Numerical studies of the Hubbard model and its strong-coupling form, the t-J model, show evidence for antiferromagnetic, $d_{x^{\text{2}} - y^2 } $ -pairing and stripe correlations which remind one of phenomena seen in the layered cuprate materials. Here, we ask what these numerical results imply about various scenarios for the pairing mechanism.

David Lewis (1969) introduced sender-receiver games as a way of investigating how meaningful language might evolve from initially random signals. In this report I investigate the conditions under which Lewis signaling games evolve to perfect signaling systems under various learning dynamics. While the 2-state/2- term Lewis signaling game with basic urn learning always approaches a signaling system, I will show that with more than two states suboptimal pooling equilibria can evolve. Inhomogeneous state distributions increase the likelihood of pooling equilibria, but (...) learning strategies with negative reinforcement or certain sorts of mutation can decrease the likelihood of, and even eliminate, pooling equilibria. Both Moran and APR learning strategies (Bereby-Meyer and Erev 1998) are shown to promote successful convergence to signaling systems. A model is presented that illustrates how a language that codes state-act pairs in an order-based grammar might evolve in the context of a Lewis signaling game. The terms, grammar, and the corresponding partitions of the state space co-evolve to generate a language whose structure appears to reflect canonical natural kinds. The evolution of these apparent natural kinds, however, is entirely in service of the rewards that accompany successful distinctions between the sender and receiver. Any metaphysics grounded on the structure of a natural language that evolved in this way would track arbitrary, but pragmatically useful distinctions. (shrink)

The paper presents a numerical interpretation of the quantifiers of traditional categorical propositions and then offers a generalization to accommodate all other numerical values. Next, it considers the implications possible on the basis of both minimum and maximum existential presuppositions; and finally, it shows that every pair of categorical premises yields multiple conclusions when appropriate minimum and maximum presuppositions are made for the terms of the premises.

This paper addresses the strength of Ramsey's theorem for pairs ($RT^2_2$) over a weak base theory from the perspective of 'proof mining'. Let $RT^{2-}_2$ denote Ramsey's theorem for pairs where the coloring is given by an explicit term involving only numeric variables. We add this principle to a weak base theory that includes weak König's Lemma and a substantial amount of $\Sigma^0_1$-induction (enough to prove the totality of all primitive recursive functions but not of all primitive recursive functionals). (...) In the resulting theory we show the extractability of primitive recursive programs and uniform bounds from proofs of $\forall\exists$-theorems. There are two components of this work. The first component is a general proof-theoretic result, due to the second author, that establishes conservation results for restricted principles of choice and comprehension over primitive recursive arithmetic PRA as well as a method for the extraction of primitive recursive bounds from proofs based on such principles. The second component is the main novelty of the paper: it is shown that a proof of Ramsey's theorem due to Erdős and Rado can be formalized using these restricted principles. So from the perspective of proof unwinding the computational content of concrete proofs based on $RT^2_2$ the computational complexity will, in most practical cases, not go beyond primitive recursive complexity. This even is the case when the theorem to be proved has function parameters f and the proof uses instances of $RT^2_2$ that are primitive recursive in f. (shrink)

Knowledge reduction of information systems is one of the most important parts of rough set theory in real-world applications. Based on the connections between the rough set theory and the theory of topology, a kind of topological reduction of incomplete information systems is discussed. In this study, the topological reduction of incomplete information systems is characterized by belief and plausibility functions from evidence theory. First, we present that a topological space induced by a pair of approximation operators in an incomplete (...) information system is pseudo-discrete, which deduces a partition. Then, the topological reduction is characterized by the belief and plausibility function values of the sets in the partition. A topological reduction algorithm for computing the topological reducts in incomplete information systems is also proposed based on evidence theory, and its efficiency is examined by an example. Moreover, relationships among the concepts of topological reduct, classical reduct, belief reduct, and plausibility reduct of an incomplete information system are presented. (shrink)

Suppose that entities composed of two distinct components can be qualitatively ordered in two ways, such that each ordering relation satisfies the axioms of conjoint measurement. Without further assumptions nothing can be said about the relation between the pair of numerical scales constructed for each component. Axioms are stated that relate the two measurement theories, and that are sufficient to establish that the two conjoint scales on each component are linearly related.

Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill1,2. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations3,4, and their performance suffers if this nonsymbolic system is impaired5. Nonsymbolic number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required6–10. (...) Here we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction11–15. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children’s difficulties learning symbolic arithmetic, and they suggest ways to enhance children’s engagement with formal mathematics. We presented children with approximate symbolic arithmetic problems in a format that parallels previous tests of non-symbolic arithmetic in preschool children8,9. In the first experiment, five- to six-year-old children were given problems such as ‘‘If you had twenty-four stickers and I gave you twenty-seven more, would you have more or less than thirty-five stickers?’’. Children performed well above chance (65.0%, t1952.77, P 5 0.012) without resorting to guessing or comparison strategies that could serve as alternatives to arithmetic. Children who have been taught no symbolic arithmetic therefore have some ability to perform symbolic addition problems. The children’s performance nevertheless fell short of performance on non-symbolic arithmetic tasks using equivalent addition problems with numbers presented as arrays of dots and with the addition operation conveyed by successive motions of the dots into a box (71.3% correct, F1,345 4.26, P 5 0.047)8.. (shrink)

In a theoretical simulation the cooperation of two insects is investigated who share a large number of maximally entangled EPR-pairs to correlate their probabilistic actions. Specifically, two distant butterflies must find each other. Each butterfly moves in a chaotic form of short flights, guided only by the weak scent emanating from the other butterfly. The flight directions result from classical random choices. Each such decision of an individual is followed by a read-out of an internal quantum measurement on a (...) spin, the result of which decides whether the individual shall do a short flight or wait. These assumptions reflect the scarce environmental information and the small brains’ limited computational capacity. The quantum model is contrasted to two other cases: In the classical case the coherence between the spin pairs gets lost and the two butterflies act independently. In the super classical case the two butterflies read off their decisions of whether to fly or to wait from the same internal list so that they always take the same decision as if they were super correlated. The numerical simulation reveals that the quantum entangled butterflies find each other with a much shorter total flight path than in both classical models. (shrink)

Pairs of sentences like the following pose a problem for ontology: (1) Jupiter has four moons. (2) The number of moons of Jupiter is four. (2) is intuitively a trivial paraphrase of (1). And yet while (1) seems ontologically innocent, (2) appears to imply the existence of numbers. Thomas Hofweber proposes that we can resolve the puzzle by recognizing that sentence (2) is syntactically derived from, and has the same meaning as, sentence (1). Despite appearances, the expressions ‘the number (...) of moons of Jupiter’ and ‘four’ do not function semantically as singular terms in (2). Hofweber’s primary evidence for this proposal concerns differences in the focus-related communicative functions of (1) and (2). In this paper I raise several serious problems for Hofweber’s proposal, and for his attempt to support it by appeal to focus-related phenomena. I conclude by offering independent evidence for an alternative, purely pragmatic resolution of the ontological puzzle. (shrink)

We show that numerous distinctive concepts of constructive mathematics arise automatically from an “antithesis” translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict and non-strict order pairs, cut-valued metrics, and apartness spaces. We also explain the constructive bifurcation of some classical concepts using the choice between multiplicative and additive affine connectives. Affine logic and the antithesis construction thus systematically “constructivize” classical definitions, handling the resulting bookkeeping automatically.

We characterize pairs of monotone generalized quantifiers Q1 and Q2 over finite domains that give rise to an entailment relation between their two relative scope construals. This relation between quantifiers, which is referred to as scope dominance, is used for identifying entailment relations between the two scopal interpretations of simple sentences of the form NP1–V–NP2. Simple numerical or set-theoretical considerations that follow from our main result are used for characterizing such relations. The variety of examples in which they hold (...) are shown to go far beyond the familiar existential-universal type. (shrink)

ABSTRACTFractions are defined by numerical relationships, and comparing two fractions’ magnitudes requires within-fraction and/or between-fraction relational comparisons. To better understand how individuals spontaneously reason about fractions, we collected eye-tracking data while they performed a fraction comparison task with conditions that promoted or obstructed different types of comparisons. We found evidence for both componential and holistic processing in this mixed-pairs task, consistent with the hybrid theory of fraction representation. Additionally, making within-fraction eye movements on trials that promoted a between-fraction comparison (...) strategy was associated with slower responses. Finally, participants who performed better on a non-numerical test of reasoning took longer to respond to the most difficult fraction trials, which suggests that those who had greater facility with non-numerical reasoning attended more to numerical relationships. These findings extend pri... (shrink)

Both and agree that there are universals—that qualities are universals. To say that the quality white is a universal is to say, in part, that one and the same thing is connected in some way to both Plato and Socrates and accounts for the truth of the sentences "Plato is white" and "Socrates is white." To put it another way, the term "white" in both sentences refers to the same entity. What arguments are there for such a view? Russell elegantly (...) put forth the classic argument in "On the Relations of Universals to Particulars." To deny universals is to assert that the quality attributed to Socrates is not one and the same with the quality attributed to Plato. The quality "in" each is numerically distinct and, furthermore, no one thing accounts for these distinct qualities being of the same kind. [I mention this latter point since one might, on a version of, hold that there are particular qualities as well as universal qualities. The former account for the whiteness of particular patches; the latter for such particular whitenesses being just that.] One must then hold that such particular qualities are related in some way, since they are the entities in virtue of which we truly assert that both things are white. One must then specify such a relation. The obvious point is that such a relation will either be taken as a universal or a particular instance. If a particular then the original problem recurs when we introduce a third white patch or a pair of black patches. If admitted as a universal then the view finally accepts universals, albeit relational ones. No other alternative can answer the original question—to account for Socrates and Plato having the same color. That is, no alternative acknowledging only individuals—that denies the two patches are connected, in some way, to one and the same entity—can prevent the recurrence of exactly the same kind of question we started out with. Let us consider the case of particulars. One may argue that just as universals account for the sameness of quality, something must account for the difference of two patches which, conceivably, have all their nonrelational qualities in common. This something, the ground of numerical difference, is considered to be a substratum which stands in a unique relation or connection with universals to form or constitute facts and the things we started out with, Plato and Socrates. These ordinary things are thought of as composed of a substratum and universals connected together. Facts about such things may be composed of the substratum and one universal. The facts are about the things since the same substratum is a constituent of both sorts of entities. Such substrata account for the difference of the two patches; for there being two and not one thing. These substrata, in turn, are held to be simply different. At this point one may balk. If substrata are held to be simply different, why bother with them at all? Why not hold that Socrates and Plato are composites, not classes, of universals, and that they are different composites of the same universals? They just simply differ. If substrata can simply differ, why may not composites of universals simply differ? The proponent of substrata must retort that since Plato and Socrates are composite entities they cannot simply differ but must be held to differ in a constituent. Only simple entities can simply differ. Let me call this assertion the axiom of difference. The first point to note is that it is a necessary assumption in the argument to establish the need for substrata in an adequate ontology. We must then inquire why some accept, implicitly or explicitly, such an axiom. (shrink)

Este trabajo se encuadra dentro de una nueva visión de la lógica de Leibniz, la cual pretende mostrar que sus escritos fueron ricos no solamente en proyectos ambiciosos sino también en desarrollos lógico-matematicos concretos. Se demuestra que su “Caracteristica Numerica” que asigna pares de números a las proposiciones categóricas es una semántiea para la cual la silogística aristotélica es correcta y completa, y que el sistema algebraico presentado en Fundamentos de un Cálculo Lógico es una lógica algebraica similar a la (...) de Boole.This work is a contribution to a new view of Leibniz’s logic, pretending to show that his writings were not only rich in projects, but also in concrete logico-mathematical developments. We prove that his “Numerical Characteristic” assigning pairs of numbers to terms of categorical propositions, is a complete and correct semantics for aristotelian syllogistic, and the algebraic system presented in Fundamentals of Logical Calculus is essentially a complete version of boolean algebraic logic. (shrink)

Tennis smashed onto the worldwide athletic scene soon after its modern rules and equipment were introduced in nineteenth-century England. Exciting, competitive, and uniquely accessible to people of all ages and talent levels, tennis continues to enjoy popularity, both as a recreational activity and a spectator sport. Life imitates sport in Tennis and Philosophy. Editor David Baggett approaches tennis not only as a game but also as a surprisingly rich resource for philosophical analysis. He assembles a team of champion scholars, including (...) David Foster Wallace, Robert R. Clewis, David Detmer, Mark Huston, Tommy Valentini, Neil Delaney, and Kevin Kinghorn, to consider numerous philosophical issues within the sport. Profiles of tennis greats such as John McEnroe, Roger Federer, the Williams sisters, and Arthur Ashe are paired with pertinent topics, from the ethics of rage to the role of rivalry. Whether entertaining metaphysical arguments or examining the nature of beauty, these essays promise insightful discussion of one of the world's most popular sports. (shrink)

Arthur C. Danto’s The Transfiguration of the Commonplace is one of the most influential recent books on philosophy of art. It is noteworthy for both his method, which emphasizes indiscernible pairs and sets of objects, and his conclusion, which is that artworks are distinguished from non-artwork counterparts by a semantic and aesthetic transfiguration that depends on their relationship to art history. In numerous contexts, Danto has confirmed that the relevant concept of art is the concept of fine art. Examples (...) of music that are not fine art demonstrate that semantic and aesthetic transfiguration does not require a relationship to art history or art theory. Appropriate interpretation and individuation of a great deal of music can be achieved by listeners who do not grasp art theory and who do not guide their interpretation by reference to the concept of art. (shrink)

""Serious philosophy is not an attempt to construct a system of beliefs, but the activity of awakening, the conversation passionately pursued. Only if professional philosophy reclaims this paradigm and finds ways to embody it, will it achieve an active place in the thought and life of our culture."" --James Conlon, ""Stanley Cavell and the Predicament of Philosophy."" This book is a collection of serious philosophical essays that aim to awaken readers, teachers, and students to a desire for conversation passionately pursued. (...) The essays in this volume speak about sex, movies, poetry, and politics, in short, about those things contemporary Americans passionately discuss. These are the subjects that were taught for forty-three years in James Conlon's classroom at Mount Mary University, a Catholic urban university for women in Milwaukee, Wisconsin. This volume celebrates Conlon's work while calling to all who continue to teach and learn about philosophy in contemporary times with the message that relevant philosophy deals with life as it is lived in the moment. ""Dr. Conlon made it his life's work to bring to consciousness an often unconscious awareness that accepts the way things are as the measure of what is real, normative, and moral. His commitment to awakening people to the wonder of common experience made a profound contribution to the mission of Mount Mary. The essays in this volume are a testament to the way he engaged students in the process of living a fully human life."" --Joan Penzenstadler, SSND, Mount Mary University ""True to the spirit of Professor Conlon's teaching, this collection illustrates how his approach made philosophy a genuine dialogue, brought diverse viewpoints and perspectives to bear on any problem, and engaged generations of women in the philosophical conversation."" --Kathleen Poorman Dougherty, Alma College ""This collection of always thoughtful and often provocative essays by James Conlon, his colleagues, and students honors Conlon's decades-long career at Mount Mary University dedicated to teaching the practice of philosophy... Both new and experienced teachers of philosophy will find insights and inspiration in this volume!"" --Donna Engelmann, Alverno College ""Just in Time celebrates the work of the philosopher James Conlon. It also honors the pedagogy of inquiry that has had a profound impact on the students he taught for over 40 years. Conlon's essays are paired with ones from his students and colleagues--testaments to the influence that his teaching has had. Readers will be challenged to pursue passionate conversations and inspire others to engage in thoughtful inquiry about the relevant topics of today."" --Eileen Schwalbach, Former president, Mount Mary University Jennifer Hockenbery Dragseth is Professor of Philosophy at Mount Mary University. She is the author of Thinking Woman: A Philosophical Approach to the Quandary of Gender and the editor of The Devil's Whore: Reason and Philosophy in the Lutheran Tradition. James Conlon is Professor of Philosophy, Emeritus at Mount Mary University where he taught for forty-three years. He is the author of numerous philosophical articles. (shrink)

Impression-based music retrieval helps users in finding musical pieces that suit their preferences, feelings, or mental states from the huge volume of a music database. We have therefore developed an impression-based music retrieval system that enables this. Users are asked to select one or more pairs of impression words from the multiple pairs presented by the system and estimate each of the selected pairs on a seven-step scale in order to input their impressions into the system. For (...) instance, if they want to locate musical pieces that will create a happy impression, they should check the radio button ``Happy'' in the impression scale, ``Very happy -- Happy -- A little happy -- Neutral -- A little sad -- Sad -- Very sad,'' where a pair of impression words with a seven-step scale is called an ``impression scale'' in this paper. The system would measure the distance between the impressions of every musical piece in a user-specified music database and the impressions inputted by the user, and determine candidate musical pieces to be presented as retrieval results. In this paper, we define the form of vectors that numerically express impressions of musical pieces, and propose a method of generating such a vector from a musical piece. The most significant attribute of this method is that it uses n-gram statistics of information on pitch, strength, and length of every tone in that musical piece as features extracted from it. We also present the results of evaluating the performance of the system. (shrink)

A methodology which enables a flexible and reusable development of mobile agent application to a mobility aware indoor environment is provided in this study. The methodology is named Workflow-awareness model based on a concept of a pair of mobile agents cooperating to perform a given task. A monolithic mobile agent application with numerous concerns in a mobility aware setting is divided into a master agent and a shadow agent according to a type of tasks. The MA executes a main application (...) logic which includes monitoring a user's physical movement and coordinating various services. The SA performs additional tasks depending on environments to aid the MA in achieving efficient execution without losing application logic. "Workflow-awareness " means that the SA knows the MA's execution state transition so that the SA can provide a proper task at a proper timing. A prototype implementation of the methodology is done with a practical use of AspectJ. AspectJ is used to automate WFA by weaving communication modules to both MA and SA. Usefulness of this methodology concerning its efficiency and software engineering aspects are analyzed. As for the effectiveness, the overhead of WFA is relatively small to the whole expenditure time. And from the view of the software engineering, WFA is possible to provide a mechanism to deploy one application in various situations. (shrink)

Este trabajo se encuadra dentro de una nueva visión de la lógica de Leibniz, la cual pretende mostrar que sus escritos fueron ricos no solamente en proyectos ambiciosos sino también en desarrollos lógico-matematicos concretos. Se demuestra que su “Caracteristica Numerica” que asigna pares de números a las proposiciones categóricas es una semántiea para la cual la silogística aristotélica es correcta y completa, y que el sistema algebraico presentado en Fundamentos de un Cálculo Lógico es una lógica algebraica similar a la (...) de Boole.This work is a contribution to a new view of Leibniz’s logic, pretending to show that his writings were not only rich in projects, but also in concrete logico-mathematical developments. We prove that his “Numerical Characteristic” assigning pairs of numbers to terms of categorical propositions, is a complete and correct semantics for aristotelian syllogistic, and the algebraic system presented in Fundamentals of Logical Calculus is essentially a complete version of boolean algebraic logic. (shrink)

Imagine a very fi ne grid or graph on which dots are placed at various coordinates so that, as a consequence, this or that shape materializes there. Depending on the coordinates of the dots, different shapes will appear, and for every shape there will be a pattern in the coordinates that guarantees its appearance. Take, for example, the diagonal line that slopes rightward and upward at an angle of 45 degrees from the origin. This line is bound to make an (...) appearance so long as the coordinates satisfy the condition or pattern that as they move away from the origin, (0,0), the coordinates are progressively larger pairs of equal numbers: (1,1), (3,3), and so on. In the world of such dots and shapes, it is going to be in principle possible, for any array of dots that realizes a relevant shape, to derive the presence of the shape from the numerical coordinates of the dots. More particularly, it is going to be possible to derive that shape without reliance on anything other than, fi rst, the empirical fact that the given array of coordinates instantiates this or that pattern; and second, the a priori knowable fact that the pattern guarantees the presence of the shape in question. The nature of the shapes on any grid—if indeed there are any relevant shapes present—is going to be a priori derivable from the positions of the dots; it is going to be possible in principle to derive the one from the other. The simplest and most appealing version of physicalism parallels this sort of doctrine about dots and shapes (Pettit 1994, 1995). It holds that just as the positions of the dots determine the nature of the shapes a priori, so the way the natural world is physically organized a priori determines the way it presents itself in psychological and other terms. The way things are physically confi gured entails the presence of psychological and other realities, and it does this without reliance on anything other than what a.. (shrink)

1. Consider a circle. It has both a radius and a circumference. There is obviously a real distinction between the properties having a radius and having a circumference. This is not because, when confining ourselves to circles,1 having a radius can ever exist apart from having a circumference. A real distinction does not depend on that. Descartes thought that a real distinction between x and y meant that x could exist without y or vice versa, if only by the power (...) of God. But Descartes was wrong. Separable existence is a sufficient but not necessary condition of there being a real distinction. The difference between a real and a conceptual distinction derives from medieval philosophy. Aquinas, for one, held that things can be really distinct even though not separable (the form and matter of a material substance or its essence and existence, for example).2 For a merely conceptual distinction between x and y to exist, it is necessary for the distinction to exist in thought only. There is only a conceptual distinction between an upward slope and a downward slope, or between a glass’s being half empty and half full. Not only are the members of such pairs inseparable (whether by God or in any other way), but there is no real distinction between them. There is no numerical distinctness between the entities or qualities between which there is only a conceptual distinction. To this extent alone is Galen Strawson (2008) correct.3 But when it comes to.. (shrink)

The vast expressive power of language is made possible by two principles: the arbitrary soundmeaning pairing underlying words, and the discrete combinatorial system underlying grammar. These principles implicate distinct cognitive mechanisms: associative memory and symbolmanipulating rules. The distinction may be seen in the difference between regular inflection (e.g., walk-walked), which is productive and open-ended and hence implicates a rule, and irregular inflection (e.g., come-came, which is idiosyncratic and closed and hence implicates individually memorized words. Nonetheless, two very different theories have (...) attempted to collapse the distinction; generative phonology invokes minor rules to generate irregular as well as regular forms, and connectionism invokes a pattern associator memory to store and retrieve regular as well as irregular forms. I present evidence from three disciplines that supports the traditional word/rule distinction, though with an enriched conception of lexical memory with some of the properties of a pattern-associator. Rules, nonetheless, are distinct from patternassociation, because a rule concatenates a suffix to a symbol for verbs, so it does not require access to memorized verbs or their sound patterns, but applies as the "default," whenever memory access fails. I present a dozen such circumstances, including novel, unusual-sounding, and rootless and headless derived words, in which people inflect the words regularly (explaining quirks like flied out, low-lifes, and Walkmans). A comparison of English to other languages shows that contrary to the connectionist account, default suffixation is not due to numerous regular words reinforcing a pattern in associative memory, but to a memory-independent, symbol-concatenating mental operation. (shrink)

Intuitively, collective nouns are pseudo-singular: a collection of things (a pair of people, a flock of birds, etc.) just is the things that make ‘it’ up. But certain facts about natural language seem to count against this view. In short, distributive predicates and numerals interact with collective nouns in ways that they seemingly shouldn’t if those nouns are pseudo-singular. We call this set of issues ‘the distribution problem’. To solve it, we propose a modification to cover-based semantics. On this semantics, (...) the interpretation of distributive predicates and numerals depends on a cover, where the choice of cover is strongly semantically constrained by the noun with which they interact. (shrink)

Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. (...) We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point. (shrink)

Nelson’s stochastic quantum mechanics provides an ideal arena to test how the Born rule is established from an initial probability distribution that is not identical to the square modulus of the wavefunction. Here, we investigate numerically this problem for three relevant cases: a double-slit interference setup, a harmonic oscillator, and a quantum particle in a uniform gravitational field. For all cases, Nelson’s stochastic trajectories are initially localized at a definite position, thereby violating the Born rule. For the double slit and (...) harmonic oscillator, typical quantum phenomena, such as interferences, always occur well after the establishment of the Born rule. In contrast, for the case of quantum particles free-falling in the gravity field of the Earth, an interference pattern is observed before the completion of the quantum relaxation. This finding may pave the way to experiments able to discriminate standard quantum mechanics, where the Born rule is always satisfied, from Nelson’s theory, for which an early subquantum dynamics may be present before full quantum relaxation has occurred. Although the mechanism through which a quantum particle might violate the Born rule remains unknown to date, we speculate that this may occur during fundamental processes, such as beta decay or particle-antiparticle pair production. (shrink)

Stereotypically, computation involves intrinsic changes to the medium of representation: writing new symbols, erasing old symbols, turning gears, flipping switches, sliding abacus beads. Perspectival computation leaves the original inscriptions untouched. The problem solver obtains the output by merely alters his orientation toward the input. There is no rewriting or copying of the input inscriptions; the output inscriptions are numerically identical to the input inscriptions. This suggests a loophole through some of the computational limits apparently imposed by physics. There can be (...) symbol manipulation without inscription manipulation because symbols are complex objects that have manipulatable elements besides their inscriptions. Since a written symbol is an ordered pair of consisting of a shape and the reader's orientation to that inscription, the symbol can be changed by changing the orientation rather than inscription. Although there are the usual physical limits associated with reading the answer, the computation is itself instantaneous. This is true even when the sub-calculations are algorithmically complex, exponentially increasing or even infinite. (shrink)

Despite advances in treatments over the last decades, a uniformly reliable and free of side effects therapy of human cancers remains to be achieved. During chromosome replication, a premature halt of two converging DNA replication forks would cause incomplete replication and a cytotoxic chromosome nondisjunction during mitosis. In contrast to normal cells, most cancer cells bear numerous DNA deletions. A homozygous deletion permanently marks a cell and its descendants. Here, we propose an approach to cancer therapy in which a pair (...) of sequence‐specific roadblocks is placed solely at two cancer‐confined deletion sites that are located ahead of two converging replication forks. We describe this method, termed “replication blocks specific for deletions” (RBSD), and another deletions‐based approach as well. RBSD can be expanded by placing pairs of replication roadblocks on several different chromosomes. The resulting simultaneous nondisjunctions of these chromosomes in cancer cells would further increase the cancer‐specific toxicity of RBSD. (shrink)

Crispin Wright in his 1982 paper argues for strict finitism, a constructive standpoint that is more restrictive than intuitionism. In its appendix, he proposes models of strict finitistic arithmetic. They are tree-like structures, formed in his strict finitistic metatheory, of equations between numerals on which concrete arithmetical sentences are evaluated. As a first step towards classical formalisation of strict finitism, we propose their counterparts in the classical metatheory with one additional assumption, and then extract the propositional part of ‘strict finitistic (...) logic’ from it and investigate. We will provide a sound and complete pair of a Kripke-style semantics and a sequent calculus, and compare with other logics. The logic lacks the law of excluded middle and Modus Ponens and is weaker than classical logic, but stronger than any proper intermediate logics in terms of theoremhood. In fact, all the other well-known classical theorems are found to be theorems. Finally, we will make an observation that models of this semantics can be seen as nodes of an intuitionistic model. (shrink)

An Invitation to Formal Reasoning introduces the discipline of formal logic by means of a powerful new system formulated by Fred Sommers. This system, term logic, is different in a number of ways from the standard system employed in modern logic; most striking is its greater simplicity and naturalness. Based on a radically different theory of logical syntax than the one Frege used when initiating modern mathematical logic in the 19th Century, term logic borrows insights from Aristotle's syllogistic, Scholastic logicians, (...) Leibniz, and the 19th century British algebraists. Term logic takes its syntax directly from natural language, construing statements as combinations of pairs of terms, where complex terms are taken to have the same syntax as statements. Whereas standard logic requires extensive 'translation' from natural language to symbolic language, term logic requires only 'transcription' into the symbolic language. Its naturalness is the result of its ability to stay close to the forms of sentences usually found in every day discourse. Written by the founders of the term logic approach, An Invitation to Formal Reasoning is a unique introduction and exploration of this new system, offering numerous exercises and examples throughout the text. Summarising the standard system of mathematical logic to set term logic in context, and showing how the two systems compare, this book presents an alternative approach to standard modern logic for those studying formal logic, philosophy of language or computer theory. Fred Sommers is Professor Emeritus, Brandeis University, USA; George Englebretsen is Professor of Philosophy, Bishop's University, Canada. (shrink)

Data increasingly drive our lives. Often presented as a new trajectory, the deep immersion of our lives in data has a history that is well over a century old. By revisiting the work of early pioneers of what would today be called data science, we can bring into view both assumptions that fund our data-driven moment as well as alternative relations to data. I here excavate insights by contrasting a seemingly unlikely pair of early data technologists, Francis Galton and W.E.B. (...) Du Bois. Galton, well known for his contributions to eugenics, was first and foremost a tinkering technician of measure. There are numerous domains of science over which Galtonian conceptions retain considerable influence, presumably without his pride in racial inequality. A more viable, because more egalitarian, alternative for the present can be found in the early data work of Du Bois. (shrink)

People often struggle with Bayesian reasoning. However, research showed that people’s performance (and rationality) can be supported by the way of representing the statistical information. First, research showed that using natural frequencies instead of probabilities as format of statistical information increases people’s performance in Bayesian situations thoroughly. Second, research also yielded that people’s performance increases through using visualization. We build our paper on existing research in this field. The main aim is to analyse people’s strategies in Bayesian situations that are (...) still erroneous although statistical information is represented by natural frequencies and visualizations. In particular, we compare two pairs of visualization with similar numerical information (tree diagram vs. unit square and double-tree diagram vs. 2x2-table) concerning their impact on people’s erroneous strategies in Bayesian situations. For this aim, we conducted an experiment with 540 university students. The students were randomly assigned to four conditions that are defined by the four different visualizations of statistical information. The students were asked to indicate a fraction as response in four Bayesian situations. We documented the numerator and the denominator of the students’ responses representing a basic set and a subset in a Bayesian situation. Our results show that people’s erroneous strategies are highly dependent on the visualization. A central finding is that the visualization’s characteristic of making the nested-sets structure of a Bayesian situation transparent has a facilitating effect on people’s Bayesian reasoning. For example, compared to the unit square, a tree diagram does not explicitly visualize the set-subset relations that are relevant in a Bayesian situation. Accordingly, compared to a unit square, a tree diagram partly hinders people to find the correct denominator in a Bayesian situation, and, in particular, triggers to select a wrong numerator. By analyzing people’s erroneous strategies in Bayesian situations, we contribute to investigating approaches to facilitate Bayesian reasoning and to further develop the teaching of Bayesian reasoning. (shrink)

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event (...) depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. (shrink)

Meditation. A man is a compositus ex mente et corpore (VII 82; II 57), a composite being consisting of a mind and a body. [Note: In parenthetical citations of Descartes's text, the first pair of numerals refers to volume and page of the Adam and Tannery edition; the second pair to volume and page of the English translation by Cottingham, Stoothoff, Murdoch, and Kenny.] These two components of a man are themselves different things. Not only are they disparate in nature, (...) having nothing in common; but they are also distinct from one another, in the sense that each can exist without the other. (shrink)

The historical formation of Brazil is distinguished from the majority of ex-colonial nations by one factor that is especially characteristic: an intense process of ethnic and cultural mixing. The Portuguese colonisers, who, unlike the English Puritans in North America, left their families and arrived in Brazil in small groups mainly composed of men, naturally tended to pair off with the women they found available - first of all indigenous women and later African women. There was nothing in Brazil to prevent (...) this spontaneous behaviour similar to the role played in the English colonies of North America by the strength of the family group or the strict religious observance of the community. Thus from the outset Brazil tended to accept racial mixing as a de facto reality. As Gilberto Freyre correctly noted in his book Casa Grande e Senzala:They mixed happily with women of colour from the very first contacts and many mixed-race children resulted, so much so that only a few thousand men were enough to colonize vast areas and compete with the greatest and most numerous peoples as regards the extent of the colonial territory and the effectiveness of colonizing activity. (shrink)

There are different Bayesian measures to calculate the degree of confirmation of a hypothesis H in respect of a particular piece of evidence E. Zalabardo (Analysis 69:630–635, 2009) is a recent attempt to defend the likelihood-ratio measure (LR) against the probability-ratio measure (PR). The main disagreement between LR and PR concerns their sensitivity to prior probabilities. Zalabardo invokes intuitive plausibility as the appropriate criterion for choosing between them. Furthermore, he claims that it favours the ordering of pairs evidence/hypothesis generated (...) by LR. We will argue, however, that the intuitive non-numerical example provided by Zalabardo does not show that prior probabilities do not affect the degree of confirmation. On account of this, we conclude that there is no compelling reason to endorse LR qua measure of degree of confirmation. On the other side, we should not forget some technicalities which still benefit PR. (shrink)

Summary In this work we elaborate on the idea of a formal theory for a limited but important part of structural chemistry, that described by Lewis’ methods and VSEPR (Valence Shell Electron Pair Repulsion). For this purpose, recursive functions and propositional functions are defined, that apply to formal expressions of the structure, based on a finite set of symbols. This approach allows for the expression of numerous questions of chemical interest. The formalization of basic structural chemistry based on Lewis/VSEPR method (...) is potentially useful for the automation of the related procedures, but possibly also of some use as complementary material in teaching and as a heuristic tool in structural chemistry. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

The concept of classical r matrices is developed from a purely canonical standpoint. The final purpose of this work is to bring about a synthesis between recent developments in the theory of integrable systems and the general theory of quantization as a deformation of classical mechanics. The concept of quantization algebra is here dominant; in integrable systems this is the set of dynamical variables that appear in the Lax pair. The nature of this algebra, a solvable Lie algebra in such (...) models as the Sine-Gordon and Toda field theories but semisimple in the case of spin systems, provides a useful scheme for the classification of integrable models. A completely different classification is obtained by the nature of the r matrix employed; there are three kinds: rational, trigonometric, and elliptic. All cases are studied in detail, with numerous examples. Some of the problems connected with quantization are discussed. (shrink)

Interactions among membrane proteins regulate numerous cellular processes, including cell growth, cell differentiation and apoptosis. We need to understand which proteins interact, where they interact and to which extent they interact. This article describes a set of novel approaches to measure, on the surface of living cells, the number of clusters of proteins, the number of proteins per cluster, the number of clusters or membrane domains that contain pairs of interacting proteins and the fraction of one protein species that (...) interacts with another protein within these domains. These data can then be interpreted in terms of the function of the protein‐protein interactions. BioEssays 26:196–203, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

Partial order optimality theory is a conservative generalization of classical optimality theory that makes possible the modeling of free variation and quantitative regularities without any numerical parameters. Solving the ranking problem for PoOT has so far remained an outstanding problem: allowing for free variation, given a finite set of input/output pairs, i.e., a dataset, \ that a speaker S knows to be part of some language L, how can S learn the set of all grammars G under some constraint (...) set C compatible with \?. Here, allowing for free variation, given the set of all PoOT grammars GPoOT over a constraint set C, for an arbitrary \, I provide set-theoretic means for constructing the actual set G compatible with \. Specifically, I determine the set of all STRICT ORDERS of C that are compatible with \. As every strict total order is a strict order, our solution is applicable in both PoOT and COT, showing that the ranking problem in COT is a special instance of a more general one in PoOT. (shrink)

In this series of papers I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Papers I and II were devoted to system A theory of the outer planets and of the planet Venus. In this third and last paper I will study system A theory of the planet Mercury. Our knowledge of the Babylonian theory of Mercury is at present based on twelveEphemeridesand sevenProcedure Texts. Three computational systems of (...) Mercury are known, all of system A. System A1is represented by nineEphemeridescovering the years 190 BC to 100 BC and system A2by twoEphemeridescovering the years 310 to 290 BC. System A3is known from aProcedure Textand from Text M, anEphemerisof the last evening visibility of Mercury for the years 424 to 403 BC. From an analysis of the Babylonian observations of Mercury preserved in theAstronomical DiariesandPlanetary Textswe find: (1) that dates on which Mercury reaches its stationary points are not recorded, (2) that Normal Star observations on or near dates of first and last appearance of Mercury are rare (about once every twenty observations), and (3) that about one out of every seven pairs of first and last appearances is recorded as “omitted” when Mercury remains invisible due to a combination of the low inclination of its orbit to the horizon and the attenuation by atmospheric extinction. To be able to study the way in which the Babylonian scholars constructed their system A models of Mercury from the available observational material I have created a database of synthetic observations by computing the dates and zodiacal longitudes of all first and last appearances and of all stationary points of Mercury in Babylon between 450 and 50 BC. Of the data required for the construction of an ephemeris synodic time intervals Δt can be directly derived from observed dates but zodiacal longitudes and synodic arcs Δλ must be determined in some other way. Because for Mercury positions with respect to Normal Stars can only rarely be determined at its first or last appearance I propose that the Babylonian scholars used the relation Δλ = Δt −3;39,40, which follows from the period relations, to compute synodic arcs of Mercury from the observed synodic time intervals. An additional difficulty in the construction of System A step functions is that most amplitudes are larger than the associated zone lengths so that in the computation of the longitudes of the synodic phases of Mercury quite often two zone boundaries are crossed. This complication makes it difficult to understand how the Babylonian scholars managed to construct System A models for Mercury that fitted the observations so well because it requires an excessive amount of computational effort to find the best possible step function in a complicated trial and error fitting process with four or five free parameters. To circumvent this difficulty I propose that the Babylonian scholars used an alternative more direct method to fit System A-type models to the observational data of Mercury. This alternative method is based on the fact that after three synodic intervals Mercury returns to a position in the sky which is on average only 17.4° less in longitude. Using reduced amplitudes of about 14°–25° but keeping the same zone boundaries, the computation of what I will call 3-synarc system A models of Mercury is significantly simplified. A full ephemeris of a synodic phase of Mercury can then be composed by combining three columns of longitudes computed with 3-synarc step functions, each column starting with a longitude of Mercury one synodic event apart. Confirmation that this method was indeed used by the Babylonian astronomers comes from Text M (BM 36551+), a very early ephemeris of the last appearances in the evening of Mercury from 424 to 403 BC, computed in three columns according to System A3. Based on an analysis of Text M I suggest that around 400 BC the initial approach in system A modelling of Mercury may have been directed towards choosing “nice” sexagesimal numbers for the amplitudes of the system A step functions while in the later final models, dating from around 300 BC onwards, more emphasis was put on selecting numerical values for the amplitudes such that they were related by simple ratios. The fact that different ephemeris periods were used for each of the four synodic phases of Mercury in the later models may be related to the selection of a best fitting set of System A step function amplitudes for each synodic phase. (shrink)

In 1655 La Peyrère was the first to substantially argue for and popularize polygenism—the view that God created multiple original human mating pairs in separate acts of creation with numerous created before Adam. Positing or rejecting polygenism has been central to modern theorizing about human types and origins. Prominent recent interpreters have maintained that La Peyrère’s polygenism does not imply a hierarchy of human types. This paper reconstructs La Peyrère’s account and, in opposition to the dominant view, argues that (...) his polygenism produces a human species hierarchy. The Adamite species is superior to the Pre-Adamite species in virtue of its material composition, mode of creation, and form. The upshot is that La Peyrère’s theological system posits a proto-racialist conception of human types. (shrink)

The Vessantara J?taka is not only the most popular of all the Buddhist J?taka tales, but is important in the tradition as a whole, generally considered by the Therav?din tradition to display the epitome of the Bodhisatta’s perfection of giving. While most studies have focused on philological approaches, numerous questions as to the text’s structure and how to interpret individual parts within that structure have remained unresolved. My study shall employ the theory of ‘chiasmus’ to shed new light on both (...) the key message of the story and also the sub-themes within it. In terms of textual criticism, I shall first elucidate the chiastic structure of the text and discuss how this structure can provide insights on text-critical readings. In terms of interpretation, I shall then see how the structure clearly demarcates the text’s scope through its prologue and conclusion with surrounding framework, its paired parallel sub-themes, and its central climax point, all in the light of its chiastic structure. Finally, considering broader implications, on comparison with other recently discovered Buddhist textual chiasmi I shall present a tentative hypothesis as to the origins of such structures in the ‘bodhisatta’ literary genre. (shrink)

Visual illusions provide a means of investigating the rules and principles through which approximate number representations are formed. Here, we investigated the developmental trajectory of an important numerical illusion – the connectedness illusion, wherein connecting pairs of items with thin lines reduces perceived number without altering continuous attributes of the collections. We found that children as young as 5 years of age showed susceptibility to the illusion and that the magnitude of the effect increased into adulthood. Moreover, individuals with (...) greater numerical acuity exhibited stronger connectedness illusions after controlling for age. Overall, these results suggest the approximate number system expects to enumerate over bounded wholes and doing so is a signature of its optimal functioning. (shrink)

The term 'essentialism' in its popular usage is usually qualified in some way, as in 'biological essentialism', 'gender essentialism' and 'social essentialism'. The essentialist theses were defended on the grounds that denying them leads, under plausible assumptions, to pairs of worlds containing objects which are intrinsic and spatio‐temporal duplicates and yet which are numerically distinct. This chapter outlines some technical difficulties in getting the definitions of 'essential property' and 'individual essence' exactly right. It explains the idea of a metaphysically (...) essential property in terms of Aristotle's 'essential/accidental' contrast. A popular idea is to invoke the notion, which has its roots in Aristotle's theory of essence and accident, of a substance sortal. A different way of developing a sortal‐based account of essential kinds is suggested by David Wiggins, who argues that it is only ultimate sortals that represent essential properties, where an ultimate sortal is the most general sortal corresponding to a given principle of individuation. (shrink)

Barsalou's contribution converges with basic ideas and empirical findings of cognitive linguistics. They posit the same general architecture. The perceptual grounding of conceptual structure is a central tenet of cognitive linguistics. Our capacity to construe the same situation in alternate ways is fundamental to cognitive semantics, and numerous parallels are discernible between conceptual construal and visual perception. Grammar is meaningful, consisting of schematized patterns for the pairing of semantic and phonological structures. The meanings of grammatical elements reside primarily in the (...) construal they impose on conceptual content. This view of linguistic structure appears to be compatible with Barsalou's proposals. (shrink)

t Intentional sampling methods are non-randomized procedures that select a group of individuals for a sample with the purpose of meeting specific prescribed criteria. In this paper we extend previous works related to intentional sampling, and address the problem of sequential allocation for clinical trials with few patients. Roughly speaking, patients are enrolled sequentially, according to the order in which they start the treatment at the clinic or hospital. The allocation problem consists in assigning each new patient to one, and (...) only one, of the alternative treatment arms. The main requisite is that the profiles in the alternative arms remain similar with respect to some relevant patients’ attributes (age, gender, disease, symptom severity and others). We perform numerical experiments based on a real case study and discuss how to conveniently set up perturbation parameters, in order to yield a suitable balance between optimality – the similarity among the relative frequencies of patients in the several categories for both arms, and decoupling – the absence of a tendency to allocate each pair of patients consistently to the same arm. (shrink)