infinitary generalizations as extensions of sequent calculi for (...) both classical and intuitionistic infinitary logic. As an application, a simple proof of the infinitary Barr’s theorem without the axioms of choice is shown. (shrink)

We argue against the dominant view in the literature that concepts are modulated in lexical modulation. We also argue against the alternative view that ‘grab bags’ of information that don’t determine extensions are the starting point for lexical modulation. In response to the problems with these views we outline a new model for lexical modulation that dispenses with the assumption that there is a standing meaning of a general term that is modified in the cases under consideration. In applying general (...) terms we intend to conform with our linguistic ancestors and in doing so we take facts about the referents of these terms for granted. In cases of lexical modulation we become aware of facts we took for granted and we need to change the facts we take for granted in order to see ourselves as continuing in a practice. These changes result in utterances of the general term referring to different properties. In general, concepts are neither the starting point for lexical modulation nor the standing meanings of words. (shrink)