In this paper we study generic complexity of undecidable problems. It turns out that some classical undecidable problems are, in fact, strongly undecidable, i.e., they are undecidable on every strongly generic subset of inputs. For instance, the classical Halting Problem is strongly undecidable. Moreover, we prove and analog of the Rice theorem for strongly undecidable problems, which provides plenty of examples of strongly undecidable problems. Then we show that there are natural super-undecidable problems. i.e., (...) problem which are undecidable on every generic (not only strongly generic) subset of inputs. In particular, there are finitely presented semigroups with super-undecidable word problem. To construct strongly- and super-undecidable problems we introducea method of generic amplification (an analog of the amplification in complexity theory). Finally, we construct absolutely undecidable problems, which stay undecidable on every non-negligible set of inputs. Their construction rests on generic immune sets. (shrink)

A pseudo-natural algorithm for the word problem of a finitely presented group is an algorithm which not only tells us whether or not a word w equals 1 in the group but also gives a derivation of 1 from w when w equals 1. In [13], [14] Madlener and Otto show that, if we measure complexity of a primitive recursive algorithm by its level in the Grzegorczyk hierarchy, there are groups in which a pseudo-natural algorithm is arbitrarily (...) more complicated than an algorithm which simply solves the word problem. In a given group the lowest degree of complexity that can be realised by a pseudo-natural algorithm is essentially the derivational complexity of that group. Thus the result separates the derivational complexity of the word problem of a finitely presented group from its intrinsic complexity. The proof given in [13] involves the construction of a finitely presented group G from a Turing machine T such that the intrinsic complexity of the word problem for G reflects the complexity of the halting problem of T, while the derivational complexity of the word problem for G reflects the runtime complexity of T. The proof of one of the crucial lemmas in [13] is only sketched, and part of the purpose of this paper is to give the full details of this proof. We will also obtain a variant of their proof, using modular machines rather than Turing machines. As for several other results, this simplifies the proofs considerably. MSC: 03D40, 20F10. (shrink)

The linguistic complexity of words has largely been studied on the behavioral level and in experimental settings. Only little is known about the neural processes underlying it in uninstructed, spontaneous conversations. We built up a multimodal neurolinguistic corpus composed of synchronized audio, video, and electrocorticographic (ECoG) recordings from the fronto-temporo-parietal cortex to address this phenomenon based on uninstructed, spontaneous speech production. We performed extensive linguistic annotations of the language material and calculated word complexity using several numeric parameters. (...) We orthogonalized the parameters with the help of a linear regression model. Then, we correlated the spectral components of neural activity with the individual linguistic parameters and with the residuals of the linear regression model, and compared the results. The proportional relation between the number of consonants and vowels, which was the most informative parameter with regard to the neural representation of word complexity, showed effects in two areas: the frontal one was at the junction of the premotor cortex, the prefrontal cortex, and Brodmann area 44. The postcentral one lay directly above the lateral sulcus and comprised the ventral central sulcus, the parietal operculum and the adjacent inferior parietal cortex. Beyond the physiological findings summarized here, our methods may be useful for those interested in ways of studying neural effects related to natural language production and in surmounting the intrinsic problem of collinearity between multiple features of spontaneously spoken material. (shrink)

Understanding arithmetic word problems involves a complex interaction of text comprehension and mathematical processes. This article presents a computer simulation designed to capture the working memory demands required in “bottomup” comprehension of arithmetic word problems. The simulation's sentence‐level parser and text integration component reflect the importance of processing the problem from its original natural language presentation. Children's probability of solution was analyzed in exploratory regression analyses as a function of the simulation's sentence‐level and text integration processes. (...) Working memory variables measuring the combined effects of concepts to remember and text integration inferences account for a significant proportion of variance in children's solution probabilities across the first four grade levels (K‐3). Consistent with previous results from others, which highlighted the significance of small changes in problem wording, the simulation offers a process‐oriented perspective as to why natural language presentation constrains the comprehension of mathematical relationships. (shrink)

The model-checking problem for a logic L on a class C of structures asks whether a given L-sentence holds in a given structure in C. In this paper, we give super-exponential lower bounds for fixed-parameter tractable model-checking problems for first-order and monadic second-order logic. We show that unless PTIME=NP, the model-checking problem for monadic second-order logic on finite words is not solvable in time f·p, for any elementary function f and any polynomial p. Here k denotes the size of (...) the input sentence and n the size of the input word. We establish a number of similar lower bounds for the model-checking problem for first-order logic, for example, on the class of all trees. (shrink)

We consider the Lambek calculus, or noncommutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an$\omega $-rule, and prove that the derivability problem in this calculus is$\Pi _1^0$-hard. This solves a problem left open by Buszkowski (2007), who obtained the same complexity bound for infinitary action logic, which additionally includes additive conjunction and disjunction. As a by-product, we prove that any context-free language without the empty word can be generated by a Lambek (...) grammar with unique type assignment, without Lambek’s nonemptiness restriction imposed (cf. Safiullin, 2007). (shrink)

Nature is complex, exceedingly so. A repercussion of this “complex world constraint” is that it is, in practice, impossible to connect words to the world in a foolproof manner. In this paper I explore the ways in which the complex world constraint makes vagueness, or more generally imprecision, in language in practice unavoidable, illuminates what vagueness comes to, and guides us to a sensible way of thinking about truth. Along the way we see that the problem of ceteris paribus laws (...) is exactly the problem of vagueness and susceptible to similar treatment. (shrink)

Nature is complex, exceedingly so. A repercussion of this “complex world constraint” is that it is, in practice, impossible to connect words to the world in a foolproof manner. In this paper I explore the ways in which the complex world constraint makes vagueness, or more generally imprecision, in language in practice unavoidable, illuminates what vagueness comes to, and guides us to a sensible way of thinking about truth. Along the way we see that the problem of ceteris paribus laws (...) is exactly the problem of vagueness and susceptible to similar treatment. (shrink)

A completeness theory for parameterized computational complexity has been studied in a series of recent papers, and has been shown to have many applications in diverse problem domains including familiar graph-theoretic problems, VLSI layout, games, computational biology, cryptography, and computational learning [ADF,BDHW,BFH, DEF,DF1-7,FHW,FK]. We here study the parameterized complexity of two kinds of problems: (1) problems concerning parameterized computations of Turing machines, such as determining whether a nondeterministic machine can reach an accept state in \documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $k$\end{document} steps (the Short TM Computation Problem), and (2) problems concerning derivations and factorizations, such as determining whether a word \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $x$\end{document} can be derived in a grammar \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $G$\end{document} in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $k$\end{document} steps, or whether a permutation has a factorization of length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $k$\end{document} over a given set of generators. We show hardness and completeness for these problems for various levels of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $W$\end{document} hierarchy. In particular, we show that Short TM Computation is complete for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $W[1]$\end{document}. This gives a new and useful characterization of the most important of the apparently intractable parameterized complexity classes. (shrink)

This paper argues for a broader understanding of complexity; an understanding that speaks to the multidimensionality of environmental problems. As argued, environmental problems rest upon ontological, epistemological, and moral claims; they rest, in other words, upon statements about what is, knowledge, and what ought to be, respectively. To develop and illustrate this argument, the GMO (genetically modified organism) controversy is broken down according to these three dimensions. Dissecting environmental problems in this manner reveals why we cannot (...) look solely toward the natural sciences for resolution: because these problems beg questions that cannot be answered with references to materiality alone. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Transcendence of WordsAkos Krassoy (bio)Levinas’s central contribution to aesthetics and the philosophy of art is his well-known and provocative attempt to ethicize art. Yet, there is hardly any certainty regarding the nature of this ethicization. As far as the realization of Levinas’s program is concerned, readers usually remember its harmful effects.1 On the other hand, there are equally appreciative tones in his reading of art. It might be (...) more correct to say that the derogatory side is part of a fundamentally ambiguous attitude. It is almost as if Levinas’s radical ethical thinking, the job of which is to tackle totalizing Western thought, should speak in two voices when it comes to the aesthetic and the arts.Most of the commentaries run into, and then set out to resolve this weird situation marked by pejoration and ambiguity in one way or another. This is no easy task to accomplish; there is surely no single way out of this labyrinth. An element of irony is definitely required on the side of the interpreter. Arguably, my text may be no exception in the long line of attempts. In the following, I shall try my hand at these complexities and, similarly to other readers, deal with the contradictory remarks and implied but underdeveloped ideas by putting them into a meaningful framework. Like others before me, I shall do my best to provide a narrative as coherent as possible in which the letter [End Page 1] and the spirit of Levinas are followed and the relevant (phenomenological) aesthetic context is taken into account. In my case, this will mean siding with those interpreters who see a fixed set of problems dominating — that is, a single consistent path winding — in Levinas’s difficult itinerary. In more concrete terms, I shall join the camp of those who show sensitivity to the introduction of the critical act and argue that the shortcomings of the aesthetic are, to some extent, reversed in its recontextualization in human communication.2 Yet, unlike these authors who touch upon the issue of criticism to varying degrees, I shall concentrate fully on placing critical activity in the center of Levinas’s aesthetic thought and thus treating art as an important segment of ethical signification. My focus will be on the reintegration of the disengaged image into reality; I shall try to determine what this development in art implies in Levinas’s ethical phenomenological project. Concerning the particular course of my text, I shall concentrate mostly on the issue of ambiguity and, gradually working my way through it, deal with pejoration at the same time. I shall first analyze what is at stake in this ambiguousness, then attempt to establish its governing logic, only to prepare the ground on which criticism as a way out of the maze can be seen in its entirety.A Real Headache: AmbiguousnessAnyone interested in Levinas’s aesthetic thought arrives at a truly interesting but nebulous field. By nebulousness I primarily mean the overly ambiguous character of Levinas’s position. What Levinas has to say is indeed quite difficult to pin down or, at least, it is highly equivocal: the noise of critique is balanced by the sound of quiet but all the more patent affirmation. In every phase of his thinking there is a suspicion felt toward artistic expression, which may on occasion reach the level of derogation; all this is nevertheless accompanied by clear-cut support. This can be sensed in chance remarks, such as, in “Reality and Its Shadow” — the essay mostly responsible for the bad reputation of [End Page 2] Levinas in aesthetics — where Levinas discusses the plasticity of literary works and mentions a “particularly admirable page” in Proust’s The Captive (RS 10). In spite of the anti-aesthetic logic and philistine-like rhetoric of the essay, the art-loving character of the author — who is beyond a doubt an affectionate reader — is revealed for a second.Remarks like this are quite suggestive with respect to Levinas’s appraisal of the arts—as are many other details of Levinas’s work. Of all these, his apparent knowledge and use of artworks in his... (shrink)

In order to solve the problem of the influence of feature word position in lyrics on music emotion classification, this paper designs a music classification and detection model in complex noise environment. Firstly, an intelligent detection algorithm for electronic music signals under complex noise scenes is proposed, which can solve the limitations existing in the current electronic music signal detection process. At the same time, denoising technology is introduced to eliminate the noise and extract the features from the signal. (...) Secondly, from the perspective of audio and lyrics of song sentiment analysis and the unique characteristics of lyrics text, a lyric sentiment analysis method based on text title and position weight is proposed. Finally, considering the influence of the weight of feature words in different positions on the classification of lyrics, the analytic hierarchy process is used to calculate the weight of feature words in different positions of text title and lyrics before, in, and after the text. The results show that in the complex noise environment, the accuracy of music classification and detection of the proposed model is more than 90%, which is far beyond the control range of the actual application of music processing. The effect of music classification and detection is better than that of the contrast model, which has a certain practical application value. (shrink)

We observe that the classification problem for countable models of arithmetic is Borel complete. On the other hand, the classification problems for finitely generated models of arithmetic and for recursively saturated models of arithmetic are Borel; we investigate the precise complexity of each of these. Finally, we show that the classification problem for pairs of recursively saturated models and for automorphisms of a fixed recursively saturated model are Borel complete.

B a c k g r o u n d. The article is devoted to the analysis of the key directions of the study of the possible influence of the specifics of Chinese language culture on the content and nature of intellectual discourse, which is recognized as philosophical. Logic and ontology are the key areas of analysis of the possible influence of linguistic determinants on the intellectual discourse of China. Three main topics that attract the attention of researchers are the (...) structure of judgment, the semantics of lexical units, and the specificity of the pragmatics of the Chinese language. M e t h o d s. The author applied general scientific methods of analysis, synthesis, comparison and description of the works of researchers of Chinese philosophy, which justify and argue the fruitfulness of studying the peculiarities of Chinese language to explain the reasons of the fundamental difference between the problems actualized in the history of Chinese philosophy and those that formed the basis of the development of the history of philosophy in the Western world. R e s u l t s. It is generally accepted that for the worldview of representatives of Chinese culture, the world is a structural whole, consisting of elements that continuously interact in the dynamics of changes and transformations, we find a reflection of this feature in the semantics of the corresponding symbolic system. Polysemy in the Chinese language mostly reveals a complex and multi-layered "web" of associative and correlative connections between meanings, which in fact cannot be argued outside the context of the relevant cultural tradition indicating common features or similarities of the signified. The doubt about the typicality of understanding the denotations as fixed and atomized for the Chinese language culture is reasonable, even in those cases when it comes to the designation of empirically accessible objectivity. The main specific features of polysemy in the Chinese language are the complete heterogeneity of what is signified, and the lack of transparent grounds for identifying the genus-species subordination of the scope of general concepts. This can also serve as an explanation for the fact that we do not find a completely obvious and nondisputable analogue of the problem of universals of the Western model in the history of Chinese philosophy. C o n c l u s i o n s. Based on the peculiarities of the Chinese language culture, we can recognize as a reasonable a statement that the seemingly natural understanding of the essence – the subject, as something that remains the same (at least for a certain time), but it undergoes some changes through its manifestations – a predicate (properties and actions). It is not as necessary and axiomatic for Chinese thinkers as, for example, for ancient Greek philosophers. In addition, we can recognize the fact that the verb "to exist" does not fulfill the role of a necessary copula in judgments in the Chinese language, as a probable reason for the lack of fundamental problematization of the concept of "being" in the Chinese history of philosophy. In general, the context of the use of a certain word-sign in the Chinese language plays a determining role. The actualization of one or another meaning in an expression is formed not only by its integration into a certain text, but also by its purpose in accordance with the specific practice of application. Therefore, this can serve as an explanation for the absence of an original and axiomatic interpretation of truth as absolute, that is, unchanging and non-relative in the history of Chinese philosophy. (shrink)

This essay presents a point of view for looking at `free will', with the purpose of interpreting where exactly the freedom lies. For, freedom is what we mean by it. It compares the exercise of free will with the making of inferences, which usually is predominantly inductive in nature. The making of inference and the exercise of free will, both draw upon psychological resources that define our ‘selves’. I examine the constitution of the self of an individual, especially the involvement (...) of personal beliefs, personal memories, affects, emotions, and the hugely important psychological value-system, all of which distinguish the self of one individual from that of another. The foundational position that adopted in this essay is that all psychological processes are correlated with corresponding ones involving large scale neural aggregates in the brain, communicating with one another through wavelike modes of excitation and de-excitation. Of central relevance is the value-network around which the affect system is organized, the latter, in turn, being the axis around which is assembled the self, with all its emotional correlates. The self is a complex system. I include a brief outline of what complexity consists of. In reality all systems are complex, for complexity is ubiquitous, and certain parts of nature appear to us to be ‘simple’ only in certain specific contexts. It is in this background that the issue of determinism is viewed in this essay. Instead of looking at determinism as a grand principle entrenched in nature independent of our interpretation of it, I look at our ability to explain and to predict events and phenomena around us, which is made possible by the existence of causal links running in a complex course that set up correlations between diverse parts of nature, in this way putting the stamp of necessity on these events. However, the complexity of systems limits our ability to explain and to predict to within certain horizons defined by contexts. Our ability to explain and predict in matters relating to acts of free will is similarly limited by the operations of the self that remain hidden from our own awareness. The aspects of necessity and determinism appear to us in the form of reason and rationality that explain and predict only within a limited horizon, while the rest depends on the complex operation of self-linked psychological resources, where the latter appear as contingent in the context of the exercise of free will. The hallmark of complex systems is the existence of amplifying factors that operate as destabilizing ones, along with inhibiting or stabilizing factors as well that generally limit the destabilizing influences to local occurrences, while preserving the global integrity of a system. This complex interplay of destabilizing and stabilizing influences lead to the possibility of an enormous number of distinct modes of behavior that appear as emergent phenomena in complex systems. Looking at the particular case of the self of an individual that guide her actions and thoughts, it is the operation of our emotions, built around the psychological value-system, that provide for the amplifying and inhibiting factors mentioned above. The operation of these self-linked factors stamps our actions and thoughts as contingent ones that do not fit with our concepts of reason and rationality. And this is what provides the basis of our idea of free will. Free will is not ‘free’ in virtue of exemption from causal links running through all our self-based processes - ones that remain hidden from our awareness, but is free of what is perceived to be ‘reason and rationality’ based on knowledge and the common pool of beliefs and principles associated with a shared world-view. When we speak of the choice involved in an act of exercise of free will what we actually refer to is the commonly observed fact that various different individuals of a similar disposition respond differently when placed under similar circumstances. In other words, free will is ‘free’ precisely because it is not subject to constraints of a commonly accepted and shared set of principles, beliefs, and values. While it is possible that, in an exercise of free will, the self-linked psychological resources are brought into action when a number of alternatives are presented to the self by the operation of the ingredients of a commonly shared world-view, it seems likely that, that set of alternatives is not of primary relevance in the final response that the mind produces, since the latter is primarily a product of the operation of the self-based psychological resources. What is of greater relevance here is the operation of emotion-driven processes, guided by the psychological value-system based on the activity of the so-called reward-punishment network in the brain. These processes lead the individual to a response that appears to be free from the shackles of determinism precisely because their mechanisms, which are hidden from us, do not conform to commonly accepted and shared rules and principles. In contrast, inductive inference is a process that is based on the ‘cognitive face’ of self, where the self-based psychological resources play a supportive role to the commonly shared world-view of an individual. There is never any freedom from the all-pervading causal links representing correlations among all objects, entities, and events in nature. In the midst of all this, the closest thing to freedom that we can have in our life comes with self-examination and self-improvement. The possibility of self-examination appears in the form of specific conjunctions between our complex self-processes and the ceaseless changes of scenario in our external world. This actually makes the emergent phenomenon of self-examination a matter of chance, but one that keeps on appearing again and again in our life. Once realized, self examination creates possibilities that would not be there in the absence of it, and these possibilities include the enhancement of further self-enrichment and further diversity in the exercise of our free will. (shrink)

Chapter 1 First Person Access to Mental States. Mind Science and Subjective Qualities -/- Abstract. The philosophy of mind as we know it today starts with Ryle. What defines and at the same time differentiates it from the previous tradition of study on mind is the persuasion that any rigorous approach to mental phenomena must conform to the criteria of scientificity applied by the natural sciences, i.e. its investigations and results must be intersubjectively and publicly controllable. In Ryle’s view, philosophy (...) of mind needs to adopt an antimentalist stance to achieve this aim. Antimentalism not only definitively rejects the idea that mind is a substance separated from the body, it also denies that mental phenomena radically differ from physical phenomena by virtue of several unique features. Most problematically, mental phenomena have a conscious character (mental states are related to specific qualitative feelings) and are accessible only to the first-person (only the subject knows directly what s/he is experiencing inside his/her mind). Ryle takes a strong stance on antimentalism going so far as to maintain that an approach to mind which aims to meet the criteria of scientificity set by the natural sciences must avoid any reference to internal, unobservable mental states. In his view (which is considered a specifically philosophical version of psychological behaviorism and also addresses questions put forward in psychological research), mental states can be redescribed in terms of behavioral dispositions. In this chapter, we address the historical roots of the antimentalist view and analyze its relation to the later tradition of research on mind. We show that, compared to the antimentalist stance, functionalism and cognitivism take a step back when they maintain that direct reference to mental states is necessary since mental states cause and therefore explain human behavior. This step backwards is often interpreted as a return to mentalism. However, this is only partially true. Indeed, we suggest that these later traditions retain one important element of Ryle’s antimentalism, i.e. the idea that mental states must be uniquely identified using external and publicly observable criteria, while excluding any reference to introspection and those qualitative dimensions of a mental state, which are accessible only to the first-person. According to the perspective we put forward, this epistemological stance has continued to influence contemporary research on mind and current philosophical and psychological theories which both tend to exclude the subjective qualities of human experience from their accounts of how the mind works. The issue we raise here is whether this is legitimate or whether subjective qualities do play a role with respect to the way our mind works. The conclusion of this chapter anticipates the argument the book makes in in favor of this latter position, starting from a particular angle, i.e. the problem of how we categorize concepts related to our internal states. -/- Chapter 2 The Misleading Aspects of the Mind/Computer Analogy. The Grounding Problem and the Thorny Issue of Propriosensitive Information -/- Abstract. After the crisis of behaviorism, cognitivism and functionalism became the predominant models in the field of psychology and of philosophy, respectively. Their success is mainly due to the new key they use for interpreting mental processes: the mind/computer analogy. On the basis of this analogy, mental operations are seen as cognitive processes based on computations, i.e. on manipulations of abstract symbols which are in turn understood as informational unities (representations). This chapter identifies two main problems with this model. The first is how these symbols can relate to and communicate with perception and thus allow us to identify and classify what we perceive through the senses. Here we limit ourselves to presenting this issue in relation to the classical symbol grounding problem originally put forward by Harnad on the basis of Searle’s Chinese room argument. An attempt to address the problem raised here will be made in chap. 3. The second point we discuss in relation to the mind/computer analogy concerns the idea of information it fosters. Indeed, following this analogy, information is something available in the external world which can be captured by the senses and transmitted to the central system without being influenced or modified by the procedures of transmission. This perspective does not take into account that – unlike computers – in living beings information is acquired by means of the body. As Ulric Neisser has already pointed out, the body is itself an informational source that provides us with additional sensory experience that influences (modifies or complements) the information extracted from the external world by the senses. To develop this line of analysis and to determine exactly what information is provided by the body and how this might influence cognition, we examine Sherrington’s and Gibson’s positions. Moving on from their views, we qualify bodily information in terms of ‘proprioception’. We use ‘proprioception’ in a broad sense to describe any kind of experience we have of our internal states (including postural information as well as sensations related to the general state of the body and its parts). Following Damasio’s and Craig’s studies, we further elaborate this position, arguing that living beings are equipped with an internal propriosensitive monitoring system which maps all the changes that constantly occur in our body and that give us perceptual (‘proprioceptive’ or propriosensitive) information about what happens inside us. Moreover, relying on Goldie’s and Ratcliffe’s view, we show that emotional information can also be considered as a form of ‘proprioception’ which contributes to determining everything we perceive. This analysis leads us to the second main thesis of this book: ‘proprioception’ is a form of internal perception and it is an essential component of the sensory information we can access and use for all cognitive purposes. -/- Chapter 3 Semantic Competence from the Inside: Conceptual Architecture and Composition -/- Abstract. Concepts are essential constituents of thought: they are the instruments we use to categorize our experience, i.e. to classify things and group them together in homogeneous sets. Here we define concepts as the internal mental information (representations) that allows us, among other things, to master words in natural language. By analyzing the way in which individuals master word meanings we explore a number of hypotheses regarding the nature of concepts. Following Diego Marconi’s research, we differentiate between two kind of abilities that underpin lexical competence – so-called ‘referential’ and ‘inferential competence’ – and we suggest that, in order to support these abilities, concepts must also include two corresponding kinds of information, i.e. inferential and referential information. We point out that the most widely used and acknowledged theories of concepts do not make this distinction, instead broadly characterizing the information used for categorization in terms of propositionally described feature lists. However, we show that while feature lists can explain inferential competence, they do not account for referential competence. To address the issue of referential competence we examine Ray Jackendoff’s hypothesis that to account for the possibility of linking perceptual and conceptual information we need to assume the existence of a (visual) representation that encodes the geometric and topological properties of objects and bridges the gap between the percept and the concept. Furthermore, we analyze the extension of this work by Jesse Prinz who introduced the notion of a proxytype, a perceptual representation of a class of objects that incorporates structural and parametric information related to their appearance. However, as we point out, proxytypes can only explain the relationship between perception and concepts with respect to instances that can be perceived through the senses and that belong to the same class by virtue of their physical similarity. We suggest that this notion be extended to include larger conceptual classes. To accomplish this, we further develop Mark Johnson, George Lakoff and Jean Mandler’s idea of a schematic image and argue that conceptual representations include a perceptual schema. Perceptual schemata are non-linguistic, structured experiential gestalts (patterns or maps) that make use of information taken from all sensory modalities, including body perception. They accomplish a quasi-conceptual function: they allow us to recognize and to classify different instances. In this work, we hypothesize that perceptual schemata are an essential component of concepts, but not identical to them. Instead, we suggest that concepts include both perceptual and propositional information with perceptual schemata providing the ‘perceptual core concept’ that grounds related propositional information. -/- Chapter 4 In the Beginning There Were Categories. The Bodily Origin of Prelinguistic Categorical Organization: The Example of Folkbiological Taxonomies -/- Abstract. Studies of categorization in psychology and the cognitive sciences have made use of the notions of ‘category’ and ‘concept’ without precisely defining what is meant by either; in fact, often these terms have been used as synonyms, making it difficult to address specific issues related to conceptual development. This chapter begins by discussing the definitions of, as well as the distinctions between, ‘categories’ and ‘concepts’ in the classical philosophical tradition (Aristotle, Kant and Husserl). We introduce our view of categories with reference to Husserl. Categorization is defined as the way in which our experience is originally (pre-linguistically) organized in a passive and fully unconscious manner on the basis of universal structuring principles. Conceptualization is explained as a later process in which the earlier categorical macro-classes are further subdivided into more specific and detailed sets; this later process also relies on linguistic learning and exposure to culture. On the basis of Ray Jackendoff, Jean Mandler, George Lakoff and Mark Johnson’s work, we hypothesize that categorization is a two-step process that begins with the formation of homogeneous sets of entities partitioned into regions that describe the ontological boundaries of the objects that humans perceive (categories) and continues at a later stage with the development of more specific classifications (concepts). In this chapter, we mainly address three related issues: Why should we assume that there is categorical organization which precedes the development of a conceptual system? How do categories and concepts relate to each other? Shall we hypothesize that categories are innate or that they are formed before concepts on the basis of information and organizational structure available at a very early developmental stage? We show that categorical partitions are necessary for categorization and, following Mandler, that the general categories we form at an early age do not match our adult superordinate concepts. As for the third issue, we argue that there might be no need to assume that categories are innately present in the human mind, since their formation can be explained – at least in certain cases – by basic mechanisms that work on body (propriosensitive) information. This hypothesis will not be discussed in general, but in relation to a particularly relevant example of categorical partition, i.e. the folk-biological dichotomy between ANIMATE/INANIMATE. This is compared with other dichotomies that derive from it, but are not directly categorical such as LIVING/NON-LIVING and BIOLOGICAL/NON-BIOLOGICAL. -/- Chapter 5 Internal States: From Headache to Anger. Conceptualization and Semantic Mastery -/- Abstract. Here we ask if we can also apply the distinction between referential and inferential competence we introduced in Chapter 3 to words that do not refer to things that are perceived using the external senses, especially to words/concepts that denote bodily experiences (such as pain, thirst, hunger, etc.) or emotions. We introduce and discuss the hypothesis that – even though such words/concepts do not refer to intersubjectively identifiable entities in the external world – they do have a kind of referent that can be accessed via direct perception, more specifically ‘proprioception’, as we have defined it in terms of all propriosensitive information we can consciously access. In the first part of the chapter, we specifically consider terms denoting bodily experiences such as ‘pain’ or ‘hunger’ and argue that their referents are identified and classified from a first-personal point of view on the basis of four main characteristics: their specific intensity, their localization in the body, their co-occurrence with other signals and above all their specific qualitative sensations. Emotions are addressed in the second part of the chapter. We suggest that there is a continuity between bodily experiences and emotions. In particular, we argue for a perceptual theory of emotions in line with that proposed by James and Lange at the end of the 19th century and developed more recently by authors such as Damasio (see also chap. 2§5, §6). The hypothesis we put forward is that the referential information that supports the categorization of emotions and therefore also our mastery of terms referring to emotions consists in the perception (i.e. the ‘proprioception’) of those bodily states and changes in bodily states which constitute our emotional experience. In the context of this discussion we examine some objections to this line of reasoning that arise from a cognitivist perspective and following authors such as Oatley, Johnson-Laird and Frijda, we distinguish between basic emotions that can be identified and classified solely on the basis on how they feel and complex emotions whose identification and classification additionally depends on cognitive factors. To describe how emotions are identified and classified on the basis of how they feel, we rely on Marcel and Lambie’s distinction between an ‘emotion state’ and an ‘emotion experience’. Both notions indicate kinds of feelings that we consciously experience. However, they describe first-order and second order emotion awareness respectively. The emotion state is the feeling we have of the bodily states and changes that occur when we are experiencing an emotion, while the emotion experience is the fully developed and integrated emotion we both experience and are, with reflection, aware of experiencing. On the basis of this differentiation, we also show that the same characteristics that aid in the identification and classification of bodily experiences (specific qualitative sensations; somatic localization; specific intensity; presence/absence of specific concomitant sensations) can also be used for the identification and classification of emotions – at least basic emotions. In the last two sections of the chapter we present some clinical evidence on the semantic competence of people who suffer from Alexithymia and Autism Spectrum Disorder which supports the conclusions of our preceding analyses. -/- Chapter 6 The ‘Proprioceptive’ Component of Abstract Concepts -/- Abstract. In this chapter, we address the issue of whether the mastery of abstract words requires only inferential knowledge and thus, if the concepts that support the mastery of abstract words include only linguistic information. We start by differentiating the notions of ‘abstract’ and ‘general’ which are often erroneously confused. We then identify a strict definition of abstract, as contrasted with ‘concrete’, that applies to words or concepts whose referent cannot be experienced by the senses. We argue that abstract words/concepts would be better described as theoretical, because they are usually conceived as structured sets of inferential knowledge expressed linguistically; that is, as small theories. Pointing out parallels with Carnap’s analysis of this issue in philosophy of science, we hypothesize that words/concepts denoting non-observable entities are not all ‘equally theoretical’, because their link to sensory experience can be stronger or weaker. We revive the distinction, inspired by Quine, between theoretical and intertheoretical concepts/words. This distinction relies on the fact that the former – unlike the latter – retains a strong, although indirect, connection with perception. In Quine’s discussion, perception is understood uniquely in terms of observability, i.e. of external sensory experience. Here we argue, however, that bodily, ‘proprioceptive’ (i.e. propriosensitive) experience can also serve to referentially ground theoretical (i.e. abstract) concepts/words. We frame this issue using the example of the theoretical concept ‘freedom’ and Lakoff’s hypothesis that this concept is developed on the basis of bodily information. We contrast this with the example of ‘democracy’ which more closely resembles an intertheoretical concept/word. Furthermore, we show that one of the classical views put forward in psycholinguistic research to explain how abstract concepts are mentally represented – i.e. Paivio’s Dual Coding Theory – points in the same direction as our analysis. The same is true of Barsalou’s work suggesting that we use internal information to understand at least some abstract words. To sustain this position, we put forward two lines of evidence: the first comes from psycholinguistic studies while the second examines deficits of semantic competence exhibited by people with Autism Spectrum Disorder. On the basis of our analysis, we put forward a classification that distinguishes between different kinds of concreteness and different degrees of abstraction: concepts/words referring to body experiences and basic emotions are described as analogous to concrete concepts/words because they are grounded in perceptual (i.e. propriosensitive) experience, while abstract concepts/words are considered more or less abstract depending on whether they are intratheoretical (and rely entirely on inferential information) or theoretical (and are partially grounded in perceptual – or more often in propriosensitive perceptual – information). In the last section of the chapter we consider two scales that have been used in psycholinguistic research to measure the degree of concreteness vs. abstractness of words and we show that – used conjointly – they can provide a measure of the internal vs. external grounding of specific words. (shrink)

The constantly accelerating progress of contemporary natural science is indissolubly associated with the development and use of mathematics and with the processes of mathematical modeling of the phenomena of nature. The essence of this diverse and highly fertile interaction of mathematics and natural science and the dialectics of this interaction can only be disclosed through analysis of the nature of theoretical notions in general. Today, above all in the ranks of materialistically minded researchers, it is generally accepted that theory possesses (...) a value of its own. Contrary to positivist concepts of the nature of our knowledge, the meaning and significance of theory do not consist merely of the recording of experimental data, their classification and notation in abbreviated form. The meaning of theory is considerably more significant and is revealed, above all, in its explanatory and predictive functions. Contemporary theoretical knowledge is quite advanced and comprises a highly complex system, relatively self-contained and capable of internal development. Mathematics is the most interesting and distinctive phenomenon in the system of theoretical knowledge, in the system of science in general. It is in its dialectical development that the internal force and dynamics of the development of theory, in the very broadest sense of that word, find expression. Paul Lafargue tells us that Karl Marx held that "science only attains perfection when it succeeds in making use of mathematics" . In many fields of research the formulation of new ideas and concepts rests upon mathematics, its concepts and notions, and "is suggested" by the latter. "Mathematics," writes F. Dyson, "is the main source of the notions and principles out of which new theories are created" . The basic significance of mathematics to theory has been noted by outstanding thinkers over the course of the entire history of development of science. Today the expressive phrase, "the mathematization of knowledge," has come into general currency as a description of the principal direction of growth of theoretical notions in natural science. However, with respect to the growth of modern theoretical physics in general, the statement that it develops primarily by the method of the mathematical hypothesis has general validity. For example, the principal findings and discoveries of quantum theory and particle physics, starting from the corpuscularwave dualism and terminating with the omega minus hyperon and hypothetical quarks, were obtained or made "at the tip of a mathematician's pen.". (shrink)

Everybody who has learned English as a second or foreign language knows that for reaching intermediate levels, English is an easy language regarding grammar and vocabulary; however, when reaching advanced levels, the learners are faced with complex forms of morphology, syntax, and most obviously, they are faced with the difficulties that pronunciation presents. These are mainly the problems that occur with the English students whose native language is other than English. An experienced teacher of non-native speakers of English can (...) easily recognize the causes of mispronunciation, which in most cases are lack of vocabulary, lack of practice, bad teaching experiences, lack of direct contact with the language, and lack of self-confidence. There are quite a lot of words in English, which are often mispronounced. Those who have just started to learn English as a foreign language, students at primary schools, adults using English as a means of communication and as a working tool, such as businessmen, politicians, administrators, doctors, accountants, and those studying English for teaching purposes, even the teachers of English are faced with the problems of proper pronunciation of words in English.The aim of this research is to identify the problems that the students in the Department of English Language and Literature in the Faculty of Languages, Cultures and Communication face with when they deal with pronunciation of lexical words. (shrink)

I consider the problem of existence of virtual objects, mainly their mode of existence, while omitting the issue of the criteria of their existence. I present and analyze the concepts of modes of existence of virtual objects proposed in the literature of the subject, and then I demonstrate my own position on the issue. My position on the existence of virtual objects has certain points coinciding with the already postulated views, but at the same time it differs from them in (...) some basic aspects. In my view virtual objects are “born” in human individual consciousness as the objects of specific creative states of the mind. So initially they are private objects belonging to the individual subjective sphere. However, their final and ready forms emerge in complex processes of objectifying and autonomizing the respective private conscious states and their objects. In these processes the private objects are transformed into objects intersubjectively accessible and existing in the collective cultural sphere. In both their forms, initial and final, virtual objects are non-material entities: first subjective, then objective. The ontic status of virtual objects is very similar to the status of intangible ideas and all the non-material objects created by the human mind. The main difference consists in that virtual objects are expressed by the use computers programmes, while other non-material objects created by human beings are expressed by use of words, pictures, literature and art works, etc. (shrink)

I consider the problem of existence of virtual objects, mainly their mode of existence, while omitting the issue of the criteria of their existence. I present and analyze the concepts of modes of existence of virtual objects proposed in the literature of the subject, and then I demonstrate my own position on the issue. My position on the existence of virtual objects has certain points coinciding with the already postulated views, but at the same time it differs from them in (...) some basic aspects. In my view virtual objects are “born” in human individual consciousness as the objects of specific creative states of the mind. So initially they are private objects belonging to the individual subjective sphere. However, their final and ready forms emerge in complex processes of objectifying and autonomizing the respective private conscious states and their objects. In these processes the private objects are transformed into objects intersubjectively accessible and existing in the collective cultural sphere. In both their forms, initial and final, virtual objects are non-material entities: first subjective, then objective. The ontic status of virtual objects is very similar to the status of intangible ideas and all the non-material objects created by the human mind. The main difference consists in that virtual objects are expressed by the use computers programmes, while other non-material objects created by human beings are expressed by use of words, pictures, literature and art works, etc. (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)

Of course, words aren’t magic. Neither are sextants, compasses, maps, slide rules and all the other paraphenelia which have accreted around the basic biological brains of homo sapiens. In the case of these other tools and props, however, it is transparently clear that they function so as to either carry out or to facilitate computational operations important to various human projects. The slide rule transforms complex mathematical problems (ones that would baffle or tax the unaided subject) into simple tasks (...) of perceptual recognition. The map provides geographical information in a format well-suited to aid complex planning and strategic military operations. The compass gathers and displays a kind of information that (most) unaided human subjects do not seem to command. These various tools and props thus act to generate information, or to store it, or to transform it, or some combination of the three. In so doing, they impact our individual and collective problem- solving capacities in much the same dramatic ways as various software packages impact the performance of a simple pc. (shrink)

Every science has its technical vocabulary, consisting in part of terms coined for explicit purposes and in part of words borrowed from ordinary discourse and used with greater or lesser degrees of precision. Words of the latter sort pose curious problems, some of them familiar to those historians of science concerned with, for example, what Galileo meant by forza and Newton by attraction. Indeed, analogous problems face any historian seeking to understand the older meanings of terms still in (...) use today. (shrink)

We consider the problem of recognizing important properties of logical calculi and find complexity bounds for some decidable properties. For a given logical system L, a property P of logical calculi is called decidable over L if there is an algorithm which for any finite set Ax of new axiom schemes decides whether the calculus L + Ax has the property P or not. In [11] the complexity of tabularity, pre-tabularity, and interpolation problems over the intuitionistic logic (...) Int and over modal logic S4 was studied, also we found the complexity of amalgamation problems in varieties of Heyting algebras and closure algebras. In the present paper we deal with positive calculi. We prove NP-completeness of tabularity, DP-hardness of pretabularity and PSPACE-completeness of interpolation problem over Int + . In addition to above-mentioned properties, we consider Beth's definability properties. Also we improve some complexity bounds for properties of superintuitionistic calculi. (shrink)

"The notion of Geschlecht - denoting gender, genre, kinship, and more - exemplifies the most pertinent questions of the transnational and transdisciplinary structures of contemporary humanities. What happens in the transference from one language, tradition, or form to another? Combining detailed case studies of "category problems" in literature, philosophy, theatre, media, cinema, and performing arts, with excerpts from canonical texts-by field-defining thinkers such as Derrida, Malabou, Nancy, and Irigaray-the volume presents "the Geschlecht complex" as a fulcrum for any interpretive (...) endeavor, as an invaluable mode of thought for the present and inevitable complexities of theorizing in the 21st century"--. (shrink)

We investigate the complexity of finding solutions to infinite recursive constraint satisfaction problems. We show that, in general, the problem of finding a solution to an infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through a recursive tree. We also identify natural classes of infinite recursive constraint satisfaction problems where the problem of finding a solution to the infinite recursive constraint satisfaction problem is equivalent to the problem of finding an (...) infinite path through finitely branching recursive trees or recursive binary trees. There are a large number of results in the literature on the complexity of the problem of finding an infinite path through a recursive tree. Our main result allows us to automatically transfer such results to give equivalent results about the complexity of the problem of finding a solution to a recursive constraint satisfaction problem. (shrink)

Earlier research by the author brought about findings suggesting that people in a special way process words related to demands of a problem they previously solved, even when they do not consciously notice this relationship. The findings concerned interference in the task in which the words appeared, a shift in affective responses to them that depended on sex of the participants, and impaired memory of the words. The aim of this study was to replicate these effects and to find out (...) whether they are related to working memory span of the participants, taken as a measure of the individual’s ability to control attention. Participants in the experimental group solved a divergent problem, then performed an ostensibly unrelated speeded affective classification task concerning each of a series of nouns, and then performed an unexpected cued recall task for the nouns. Afterwards, a task measuring WM span was administered. In the control group there was no problem-solving phase. Response latencies for words immediately following problem-related words in the classification task were longer in the experimental than in the control group, but there was no relationship between this effect and WM span. Solving the problem, in interaction with sex of the participants and, independently, with their WM span, influenced affective responses to problem-related words. Recall of these words, however, was not impaired in the experimental group. (shrink)

Two experiments were conducted to investigate children’s interpretations of standard arithmetic word problems and the factors that influence their interpretations. In Experiment 1, children were required to solve a series of problems and then to draw and select pictures that represented the problems’ structures. Solution performance was found to vary systematically with the nature of the representations drawn and chosen. The crucial determinant of solution success was the interpretation a child assigned to certain phrases used in (...) the problems. In Experiment 2, solution and drawing accuracy were found to be significantly improved by rewording problems to avoid ambiguous linguistic forms. Together, these results imply that (a) word-problem solution errors are caused by misinterpretations of certain verbal expressions commonly used in problem texts, and (b) these misinterpretations are the result of missing or inadequate mappings of these verbal expressions to partwhole knowledge. (shrink)

I was more excited by Jacques Ranciere’s idea about aesthetics being, in his opinion, a special way of thinking (mode de pensee) that works of art provoke and that tends to show what they are like as art objects. Aesthetics then (following this intention) would not be viewed as a discipline akin to art theory that wouldexamine the structure of the work of art, its peculiarities, conditions of arising, et cetera, all that attests either to its objectivity or subjectivity. Ranciere (...) underscores the special (in the style of Hegel and Romanticist philosophy) regime of thinking about art where the idea is not yet an idea, but is what is not yet being thought. In spite of the fact that Ranciere’s declarations refer to S. Freud’s theory of the unconscious that, in his opinion, is closely linked with the way of artistic thinking and possibly can be expressed in no other way but through the medium of artistic thinking. The same way refers to the basic concepts of Freud’s psychoanalysis including also the unconscious and the ideas on complexes, especially on the Oedipus complex. It is interesting that Ranciere compares the framework ofthe dramatic nature of Oedipus’ fate with the basic fluctuations of aesthetics and art and namely – just like Oedipus is also the one who experiences everything absolutely and is completely expressed in action so the character of aesthetics and art is hidden in the contradictions between activities and sufferings or action and passions. This theme just like the question of the extreme poles of understanding aesthetics – pleasure and pain is comparable with the question of the determination of aesthetics and also art that grasps human experience in figural bodily shapes because that is the way of discerning the thought that is not yet being thought, but is hidden in bodily or animated figures. This tradition or historical regime, I think, is not to be discovered as a rectilinear trajectory; it manifests itself in a contradictory and sporadic way, frequently as an interlude between crucial conclusions and an essential interest pointing towards the ambivalence of art that referring to the words of the early modernist poet Charles Baudelaire: “I am the wound and the knife” would mark these relationships between action and its effect that could also attest to the painful birth of the thought in the not thought yet or else the negative character of aistheton. (shrink)

This paper does not purport to present a fully developed argument. Rather, it intends to delineate, in broad strokes and in a synoptic manner, the total frame of reference of Scientific Empiricism as far as it is necessary for an integration of the several contributory clarifications of the complex, usually referred to as the psychophysical problem. Several considerations seem to justify such an attempt. It is desirable, from time to time, to free the results of logical and methodological analysis from (...) their specialized contexts. Only thus can they be presented in a way which brings to the fore their continuity with more traditionally worded epistemological thought. By doing this such a presentation should also help to dissolve the current objections of formalism, scientism, and philosophical irrelevance so frequently based on misunderstanding. It is only fair to admit, however, that these misunderstandings have been facilitated by the preoccupation with the technical, and the brevity with regard to the nontechnical, which characterize the modern analysts. (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, (...) neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

Word problems are notoriously difficult to solve. We suggest that much of the difficulty children experience with word problems can be attributed to difficulty in comprehending abstract or ambiguous language. We tested this hypothesis by (1) requiring children to recall problems either before or after solving them, (2) requiring them to generate f'mal questions to incomplete word problems, and (3) modeling performance pattems using a computer simulation. Solution performance was found to be systematically (...) related to recall and question generation performance. Correct solutions were associated with accurate recall of the problem structure and with appropriate question generation. Solution "errors" were found to be correct solutions to miscomprehended problems. Word problems that contained abstract or ambiguous language tended to be miscomprehended more often than those using simpler language, and there was a great deal of systematicity in the way these problems were miscomprehended. Solution error pattems were successfully simulated by manipulating a computer model’s language comprehension strategies, as opposed to its knowledge of logical set relations. o was.. (shrink)