We construct a 2-equivalence $\mathfrak {CohTheory}^{op }\simeq \mathfrak {TypeSpaceFunc}$. Here $\mathfrak {CohTheory}$ is the 2-category of positive theories and $\mathfrak {TypeSpaceFunc}$ is the 2-category of type space functors. We give a precise definition of interpretations for positive logic, which will be the 1-cells in $\mathfrak {CohTheory}$. The 2-cells are definable homomorphisms. The 2-equivalence restricts to a duality of categories, making precise the philosophy that a theory is ‘the same’ as the collection of its type spaces (i.e. its (...) type space functor). In characterising those functors that arise as type space functors, we find that they are specific instances of (coherent) hyperdoctrines. This connects two different schools of thought on the logical structure of a theory. The key ingredient, the Deligne completeness theorem, arises from topos theory, where positive theories have been studied under the name of coherent theories. (shrink)

In this paper I compare two well studied approaches to topological semantics – the domain-theoretic approach, exemplified by the category of countably based equilogical spaces, Equ and Typ Two Effectivity, exemplified by the category of Baire space representations, Rep . These two categories are both locally cartesian closed extensions of countably based T0-spaces. A natural question to ask is how they are related.First, we show that Rep is equivalent to a full coreflective subcategory of Equ, consisting of the so-called (...) 0-equilogical spaces. This establishes a pair of adjoint functors between Rep and Equ. The inclusion Rep → Equ and its coreflection have many desirable properties, but they do not preserve exponentials in general. This means that the cartesian closed structures of Rep and Equ are essentially different. How ever, in a second comparison we show that Rep and Equ do share a common cartesian closed subcategory that contains all countably based-T0 spaces. Therefore, the domain-theoretic approach and TTE yield equivalent topological semantics of computation for all higher-order types over countably based T0-spaces. We consider several examples involving the natural numbers and the real numbers to demonstrate how these comparisons make it possible to transfer results from one setting to another. (shrink)

By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.

Our conscious experiences are qualitative and unitary. The qualitative universals given in particular experiences, i.e. qualia, combine into the seamless unity of our conscious experience. The problematics of quality and cohesion are not unique to consciousness studies. In mathematics, the study of qualities (e.g., shape) resulting from quantitative variations in cohesive spaces led to the axiomatization of cohesion and quality. Using the mathematical definition of quality, herein we model qualia space as a categorical product of qualities. Thus modeled qualia (...) space is a codomain space wherein composite qualities (e.g. shape AND color) of conscious experiences can be valued. As part of characterizing the qualia space, we provide a detailed exemplification of the mathematics of quality and cohesion in terms of the categories of idempotents and reflexive graphs. More specifically, with qualities as commutative triangles formed of cohesion-preserving functors, first we calculate the product of commutative triangles. Next, we explicitly show that the category of idempotents is a quality type. Lastly, as part of showing that the category of reflexive graphs is cohesive, we characterize the adjointness between functors relating cohesive graphs to discrete sets. In conclusion, our category theoretic construction of qualia space is a formalization of the binding of qualitative features (colors and shapes) into the cohesive objects (colored-shapes) of conscious experiences. Compared to the feature-vector accounts of conscious experiences, our product-of-qualities account of consciousness is a substantial theoretical advance. (shrink)

In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers :149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42:863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison (...) between the two and a statement of semantic equivalence with respect to two different logical systems: a doxastic logic for belief and an epistemic–doxastic logic for belief and knowledge. Moreover, a sound and complete axiomatization of these logics with respect to the two equivalent Kripke semantics and type spaces semantics is provided. Finally, a probabilistic extension of the result is also presented. A further result of the paper is a study of the relationship between the epistemic–doxastic logic for belief and knowledge and the logic STIT by Belnap and colleagues. (shrink)

In this article we give a general categorical construction via reflection functors for various completions of T0-spaces subordinate to sobrification, with a particular emphasis on what we call the -completion, a type of directed completion introduced by Wyler [O. Wyler, Dedekind complete posets and Scott topologies, in: B. Banaschewski, R.-E. Hoffmann , Continuous Lattices Proceedings, Bremen 1979, in: Lecture Notes in Mathematics, vol. 871, Springer Verlag, 1981, pp. 384–389]. A key result is that all completions of a certain (...) class='Hi'>type are universal, hence unique . We give a direct definition of the -completion and develop its theory by introducing a variant of the Scott topology, which we call the d-topology. For partially ordered sets the -completion turns out to be a natural dcpo-completion that generalizes the rounded ideal completion. In the latter part of the paper we consider settings in which the -completion agrees with the sobrification respectively the closed ideal completion. (shrink)

Many different approaches to describing the players’ knowledge and beliefs can be found in the literature on the epistemic foundations of game theory. We focus here on non-probabilistic approaches. The two most prominent are the so-called Kripkeor Aumann- structures and knowledge structures (non-probabilistic variants of Harsanyi type spaces). Much of the recent work on Kripke structures has focused on dynamic extensions and simple ways of incorporating these. We argue that many of these ideas can be applied to knowledge structures (...) as well. Our main result characterizes precisely when one type can be transformed into another type by a specific type of information update. Our work in this paper suggest that it would be interesting to pursue a theory of “information dynamics” for knowledge structures (and eventually Harsanyi type spaces). (shrink)

Several Gentzen-style syntactic type calculi with product are considered. They form a hierarchy in such a way that one calculus results from another by imposing a new condition upon the sequent-forming operation. It turns out that, at some steps of this process, two different functors collapse to a single one. For the remaining stages of the hierarchy, analogues of Wajsbergs's theorem on non-mutual-definability are proved.

We discuss the externally definable Ramsey property, a weakening of the Ramsey property for relational structures, where the only colourings considered are those that are externally definable: that is, definable with parameters in an elementary extension. We show a number of basic results analogous to the classical Ramsey theory, and show that, for an ultrahomogeneous structure M with countable age, the externally definable Ramsey property is equivalent to the dynamical statement that, for all $$n \in \mathbb {N}$$, every subflow (...) of the space $$S_n(M)$$ of n-types has a fixed point. We discuss a range of examples, including results regarding the lexicographic product of structures. (shrink)

The basic concept of Type-2 Theory of Effectivity to define computability on topological spaces or limit spaces are representations, i. e. surjection functions from the Baire space onto X. Representations having the topological property of admissibility are known to provide a reasonable computability theory. In this article, we investigate several additional properties of representations which guarantee that such representations induce a reasonable Type-2 Complexity Theory on the represented spaces. For each of these properties, we give a nice (...) characterization of the class of spaces that are equipped with a representation having the respective property. (shrink)

We study connections between asymptotic structure in a Banach space and model theoretic properties of the space. We show that, in an asymptotic sense, a sequence $$ in a Banach space X generates copies of one of the classical sequence spaces $\ell_p$ or $c_0$ inside X if and only if the quantifier-free types approximated by $$inside X are quantifier-free definable. More precisely, if$$ is a bounded sequence X such that no normalized sequence of blocks of (...) $$converges, then the following two conditions are equivalent. There exists a sequence$$ of blocks of $$ such that for every finite dimensional subspace E of X, every quantifier-free type over $E +\overline{\rm span}\{y_n\mid n\in \mathbb{N}\}$ is quantifier-free definable. One of the following two conditions holds: there exists $1\le p 0$ and every finite dimensional subspace E of X there exists a sequence of blocks of $$which is$$-equivalent over E to the standard unit basis of $\ell_p$; for every $\epsilon>0$ and every finite dimensional subspace E of X there exists a sequence of blocks of $$which is$$-equivalent over E to the standard unit basis of $c_0$. Several byproducts of the proof are analyzed. (shrink)

Using Type‐2 theory of effectivity, we define computability notions on the spaces of Lebesgue‐integrable functions on the real line that are based on two natural approaches to integrability from measure theory. We show that Fourier transform and convolution on these spaces are computable operators with respect to these representations. By means of the orthonormal basis of Hermite functions in L2, we show the existence of a linear complexity bound for the Fourier transform. (© 2004 WILEY‐VCH Verlag GmbH & Co. (...) KGaA, Weinheim). (shrink)

We introduce a notion of the space of types in positive model theory based on Stone duality for distributive lattices. We show that this space closely mirrors the Stone space of types in the full first-order model theory with negation (Tarskian model theory). We use this to generalise some classical results on countable models from the Tarskian setting to positive model theory.

A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a $\mathbf {0}'$ -computable low $_3$ compact Polish space which is not homeomorphic to a computable one, and that, for any natural number $n\geq 2$, there exists a Polish space $X_n$ such that exactly the high $_{n}$ -degrees are required to present the (...) homeomorphism type of $X_n$. Along the way we investigate the computable aspects of Čech homology groups. We also show that no compact Polish space has a least presentation with respect to Turing reducibility. (shrink)

Summary I outline an approach to the phenomenology of improvised music which takes typification and the development of multi‐ordered phenomenological structures as central. My approach here is firmly in line with classical Husserlian phenomenology, taking the discussion of types in Experience and Judgment (Husserl, 1973) and Brudzińska (2015) as guide. I provide a phenomenological analysis of musical types as they are found in improvisational contexts, focusing on jazz in the 20th century. Styles are higher‐order musical types. Musical types are structures (...) that are temporally “thick,” relying on sedimented typification and knowledge, driving expectations as definitional. In most forms of music (including improvised music), musical styles involve maintaining a balance between confirming expectations and flouting expectations. I show that improvised music has a phenomenal structure which is enriched by the communicative and “ real‐time” nature of improvised music. Improvised music can be seen as an exploration of a possibility space rendered by the juxtaposition of the musical types afforded by a performance environment (instrumentation, harmonic and melodic traditions, etc.). I show that improvisation in music is a multi‐vectoral form of communication. The communication is founded in what Dieter Lohmar calls “non‐linguistic thinking.” The expression is constituted in the results of active and synthesis. The culmination of improvisational exploration of possibility spaces is the precisification and enrichment of styles‐as‐types, while in some cases developing new styles in the process. (shrink)

This paper deals with Gärdenfors’ theory of conceptual spaces. Let ${\mathcal {S}}$ be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes $\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}$ be given. Our main result is the construction of a classification algorithm. That is, given an element ${\tilde{A}}\in \mathcal {S},$ our algorithm classifies it into the conceptual field determined by one of the given prototypes $\tilde{P}_i.$ The construction of our algorithm uses some (...) physical analogies and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space $\mathcal {S}$ is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

In set theory without the axiom of choice math formula, three-space type results for the Hahn-Banach property are provided. We deduce that for every Hausdorff compact scattered space K, the Banach space C of real continuous functions on K satisfies the continuous Hahn-Banach property in math formula. We also prove in math formula Rudin's theorem: “Radon measures on Hausdorff compact scattered spaces are discrete”.

We give a characterisation of an extension of the Kleene-Kreisel continuous functionals to objects of transfinite types using limit spaces of transfinite types.

Barendregt gave a sound semantics of the simple type assignment system λ → by generalizing Tait’s proof of the strong normalization theorem. In this paper, we aim to extend the semantics so that the completeness theorem holds.

A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing the (...) Pudlák–Rödl Theorem to this class of topological Ramsey spaces. To each topological Ramsey space in this framework corresponds an associated ultrafilter satisfying some weak partition property. By using the correct Fraïssé classes, we construct topological Ramsey spaces which are dense in the partial orders of Baumgartner and Taylor generating p-points which are k-arrow but not \-arrow, and in a partial order of Blass producing a diamond shape in the Rudin-Keisler structure of p-points. Any space in our framework in which blocks are products of n many structures produces ultrafilters with initial Tukey structure exactly the Boolean algebra \\). If the number of Fraïssé classes on each block grows without bound, then the Tukey types of the p-points below the space’s associated ultrafilter have the structure exactly \. In contrast, the set of isomorphism types of any product of finitely many Fraïssé classes of finite relational structures satisfying the Ramsey property and the OPFAP, partially ordered by embedding, is realized as the initial Rudin-Keisler structure of some p-point generated by a space constructed from our template. (shrink)

The paper sets out to offer an alternative to the function/argument approach to the most essential aspects of natural language meanings. That is, we question the assumption that semantic completeness (of, e.g., propositions) or incompleteness (of, e.g., predicates) exactly replicate the corresponding grammatical concepts (of, e.g., sentences and verbs, respectively). We argue that even if one gives up this assumption, it is still possible to keep the compositionality of the semantic interpretation of simple predicate/argument structures. In our opinion, compositionality presupposes (...) that we are able to compare arbitrary meanings in term of information content. This is why our proposal relies on an ‘intrinsically’ type free algebraic semantic theory. The basic entities in our models are neither individuals, nor eventualities, nor their properties, but ‘pieces of evidence’ for believing in the ‘truth’ or ‘existence’ or ‘identity’ of any kind of phenomenon. Our formal language contains a single binary non-associative constructor used for creating structured complex terms representing arbitrary phenomena. We give a finite Hilbert-style axiomatisation and a decision algorithm for the entailment problem of the suggested system. (shrink)

We develop the general theory of topometric spaces, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric. Spaces of global and local types in continuous logic are the motivating examples for the study of such spaces. In particular, we develop Cantor-Bendixson analysis of topometric spaces, which can serve as a basis for the study of local stability (extending the ad hoc development in Ben Yaacov I and Usvyatsov A, Continuous first order logic and local stability. Trans Am Math Soc, (...) in press), as well as of global ${\aleph_0}$ -stability. We conclude with a study of perturbation systems (see Ben Yaacov I, On perturbations of continuous structures, submitted) in the formalism of topometric spaces. In particular, we show how the abstract development applies to ${\aleph_0}$ -stability up to perturbation. (shrink)

Structural representations are likely the most talked about representational posits in the contemporary debate over cognitive representations. Indeed, the debate surrounding them is so vast virtually every claim about them has been made. Some, for instance, claimed structural representations are different from indicators. Others argued they are the same. Some claimed structural representations mesh perfectly with mechanistic explanations, others argued they can’t in principle mash. Some claimed structural representations are central to predictive processing accounts of cognition, others rebuked predictive processing (...) networks are blissfully structural representation free. And so forth. Here, I suggest this confusing state of affairs is due to the fact that the term “structural representations” is applied to a number of distinct conceptions of representations. In this paper, I distinguish four such conceptions, argue that these four conceptions are actually distinct, and then show that such a fourfold distinction can be used to clarify some of the most pressing questions concerning structural representations and their role in cognitive theorizing, making these questions more easily answerable. (shrink)

RESUMEN Esta investigación aborda la validez del espacio público como auspiciador de la participación política, centrándose en las diversas formas de apropiación del espacio que pueden fomentar dicha participación. El objetivo principal consiste en demostrar las posibilidades de acción política de las y los ciudadanos al expresar su desacuerdo a través de distintos procesos de apropiación del espacio público: la apropiación por dominación, por rebelión, la apropiación vandálica y artística. Se sostiene que la legitimidad de un sistema de gobierno puede (...) cuestionarse o debilitarse según la actuación pública del cuerpo ciudadano contra el Estado o la entidad que ejerce la soberanía sobre el espacio. El análisis se llevará a cabo desde la filosofía política de la vertiente disociativa y el realismo político a través de los conceptos de conflicto, soberanía y desacuerdo. ABSTRACT This research addresses the validity of public space as a promoter of political participation, focusing on the various forms of appropriation of space that can foster said participation. The main objective is to demonstrate the possibilities of political action of citizens by expressing their disagreement through different processes of appropriation of public space: appropriation by domination, appropriation by rebellion, vandalic, and artistic appropriation. It will be argued that the legitimacy of a government system can be questioned or weakened depending on the public actions of the citizen body against the State or the entity that exercises sovereignty over space. The analysis will be carried out from the political philosophy of the dissociative aspect and political realism, through the concepts of conflict, sovereignty, and disagreement. (shrink)

Inspired by a construction of the Tsirelson space , we prove a general theorem for omitting countably many positive formulas in normed spaces. This theorem can be used in functional analysis as a tool to guarantee the existence of complicated normed spaces without having to construct them. The proof of this result is based on the notion of approximate truth and on a study of the relationship between approximate truth and convergence in normed spaces. We illustrate the power of (...) this result with an application to functional analysis. (shrink)

This article investigates the construction of urban/rural binary distinctions in 18th - and 19th-century social scientific literature, and in particular in the writings of the statistical societies in England. The 18th-century writers were primarily concerned with the spread of luxury, vice and effeminacy among the upper social strata in large cities. Later on, statisticians began to focus on moral hazards among the urban working poor. These writings are significant in several respects: they contributed to the spatial mapping of moral character, (...) played a role in the development of quantitative social scientific techniques, and foreshadowed later sociological debates over the nature and consequences of social evolution from simpler to more complex societies. (shrink)

What is the relationship between space and time in the human mind? Studies in adults show an asymmetric relationship between mental representations of these basic dimensions of experience: Representations of time depend on space more than representations of space depend on time. Here we investigated the relationship between space and time in the developing mind. Native Greek‐speaking children watched movies of two animals traveling along parallel paths for different distances or durations and judged the spatial and (...) temporal aspects of these events (e.g., Which animal went for a longer distance, or a longer time?). Results showed a reliable cross‐dimensional asymmetry. For the same stimuli, spatial information influenced temporal judgments more than temporal information influenced spatial judgments. This pattern was robust to variations in the age of the participants and the type of linguistic framing used to elicit responses. This finding demonstrates a continuity between space‐time representations in children and adults, and informs theories of analog magnitude representation. (shrink)

In this paper I argue that empty space can be heard. This position contrasts with the generally held view that the only things that can be heard are sounds, their properties, echoes, and perhaps sound sources. Specifically, I suggest that when sounds reverberate in enclosed environments we auditorily represent the volume of space surrounding us. Clearly, we can learn the approximate size of an enclosed space through hearing a sound reverberate within it, and so any account that (...) denies that we hear empty space must instead show how beliefs about volumes of space can be derived indirectly from what is heard. That is, if space is not auditorily represented when we hear sounds reverberate, what is? I consider whether hearing reverberation can be thought of as hearing a distinct sound, hearing echoes, or hearing a property of a sound. I argue that experiences of reverberation cannot be reduced to the perception of any of these types and that therefore empty space is represented in auditory perceptual content. In the final section I outline two ways in which space might be represented. (shrink)

0. The ancient and honorable role of philosophy as a servant to the learning, development and use of scientific knowledge, though sadly underdeveloped since Grassmann, has been re-emerging from within the particular science of mathematics due to the latter's internal need; making this relationship more explicit (as well as further investigating the reasons for the decline) will, it is hoped, help to germinate the seeds of a brighter future for philosophy as well as help to guide the much wider learning (...) of mathematics and hence of all the sciences. 1. The unity of interacting opposites "space vs. quantity", with the accompanying "general vs. particular" and the resulting division of variable quantity into the interacting opposites "extensive vs. intensive", is susceptible, with the aid of categories, functors, and natural transformations, of a formulation which is on the one hand precise enough to admit proved theorems and considerable technical development and yet is on the other hand general enough to admit incorporation of almost any specialized hypothesis. Readers armed with the mathematical definitions of basic category theory should be able to translate the discussion in this section into symbols and diagrams for calculations. 2. The role of space as an arena for quantitative "becoming" underlies the qualitative transformation of a spatial category into a homotopy category, on which extensive and intensive quantities reappear as homology and cohomology. 3. The understanding of an object in a spatial category can be approached through definite Moore-Postnikov levels; each of these levels constitutes a mathematically precise "unity and identity of opposites", and their ensemble bears features strongly reminiscent of Hegel's Science of Logic. This resemblance suggests many mathematical and philosophical problems which now seem susceptible of exact solution. (shrink)

We investigate the use of coalgebra to represent quantum systems, thus providing a basis for the use of coalgebraic methods in quantum information and computation. Coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. (...) We use this structure to give a universal semantics for quantum systems based on a final coalgebra construction. We characterize equality in this semantics as projective equivalence. We also define an analogous indexed structure for Chu spaces, and use this to obtain a novel categorical description of the category of Chu spaces. We use the indexed structures of Chu spaces and coalgebras over a common base to define a truncation functor from coalgebras to Chu spaces. This truncation functor is used to lift the full and faithful representation of the groupoid of physical symmetries on Hilbert spaces into Chu spaces, obtained in our previous work, to the coalgebraic semantics. (shrink)

We present a formal analysis of Douglas Hofstadter’s concept of superrationality. We start by defining superrationally justifiable actions, and study them in symmetric games. We then model the beliefs of the players, in a way that leads them to different choices than the usual assumption of rationality by restricting the range of conceivable choices. These beliefs are captured in the formal notion of type drawn from epistemic game theory. The theory of coalgebras is used to frame type spaces (...) and to account for the existence of some of them. We find conditions that guarantee superrational outcomes. (shrink)

Several reaction time (RT) studies report faster responses when responses to temporal information are arranged in a spatially congruent manner than when this arrangement is incongruent. The resulting space–time congruency effect is commonly attributed to a culturally salient localization of temporal information along a mental timeline (e.g., a mental timeline that runs from left to right). The present study aims to provide a compilation of the published RT studies on this time–space association in order to estimate the size (...) of its effect and the extent of potential publication bias in this field of research. In this meta-analysis, three types of task are distinguished due to hitherto existing empirical findings. These findings suggest that the extent to which time is made relevant to the experimental task has a systematic impact on whether or not the mental timeline is activated. The results of this meta-analysis corroborate these considerations: First, experiments that make time a task-relevant dimension have a mean effect size of d = 0.46. Second, in experiments in which time is task irrelevant, the effect size does not significantly deviate from zero. Third, temporal priming studies have a surprisingly high mean effect size of d = 0.47, which, however, should be adjusted to d = 0.36 due to publication bias. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large – it is the space of applicable Turing machines. As a result, mappings that pivot on such attenuated regularities cannot, in general, be found by brute-force search. The class of problems that present such mappings we call the class of “type-2 problems.” (...) Type-1 problems, by contrast, present tractable problems of search insofar as the relevant regularities can be found by sampling the input data as originally coded. Type-2 problems, we suggest, present neither rare nor pathological cases. They are rife in biologically realistic settings and in domains ranging from simple animat behaviors to language acquisition. Not only are such problems rife – they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding biases so as to reduce specific type-2 problems to type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy – namely, the maximal exploitation of states of representation already achieved by prior, simpler learning so as to reduce the amount of subsequent computational search. Such exploitation both characterizes and helps make unitary sense of a diverse range of mechanisms. These include simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription”. In addition, the most distinctive features of human cognition – language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large type-2 problems. they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right (...) set of recoding biases so as to reduce specific type-2 problems to (tractable) type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general (not task-specific) strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy representational redescription language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

Urban spaces require increasing their attractiveness by exploring the social and spatial implications of new lifestyles. Broad civic knowledge is the basis for placemaking to shape user-centred and inclusive spaces of everyday life. Gathering information on the sense of the place is crucial to finding out and understanding the place-related identity of its users to make the place more appealing and usable. The most popular survey tool is a questionnaire constructed as a series of questions and used for collecting information (...) about a population’s attributes, attitudes or actions. Administered in person or online, questionnaire surveys may provide broad coverage of urban communities – however, they require significantly large human resources to carry out. The survey based on personal contact with the respondent may limit time allocated to its implementation, thus affecting the sample selection. Also, the researcher’s involvement in the questionnaire-filling process can be problematic if he or she reveals the topic of interest and if the sequencing of questionnaire themes influences responses. Similarly, an online questionnaire may not reach some potential respondents due to their reduced access to the internet etc. These limitations may affect the results’ reliability. Taking into account the above-mentioned aspects, the idea of this chapter is to present selected types of questionnaires (textual, visual, in-VR and survey gamification). The main aim is to discuss these questionnaires in the context of their main advantages and disadvantages resulting from the specifics of a type and a form of survey (in-depth and online) to facilitate their use in the process of data collection in placemaking research. The results show that the variety of types of questionnaires, as well as the form of the conducted survey, allow their better selection to the specificity of the community, increasing the place-related identity, thus may provide a more reliable and complete set of information possible to be used in placemaking. (shrink)

Already in 1835 Lobachevski entertained the possibility of multiple geometries of the same type playing a role. This idea of rival geometries has reappeared from time to time but had yet to become a key idea in space-time philosophy prior to Brown's _Physical Relativity_. Such ideas are emphasized towards the end of Brown's book, which I suggest as the interpretive key. A crucial difference between Brown's constructivist approach to space-time theory and orthodox "space-time realism" pertains to (...) modal scope. Constructivism takes a broad modal scope in applying to all local classical field theories---modal cosmopolitanism, one might say, including theories with multiple geometries. By contrast the orthodox view is modally provincial in assuming that there exists a _unique_ geometry, as the familiar theories have. These theories serve as the "canon" for the orthodox view. Their historical roles also suggest a Whiggish story of inevitable progress. Physics literature after c. 1920 is relevant to orthodoxy primarily as commentary on the canon, which closed in the 1910s. The orthodox view explains the spatio-temporal behavior of matter in terms of the manifestation of the real geometry of space-time, an explanation works fairly well within the canon. The orthodox view, Whiggish history, and the canon have a symbiotic relationship. If one happens to philosophize about a theory outside the canon, space-time realism sheds little light on the spatio-temporal behavior of matter. Worse, it gives the _wrong_ answer when applied to an example arguably _within_ the canon, a sector of Special Relativity, namely, _massive_ scalar gravity with universal coupling. Which is the true geometry---the flat metric from the Poincare' symmetry group, the conformally flat metric exhibited by material rods and clocks, or both---or is the question faulty? How does space-time realism explain the fact that all matter fields see the same curved geometry, when so many ways to mix and match exist? Constructivist attention to dynamical details is vindicated; geometrical shortcuts can disappoint. The more exhaustive exploration of relativistic field theories in particle physics, especially massive theories, is a largely untapped resource for space-time philosophy. (shrink)

What is consciousness? Some philosophers have contended that ‘qualia’, or an experiential medium from which consciousness is derived, exists as a fundamental component of reality. Whitehead, for example, described the universe as being comprised of ‘occasions of experience’. To examine this possibility scientifically, the very nature of physical reality must be re-examined. We must come to terms with the physics of space-time -- as is described by Einstein's general theory of relativity -- and its relation to the fundamental theory (...) of matter -- as described by quantum theory. This leads us to employ a new physics of objective reduction: OR which appeals to a form of ‘quantum gravity’ to provide a useful description of fundamental processes at the quantum/classical borderline . Within the OR scheme, we consider that consciousness occurs if an appropriately organized system is able to develop and maintain quantum coherent superposition until a specific ‘objective’ criterion is reached; the coherent system then self-reduces . We contend that this type of objective self-collapse introduces non-computability, an essential feature of consciousness. OR is taken as an instantaneous event -- the climax of a self-organizing process in fundamental space-time -- and a candidate for a conscious Whitehead-like ‘occasion’ of experience. How could an OR process occur in the brain, be coupled to neural activities, and account for other features of consciousness? We nominate an OR process with the requisite characteristics to be occurring in cytoskeletal microtubules within the brain's neurons. (shrink)

2Public space is an old habit. The words public space are deceptive; when I hear the words, when I say the words, I’m forced to have an image of a physical place I can point to and be in. I should be thinking only of a condition; but, instead, I imagine an architectural type, and I think of a piazza, or a town square, or a city commons. Public space, I assume, without thinking about it, is (...) a place where the public gathers. The public gathers in two kinds of spaces. The first is a space that is public, a place where the public gathers because it has a right to the place; the second is a space that is made public, a place where the public gathers precisely because it doesn’t have the right—a place made public by force.3In the space that is public, the public whose space this is has agreed to be a public; these are people “in the form of the city,” they are public when they act “in the name of the city.” They “own” the city only in quotes. The establishment of certain space in the city as “public” is a reminder, a warning, that the rest of the city isn’t public. New York doesn’t belong to us, and neither does Paris, and neither does Des Moines. Setting up a public space means setting aside a public space. Public space is a place in the middle of the city but isolated from the city. Public space is the piazza, an open space separated from the closure of alleys and dead ends; public space is the piazza, a space in the light, away from the plots and conspiracies in dark smokey rooms. Vit Acconci’s latest show, entitled “Public Places,” was held in 1988 at the Museum of Modern Art, New York. He is currently at work on a park in Detroit, a pedestrian mall in Baltimore, and a housing project in Regensburg, Germany. (shrink)

In connection with the "Philosophy of Science" research program conducted by the Deutsche Forschungsgemeinschaft a colloquium was held in Munich from 18th to 20th May 1919. This covered basic structures of physical theories, the main emphasis being on the interrelation of space, time and mechanics. The present volume contains contributions and the results of the discussions. The papers are given here in the same order of presentation as at the meeting. The development of these "basic structures of physical theories" (...) involved diverging trends arising from different starting points in philosophy and physics. In order to obtain a clear comparison between these schools of thought, it was appropriate to concentrate discussion on geometry and chronology as the common foundation of classical and quantum mechanics. As a rather simple and "Tell prepared field of study, geochronometry seemed suited to analysing these mutually exclusive positions. vii D. Mayr and G. Sussmann (eds.), Space, Time, and Mechanics, vii. Copyright © 1983 by D. Reidel Publishing Company. ACKNOWLEDGEMENT The editors gratefully appreciate the sponsorship of the Deutsche Forschungsgemeinschaft and the cooperation of the authors and publisher. It is also a pleasure to thank Frau M.-L. Grohmann and Frau I. Thies for their organisational and especially Frau B. Grund for typing and clerical work. D. MAYR G. SUSSMANN 1982 University of Munich viii INTRODUCTION The distinct positions present at the symposium may be roughly divided into three schools that differ in their philosophical interpretation of physics and their meta-... ~. (shrink)

We examine two different descriptions of the behavioral functions of the hippocampal system. One emphasizes spatially organized behaviors, especially those using cognitive maps. The other emphasizes memory, particularly working memory, a short-term memory that requires iexible stimulus-response associations and is highly susceptible to interference. The predictive value of the spatial and memory descriptions were evaluated by testing rats with damage to the hippocampal system in a series of experiments, independently manipulating the spatial and memory characteristics of a behavioral task. No (...) dissociations were found when the spatial characteristics of the stimuli to be remembered were changed; lesions produced a similar deficit in both spatial and nonspatial test procedures, indicating that the hippocampus was similarly involved regardless of the spatial nature of the task. In contrast, a marked dissociation was found when the memory requirements were altered. Rats with lesions were able to perform accurately in tasks that could be solved exclusively on the basis of reference memory. They performed at chance levels and showed no signs of recovery even with extensive postoperative training in tasks that required working memory. In one experiment all the characteristics of the reference memory and working memory procedures were identical except the type of memory required. Consequently, the behavioral dissociation cannot be explained by differences in attention, motivation, response inhibition, or the type of stimuli to be remembered. As a result of these experiments we propose that the hippocampus is selectively involved in behaviors that require working memory, irrespective of the type of material that is to be processed by that memory. (shrink)

This paper takes up the themes in the articles and examines not only the environmental changes that are taking place in relation to universities, but also the dynamics of their organizational implications. It argues that there are parallels between managerially and academic professionalism in that both deny context. Arguing for a context-sensitivity that is not dependant, issues of space and governance become important in order to understand forms of knowledge and the relationship between the contexts of production and the (...) contents of what is produced. Universities have different capacities to play at the game of scales and they are judged according to abstract indicators that provide little or no opportunity for learning. Instead of examining these relations, expertise is assumed to be spatial, whilst universities transform themselves in the slipstream of imagined futures as if they were separate from the present and past. Understanding is lost in the process and so too are the opportunities to adequately examine the differences in types of knowledge's that are produced for sustainable futures in contemporary societies. (shrink)

We study invariant types in NIP theories. Amongst other things: we prove a definable version of the [Formula: see text]-theorem in theories of small or medium directionality; we construct a canonical retraction from the space of [Formula: see text]-invariant types to that of [Formula: see text]-finitely satisfiable types; we show some amalgamation results for invariant types and list a number of open questions.

We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures, as opposed to the restricted class of orthogonal projection-valued measures used in the original theorem. The advantage of this method is that it works for two-dimensional quantum systems and even for vector spaces over rational fields—settings where the standard theorem fails. Furthermore, unlike the method necessary for proving the original result, the present one is rather elementary. In the case of a qubit, (...) we investigate similar results for frame functions defined upon various restricted classes of POVMs. For the so-called trine measurements, the standard quantum probability rule is again recovered. (shrink)

The article examines space as a hierarchy of differences and as a basic phenomenon of the world, while calling into question the existence of time as a natural process and basis for human experience. It analyses the functionality of time in connection with various types of individual spaces and reveals the correlativity of space and consciousness.

Video game spaces have vastly expanded the built environment, offering new worlds to explore and inhabit. Like buildings, cities, and gardens before them, these virtual environments express meaning and communicate ideas and affects through the spatial experiences they afford. Drawing on the emerging field of embodied cognition, this book explores the dynamic interplay between mind, body, and environment that sits at the heart of spatial communication. To capture the wide diversity of forms that spatial expression can take, the book builds (...) a comparative analysis of twelve video games across four types of space, spanning ones designed for exploration and inhabitation, kinetic enjoyment, enacting a situated role, and enhancing perception. Together, these diverse virtual environments suggest the many ways that video games enhance and extend our embodied lives."--Publisher's website. (shrink)

We distinguish three qualitatively different types of uncertainty—ethical, option and state space uncertainty—that are distinct from state uncertainty, the empirical uncertainty that is typically measured by a probability function on states of the world. Ethical uncertainty arises if the agent cannot assign precise utilities to consequences. Option uncertainty arises when the agent does not know what precise consequence an act has at every state. Finally, state space uncertainty exists when the agent is unsure how to construct an exhaustive (...) state space. These types of uncertainty are characterised along three dimensions—nature, object and severity—and the relationship between them is examined. We conclude that these different forms of uncertainty cannot be reduced to empirical uncertainty about the state of the world without inducing an increase in its severity. (shrink)