Different analyses of complex cardinal numerals have been proposed in Generative Grammar. This article provides an analysis of these expressions based on the Strong Minimalist Thesis, according to which the derivations of linguistic expressions are generated by a simple combinatorial operation, applying in accord with principles external to the language faculty. The proposed derivations account for the asymmetrical structure of additive and multiplicative complexes and for the instructions they provide to the external systems for their interpretation. They (...) harmonize with those of coordinate nouns, and thus offer a unified Minimalist account of their core properties. Firstly, the empirical problem addressed is stated. Secondly, the theoretical framework is presented. Thirdly, Minimalist derivations for additive and multiplicative complexes are provided. Fourthly, the proposed derivations are contrasted with derivations not relying on the Strong Minimalist Thesis. Lastly, consequences for linguistic theory are identified as well as questions open to further inquiry. (shrink)

The present study analyzes the English diaries written by a young Chinese English as a foreign language learner over a 1-year period in an attempt to determine the developmental process of Chinese EFL young learners’ written language in terms of syntactic complexity. This study aimed to use a wide range of metrics to explore densely collected data based on Dynamic Systems Theory. The longitudinal study data were analyzed through eight large-grained measures related to sentential, clausal, and phrasal features by using (...) L2 Syntactic Complexity Analyzer, as well as fine-grained measures related to seven modifiers, an adjective placed before a noun, ordinal numerals are indicated, cardinal numeral, predicative adjective, adverbial adjective, adverbs, prepositional phrases, subordinate, and relative clause, through manual annotations. The results show that, first, the developmental process was not linear but spiral in terms of large-grained measures. The sentential level varied, and the development process of the young learner is different from Chinese English learners studying in colleges. Second, the dynamic features of fine-grained measures are also prominent in the seven indicators. ADJA, PREP, and REL showed a steady increase, ADJP showed an obvious decline, while ADV and SUB first increased and then declined. Third, the correlation analysis revealed a competitive interaction within fine-grained measures and between large-grained and fine-grained measures. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy of Music Education Review 12.1 (2004) 89-93 [Access article in PDF] Richard Shusterman, Performing Live: Aesthetic Alternatives for the Ends of Art (New York: Cornell University Press, 2000) Performing Live can be ascribed to post-modern American pragmatism in its widest expression. The author's intention is to revalue aesthetic experience, as well as to expand its realm to the extent where such experience also encompasses areas alien to traditional (...) aesthetics (for example, popular art or the somatic arts of self-improvement), reaching "the art of living" and reclaiming life itself as performance.After the introduction, titled "Aesthetic Renewal for the Ends of Art: An Overture," the text is organized in two main parts: "Aesthetic Experience and Popular Art" and "Soma, Self, and Society." Along with its ambitious title, the book's organization and structure promise a consistency of approach and narrative that somewhat dissolves during the reading. Shusterman recognizes that the stylistic problems that arise from a compilation of articles spanning ten years, mixing newly written and revised articles, but appeals to the reader's appreciation of the "quality of the mix" (11). Despite this feature, he is a lucid and thoughtful communicator and his writing style is excellent.In order to propose new or revitalized alternatives for the ends of art, Shusterman [End Page 89] explores the crisis in traditional visions of art, pointing to the compartmentalization and lack of credibility in current artistic thought and practice. Hegel, Walter Benjamin, Gianni Vattimo, and Arthur Danto provide him with the philosophical arguments accounting for the modern "exhaustion" of art. He supports a dialectical approach, both naturalistic and historicist, and builds a solid case for the possibility of alternatives in aesthetic thought and experience. He proposes two alternatives in his introduction: The two most prominent sites for today's aesthetic alternatives are clearly the mass-media popular arts and the complex cluster of disciplines devoted to bodily beauty and the art of living as expressed in today's preoccupation with aesthetic lifestyles. (7) It is unclear why these alternatives are "clearly" "the two most prominent." The author does not build a case for this assumption or for the "newness" of these alternatives. The "compilation style" mentioned above and this lack of justification for one of the most original elements in the book make this text often read as a philosophical drafting board. Keeping these characteristics in mind and also critically pondering the degrees of success in the enterprise, the reader must give Shusterman credit for taking risks while suggesting concrete examples for an experiential, holistic philosophy. In this sense, he mentions (in a different context) that "all of us [are caught] between conceptual history and futuristic speculation" (145), and he takes to heart this situation and its challenges.The first chapter in Performing Live aims to redeem or revalue the concept of aesthetic experience. For Shusterman, the loss of "felt experience" in art makes the interest in this concept utterly relevant for art's survival. He traces the lineage of this aesthetic philosophy to John Dewey, Monroe Beardsley, Nelson Goodman, and Arthur Danto. Besides focusing on these authors, his analysis revisits some of the main currents of thought in Western philosophy on the topic (for example, Plato, Hume, Kant, Dickie, Adorno, Benjamin, Gadamer). He concludes that a pragmatic approach to aesthetics, applying the concept of aesthetic experience directionally (as a means towards the actual experience rather than as a definable concept), can provide new paths for revitalizing art. Throughout the text this concept is also used expansively. The post-modern justification of the proposed aesthetics, by allowing the extension of aesthetic experience to embrace "the art of living," can leave the reader wondering if Shusterman has not simply turned Kierkegaard's existentialist stages to self-realization upside down.The second chapter is an open defense of popular art, carried out by contesting the main complaints found in current art criticism. Shusterman's defense is not directed to the products of popular art, but against the claim that popular art is aesthetically "worthless." His definition of "popular art... (shrink)

Most participatory strands of democratic theory hold a conception of the transformative potential of democratic participation. According to those theories, involvement in deliberative or decision-making processes makes better citizens by teaching them political skills and orienting them towards the common good. This article draws from original interviews with residents of housing coops to argue that this phenomenon can also be found outside formal decision-making forums, in menial and quotidian tasks undertaken for the preservation and maintenance of the organization. Using the (...) political theory of Mary Parker Follett, we suggest that involvement in practical concrete activities is an overlooked but significant element of democratic life. Residents of the coops we studied grew ‘power-with’ by joining others in accomplishing everyday tasks, such as blowing snow, gardening, or fixing shelves, and this collective power made them feel responsible for the organization they were a part of. Broadening our understanding of political participation to include those practical activities could be useful in assessing and devising plans for participatory reforms in small-scale local democracies, but also possibly at a larger scale that would produce the benefits of participation without requiring individuals to overly engage in demanding and complex procedures. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Inspiration and Institution in John of Rupescissa's Liber Ostensor XI1Graziana S. CiolaIntroductionThe present study proposes a philosophical analysis of John of Rupescissa's Liber Ostensor [=LO], Treatise XI. John of Rupescissa (OFM, 1310 ca. – 1366)2 is a particularly interesting, eclectic and somewhat extraordinary [End Page 7] author writing around the second third of the 14th century in the wake of the Spiritual Franciscan movement in the South of France.3 (...) In LO XI, Rupescissa theorizes and systematically articulates a complex relationship between inspired knowledge and the normative portrait of what he believes the Franciscan Order should ideally be; he does so against the background of his eschatological concerns. Per Rupescissa's style of exposition and argumentation, these different elements — i.e., inspired epistemology, eschatology, and ecclesiology — are tightly intertwined on a theoretical and foundational level that goes beyond that of mere rhetorics.These themes are both recurrent and pivotal throughout Rupescissa's extremely prolific intellectual output, which counts numerous theological, ecclesiological, eschatological and alchemical treatises.4 LO, composed in [End Page 8] 1356 during Rupescissa's own "Avignon Captivity," is in many ways a sum of Rupescissa's prophetical and eschatological thought within the framing of the author's self-apologetic aims and of his ecclesiological views, in particular concerning the future of the Franciscan Order.5 [End Page 9]Treatise XI is undoubtedly the most theoretical book in LO; with its 489 paragraphs, it is also the longest. While this extremely dense text broaches on a great variety of topics, it is first and foremost about and for Spiritual Franciscans. Overall, LO XI is both a great portrayal of the Franciscan order as it is and as it should be, as well as a handbook addressed to the elect among the Spirituals, in order to help them face the eschaton and the tribulations to come. Per Rupescissa's eschatological views, such trials would affect the Franciscan Order the hardest and for the longest — hence the need for a detailed guide. At its core, then, LO XI is a deeply ecclesiological treatise and as such it is complementary to the larger systematization established in the Sexdequiloquium.6 It is in this framework that LO XI offers a complex theory of prophecy and illuminative knowledge as they should be embodied in the practices of a true Franciscan.7Given its highly abstract nature and cardinal function within one the most complex works of Rupescissa's maturity, LO XI, combining relevant insights on Rupescissa's ecclesiological, epistemological and prophetical positions, constitutes the ideal case study in order to assess Rupescissa's most refined and articulated account on inspired knowledge, particularly insofar as true and actual prophecy is concerned. This inspired knowledge, according to Rupescissa, is an indispensable tool for the elect to be able to victoriously face the imminent end of times. In the account presented in LO XI, such knowledge is possible exclusively through a form of institutional embedding: divine inspiration, culminating in true prophecy, is in service of the Franciscan Order's soteriological role within the Church as a whole, and can only be achieved by those who are faithful to the spirit of Francis's Rule.8 [End Page 10]Here, I analyze Rupescissa's theory of evangelical poverty and its role as a necessary condition for inspired knowledge, following the internal articulation of LO XI.Overall, in Rupescissa's view, Franciscan poverty and inspiration are two inseparable sides of the same coin. On the one hand, inspired knowledge is only achievable through a rigorous practice and thorough understanding of Franciscan poverty. On the other hand, the true institutional role of the Franciscan Order and its soteriological aims can be fulfilled exclusively by the true Spiritual Franciscans, whose moral, spiritual and epistemic perfection is divinely inspired. For Rupescissa, not only is poverty the source of all virtues both for the Franciscan Order and for the rest of the Church, but it also constitutes the ideal moral and social model, tout court. But most importantly, evangelical poverty has a genuinely epistemic role; this role is essential for Rupescissa's illuminative epistemology and for his account of prophetical exegesis — or exegetical prophecy. In turn, the... (shrink)

Human languages vary in terms of which meanings they lexicalize, but this variation is constrained. It has been argued that languages are under two competing pressures: the pressure to be simple (e.g., to have a small lexicon) and to allow for informative (i.e., precise) communication, and that which meanings get lexicalized may be explained by languages finding a good way to trade off between these two pressures. However, in certain semantic domains, languages can reach very high levels of informativeness even (...) if they lexicalize very few meanings in that domain. This is due to productive morphosyntax and compositional semantics, which may allow for construction of meanings which are not lexicalized. Consider the semantic domain of natural numbers: many languages lexicalize few natural number meanings as monomorphemic expressions, but can precisely convey very many natural number meanings using morphosyntactically complex numerals. In such semantic domains, lexicon size is not in direct competition with informativeness. What explains which meanings are lexicalized in such semantic domains? We will propose that in such cases, languages need to solve a different kind of trade‐off problem: the trade‐off between the pressure to lexicalize as few meanings as possible (i.e, to minimize lexicon size) and the pressure to produce as morphosyntactically simple utterances as possible (i.e, to minimize average morphosyntactic complexity of utterances). To support this claim, we will present a case study of 128 natural languages' numeral systems, and show computationally that they achieve a near‐optimal trade‐off between lexicon size and average morphosyntactic complexity of numerals. This study in conjunction with previous work on communicative efficiency suggests that languages' lexicons are shaped by a trade‐off between not two but three pressures: be simple, be informative, and minimize average morphosyntactic complexity of utterances. (shrink)

This article presents two approaches for computer simulations of virtue ethics in the context of agent-based modeling, a simple way and a complex way. The simple way represents virtues as numeric variables that are invoked in specific events or situations. This way can easily be implemented and included in social simulations. On the other hand, the complex way requires a PECS framework: physical, cognitive, emotional, and social components need to be implemented in agents. Virtue is the result of (...) the interaction of these internal components rather than a single variable. I argue that the complex way using the PECS framework is more suitable for simulating virtue ethics theory because it can capture the internal struggle and conflict sometimes involved in the practice of virtue. To show how the complex way could function, I present a sample computer simulation for the cardinal virtue of temperance, the virtue that moderates physical desires such as food, drink, and sex. This computer simulation is programmed in Python and builds upon the well-known Sugarscape simulation.1. (shrink)

Modern mathematical sciences are hard to imagine without appeal to efficient computational algorithms. We address several conceptual problems arising from this interaction by outlining rival but complementary perspectives on mathematical tractability. More specifically, we articulate three alternative characterizations of the complexity hierarchy of mathematical problems that are themselves based on different understandings of computational constraints. These distinctions resolve the tension between epistemic contexts in which exact solutions can be found and the ones in which they cannot; however, contrary to a (...) persistent myth, we conclude that having an exact solution is not generally more epistemologically beneficial than lacking one. (shrink)

The numerically definite syllogistic is the fragment of English obtained by extending the language of the classical syllogism with numerical quantifiers. The numerically definite relational syllogistic is the fragment of English obtained by extending the numerically definite syllogistic with predicates involving transitive verbs. This paper investigates the computational complexity of the satisfiability problem for these fragments. We show that the satisfiability problem (= finite satisfiability problem) for the numerically definite syllogistic is strongly NP-complete, and that the satisfiability problem (= finite (...) satisfiability problem) for the numerically definite relational syllogistic is NEXPTIME-complete, but perhaps not strongly so. We discuss the related problem of probabilistic (propositional) satisfiability, and thereby demonstrate the incompleteness of some proof-systems that have been proposed for the numerically definite syllogistic. (shrink)

This paper presents a formalization of first-order arithmetic characterizing the natural numbers as abstracta of the equinumerosity relation. The formalization turns on the interaction of a nonstandard cardinality quantifier with an abstraction operator assigning objects to predicates. The project draws its philosophical motivation from a nonreductionist conception of logicism, a deflationary view of abstraction, and an approach to formal arithmetic that emphasizes the cardinal properties of the natural numbers over the structural ones.

One of the numerous characterizations of a Ramsey cardinal κ involves the existence of certain types of elementary embeddings for transitive sets of size κ satisfying a large fragment of ZFC. We introduce new large cardinal axioms generalizing the Ramsey elementary embeddings characterization and show that they form a natural hierarchy between weakly compact cardinals and measurable cardinals. These new axioms serve to further our knowledge about the elementary embedding properties of smaller large cardinals, in particular those still (...) consistent with V = L. (shrink)

Complex adaptive systems and nursingThere have been numerous references to complexity theory and complex systems in the recent healthcare literature, including nursing. However, exaggerated claims have (in my view) been made about how they can be applied to health service delivery, and there is a widespread tendency to misunderstand some of the concepts associated with complexity thinking (usually justified by describing the misconception as a metaphor). These conceptscanbe extended to systems and structures in healthcare organisations but, at this (...) stage in the development of complexity science, only in a modest and very cautious way. In this paper I first outline some of the key ideas in the theory of complex adaptive systems, and then suggest that they have been distorted by a series of influential articles in the medical literature. I go on to present a simple case study of my own and undertake a complexity analysis of it. In the conclusion I suggest that we should beware of some outdated ideas being trotted out in the guise of complexity — an exciting and diverse area of enquiry that those old ideas do not, in fact, resemble. (shrink)

The cardinal role that notions of respect and self-respect play in Rawls’s A Theory of Justice has already been abundantly examined in the literature. In contrast, it has hardly been noticed that these notions are also central to Michael Walzer’s Spheres of Justice. Respect and self-respect are not only central topics of his chapter “Recognition”, but constitute a central aim of a “complex egalitarian society” and of Walzer’s theory of justice. This paper substantiates this thesis and elucidates Walzer’s (...) criticism of Rawls that we need to distinguish between “self-respect” and “self-esteem”. (shrink)

We present results from numerical studies of supervised learning operations in recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for particular inputs with respect to predetermined outputs are asymptotically stable and can be characterized by attractors which form a representation space for an associative multiplicative structure of input operations. As the mapping from a series of inputs onto a series of such attractors generally depends on the (...) sequence of inputs, this structure is generally noncommutative. Moreover, the size of the set of attractors, indicating the complexity of learning, is found to behave non-monotonically as learning proceeds. A tentative relation between this complexity and the notion of pragmatic information is indicated. (shrink)

How do we acquire the notions of cardinality and cardinal number? In the (neo-)Fregean approach, they are derived from the notion of equinumerosity. According to some alternative approaches, defended and developed by Husserl and Parsons among others, the order of explanation is reversed: equinumerosity is explained in terms of cardinality, which, in turn, is explained in terms of our ordinary practices of counting. In their paper, ‘Cardinality, Counting, and Equinumerosity’, Richard Kimberly Heck proposes that instead of equinumerosity or counting, (...) cardinality is derived from a cognitively earlier notion of _just as many_. In this paper, we assess Heck’s proposal in terms of contemporary theories of number concept acquisition. Focusing on bootstrapping theories, we argue that there is no evidence that the notion of _just as many_ is cognitively primary. Furthermore, since the acquisition of cardinality is an enculturated process, the cognitive primariness of these notions, possibly including _just as many_, depends on various external cultural factors. Therefore, being possibly a cultural construction, _just as many_ could be one among several notions used in the acquisition of cardinality and cardinal number concepts. This paper thus challenges those accounts which seek for a fundamental concept underlying all aspects of numerical cognition. (shrink)

We define a generic Vopěnka cardinal to be an inaccessible cardinal \ such that for every first-order language \ of cardinality less than \ and every set \ of \-structures, if \ and every structure in \ has cardinality less than \, then an elementary embedding between two structures in \ exists in some generic extension of V. We investigate connections between generic Vopěnka cardinals in models of ZFC and the number and complexity of \-Suslin sets of reals (...) in models of ZF. In particular, we show that ZFC + is equiconsistent with ZF + \\) where \ is the pointclass of all \-Suslin sets of reals, and also with ZF + \\) + \\) where \ is the least ordinal that is not a surjective image of the reals. (shrink)

A set $B\subseteq\mathbb{N}$ is called low for Martin-Löf random if every Martin-Löf random set is also Martin-Löf random relative to B . We show that a $\Delta^0_2$ set B is low for Martin-Löf random if and only if the class of oracles which compress less efficiently than B , namely, the class $\mathcal{C}^B=\{A\ |\ \forall n\ K^B(n)\leq^+ K^A(n)\}$ is countable (where K denotes the prefix-free complexity and $\leq^+$ denotes inequality modulo a constant. It follows that $\Delta^0_2$ is the largest arithmetical (...) class with this property and if $\mathcal{C}^B$ is uncountable, it contains a perfect $\Pi^0_1$ set of reals. The proof introduces a new method for constructing nontrivial reals below a $\Delta^0_2$ set which is not low for Martin-Löf random. (shrink)

Numerical identity is the non-relational sameness of an object to itself. It is concerned with understanding how entities undergo change and maintain their identity. In substance metaphysics, an entity is considered a substance with an essence and such an essence is the source of its power. However, such a framework fails to explain the sense in which an entity is still the entity it was, amidst changes. Those who claim that essence is unaffected by existence are faced with challenge of (...) exploring the epistemic access to such an essence, which is questionable at best. Process metaphysics is a strong candidate for a theory that can ontologically explain regularity and change without appeal to essence. Process and its interactions is the main category. Every process is an emergent organization of constitutive interactions and is individuated on the basis of its interactive powers, that is, the ways in which it interacts with the world around it. Interactions are situated adaptation to changes. In this way, changes are crucial within process metaphysics and are included in the starting point of its investigation. What seems to the naked eyes as one-ness/singularity is a complex process where an organization of interactions is emerging from moment to moment by continually adapting to the changes around and within it. The question of numerical identity over time becomes valid only within substance metaphysics which has no space to accommodate change, due to its allegiance to essence. (shrink)

Blasting in water-conveyance tunnels that cross rivers is vital for the safety and stability of embankments. In this work, a tunnel project that crosses the Yellow River in the north district of the first-phase Eastern Line of the South-to-North Water Diversion Project was selected as the research object. A complex modeling and numerical simulation on embankment stability with regard to the blasting power of the tunnel was conducted using the professional finite difference software FLAC3D to disclose the relationships between (...) the blasting seismic waves with vibration velocity and embankment displacement under different excavation steps. Calculation results demonstrated that displacement generally attenuated from the tunnel wall to the internal structure of rocks under the effect of blasting seismic waves. The tunnel wall was in tension, and tensile stress gradually transformed into compressive stress with increased depth into the rocks. The curtain-grouting zone was mainly concentrated in the compressive zones. For different excavation steps, the vibration velocity at different feature points was high at the beginning of blasting and then gradually decreased. The resultant displacement was relatively small in the early excavation period and slowly increased as blasting progressed. The effects of different excavation steps on the safety of surrounding rocks and embankment under blasting seismic waves were simulated. We found that the blasting-induced vibration velocity was within the safe range of the code and that the calculated displacement was within the allowed range. Numerical simulation was feasible to assess the safety and stability of engineering projects. (shrink)

We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exists seem to be very rare. It is the main purpose of this paper to prove that, nevertheless, the (...) definition has a large number of important applications. Using the framework of TTE [40], we introduce computable metric spaces and computability on the compact subsets. We prove that every computable metric space has a c-proper c-admissible representation. We prove that Turing machine time complexity of a function computable relative to c-admissible c-proper representations has a computable bound on every computable compact subset. We prove that computably compact computable metric spaces have concise c-proper c-admissible representations and show by examples that many canonical representations are of this kind. Finally, we compare our definition with a similar one by Labhalla et al. [22]. Several examples illustrate the concepts. By these results natural and realistic definitions of computational complexity are now available for a variety of numerical problems such as image processing, integration, continuous Fourier transform or wave propagation. (shrink)

In this article, I will discuss possible differences between ecosystems and organisms on the basis of their intrinsic complexity. As the concept of complexity still remains highly debated, I propose here a practical and original way to measure the complexity of an ecosystem or an organism. For this purpose, I suggest using the concept of logical depth (LD) in a specific manner, in order to take into account the difficulty as well as the time needed to generate the studied object. (...) I illustrate this method with fully controlled Daisyworld simulations (i.e., simulations based on the Gaia hypothesis) that have often been proposed to mimic living systems. The method consists of the following sequential stages: (1) identification of the shortest program able to numerically model the studied system (also called the Kolmogorov–Solomonoff complexity); (2) running the program, once if there are no stochastic components in the system, several times if stochastic components are there; and (3) computing the time needed to generate the system with LD complexity. This measure is supposed to estimate the system complexity. It appears in this study that LD estimations fit well with the intuition we have of complex systems, with higher complexities being found for more realistic Daisyworlds. With such a method of capturing the time needed to build a system, we expect to detect in future studies any quantified differences between complex ecosystems and organisms. (shrink)

In this paper, we investigate the numerical solution of the coupled fractional massive Thirring equation with the aid of He’s fractional complex transform. This study plays a significant aspect in the field of quantum physics, weakly nonlinear thrilling waves, and nonlinear optics. The main advantage of FCT is that it converts the fractional differential equation into its traditional parts and is also capable to handle the fractional order, whereas the homotopy perturbation method is employed to tackle the nonlinear terms (...) in the coupled fractional massive Thirring equation. An example is illustrated to present the efficiency and validity of the two-scale theory. The solutions are obtained in the form of series with simple and easy computations which confirm that the present approach is good in agreement and is easy to implement for such type of complex systems in science and engineering. (shrink)

Memory for numbers improves with age. One source of this improvement may be learning linear spatial-numeric associations, but previous evidence for this hypothesis likely confounded memory span with quality of numerical magnitude representations and failed to distinguish spatial-numeric mappings from other numeric abilities, such as counting or number word-cardinality mapping. To obviate the influence of memory span on numerical memory, we examined 39 3- to 5-year-olds’ ability to recall one spontaneously produced number (1-20) after a delay, and the relation between (...) numeric recall (controlling for non-numeric recall) and quality of mapping between symbolic and non-symbolic quantities using number-line estimation, give-a-number estimation, and counting tasks. Consistent with previous reports, mapping of numerals to space, to discrete quantities, and to numbers in memory displayed a logarithmic-to-linear shift. Also, linearity of spatial-numeric mapping correlated strongly with multiple measures of numeric recall (percent correct and percent absolute error), even when controlling for age and non-numeric memory. Results suggest that linear spatial-numeric mappings may aid memory for number over and above children’s other numeric skills. (shrink)

The proposal of Rips et al. is motivated by discontinuity and input claims. The discontinuity claim is that no continuity exists between early (nonverbal) numerical representations and natural number. The input claim is that particular experiences (e.g., cardinality-related talk and object-based activities) do not aid in natural number construction. We discuss reasons to doubt both claims in their strongest forms.

SWORD W, CLARK AM, HEGADOREN K, BROOKS S and KINGSTON D. Nursing Inquiry 2012; 19: 51–62 The complexity of postpartum mental health and illness: a critical realist studyPostpartum depression (PPD) is a major public health issue that profoundly impacts the woman, her infant and family. Although it may be linked to hormone changes, no direct hormonal aetiology has been established. A large body of evidence implicates numerous psychosocial predictors of PPD. While a history of depression predicts about 50% of cases (...) of PPD, it remains unclear why some women with a history do not develop depression following childbirth, even taking psychosocial factors into account. The aim of this study was to identify the main mechanisms and factors associated with the presence or absence of PPD in women with a history of depression, and the presence of PPD in women without a history, using a critical realist approach. The findings indicate a number of personal and contextual factors that influence postpartum mental health and illness. In addition, and perhaps most importantly, women who did not develop depression identified goal‐oriented actions that were protective. These factors and processes did not exist in isolation and the interplay among them in influencing health was apparent. More research is needed to explore the effects of these mechanisms in different contexts. (shrink)

This paper investigates a certain puzzling argument concerning number expressions and their meanings, the Easy Argument for Numbers. After finding faults with previous views, I offer a new take on what’s ultimately wrong with the Argument: it equivocates. I develop a semantics for number expressions which relates various of their uses, including those relevant to the Easy Argument, via type-shifting. By marrying Romero ’s :687–737, 2005) analysis of specificational clauses with Scontras ’ semantics for Degree Nouns, I show how to (...) extend Landman ’s Adjectival Theory to numerical specificational clauses. The resulting semantics can explain various contrasts observed by Moltmann, but only if Scontras’ contention that degrees and numbers are sortally distinct is correct. At the same time, the Easy Argument can establish its intended conclusion only if numbers and degrees are mistakenly assumed to be identical. (shrink)

In 1939, the influential psychophysicist S. S. Stevens proposed definitional distinctions between the terms ‘number,’ ‘numerosity,’ and ‘numerousness.’ Although the definitions he proposed were adopted by syeveral psychophysicists and experimental psychologists in the 1940s and 1950s, they were almost forgotten in the subsequent decades, making room for what has been described as a “terminological chaos” in the field of numerical cognition. In this paper, I review Stevens’s distinctions to help bring order to this alleged chaos and to shed light on (...) two closely related questions: whether it is adequate to speak of a number sense and how philosophers can make sense of the claim by cognitive scientists that numbers are perceptual entities. Moreover, I offer further support to Stevens’s distinction between numerosity and numerousness by showing that they are relational properties that emerge through different relationships between agents and their environments. The final conclusion is that, by adopting Stevens’s distinctions, numbers do not need to be seen as perceptual entities, since the so-called number sense is better described as a sense of numerousness. (shrink)

According to Rips et al., numerical cognition develops out of two independent sets of cognitive primitives – one that supports enumeration, and one that supports arithmetic and the concepts of natural numbers. I argue against this proposal because it incorrectly predicts that natural number concepts could develop without prior knowledge of enumeration.

We introduce the notion of complexity, first at an intuitive level and then in relatively more concrete terms, explaining the various characteristic features of complex systems with examples. There exists a vast literature on complexity, and our exposition is intended to be an elementary introduction, meant for a broad audience. -/- Briefly, a complex system is one whose description involves a hierarchy of levels, where each level is made of a large number of components interacting among themselves. The (...) time evolution of such a system is of a complex nature, depending on the interactions among subsystems in the next level below the one under consideration and, at the same time, conditioned by the level above, where the latter sets the context for the evolution. Generally speaking, the interactions among the constituents of the various levels lead to a dynamics characterized by numerous characteristic scales, each level having its own set of scales. What is more, a level commonly exhibits ‘emergent properties’ that cannot be derived from considerations relating to its component systems taken in isolation or to those in a different contextual setting. In the dynamic evolution of some particular level, there occurs a self-organized emergence of a higher level and the process is repeated at still higher levels. -/- The interaction and self-organization of the components of a complex system follow the principle commonly expressed by saying that the ‘whole is different from the sum of the parts’. In the case of systems whose behavior can be expressed mathematically in terms of differential equations this means that the interactions are nonlinear in nature. -/- While all of the above features are not universally exhibited by complex systems, these are nevertheless indicative of a broad commonness relative to which individual systems can be described and analyzed. There exist measures of complexity which, once again, are not of universal applicability, being more heuristic than exact. The present state of knowledge and understanding of complex systems is itself an emerging one. Still, a large number of results on various systems can be related to their complex character, making complexity an immensely fertile concept in the study of natural, biological, and social phenomena. -/- All this puts a very definite limitation on the complete description of a complex system as a whole since such a system can be precisely described only contextually, relative to some particular level, where emergent properties rule out an exact description of more than one levels within a common framework. -/- We discuss the implications of these observations in the context of our conception of the so-called noumenal reality that has a mind-independent existence and is perceived by us in the form of the phenomenal reality. The latter is derived from the former by means of our perceptions and interpretations, and our efforts at sorting out and making sense of the bewildering complexity of reality takes the form of incessant processes of inference that lead to theories. Strictly speaking, theories apply to models that are constructed as idealized versions of parts of reality, within which inferences and abstractions can be carried out meaningfully, enabling us to construct the theories. -/- There exists a correspondence between the phenomenal and the noumenal realities in terms of events and their correlations, where these are experienced as the complex behavior of systems or entities of various descriptions. The infinite diversity of behavior of systems in the phenomenal world are explained within specified contexts by theories. The latter are constructs generated in our ceaseless attempts at interpreting the world, and the question arises as to whether these are reflections of `laws of nature' residing in the noumenal world. This is a fundamental concern of scientific realism, within the fold of which there exists a trend towards the assumption that theories express truths about the noumenal reality. We examine this assumption (referred to as a ‘point of view’ in the present essay) closely and indicate that an alternative point of view is also consistent within the broad framework of scientific realism. This is the view that theories are domain-specific and contextual, and that these are arrived at by independent processes of inference and abstractions in the various domains of experience. Theories in contiguous domains of experience dovetail and interpenetrate with one another, and bear the responsibility of correctly explaining our observations within these domains. -/- With accumulating experience, theories get revised and the network of our theories of the world acquires a complex structure, exhibiting a complex evolution. There exists a tendency within the fold of scientific realism of interpreting this complex evolution in rather simple terms, where one assumes (this, again, is a point of view) that theories tend more and more closely to truths about Nature and, what is more, progress towards an all-embracing ‘ultimate theory’ -- a foundational one in respect of all our inquiries into nature. We examine this point of view closely and outline the alternative view -- one broadly consistent with scientific realism -- that there is no ‘ultimate’ law of nature, that theories do not correspond to truths inherent in reality, and that successive revisions in theory do not lead monotonically to some ultimate truth. Instead, the theories generated in succession are incommensurate with each other, testifying to the fact that a theory gives us a perspective view of some part of reality, arrived at contextually. Instead of resembling a monotonically converging series successive theories are analogous to asymptotic series. -/- Before we summarize all the above considerations, we briefly address the issue of the complexity of the {\it human mind} -- one as pervasive as the complexity of Nature at large. The complexity of the mind is related to the complexity of the underlying neuronal organization in the brain, which operates within a larger biological context, its activities being modulated by other physiological systems, notably the one involving a host of chemical messengers. The mind, with no materiality of its own, is nevertheless emergent from the activity of interacting neuronal assemblies in the brain. As in the case of reality at large, there can be no ultimate theory of the mind, from which one can explain and predict the entire spectrum of human behavior, which is an infinitely rich and diverse one. (shrink)

This paper argues that, given a simple [DP VP] sentence, the availability of a collective interpretation crucially depends on the syntactic and semantic properties of the subject DP, specifically the presence versus absence of a pluralizing function that makes the collective interpretation available. In support of my claim, I present Lebanese Arabic and Western Armenian examples in which an indefinite DP contains a cardinal numeral and there is no overt distributivity operator but the interpretation of the sentence is nevertheless (...) obligatorily distributive, regardless of the predicate. I show that neither a distributivity operator within the DP nor one on the predicate can explain this strictly distributive interpretation. Instead, I argue that in order to allow a collective interpretation, an indefinite DP must denote a quantifier over pluralities, a condition that is not always met in numeral-containing indefinite DPs. While the claims in this paper are based primarily on observations from Lebanese Arabic and Western Armenian, because both are morphologically rich languages, the fact that this constraint is operative in these two unrelated languages, in addition to striking similarities to the Russian gender system, suggest that it is an inherent property of DPs crosslinguistically. (shrink)

There are three main types of number used in modern, industrialized societies. Cardinals count sets (e.g., people, objects) and quantify elements of conventional scales (e.g., money, distance), ordinals index positions in ordered sequences (e.g., years, pages), and nominals serve as unique identifiers (e.g., telephone numbers, player numbers). Many studies that have cited number frequencies in support of claims about numerical cognition and mathematical cognition hinge on the assumption that most numbers analyzed are cardinal. This paper is the first to (...) investigate the relative frequencies of different number types, presenting a corpus analysis of morphologically unmarked numbers (not, e.g., “eighth” or “21st”) in which we manually annotated 3,600 concordances in the Corpus of Contemporary American English. Overall, cardinals are dominant—both pure cardinals (sets) and measurements (scales)—except in the range 1,000–10,000, which is dominated by ordinal years, like 1996 and 2004. Ordinals occur less often overall, and nominals even less so. Only for cardinals do round numbers, associated with approximation, dominate overall and increase with magnitude. In comparison with other registers, academic writing contains a lower proportion of measurements as well as a higher proportion of ordinals and, to some extent, nominals. In writing, pure cardinals and measurements are usually represented as number words, but measurements—especially larger, unround ones—are more likely to be numerals. Ordinals and nominals are mostly represented as numerals. Altogether, this paper reveals how numbers are used in American English, establishing an initial baseline for any analyses of number frequencies and shedding new light on the cognitive and psychological study of number. (shrink)

A generalization of a Burridge-Knopoff spring-block model is investigated to illustrate the dynamics of transform faults. The model can undergo Hopf bifurcation and fold bifurcation of limit cycles. Considering the cyclical nature of the spring stiffness, the model with periodic perturbation is further explored via a continuation technique and numerical bifurcation analysis. It is shown that the periodic perturbation induces abundant dynamics, the existence, the switch, and the coexistence of multiple attractors including periodic solutions with various periods, quasiperiodic solutions, chaotic (...) solutions through torus destruction, or cascade of period doublings. Throughout the results obtained, one can see that the system manifests complex dynamical behaviors such as chaos, self-organized criticality, and the transition of dynamical behaviors when it comes to periodic perturbations. Even very small variation of a parameter can result in radical changes of the dynamics, which provides a new insight into the fault dynamics. (shrink)

Socio-economic status and mathematical performance seem to be risk factors of mathematics anxiety in both children and adults. However, there is little evidence about how exactly these three constructs are related, especially during early stages of mathematical learning. In the present study, we assessed longitudinal performance in symbolic and non-symbolic basic numerical skills in pre-school and second grade students, as well as MA in second grade students. Participants were 451 children from 12 schools in Chile, which differed in school vulnerability (...) index, an indicator of SES. We tested an explanatory model of MA that included SES and longitudinal performance in basic numerical skills as predictors. The results showed a direct effect of SES on MA and a mediating effect of performance in symbolic and non-symbolic comparison tasks in pre-school. However, in second grade, only performance in symbolic comparison significantly mediated the SES-MA relationship. These findings suggest that performance in non-symbolic comparison plays an important role in explaining MA at initial stages, but that its influence is no longer significant by the time children reach formal instruction in second grade. By contrast, as children’s formal educational experience in mathematics increases, MA becomes linked primarily to symbolic numerical tasks. In sum, SES affects MA and this is due in part to the effect of SES on the development of numerical learning in pre-school, which in turn has an impact on subsequent, more complex learning, ultimately leading to differences in MA. We discuss the implications of these findings for preventing and acting upon the emergence of MA. (shrink)

Solid-state processing of metal material is a very complex physical and chemical process, which is coupled by a series of variations including heat transfer, momentum transfer, mass transfer, and phase change. Applying three-dimensional finite element numerical method to the simulation of solid-state processing can perform analysis of metal material’s forging processes before production trial production, can obtain their relevant information such as material flow law, temperature field, and strain field under the minimum physical test conditions, thereby predicting metal material’s (...) forming defects and improving their forging quality. On the basis of summarizing and analyzing previous research works, this paper expounded the current status and significance of solid-state processing of metal materials, elaborated the development background, current status, and future challenges of 3D finite element numerical simulation, introduced the discrimination method and free surface solution method of numerical simulation calculation, conducted finite element model’s geometric assumptions, material selection, element division, model establishment, parameter selection, and initial and boundary condition determination, and simulated and analyzed rheological casting, remelting heating, thixoforming, and rotary piercing processes of metal materials. The results show that the 3D finite element numerical method can not only simulate various processes of flow field, temperature field, stress field, and microstructure in solid-state processing but also can provide a reliable basis for effectively obtaining a reasonable description and finding a more optimized design plan for metal material processing in a short time, which plays an important role in understanding and analyzing solid metal forming process, controlling and optimizing process parameters, guiding and mastering rheological casting, and secondary heating and rotary piercing of metal materials. (shrink)

A mass problem is a set of functions$\omega \to \omega $. For mass problems${\mathcal {C}}, {\mathcal {D}}$, one says that${\mathcal {C}}$is Muchnik reducible to${\mathcal {D}}$if each function in${\mathcal {C}}$is computed by a function in${\mathcal {D}}$. In this paper we study some highness properties of Turing oracles, which we view as mass problems. We compare them with respect to Muchnik reducibility and its uniform strengthening, Medvedev reducibility.For$p \in [0,1]$let${\mathcal {D}}(p)$be the mass problem of infinite bit sequencesy(i.e.,$\{0,1\}$-valued functions) such that for each (...) computable bit sequencex, the bit sequence$ x {\,\leftrightarrow\,} y$has asymptotic lower density at mostp(where$x {\,\leftrightarrow\,} y$has a$1$in positionniff$x(n) = y(n)$). We show that all members of this family of mass problems parameterized by a realpwith$0 p$for each computable setx. We prove that the Medvedev (and hence Muchnik) complexity of the mass problems${\mathcal {B}}(p)$is the same for all$p \in (0, 1/2)$, by showing that they are Medvedev equivalent to the mass problem of functions bounded by${2^{2}}^{n}$that are almost everywhere different from each computable function.Next, together with Joseph Miller, we obtain a proper hierarchy of the mass problems of type$\text {IOE}$: we show that for any order functiongthere exists a faster growing order function$h $such that$\text {IOE}(h)$is strictly above$\text {IOE}(g)$in the sense of Muchnik reducibility.We study cardinal characteristics in the sense of set theory that are analogous to the highness properties above. For instance,${\mathfrak {d}} (p)$is the least size of a setGof bit sequences such that for each bit sequencexthere is a bit sequenceyinGso that$\underline \rho (x {\,\leftrightarrow\,} y)>p$. We prove within ZFC all the coincidences of cardinal characteristics that are the analogs of the results above. (shrink)

In the period 4800-3600 BC. in the eastern part of the Trypillia area arose "giant settlements" or "megasites" / "mega-settlements" with thousands of buildings. In the central parts of these living conglomerates, scientists found special buildings that were recognized as sanctuaries, sacred complexes or temples. In the late period of the Trypillia culture they disappeared. These religious buildings were built with a focus visible processes of celestial bodies and the laws of cyclic rotation of the Earth in space, and included (...) in their internal filling usually cruciform altars, ritual utensils, troughs with graters for the preparation of ritual bread and numerous other ceremonial and religious artifacts. There were also unique finds, such as gold jewelry and a perforated clay disk with tockins to it from the space of the Nebelivka Temple. The interior and exterior walls of the Trypillia sacral centers were painted with natural colors with a predominance of red. The wood carving for decoration of elements of a skeleton of a construction was investigated also. The first Temples on the European continent show that even at that time there was a cult of architecture. In general, it is clear that such Trypillia objects of religious worship carried encoded astronomical information in symbolic form. The building itself was oriented with regard to worldsides and designed relative to visible celestial bodies. This indicates that the people of Trypillia had a fairly clear worldview, which allowed them to reach the level of understanding the structure and mechanisms of many natural cyclical processes on Earth. Trypillia cosmology united the celestial and terrestrial spheres, and the Temple was the point of contact of the earth with the visible Universe. In his work, the author traces the existing analogies in the structure of construction of Trypillia and sacred complexes of the ancient Middle East and biblical ideas about the Tabernacle and the House of the Lord in the ancient Jews, given the fact, that the Trypillia temple building is known from 4,000 years BC. and several thousand years older than the Middle Eastern counterparts. There are also significant parallels in the construction of temples in the context of Indo-European religious heritage. It is noted that the Temple was not only a metaphysical reflection of the annual cycle with a focus on the points of the equinoxes and solstices, but also had a higher religious function, which consisted in the combination of the terrestrial sphere with the celestial, the connection of man with the mystery of the cosmos. (shrink)

In this very readable and interesting book Mr. Weatherby explores the thesis that Newman, while remaining true to Catholic doctrinal orthodoxy, nevertheless, compromised philosophically with the subjectivism, relativism, and individualism inherent in modern thought. Mr. Weatherby further claims that Newman treated these premises of modern thought as though "they were capable of synthesis with Catholic dogma." In coming to this position, Newman rejected the fifteen hundred-year old idea of a unified Christian society and accepted instead the fragmentation on which modern (...) culture is based. To develop his main point, Weatherby divides his book into four parts. Part One, "Newman and the Old Orthodoxy," reveals Newman’s divergence philosophically from the Caroline theological tradition and the Metaphysical poets. Newman did not deny that the Creation reflects the mind of God, but he personally could not find it. He was forced, therefore, to look for the "Paradise within" since he was unable to find God’s Paradise without. In Part Two, "The Spirit Afloat," after examining Newman’s Idealism and his relation to the Alexandrian Fathers, who were essentially mystic and idealist, Weatherby shows that Newman was a man of his times in that he had a much greater affinity with the Romantic poets than with the Metaphysical poets or those of the Middle Ages and Renaissance. These latter expressed metaphorically their full accord with the Thomist and Caroline outlook that God’s operations were visible in every detail of nature and that man by reason can proceed from the order and beauty of the visible world to a knowledge of God. The Romantics, on the other hand, with their more subjective view of life and nature, stressed not so much the external reality as man’s individual apprehension of it. The Romantics’ dominant impulse was their search for the "Paradise within." In Part Three, "Newman’s Modernism: A Theology of Safeguards," a study of Newman’s orthodox subjectivism, individualism, and relativism is presented, and Weatherby uses William R. Ingel’s words on Newman to point out that "one side of religion was based on principles which, when logically drawn out, must lead away from Catholicism in the direction of an individualistic religion of experience, and a substitution of history for dogma which makes all truth relative and all values fluid." Weatherby in Part Four, "The Consequences," articulates his criticism of Newman’s stand. It is, he claims, too radical one. Although Weatherby takes care not to call Newman a revolutionary—only a radical in his thinking—he points out that had Newman followed his anti-traditional mode of thought to its logical conclusion, political and social revolution could have resulted. Weatherby claims that Newman attempts to escape from the revolutionary consequences of his philosophy in that his "radicalism is never translated into religious or political activism." One of the strengths of Mr. Weatherby’s book is the great thoroughness with which he supports his stand. He gives specific and numerous examples and quotations from Newman’s works and from those of the other writers and philosophers he is using to make his point. This method, while admirable on the whole, occasionally results in repetition since Weatherby makes certain to give a summary after each comparison that is made.—M. L. F. (shrink)

There are long-standing doubts about whether data from subjective scales—for instance, self-reports of happiness—are cardinally comparable. It is unclear how to assess whether these doubts are justified without first addressing two unresolved theoretical questions: how do people interpret subjective scales? Which assumptions are required for cardinal comparability? This paper offers answers to both. It proposes an explanation for scale interpretation derived from philosophy of language and game theory. In short: conversation is a cooperative endeavour governed by various maxims (Grice (...) 1989); because subjective scales are vague and individuals want to make themselves understood, scale interpretation is a search for a focal point (Schelling 1960). A specific focal point it hypothesised; if this hypothesis is correct, subjective data will be cardinally comparable. Four individually necessary and jointly sufficient conditions for cardinal comparability are specified. The paper then argues this hypothesis can be empirically be tested, makes an initial attempt to do so using subjective well-being data, and concludes it is supported. Numerous areas for further research are identified including, at the end of the paper, how certain tests could be used to ‘correct’ subjective data if they are not cardinal. (shrink)

This paper conducts a numerical simulation of the antiseismic performance for single-layer masonry structures, completes a study on crack distributions and detailed characteristics of masonry structures, and finally verifies the correctness of the numerical model by experimental tests. This paper also provides a reinforced proposal to improve the antiseismic performance of single-layer masonry structures. Results prove that the original model suffers more serious damage than the reinforced model; in particular, longitudinal cracks appear on bottoms of two longitudinal walls in the (...) original model, while these cracks appear later in the reinforced model; a lot of cracks appear on the door hole of the original model, and no crack appears in the reinforced model till the end of seismic waves; seismic damage of walls in the reinforced model is obviously lighter than that in the original model; dynamic responses at all observed points of the reinforced masonry are obviously less than those of the original model. Strains at all positions of the reinforced model are obviously smaller than those of the original model. From macroscopic and microscopic perspectives, the computational results prove that the reinforced proposal proposed in this paper can effectively improve the antiseismic performance of the masonry structure. (shrink)

Nonhuman primates represent the most significant extant species for comparative studies of cognition, including such complex phenomena as numerical competence, among others. Studies of numerical skills in monkeys and apes have a long, though somewhat sparse history, although questions for current empirical studies remain of great interest to several fields, including comparative, developmental, and cognitive psychology; anthropology; ethology; and philosophy, to name a few. In addition to demonstrated similarities in complex information processing, empirical studies of a variety of (...) potential cognitive limitations or constraints have provided insights into similarities and differences across the primate order, and continue to offer theoretical and pragmatic directions for future research. An historical overview of primate numerical studies is presented, as well as a summary of the 17‐year research history, including recent findings, of the Comparative Cognition Project at The Ohio State University Chimpanzee Center. Overall, the archival literature on number‐related skills and counting in nonhuman primates offers important implications for revising our thinking about comparative neuroanatomy, cross‐species (human/ape) cognitive similarities and differences, and the evolution of cognition represented by the primate continuum. (shrink)

This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm’s preference is represented by a utility function that is derived from a constant elasticity of substitution production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their complex characteristics (...) due to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations. (shrink)

Robot-assisted retinal cannulation is an eye surgical procedure which can dissolve the obstruction by using robot to inject anticoagulant into occluded vessel. The current research on the critical parameters of cannulation for human is scarce because of the immature technology. Considering the influence of microneedle, this work investigated the effects of drug concentration, injection velocity, injection position, and size of clot on cannulation by theoretical analysis and finite element analysis. For finite element analysis, the multiphysics continuum model was established to (...) demonstrate species transport and reaction which simulates the entire lytic process of the occlusive clot, and four cell zones were established to describe the generation of plasmin with the addition of tissue-type plasminogen activator and fibrinolysis of clot by importing subroutines into each cell zone under the conditions of constant clot size and variable size, respectively. The results imply that the most efficient value of tPA concentration is 50 nM, injection velocity is 60 mm/s for clot length of 0.1 mm, and the best position to insert the cannula is 0.5 mm in front of the thrombus. For different clot lengths of 0.1 mm to 0.6 mm, the optimal range of tPA concentration and injection velocity is from 20 nM to 70 nM and from 40 mm/s to 60 mm/s, respectively, and explores the reasonable injection position of 0.3 mm to 0.5 mm in front of clot in a vein of 100 μm. This conclusion can be used to perform robot-assisted cannulation surgery to improve fibrinolytic efficiency. (shrink)