The quantum formalism ofdistinguishable, yetequivalent particles (with symmetric or antisymmetric wave functions) is here worked out. The result is an entirely explicit formulation of the way in which classical mechanics emerges from quantum mechanics for such particles. Distinguishability is achieved at the cost of dynamical precision; the two are, in fact, complementary.

Disability and enhancement are often treated as opposing concepts. To become disabled in some respect is to move away from those who are enhanced in that same respect; to become enhanced is to move away from the corresponding state of disability. This chapter examines how best to understand the concepts of disability and enhancement in this symmetrical way. After considering various candidates, two types of accounts are identified as the most promising: welfarist accounts and typical-functioning accounts. The authors ultimately defend (...) a complex typical-functioning account as the best way to achieve a symmetrical understanding of disability and enhancement. (shrink)

This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some inconsistencies (...) of the CI, and gives intuitive explanations of some previously mysterious quantum effects. (shrink)

The main purpose of this paper is to introduce a class of algebraic structures related to many-valued ukasiewicz algebras. They are symmetrical Heyting algebras with a set of modal operators indexed by a finite completely symmetric poset. A representation theorem is given for these (not functionally complete) algebras.

Theories of scientific representation, following Chakrawartty's categorization, are divided into two groups. Whereas cognitive-functional views emphasize agents' intentions, informational theories stress the objective relation between represented and representing. In the first part, a modified structuralist theory is introduced that takes into account agents' intentions. The second part is devoted to dismissing a criticism against the structural account of representation on which similarity as the backbone of representation raises serious problems, since it has definite logical features, i.e. reflexivity, symmetry and transitivity, (...) which representation lacks. Drawing on the representational relation between quantum and statistical field theories, I argue that scientific representation displays these logical features, although depending on the context they may be used or not. (shrink)

Why must incompatibility be symmetric? An odd question, but recent work in the semantics of non-classical logic, which appeals to the notion of incompatibility as a primitive and defines negation in terms of it, has brought this question to the fore. Francesco Berto proposes such a semantics for negation argues that, since incompatibility must be symmetric, double negation introduction must be a law of negation. However, he offers no argument for the claim that incompatibility really must be (...) class='Hi'>symmetric. Here, I provide such an argument, showing that, insofar as we think of incompatibility in normative pragmatic terms, it can play its basic pragmatic function only if it is symmetric. The upshot is that we can vindicate Berto’s claim about the symmetry of incompatibility but only if we, pace Berto, think about incompatibility, in the first instance, as a pragmatic relation between acts rather than a semantic relation between contents. (shrink)

We study the sets of symmetric continuity of real functions in connection with the sets of continuity. We prove that sets of reals of cardinality symmetric continuity. The latter strengthens a similar result of Darji. We improve results of Fried and Belna saying that the (...) set of points of symmetric continuity of a real function that are not continuity points does not contain a nonmeager set with Baire property and has inner measure zero by introducing another notion of smallness below meager and measure zero. (shrink)

The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? I review the debate between 3N-Fundamentalists and 3D-Fundamentalists and evaluate it based on three criteria. I argue that when we consider which view leads to a deeper understanding of the physical world, especially given the deeper topological (...) explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons in favor of 3D-Fundamentalism. I conclude that our evidence favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I outline lines of future research where the evidential balance can be restored or reversed. Finally, I draw lessons from this case study to the debate about theoretical equivalence. (shrink)

The core structures of d 111 ¢ screw dislocations in bcc metals are studied using density functional theory in the local-density approximation. For Mo and Fe, direct calculations of the core structures show the cores to be symmetric with respect to 180° rotations around an axis perpendicular to the dislocation line. The magnetic moment in the Fe core is shown to be reduced relative to the bulk value. Calculations of n surfaces and the elastic constants B , C ' (...) and c 44 are reported for Fe and all group VB and VIB metals. Using a criterion suggested by Vitek and Duesbery the calculations point to symmetric core structures for all the studied metals. (shrink)

This is an exciting time for brain science. Recent progress has been such that it now seems realistic to look toward an explanation of mind in terms of the brain's anatomy and physiology. Models based on artificially symmetrical arrays of idealized neurons are now being superseded by ones which properly take into account the brain's actual circuitry. This book presents a comprehensive overview of the current state of brain modeling, containing contributions from many leading researchers in this field. It will (...) be of interest not only to researchers in the fields of brain science and neurobiology, but also to psychologists and those involved in the study of artificial intelligence. (shrink)

In this article we present symmetric diffusion networks, a family of networks that instantiate the principles of continuous, stochastic, adaptive and interactive propagation of information. Using methods of Markovion diffusion theory, we formalize the activation dynamics of these networks and then show that they can be trained to reproduce entire multivariate probability distributions on their outputs using the contrastive Hebbion learning rule (CHL). We show that CHL performs gradient descent on an error function that captures differences between desired and (...) obtained continuous multivariate probability distributions. This allows the learning algorithm to go beyond expected values of output units and to approximate complete probability distributions on continuous multivariate activation spaces. We argue that learning continuous distributions is an important task underlying a variety of real‐life situations that were beyond the scope of previous connectionist networks. Deterministic networks, like back propagation, cannot learn this task because they are limited to learning average values of independent output units. Previous stochastic connectionist networks could learn probability distributions but they were limited to discrete variables. Simulations show that symmetric diffusion networks can be trained with the CHL rule to approximate discrete and continuous probability distributions of various types. (shrink)

This paper aims at investigating the dynamic characteristics of a microring driven by dual arch electrodes because they are basic elements of microelectrostatic motors. The dual arch electrodes surround the periphery of the microring and are arranged symmetrically to the center of the ring. The electrodes are fixed while the microring is flexible. The electrostatic force will deform the microring, while the deflection of the microring changes the gap between the microring and the electrodes, thereby changing the electrostatic force. Therefore, (...) this is an electromechanical coupling effect. The nonlinear partial-differential equation that governs the motion of the microring is derived based on thin shell theory. Then, based on the assumption of small deflection, the nonlinear governing equation is linearized by truncating the higher-order terms of the Taylor series expansion of the nonlinear electrostatic force. After that, the linearized governing equation is discretized into a set of ordinary differential equations using Galerkin method in which the mode shape functions of the ring are adopted. The influences of the structural damping of the microring and the span of the arch electrodes on the forced response and dynamical stabilities of the microring are investigated. The results show that the damping ratio has a great influence on the system instability during high-frequency excitation. The unstable region of the system can increase with the increase of the electrode span; the response amplitude can also be increased within a certain range. (shrink)

Machine learning, deep learning and neural networks are extensively applied for the development of many fields. Though their technologies are improved greatly, they are often said to be opaque in terms of explainability. Their explainable neural functions will be essential to realization in the networks. In this paper, it is shown that the bio-inspired networks are useful for the explanation of tracking and classification of features. First, the asymmetric network with nonlinear functions is created based on the bio-inspired (...) retinal network. They have orthogonal properties useful for the tracking of features compared with the conventional symmetric networks, which is also proposed on the biological functions. Next, the analysis for the independence of the subspaces between the Fourier bases and the asymmetric network bases is performed. It was that the asymmetric networks have better performances in the classification compared with the symmetric ones. Further, the layered asymmetric networks generate the higher dimensional orthogonal bases that improve the classification accuracies by the replacements of bases. Finally, we classified Reuters collections data applying the explainable processing steps, which consist of the linear discriminations and the sparse coding with nearest neighbor relation for classification. (shrink)

We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only if the ‘usual’ first order (...) formula translating the sentence holds. The examples include negation, universal quantifiers and relative pronouns. (shrink)

We show that from a supercompact cardinal $\kappa$, there is a forcing extension $V[G]$ that has a symmetric inner model $N$ in which $\mathrm {ZF}+\lnot\mathrm {AC}$ holds, $\kappa$ and $\kappa^{+}$ are both singular, and the continuum function at $\kappa$ can be precisely controlled, in the sense that the final model contains a sequence of distinct subsets of $\kappa$ of length equal to any predetermined ordinal. We also show that the above situation can be collapsed to obtain a model of (...) $\mathrm {ZF}+\lnot\mathrm {AC}_{\omega}$ in which either $\aleph_{1}$ and $\aleph_{2}$ are both singular and the continuum function at $\aleph_{1}$ can be precisely controlled, or $\aleph_{\omega}$ and $\aleph_{\omega+1}$ are both singular and the continuum function at $\aleph_{\omega}$ can be precisely controlled. Additionally, we discuss a result in which we separate the lengths of sequences of distinct subsets of consecutive singular cardinals $\kappa$ and $\kappa^{+}$ in a model of $\mathrm {ZF}$. Some open questions concerning the continuum function in models of $\mathrm {ZF}$ with consecutive singular cardinals are posed. (shrink)

In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved , and the solution to the third (...) problem boils down to determining all maximal subgroups in the k-degree symmetric group Sk, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p-valued logic functions are determined, where p is a prime. (shrink)

Two different concepts of distinguishability are often mixed up in attempts to derive in quantum mechanics the symmetry of the wave function from indistinguishability of identical particles. Some of these attempts are analyzed and shown to be defective. It is argued that, although identical particles should be considered as observationally indistinguishable in symmetric states, they may be considered to be conceptually distinguishable. These two notions of distinguishability have quite different physical origins, the former one being related to observations while (...) the latter has to do with the preparation of the system. (shrink)

The article discusses the notion of metrical dualism as a phenomenon of the reader’s perception of verse. The author analyzes the prosody and metrics of Marina Tsvetayeva’s poems “Неподражаемо лжет жизнь” (“How perfectly deceitful life is ….”, 1922). However, the aim of this study is not to interpret the metre of Tsvetayeva’s verse, but rather to obtain a model of reading verse and thus show how the reader’s perception of metre changes. Thus, the author consciously has not considered the metric (...) or the logaoedic interpretations of this poem, while approaching the text from the point of view of the reader’s perception which is always aimed at the revealing of symmetric structures. This approach makes it possible to take into account such aspects as the variety of metric interpretations, the dynamic development of verse metre, the internal and external metrical boundaries in text, etc. The analysis of Tsvetayeva’s verse reveals the interaction of two rhythmic patterns in the text, which is connected to the general meaning of the poem that tells the reader about the deceitfulness of life. (shrink)

The article discusses the notion of metrical dualism as a phenomenon of the reader’s perception of verse. The author analyzes the prosody and metrics of Marina Tsvetayeva’s poems “Неподражаемо лжет жизнь” (“How perfectly deceitful life is ….”, 1922). However, the aim of this study is not to interpret the metre of Tsvetayeva’s verse, but rather to obtain a model of reading verse and thus show how the reader’s perception of metre changes. Thus, the author consciously has not considered the metric (...) or the logaoedic interpretations of this poem, while approaching the text from the point of view of the reader’s perception which is always aimed at the revealing of symmetric structures. This approach makes it possible to take into account such aspects as the variety of metric interpretations, the dynamic development of verse metre, the internal and external metrical boundaries in text, etc. The analysis of Tsvetayeva’s verse reveals the interaction of two rhythmic patterns in the text, which is connected to the general meaning of the poem that tells the reader about the deceitfulness of life. (shrink)

A central aspect of the relation between biosemiotics and biology is investigated by asking: Is a biological concept of function intrinsically related to a biosemiotic concept of sign action, and vice versa? A biological notion of function (as some process or part that serves some purpose in the context of maintenance and reproduction of the whole organism) is discussed in the light of the attempt to provide an understanding of life processes as being of a semiotic nature, i.e., constituted by (...) sign actions. Does signification and communication in biology (e.g., intracellular communication) always presuppose an organism with distinct semiotic or quasi-semiotic functions? And, symmetrically, is it the case that functional relations are simply not conceivable without living sign action? The present note is just an introduction to a project aiming at elucidating the relations between biofunction and biosemiosis. (shrink)

We exploit the properties of homogeneous functions to characterize the symmetric pure-strategy Nash equilibria of n-player symmetric games in which each player’s revenue function is not homogeneous but it can be decomposed into the sum of homogeneous functions with different degrees of homogeneity. Our results aim to provide a pathway for an easy computation of symmetric equilibria for this type of games. We discuss our results in a Cournot game, a contest game, and a public (...) good game. (shrink)

Two different concepts of distinguishability are often mixed up in attempts to derive in quantum mechanics the (anti)symmetry of the wave function from indistinguishability of identical particles. Some of these attempts are analyzed and shown to be defective. It is argued that, although identical particles should be considered as observationally indistinguishable in (anti)symmetric states, they may be considered to be conceptually distinguishable. These two notions of (in)distinguishability have quite different physical origins, the former one being related to observations while (...) the latter has to do with the preparation of the system. (shrink)

We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual, these constructions involve the splitting of symmetric idempotents.

Just as intuitionistic proofs can be modeled by functions, linear logic proofs, being symmetric in the inputs and outputs, can be modeled by relations . However generic relations do not establish any functional dependence between the arguments, and therefore it is questionable whether they can be thought as reasonable generalizations of functions. On the other hand, in some situations one can speak in some precise sense about an implicit functional dependence defined by a relation. It turns out (...) that it is possible to model linear logic with implicit functions rather than general relations, an adequate language for such a semantics being differential calculus. This results in a non-degenerate model enjoying quite strong completeness properties. (shrink)

Adherens junctions play pivotal roles in cell and tissue organization and patterning by mediating cell adhesion and cell signaling. These junctions consist of large multiprotein complexes that join the actin cytoskeleton to the plasma membrane to form adhesive contacts between cells or between cells and extracellular matrix. The best-known adherens junction is the zonula adherens (ZA) that forms a belt surrounding the apical pole of epithelial cells. Recent studies in Drosophila have further illuminated the structure of adherens junctions. Scaffolding proteins (...) encoded by the stardust gene are novel components of the Crumbs complex, which plays a critical role in ZA assembly.1-3 The small GTPase Rap1 controls the symmetric re-assembly of the ZA after cell division.4 Finally, the asymmetric distribution of adherens junction material regulates spindle orientation during asymmetric cell division in the sensory organ lineage.5 BioEssays 24:690–695, 2002. © 2002 Wiley Periodicals, Inc. (shrink)

Paraconsistent logics are logics that can be used to base inconsistent but non-trivial systems. In paraconsistent set theories, we can quan- tify over sets that in standard set theories, if consistent, would lead to contradictions, such as the Russell set, R = fx : x =2 xg. Quasi-set theories are mathematical systems built for dealing with collections of indiscernible elements. The basic motivation for the development of quasi-set theories came from quantum physics, where indiscernible entities need to be considered. Usually, (...) the way of dealing with indiscernible objects within clas- sical logic and mathematics is by restricting them to certain structures, in a way so that the relations and functions of the structure are not sufficient to individuate the objects; in other words, such structures are not rigid. In quantum physics, this idea appears when symmetry conditions are introduced, say by choosing symmetric and anti-symmetric functions in the relevant Hilbert spaces. But in standard mathematics, such as that built in Zermelo-Fraenkel set theory, any structure can be extended to a rigid structure. That means that, although we can deal with certain objects as they were indiscernible, we realize that from out- side of these structures these objects are no more indiscernible, for they can be individualized in the extended rigid structures: ZF is a theory of individuals, distinguishable objects. In quasi-set theory, it seems that there are structures that cannot be extended to rigid ones, so it seems that they provide a natural mathematical framework for expressing quantum facts without certain symmetry suppositions. There may be situations, however, in which we may need to deal with inconsistent bits of infor- mation in a quantum context, even if these informations are concerned with ways of speech. Furthermore, some authors think that superposi- tions may be understood in terms of paraconsistent logics, and even the notion of complementarity was already treated by such a means. This is, apparently, a nice motivation to try to merge these two frameworks. In this work, we develop the technical details, by basing our quasi-set theory in the paraconsistent system C1. We also elaborate a new hierarchy of paraconsistent calculi, the paraconsistent calculi with indiscernibility. For the finalities of this work, some philosophical questions are outlined, but this topic is left to a future work. (shrink)

Dual functional brain asymmetry refers to the notion that in most individuals the left cerebral hemisphere is specialized for language functions, whereas the right cerebral hemisphere is more important than the left for the perception, construction, and recall of stimuli that are difficult to verbalize. In the last twenty years there have been scattered reports of sex differences in degree of hemispheric specialization. This review provides a critical framework within which two related topics are discussed: Do meaningful sex differences (...) in verbal or spatial cerebral lateralization exist? and, if so, Is the brain of one sex more symmetrically organized than the other? Data gathered on right-handed adults are examined from clinical studies of patients with unilateral brain lesions; from dichotic listening, tachistoscopic, and sensorimotor studies of functional asymmetries in non-brain-damaged subjects; from anatomical and electrophysiological investigations, as well as from the developmental literature. Retrospective and descriptive findings predominate over prospective and experimental methodologies. Nevertheless, there is an impressive accummulation of evidence suggesting that the male brain may be more asymmetrically organized than the female brain, both for verbal and nonverbal functions. These trends are rarely found in childhood but are often significant in the mature organism. (shrink)

I consider a problem for functional reductionism, based on the following tension. Say that b is functionally reduced to a. On the one hand, a and b turn out to be identical, and identity is a symmetric relation. On the other hand, functional reductionism implies that a and b are asymmetrically related: if b is functionally reduced to a, then a is not functionally reduced to b. Thus, we ask: how can a and b be asymmetrically related if they (...) are the same thing? I propose a solution to this tension, by distinguishing between ontological levels and levels of description. (shrink)

There has recently been some literature on the properties of a Health-Related Social Welfare Function (HRSWF). The aim of this article is to contribute to the analysis of the different properties of a HRSWF, paying particular attention to the monotonicity principle. For monotonicity to be fulfilled, any increase in individual health—other things equal—should result in an increase in social welfare. We elicit public preferences concerning trade-offs between the total level of health (concern for efficiency) and its distribution (concern for equality), (...) under different hypothetical scenarios through face-to-face interviews. Of key interests are: the distinction between non-monotonic preferences and Rawlsian preferences; symmetry of HRSWF; and the extent of inequality neutral preferences. The results indicate strong support for non-monotonic preferences, over Rawlsian preferences. Furthermore, the majority of those surveyed had preferences that were consistent with a symmetric and inequality averse HRSWF. (shrink)

Two complementary bodies of literature either claim explicitly or imply that human cruelty is rooted in asymmetrical relationships. The first describes and analyzes various forms of domination and acquiescence, including colonialism, racism, imperialism, sexism, and interpersonal power dynamics, among others. The second attempts to describe what would constitute the antidote, namely symmetrical relationships of mutuality and equality. Both of these literatures counsel abandoning asymmetrical relationships in favor of the symmetrical. To the contrary, this paper argues that it is only in (...) the context of asymmetrical relationships that humans can learn the basics of equality and mutual regard that undergird democracy. More particularly, the moral use of asymmetrical relations would be to help the young acquire, inter alias, the kinds of self-awareness and self-understanding that would enable them to function as responsible parties in symmetrical relations. (shrink)

Based on the theoretical analysis of self-consciousness concepts, we hypothesized that the spatio-temporal pattern of functional connectivity within the default-mode network (DMN) should persist unchanged across a variety of different cognitive tasks or acts, thus being task-unrelated. This supposition is in contrast with current understanding that DMN activated when the subjects are resting and deactivated during any attention-demanding cognitive tasks. To test our proposal, we used, in retrospect, the results from our two early studies ([Fingelkurts, 1998] and [Fingelkurts et al., (...) 2003]). In both studies for the majority of experimental trails we indeed found a constellation of operationally synchronized cortical areas (indexed as DMN) that was persistent across all studied experimental conditions in all subjects. Furthermore, we found three major elements comprising this DMN: two symmetrical occipito-parieto-temporal and one frontal spatio-temporal patterns. This new data directly supports the notion that DMN has a specific functional connotation – it provides neurophysiologic basis for self-processing operations, namely first-person perspective taking and an experience of agency. (shrink)

One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. (...) All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). (shrink)

In this paper, first the term 'prioritarianism' is defined, with some mathematical precision, on the basis of intuitive conceptions of prioritarianism, especially the idea that "benefiting people matters more the worse off these people are". (The prioritarian weighting function is monotonously ascending and concave, while its first derivation is smoothly descending and convex but positive throughout.) Furthermore, (moderate welfare) egalitarianism is characterized. In particular a new symmetry condition is defended, i.e. that egalitarianism evaluates upper and lower deviations from the social (...) middle symmetrically and equally negatively (as do e.g. variance and Gini). Finally, it is shown that this feature distinguishes egalitarianism also extensionally from prioritarianism. (shrink)

According to the truth-functional analysis of conditions, to be ‘necessary for’ and ‘sufficient for’ are converse relations. From this, it follows that to be ‘necessary and sufficient for’ is a symmetric relation, that is, that if P is a necessary and sufficient condition for Q, then Q is a necessary and sufficient condition for P. This view is contrary to common sense. In this paper, I point out that it is also contrary to a widely accepted ontological view of (...) conditions, according to which if P is a necessary and sufficient condition for Q, then Q is in no sense a condition for P; it is a mere consequence of P. (shrink)

When Gödel developed his functional interpretation, also known as the Dialectica interpretation, his aim was to prove consistency of first order arithmetic by reducing it to a quantifier-free theory with finite types. Like other functional interpretations Gödel’s Dialectica interpretation gives rise to category theoretic constructions that serve both as new models for logic and semantics and as tools for analysing and understanding various aspects of the Dialectica interpretation itself. Gödel’s Dialectica interpretation gives rise to the Dialectica categories , in: Contemp. (...) Math., vol. 92, Amer. Math. Soc., Providence, RI, 1989, pp. 47–62] and J.M.E. Hyland in [J.M.E. Hyland, Proof theory in the abstract, Ann. Pure Appl. Logic 114 43–78, Commemorative Symposium Dedicated to Anne S. Troelstra ]). These categories are symmetric monoidal closed and have finite products and weak coproducts, but they are not Cartesian closed in general. We give an analysis of how to obtain weakly Cartesian closed and Cartesian closed Dialectica categories, and we also reflect on what the analysis might tell us about the Dialectica interpretation. (shrink)

We show that any symmetric, Baire measurable function from the complement of $\ezero$ to a finite set is constant on an $\ezero$-nonsmooth square. A simultaneous generalization of Galvin's theorem that Baire measurable colorings admit perfect homogeneous sets and the Kanovei-Zapletal theorem canonizing Borel equivalence relations on $E_0$-nonsmooth sets, this result is proved by relating $\ezero$-nonsmooth sets to embeddings of the complete binary tree into itself and appealing to a version of Hindman's theorem on the complete binary tree. We also (...) establish several canonization theorems which follow from the main result. (shrink)

The discovery of so-called ‘mirror neurons’ - found to respond both to own actions and the observation of similar actions performed by others - has been enormously influential in the cognitive sciences and beyond. Given the self-other symmetry these neurons have been hypothesized as underlying a ‘mirror mechanism’ that lets us share representations and thereby ground core social cognitive functions from intention understanding to linguistic abilities and empathy. I argue that mirror neurons are important for very different reasons. Rather (...) than a symmetric ubiquitous or context- independent mechanism, I propose that these neurons are part of broader sensorimotor circuits, which help us navigate and predict the social affordance space that we meet others in. To develop both the critical and positive project I analyze the interpretive choices and the debate surrounding the mirror neuron research and show how the field is marred by highly questionable assumptions about respectively motor and social cognition. The discovery of mirror neurons - and the sensorimotor circuits of which these neurons are a part – actually empirically challenge many of these tacit assumptions. Findings of sensorimotor goal representations at levels of abstraction well beyond actual sensory information and kinetic movements challenge the idea of motor cognition as primarily output production. Additionally, the focus on 3rd person mindreading of hidden mental states is misguiding the field of social cognition. Much ‘mind-reading’ seems rooted in sensorimotor representations and a developmentally primary 2nd person understanding of actions and the mental lives of others, which precisely breaks the assumed dichotomy between mind and behavior. I propose a Social Affordance model where parallel fronto-parietal sensorimotor circuits support representations not just of other people’s actions but of the overall social affordance space. It is a process that monitors concrete goals and teleological possibilities that the environment affords respectively oneself and other present agents. With this model I hypothesize that the complex spectrum of sensorimotor integrations are indeed essential not only to normal action choice calibration but also to social cognitive abilities, as the sensorimotor teleological representations let us relate to others and understand their action choices in a shared pragmatic and intentional context. (shrink)

with the meaning function [[·]] appearing on both sides. (1) is commonly construed as a prescription for computing the meaning of a based on the parts of a and their mode of combination. As equality is symmetric, however, we can also read (1) from right to left, as a constraint on the meaning [[b]] of a term b that brings in the wider context where b may occur, in accordance with what Dag Westerst˚ahl has recently described as “one version (...) of Frege’s famous Context Principle”. (shrink)

In this paper I shall debate the thesis according to which in the Aristotelian treatise On Soul the sense of touch works as a kind of knot for the knowledge faculties and, implicitly, as a unity for the entire treatise: it has a primitive function in the feeding process, it also represents a starting point for both the faculty of motion and knowledge, then relates itself symmetrical to the sense of vision through the typology of the intermediaries and to the (...) intellect through the criterion of nonbeing, and finally reveals to the receiver a kind of truth that has no more the false as an alternative. On the other hand, the intellect recovers in its own faculty the sense of touch by recreating its functions in the connection between intellect and the indivisible intelligibles. Given these relations, the sense of touch represents the main connection of the treatise's large themes from the question of motion to that of knowledge and it is also literally (certain aristotelian remarksover the theme of earth being taken into consideration here) related to the living body. (shrink)

A universally acknowledged, core property of language is its complexity, at each level of structure – sounds, words, phrases, clauses, utterances, and higher levels of discourse. How does this complexity originate and develop in a language? We cannot fully answer this question from spoken languages, since they are all thousands of years old or descended from old languages. However, sign languages of deaf communities can arise at any time and provide empirical data for testing hypotheses related to the emergence of (...) language complexity. An added advantage of the signed modality is a direct correspondence between visible physical articulations and linguistic structures, providing a more transparent view of linguistic complexity and its emergence (Sandler 2012). These essential characteristics of sign languages allow us to address the issue of emerging complexity by documenting the use of the body for linguistic purposes. We look at three types of discourse relations of increasing complexity motivated by research on spoken languages – additive, symmetric and asymmetric (Mann and Thompson 1988; Sanders, Spooren, and Noordman 1992), Each relation type can connect units at two different levels: within propositions (simpler) and across propositions (more complex). We hypothesized that these relations provide a measure for charting the time course of emergence of complexity, from simplest to most complex, in a new sign language. We test this hypothesis on Israeli Sign Languages (ISL), a young language, some of whose earliest users are still available for recording. Taking advantage of the unique relation in sign languages between bodily articulations and linguistic form, we study fifteen ISL signers from three different generations, and demonstrate that the predictions indeed hold. We also find that younger signers tend to converge on more systematic marking of relations, that they use fewer articulators for a given linguistic function than older signers, and that the form of articulations becomes reduced, as the language matures. Mapping discourse relations to the bodily expression of linguistic components across age groups reveals how simpler, less constrained, and more gesture-like expressions, become language. (shrink)