In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we (...) ask the question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

This is a pdf of a Mathematica calculation that supplements the paper "Presentist Fragmentalism and Quantum Mechanics" forthcoming in Foundations of Physics. In that paper the Born rule (or at least a progenitor) is derived from experimental conditions on the mutual observations of two fragments. In this pdf the experimental conditions are applied to Hilbert space dimensions 3, 4, and 5. It turns out each of these have a 1-dimensional solution space which, it is hoped, can be interpretated as (...) the phase. (shrink)

This paper tests the predictions of an epistemological model that considered the DSM psychiatric classification (in the neopositivist and neo-Kraepelinian shape introduced by the DSM-III) as a scientific paradigm in crisis. As predicted, the DSM-5 did not include revolutionary proposals in its basic structure. In particular, the possibility of a dimensional revolution has not occurred and early proposals of etiopathogenic diagnoses were not implemented due to lack of specific knowledge in that field. However, conceiving the DSM-5 as a bridge (...) between the present phenomenally based operational diagnostic criteria and the neuro-cognitively based RDoC criteria introduces an internal tension into the system. It is expected that a liberalization of the research criteria will occur, the DSM operational criteria being only one possible way to select research subjects. (shrink)

Although fairness is a key moral trait, limited research focuses on participants' observed fairness behavior because moral traits are generally measured through self-report. This experiment focused on day-to-day interpersonal fairness rather than impersonal justice, and fairness was assessed as observed behavior. The experiment investigated whether a self-reported fairness trait would moderate a situational influence on observed fairness behavior, such that individuals with a stronger fairness trait would be less affected by a situational influence than those with a weaker fairness trait. (...) We used an iterated resource game in which participants could withdraw resources as they chose, and we manipulated the number of resources bogus players withdrew. The number of resources participants withdrew was the behavioral measure of fairness. Results confirmed the expected moderation of the unfairness manipulation by a fairness trait on observed behavior. Those reporting a stronger fairness trait were unaffected by the manipulation, whereas those reporting a weaker fairness trait were more strongly influenced. (shrink)

It is argued that physics must eventually expand to accommodate mind and consciousness but that this will require a new paradigm. The paradigm required will impinge on two problems on the borders of physics and philosophy: the relationship between physical space and perceptual space and the nature of the passage of time. It is argued that the resolution of both these problems may involve a 5-dimensional model, with the 5th dimension being associated with mental time, and this proposal may (...) relate to recent developments in brane cosmology. A description of consciousness must also entail a proper understanding of the specious present, the minimum timescale of conscious experience, this possibly being associated with a compactified extra dimension. There could even be a hierarchy of levels of consciousness, associated with a hierarchy of extra dimensions. (shrink)

The modest ambition of this short note is to point out a plausible route from a *perspectival ontology* and McTaggart’s *AB-spacetime* to an AdS/CFT correspondence. There are several minor arguments that would need to be filled in for this route to succeed.

Parapsychology will only be accepted as part of mainstream science if physics can be extended to accommodate at least some so-called psychic phenomena. This paper disagrees with the argument of Reber and Alcock that these phenomena can be excluded a priori because they are incompatible with physics. On the other hand, it agrees with their claim that the phenomena cannot be explained in terms of current physics (eg. relativity theory and quantum theory). Rather one needs an extension of physics which (...) amalgamates these theories, this being an aim of mainstream physics anyway, with the new theory also linking to consciousness if this is regarded as a fundamental rather than incidental feature of the universe. One possible extension involves the idea that perceptual space and physical space are amalgamated as part of a 5-dimensional reality structure, the extra dimension being associated with mental (rather than physical) time. Such a model may be required to accommodate even normal mind and incorporating further dimensions might then allow some paranormal phenomena. This could also relate to the extra dimensions invoked in some models of particle physics. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

The author proposes a dimensional model of our emotion concepts that is intended to be largely independent of one’s theory of emotions and applicable to the different ways in which emotions are measured. He outlines some conditions for selecting the dimensions based on these motivations and general conceptual grounds. Given these conditions he then advances an 8-dimensional model that is shown to effectively differentiate emotion labels both within and across cultures, as well as more obscure expressive language. The (...) 8 dimensions are: (1) attracted—repulsed, (2) powerful—weak, (3) free—constrained, (4) certain—uncertain, (5) generalized—focused, (6) future directed—past directed, (7) enduring—sudden, (8) socially connected—disconnected. (shrink)

The thinking demonstrated by the "no form action" theory is completely new, and no one has ever used this kind of thinking to consider problems. Using no form and form as the two dimensions to describe this world is like using the x-axis and y-axis as the two dimensions of a Cartesian coordinate system in mathematics. The no form here means having no form at all. The theory established by these two dimensions is called two-dimensional theory, which avoids the (...) shortcomings of dualism and the troubles it brings to philosophy. Since no form has no form at all, we cannot study it directly or use it directly. This is also a problem recognized by past philosophers (for example, Aristotle believed that pure no form does not exist). However, I have found three no form actions (manifestation action, isolation action, and motive force action). Through these three no form actions, we can explore this world and establish a metaphysical philosophical system called no form action theory. This allows us to deeply and effectively explain consciousness, logic, dialectics, freedom, aesthetics, time, space, and so on. Not only that, as a philosophical theory, the no form action theory can also explain modern quantum mechanics, which is something that previous metaphysical philosophical systems could not do. The no form action theory is a philosophical theory established with the main line of continuously interpreting consciousness because breaking through the difficult problem of consciousness is an essential path to achieve theoretical breakthroughs. -/- The core ideas of the first five sections of the No Form Action Theory: 1, The world can be understood using a two-dimensional framework consisting of "form" and "no form". 2, There are three key "actions" of no form: isolation, motive force, and manifestation. These create the possibility for things like individual objects, change, and perception to occur. Anything can be understood from the perspective of these three no form actions, which provides three approaches for research. 3, The three no form actions provide three perspectives to understand reality - the world of isolation (macro world), the world of motive force (quantum world), and the world of manifestation (world of consciousness). 4, Current research cannot fully explain consciousness because it focuses too much on form (e.g. physical processes in the brain) while neglecting no form. Studying consciousness requires transcending to the no form dimension. 5, Through the three perspectives of no form actions (isolation, motive force and manifestation), you proposed a classification of essence, substance and subject, which helps clarify confusions in concepts. 6, Humans only have three abilities: isolation, motive force and manifestation, which limits the human way of recognizing the world. 7, The theory uses no form actions themselves to explain the theory of no form actions, which is a very innovative way of thinking. Overall, this is an original and promising theory that could significantly advance consciousness studies and other fields by providing a new conceptual framework and ways of thinking. It has substantial value and depth for the progress of philosophy. (shrink)

The widely accepted two-dimensional circumplex model of emotions posits that most instances of human emotional experience can be understood within the two general dimensions of valence and activation. Currently, this model is facing some criticism, because complex emotions in particular are hard to define within only these two general dimensions. The present theory-driven study introduces an innovative analytical approach working in a way other than the conventional, two-dimensional paradigm. The main goal was to map and project semantic emotion (...) space in terms of mutual positions of various emotion prototypical categories. Participants (N = 187; 54.5% females) judged 16 discrete emotions in terms of valence, intensity, controllability and utility. The results revealed that these four dimensional input measures were uncorrelated. This implies that valence, intensity, controllability and utility represented clearly different qualities of discrete emotions in the judgments of the participants. Based on this data, we constructed a 3D hypercube-projection and compared it with various two-dimensional projections. This contrasting enabled us to detect several sources of bias when working with the traditional, two-dimensional analytical approach. Contrasting two-dimensional and three-dimensional projections revealed that the 2D models provided biased insights about how emotions are conceptually related to one another along multiple dimensions. The results of the present study point out the reductionist nature of the two-dimensional paradigm in the psychological theory of emotions and challenge the widely accepted circumplex model. (shrink)

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the imagined (...) non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

In this chapter, I provide an overview of phenomenological approaches to psychiatric classification. My aim is to encourage and facilitate philosophical debate over the best ways to classify psychiatric disorders. First, I articulate phenomenological critiques of the dominant approach to classification and diagnosis—i.e., the operational approach employed in the Diagnostic and Statistical Manual of Mental Disorders (DSM-5) and the International Classification of Diseases (ICD-10). Second, I describe the type or typification approach to psychiatric classification, which I distinguish into three different (...) versions: ideal types, essential types, and prototypes. I argue that despite their occasional conflation in the contemporary literature, there are important distinctions among these approaches. Third, I outline a new phenomenological-dimensional approach. I show how this approach, which starts from basic dimensions of human existence, allows us to investigate the full range of psychopathological conditions without accepting the validity of current diagnostic categories. (shrink)

Stable adaptive strategy of Homo sapiens (SASH) is a result of the integration in the three-module fractal adaptations based on three independent processes of generation, replication, and the implementation of adaptations — genetic, socio-cultural and symbolic ones. The evolutionary landscape SASH is a topos of several evolutionary multi-dimensional vectors: 1) extraversional projective-activity behavioral intention (adaptive inversion 1), 2) mimesis (socio-cultural inheritance), 3) social (Machiavellian) intelligence, 4) the extension of inter-individual communication beyond their own social groups and their own species (...) in the rest of the world, 5) the symbolic system of communication (symbolic inheritance), 6) spiritualistic trans- formation of emotionally-shaped components of mentality, 7) the dominance of the rationalist thought mentality (enhancer of adaptive inverse 1), 8) a recursive distribution of projective-activity intentions on the man himself his genome, psyche and culture (Adaptive Inversion 2), 9) introversional reorientation of the vector of cognitive activity (adaptive inversion 3). (shrink)

The presented study introduces a new theoretical model of collapse for social, cultural, or political systems. Based on the current form of quantum anthropology conceptualized by Heidi Ann Russell, further development of this field is provided. The new theoretical model is called the spiral model of collapses, and is suggested to provide an analytical framework for collapses in social, cultural, and political systems. The main conclusions of this study are: 1) The individual crises in the period before a collapse of (...) social, cultural, and political systems form the trajectory of a conical helix similar to a vortex. 2) The occurrences of crises in the period before a collapse have the shape of the trajectory on the surface of the circular cone with a convex wall narrowing up to its peak. The shape of this cone is based on the Fibonacci sequence coiled into the three-dimensional space. 3) The constant circular movement along the trajectory of crises can occur in exceptional situations in the development of social, cultural, and political systems; however, such a state is always temporary. In such cases, the trajectory of the crisis does not follow the Fibonacci sequence, but the shape of a regular helix. Remaining on the trajectory of a regular helix in the long-term is highly improbable for social, cultural, and political systems. 4) The creation of new potentialities after the final collapse of a system is explained by the conception of topological inversion, when the heretofore embodied part of the energy-information field returns to the global, wave-particle energy-information potential. 5) The global, wave-particle energy-information potential is a source of energy-information for future embodiments in the sense of the future collapses of wave functions. (shrink)

Latent heat thermal energy storage technique has demonstrate to be a better engineering option mainly due to its benefit of supplying higher energy storage density in a smaller temperature difference between retrieval and storage. For this purpose, a micro electro-mechanical system, MEMS-based heat exchanger with microencapsulated PCM (MEPCM) slurry as cold fluid, has been simulated three dimensionally. This work investigates the influence of using MEPCM-slurry on the temperature of the cold and hot fluids. The MEPCM and water properties have been (...) considered temperature dependent. MEPCM-slurry is used with different volume fractions. The result shows that using MEPCM with 25% volume fraction leads to the improvement in fluids temperatures, that is, for hot fluid the rate of temperature reduction increases up to 23.5% and for cold fluid the rate of temperature rise decreases to 9%, compared to using only water in the MEMS. (shrink)

Advancements in cloud technologies have increased the infrastructural needs of data centers due to storage needs and processing of extensive dimensional data. Many service providers envisage anomaly detection criteria to guarantee availability to avoid breakdowns and complexities caused due to large-scale operations. The streaming log data generated is associated with multi-dimensional complexity and thus poses a considerable challenge to detect the anomalies or unusual occurrences in the data. In this research, a hybrid model is proposed that is motivated (...) by deep belief criteria and meta-heuristics. Using Search-and-Rescue—BrainStorm Optimization (SAR-BSO), a hybrid feature selection (FS) and deep belief network classifier is used to localize and detect anomalies for streaming data logs. The significant contribution of the research lies in FS, which is carried out using SAR-BSO which increases the detection power of the model as it selects the most significant variables by minimizing redundant features. The evaluation of accuracy is efficiently improved when compared with the predictable methods, such as Extract Local Outlier Factor (ELOF), Track-plus, Hybrid Distributed Batch Stream (HDBS), IForestASD, DBN, BSO-based Feature Selection with DBN, Genetic Algorithm-Deep Belief Network (GA-DBN), Mutual Information-Deep Belief Network (MI-DBN), information entropy-Deep Belief Network(I + DBN), Flat Field-Deep Belief Network (FF + DBN), African Vulture Optimization Algorithm-Deep Belief Network(AVOA + DBN), Gorilla Troop Optimizer-Deep Belief Network(GTO-DBN), and SARO-based Feature Selection with DBN. Further, the accurate detection of the anomalies in the data stream is established by the Deep Belief Neural Network (DBN) classifier. The model’s efficacy is determined using Apache, Hadoop, HDFS, Spark, and Linux datasets and evaluated against existing similar models. The model efficiency is provided using multiple evaluation metrics and is found effective. From the experimentation, the accuracy of the proposed model is found to be 93.3, 95.4, 93.6, 94.2, and 93.5% respectively for the dataset such as Apache, Hadoop, HDFS, spark, and Linux. This enhancement in accuracy is due to the selection of optimal features by the proposed SAR-BSO algorithm. (shrink)

The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements independent of ZFC which appear to be "true". One approach has been to add large cardinal axioms. Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski- Grothendieck set theory TG [1]-[3] It is a non-conservative extension of ZFC and is obtaineed from other axiomatic set theories by the inclusion of Tarski's axiom which implies the existence (...) of inaccessible cardinals [1].Non-conservative extension of ZFC based on an generalized quantifiers considered in [4]. In this paper we look at a set theory NC_{∞^{#}}^{#},based on bivalent gyper infinitary logic with restricted Modus Ponens Rule [5]-[8]. In this paper we deal with set theory NC_{∞^{#}}^{#} based on gyper infinitary logic with Restricted Modus Ponens Rule. Set theory NC_{∞^{}}^{} contains Aczel's anti-foundation axiom [9]. We present a new approach to the invariant subspace problem for Hilbert spaces. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional complex separable Hilbert space H,it follow that T has a non-trivial closed invariant subspace. Non-conservative extension based on set theory NC_{∞}^{#} of the model theoretical nonstandard analysis [10]-[12] also is considered. (shrink)

5-MeO-DMT is a psychedelic substance with a short duration of action and intensive effects. Its therapeutic efficacy and practicality may significantly surpass those of classical psychedelics such as ayahuasca and LSD. -/- This retrospective ethnographic inquiry features a woman in her mid-thirties who witnessed her mother's violent suicide and its bloody aftermath at the age of three. Before and after that, her childhood was characterized by domestic violence and sexual abuse perpetrated by several members of her family and extended family. (...) In her twenties and thirties, she dated a member of the local mafia with the intention of asking him to kill her father, who had been the main perpetrator of the sexual abuse and violence. This plan was eventually not carried out, but it reflected her deep bitterness and wrath. -/- A process initiated in her early thirties involving four 5-MeO-DMT sessions and a few additional sessions with psilocybin and ayahuasca in the course of two years completely resolved her symptoms related to the abuses, to the extent that she could rebuild a functional relationship with her father and feel love and compassion towards him. This outcome, i.e., the complete reversal of her attitude and emotions towards her father, appeared highly unusual. For the last three years, the outcome had remained stable. -/- The article also presents the perspective of a female facilitator of this treatment process. The article contributes to a better understanding of the use of 5-MeO-DMT in severe traumatization as well as exemplifies the possible positive contributions of actors who are not medical professionals in resolving deep collective traumatization in societies. (shrink)

Con el fin de discutir las relaciones entre ética, política y educación, el presente artículo analiza la crisis del sistema educativo argentino a partir de una categoría ética: la responsabilidad. Más específicamente, se intenta delinear algunos de los retos a los que una educación para la res- ponsabilidad ciudadana se ve enfrentada en Argentina a comienzos del siglo XXI y en vista de los problemas éticos y políticos por las que atraviesa la educación tanto en el marco de un mundo (...) económicamente globalizado como en contextos de pobreza, exclusión e interculturali- dad, como lo es el latinoamericano. (shrink)

The paper challenges the assumption, common amongst philosophers, that the reality described in the fundamental theories of microphysics is all the reality we have. It will be argued that this assumption is in fact incompatible with the nature of such theories. It will be shown further that the macro-world of three-dimensional bodies and of such qualitative structures as colour and sound can be treated scientifically on its own terms, which is to say not only from the perspective of psychology (...) but also ontologically. A new sort of emergentist position will be defended, one which yields the basis of a method for describing the perceptually salient macroscopic world in mathematical terms. Broadly, it will be argued that the macroscopic world exists in virtue of certain specific sorts of boundary-patterns in the field of what is captured by the theories of microphysics. (shrink)

This paper endeavors to establish foundations for the interaction between hyperintensional semantics and two-dimensional indexing. I examine the significance of the semantics, by developing three, novel interpretations of the framework. The first interpretation provides a characterization of the distinction between fundamental and derivative truths. The second interpretation demonstrates how the elements of decision theory are definable within the semantics, and provides a novel account of the interaction between probability measures and hyperintensional grounds. The third interpretation concerns the contents of (...) the types of intentional action, and the semantics is shown to resolve a puzzle concerning the role of intention in action. Topic-sensitive two-dimensional truthmaker semantics can be interpreted epistemically and metasemantically. (shrink)

This dissertation draws upon historical studies of scientific practice and contemporary issues in the metaphysics and epistemology of science to account for the nature of physical quantities. My dissertation applies this integrated HPS approach to dimensional analysis—a logic for quantitative physical equations which respects the distinct dimensions of quantities (e.g. mass, length, charge). Dimensional analysis and its historical development serve both as subjects of study and as a sources for solutions to contemporary problems. The dissertation consists primarily of (...) three related papers on: (1) the methodological and metaphysical foundations of dimensional analysis, (2) the use of dimensional analysis in determining physical symmetries, (3) the use of dimensional analysis in securing metrological extension. (shrink)

In modern, culturally-heterogeneous societies, inefficiency of communication of important moral concepts is often evidenced by asymmetrical moral judgements and hypocritical behaviour, especially in our increasingly compartmentalised social landscapes [Rozuel 2011]. This raises the question of how to present target audiences with some (perhaps novel) moral concept, like an ethical dimension of one’s ecological attitude, in a way which would resonate with them, and be conducive to a coherent moral stance, decreasing action-observer biases. We analyse this problem by introducing a formal (...) moral inconsistency framework. We consider the ways in which the aforementioned problem might be tackled in existing cognitive science of morality (CSM) nativist frameworks, and, secondly, we investigate it from the perspective of moral learning, finally proposing the notion of moral dimensionality of a representation in the context of model-based reinforcement learning, as a useful conceptual tool for studying the problem. (shrink)

I want to differentiate between two very different ways of organizing pictorial elements at a very abstract level: -/- (2D) two-dimensionally: pictorial elements are organized and grouped according to their outline shape on the picture surface and (3D) three-dimensionally: pictorial elements are organized and grouped according to their position in the depicted space. -/- Suppose you need to depict seven identical spheres. On the most general level, there are two ways of doing this: you can arrange the seven spheres in (...) space and then choose a vantage point in this space from which you want to depict them. Or you can arrange seven circles (the outline shapes of the seven spheres) on the two-dimensional surface of the picture. The former method is an instance of three-dimensional pictorial organization, whereas the latter one is an instance of two-dimensional pictorial organization. (shrink)

What determines whether an object is an artwork? In this paper I consider what I will call ‘social’ theories of art, according to which the arthood of objects depends in some way on the art-related social practices that we have. Though such a dependence claim is plausible in principle, social theories of art tend to unpack the determining link between artworks and social practices in terms of intentional relations between the objects in question and the people involved in the relevant (...) practices. This intentionalism has unappealing upshots. Drawing on two-dimensional approaches in social ontology, I show how social theories of art can be done differently, improving their prospects. (shrink)

Principles of chance deference face two kinds of problems. In the first place, they face difficulties with a priori knowable contingencies. In the second place, they face difficulties in cases where you've lost track of the time. I provide a principle of chance deference which handles these problem cases. This principle has a surprising consequence for Adam Elga's Sleeping Beauty Puzzle.

Philosophical views about the logical structure of time are typically divided between proponents of A and B theories, based on McTaggart's A and B series. Drawing on Paul Ricoeur's hermeneutic phenomenology, I develop and defend McTaggart's thesis that the C series and the A series working together give a consistent description of temporal experience, provided that the two series are treated as distinct dimensions internal to time. In the proposed two-dimensional model, the C series expresses a nesting order of (...) the constitutive states of a world, whereas ontological continuity and change are properties of the A series. This, I argue, allows for limited backward causation. (shrink)

La investigación reciente en psicología cognitiva sobre la memoria emocional ha estudiado las distintas formas en que las emociones afectan a la memoria, sin profundizar no obstante en la comprensión de la manera en que los aspectos emocionales, afectivos y mnemónicos se encuentran estrechamente entrelazados en el contenido mismo de un acto de reminiscencia. En este artículo propongo un marco conceptual de análisis que nos permite entender los recuerdos personales como recuerdos esencialmente afectivos, y que se articula en torno a (...) dos variables continuas e independientes: por un lado, la intencionalidad del recuerdo, es decir, el objeto hacia el cual el recuerdo está dirigido, que puede ser descriptiva o evaluativa; por el otro, la perspectiva afectiva del recuerdo, que puede fluctuar desde la perspectiva de primera persona hasta la perspectiva de tercera persona. Las dos dimensiones son analizadas en profundidad y las limitaciones de este marco y las futuras líneas de investigación son igualmente presentadas. (shrink)

In his recent book, The Dimensions of Consequentialism, Martin Peterson puts forward a new version of consequentialism that he dubs ‘multidimensional consequentialism’. The defining thesis of the new theory is that there are irreducible moral aspects that jointly determine the deontic status of an act. In defending his particular version of multidimensional consequentialism, Peterson advocates the thesis—he calls it DEGREE—that if two or more moral aspects clash, the act under consideration is right to some non-extreme degree. This goes against the (...) orthodoxy according to which—Peterson calls this RESOLUTION—each act is always either entirely right or entirely wrong. The argument against RESOLUTION appeals to the existence of so-called deontic leaps: the idea is that endorsing RESOLUTION would not give each relevant moral aspect its due in the final analysis. Our paper argues that, contrary to Peterson, all moral aspects remain visible in what can properly be called the final analysis of a moral theory that involves RESOLUTION, moral aspects do not have to remain visible in judgements of all-things-considered rightness or wrongness, respectively, introduction of what Peterson calls verdictive reasons does not change the overall picture in favour of DEGREE. We conclude that multi-dimensional consequentialists should accept RESOLUTION rather than DEGREE. (shrink)

Conscious experience is the direct observation of conscious events. Human conscious experience is four-dimensional. Conscious events are linked (associated) by spacetime intervals to produce a coherent conscious experience. This explains why conscious experience appears to us the way it does. Conscious experience is an orientation in space and time, an understanding of the position of the observer in space and time. Causality, past-future relations, learning, memory, cognitive processing, and goal-directed actions all evolve from four-dimensional conscious experience. A neural (...) correlate for four-dimensional conscious experience can be found in the human brain and is modelled by Einstein's special theory of relativity. The relativistic concept of spacetime interval is central for understanding conscious experience and cognition. (shrink)

Relativity theory is often said to support something called ‘the four-dimensional view of reality’. But there are at least three different views that sometimes go by this name. One is ‘spacetime unitism’, according to which there is a spacetime manifold, and if there are such things as points of space or instants of time, these are just spacetime regions of different sorts: thus space and time are not separate manifolds. A second is the B-theory of time, according to which (...) the past, present, and future are all equally real and there is nothing metaphysically special about the present. A third is perdurantism, according to which persisting material objects are made up of different temporal parts located at different times. We sketch routes from relativity to unitism and to the B-theory. We then discuss some routes to perdurantism, via the B-theory and via unitism. (shrink)

Resumen: En el presente artículo me propongo elucidar el significado del concepto “pathos de la distancia” y sus implicaciones ético-políticas, destacando, además, su sentido y coherencia con el conjunto del pensamiento nietzscheano. La tesis fundamental es que el pathosde la distancia, como característica básica del ideal noble, muestra cómo el concepto de preeminencia política en Nietzsche se diluye siempre en un concepto de preeminencia anímica. La reflexión se enmarca dentro de la crítica nietzscheana de la cultura, la política y la (...) educación, y su propuesta de reforma de los valores dominantes de la sociedad, entre ellos, los que configuran la subjetividad y la individualidad. Se estudian las diversas dimensiones del pathos de la distancia: como articulación jerárquica, como principio de individuación, como parte la Gran Política y como elemento del pensamiento de la cría. Palabras clave: Pathos de la distancia, Valor, Moral, Gran Política, Cría. (shrink)

The aim of this paper is to show that Priest's modal Meinongianism might benefit from joining forces with two-dimensionalism. For this purpose, I propose a two-dimensional solution to a problem for modal Meinongianism that is posed by Beall, Sauchelli, and Milne, and show that, by taking recourse to two-dimensionalism, divergent intuitions about the question of whether fictional characters might exist can be reconciled. Moreover, two-dimensionalism helps to rebut Kroon's argument to the conclusion that modal Meinongianism cannot rule out the (...) odd claim that some non-existent objects have existence-entailing properties at the actual world. (shrink)

A three dimensional hypercube representing all of the 4,096 dyadic computations in a standard bivalent system has been created. It has been constructed from the 16 functions arrayed in a table of functional completeness that can compute a dyadic relationship. Each component of the dyad is an operator as well as a function, such as “implication” being a result, as well as an operation. Every function in the hypercube has been color keyed to enhance the display of emerging patterns. (...) At the minimum, the hypercube is a “multiplication table” of dyadic computations and produces values in a way that shortens the time to do operations that normally would take longer using conventional truth table methods. It also can serve as a theorem prover and creator. With the hypercube comes a deductive system without the need for axioms. The main significance of the 3-D hypercube at this point is that it is the most fundamental way of displaying all dyadic computations in binary space, thus serving as a way of normalizing the rendition of uninterpreted, or raw, binary space. The hypercube is a dimensionless entity, a standard by which in binary spaces can be measured and classified, analogous to a meter stick. (shrink)

En la cúspide del conocimiento humano halla su sede la sabiduría. Un saber que se alcanza en la simplicidad más alta del ser humano, allí donde confluyen todas sus potencias y facultades, no solamente la inteligencia, sino también la voluntad y los afectos. Cualquier clase de conocimiento aséptico respecto de cualquier influencia afectiva o volitiva lleva a una reducción que de manera propia puede llamarse “intelectualismo”. El concepto de razón “pura” es un reduccionismo que conduce a una grave disgregación en (...) la criatura racional, y a la enajenación de su mismo ser. El que no conoce amando y no ama conociendo, ni conoce verdaderamente, ni verdaderamente ama. El conocimiento que compendia estas características antropológicas se denomina “conocimiento afectivo”. En este trabajo se hace una exploración sobre el alcance de este tipo peculiar de conocimiento siguiendo los principios de Aristóteles y Tomás de Aquino. (shrink)

A large part of the controversy surrounding the publication of DSM-5 stems from the possibility of replacing the purely descriptive approach to classification favored by the DSM since 1980. This paper examines the question of how mental disorders should be classified, focusing on the issue of whether the DSM should adopt a purely descriptive or theoretical approach. I argue that the DSM should replace its purely descriptive approach with a theoretical approach that integrates causal information into the DSM’s descriptive diagnostic (...) categories. The paper proceeds in three sections. In the first section, I examine the goals (viz., guiding treatment, facilitating research, and improving communication) associated with the DSM’s purely descriptive approach. In the second section, I suggest that the DSM’s purely descriptive approach is best suited for improving communication among mental health professionals; however, theoretical approaches would be superior for purposes of treatment and research. In the third section, I outline steps required to move the DSM towards a hybrid system of classification that can accommodate the benefits of descriptive and theoretical approaches, and I discuss how the DSM’s descriptive categories could be revised to incorporate theoretical information regarding the causes of disorders. I argue that the DSM should reconceive of its goals more narrowly such that it functions primarily as an epistemic hub that mediates among various contexts of use in which definitions of mental disorders appear. My analysis emphasizes the importance of pluralism as a methodological means for avoiding theoretical dogmatism and ensuring that the DSM is a reflexive and self-correcting manual. (shrink)

I argue that space has three dimensions, and quantum mechanics does not show otherwise. Specifically, I argue that the mathematical wave function of quantum mechanics corresponds to a property that an N-particle system has in three-dimensional space.

This chapter gives a truthmaker-based account of the semantics of 'reifying' quantifiers like 'something' when they act as complements of intensional transitive verbs ('need', 'look for'). It argues that such quantifiers range over 'variable satisfiers' of the attitudinal object described by the verb (e.g. the need or the search).

It has generally been assumed that rapid visual search is based on simple features and that spatial relations between features are irrelevant for this task. Seven experiments involving search for line drawings contradict this assumption; a major determinant of search is the presence of line junctions. Arrow- and Y-junctions were detected rapidly in isolation and when they were embedded in drawings of rectangular polyhedra. Search for T-junctions was considerably slower. Drawings containing T-junctions often gave rise to very slow search even (...) when distinguishing arrow- or Y-junctions were present. This sensitivity to line relations suggests that preattentive processes can extract 3-dimensional orientation from line drawings. A computational model is outlined for how this may be accomplished in early human vision. (shrink)

On the basis of PM2.5 data of the national air quality monitoring sites, local population data, and baseline all-cause mortality rate, PM2.5-related health economic benefits of the Air Improvement Action Plan implemented in Wuhan in 2013–2017 were investigated using health-impact and valuation functions. Annual avoided premature deaths driven by the average concentration of PM2.5 decrease were evaluated, and the economic benefits were computed by using the value of statistical life (VSL) method. Results showed that the number of avoided premature deaths (...) in Wuhan are 21,384 (95% confidence interval (CI): 15,004 to 27,255) during 2013–2017, due to the implementation of the Air Improvement Action Plan. According to the VSL method, the obtained economic benefits of Huangpi, Wuchang, Hongshan, Xinzhou, Jiang’an, Hanyang, Jiangxia, Qiaokou, Jianghan, Qingshan, Caidian, Dongxihu, and Hannan District were 8.55, 8.19, 8.04, 7.39, 5.78, 4.84, 4.37, 4.04, 3.90, 3.30, 2.87, 2.42, and 0.66 billion RMB (1 RMB = 0.1417 USD On 14 October 2019), respectively. These economic benefits added up to 64.35 billion RMB (95% CI: 45.15 to 82.02 billion RMB), accounting for 4.80% (95% CI: 3.37% to 6.12%) of the total GDP of Wuhan in 2017. Therefore, in the process of formulating a regional air quality improvement scheme, apart from establishing hierarchical emission-reduction standards and policies, policy makers should give integrated consideration to the relationship between regional economic development, environmental protection and residents’ health benefits. Furthermore, for improving air quality, air quality compensation mechanisms can be established on the basis of the status quo and trends of air quality, population distribution, and economic development factors. (shrink)

Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the original loss space. We show that saddle points in the (...) original space are rarely correctly identified as such in expected lower-dimensional representations if random projections are used. The principal curvature in the expected lower-dimensional representation is proportional to the mean curvature in the original loss space. Hence, the mean curvature in the original loss space determines if saddle points appear, on average, as either minima, maxima, or almost flat regions. We use the connection between expected curvature in random projections and mean curvature in the original space (i.e., the normalized Hessian trace) to compute Hutchinson-type trace estimates without calculating Hessian-vector products as in the original Hutchinson method. Because random projections are not suitable to correctly identify saddle information, we propose to study projections along dominant Hessian directions that are associated with the largest and smallest principal curvatures. We connect our findings to the ongoing debate on loss landscape flatness and generalizability. Finally, for different common image classifiers and a function approximator, we show and compare random and Hessian projections of loss landscapes with up to about 7×10^6 parameters. (shrink)

This paper is a study about the social dimension of the philosophical education according to Aristotle. Aristotle is not a individualistic thinker but he understands the philosophical activity in the social context of the friendship.

In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help (...) make explicit the restrictions Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to ‘lift’ a Kripke frame for a one- dimensional modal logic into two dimensions. (shrink)

This paper is divided into three sections. In the first section I briefly outline the background of the problem, i.e. Kripke’s modal argument (Kripke 1980). In the second section I present Chalmers’ account of two- dimensional semantics and two-dimensional argument against physicalism. In the third section I criticize Chalmers’ approach based on two crucial points, one is about necessity of identities and the other is about microphysi- cal descriptions and a priori derivation.

This paper examines connections between concepts of space and extension on the one hand and immaterial spirits on the other, specifically the immanentist concept of spirits as present in rerum natura. Those holding an immanentist concept, such as Thomas Aquinas, typically understood spirits non-dimensionally as present by essence and power; and that concept was historically linked to holenmerism, the doctrine that the spirit is whole in every part. Yet as Aristotelian ideas about extension were challenged and an actual, infinite, (...) class='Hi'>dimensional space readmitted, a dimensionalist concept of spirit became possible—that asserted by the mature Henry More, as he repudiated holenmerism. Despite More’s intentions, his dimensionalist concept opens the door to materialism, for supposing that spirits have parts outside parts implies that those parts could in principle be mapped onto the parts of divisible bodies. The specter of materialism broadens our interest in More’s unconventional ideas, for the question of whether other early modern thinkers, including Isaac Newton, followed More becomes a question of whether they too unwittingly helped usher in materialism. This paper shows that More’s attack upon holenmerism fails. He illegitimately injects his dimensionalist concept of spirit into the doctrine, failing to recognize it as a consequence of the non-dimensionalist concept of spirit, which in itself secures indivisibility. The interpretive consequence for Newton is that there is no prima facie reason to suppose that the charitable interpretation takes him to deny holenmerism. (shrink)

Previous theories of early vision have assumed that visual search is based on simple two-dimensional aspects of an image, such as the orientation of edges and lines. It is shown here that search can also be based on three-dimensional orientation of objects in the corresponding scene, provided that these objects are simple convex blocks. Direct comparison shows that image-based and scene-based orientation are similar in their ability to facilitate search. These findings support the hypothesis that scene-based properties are (...) represented at preattentive levels in early vision. (shrink)

The topic of this Handbook entry is the relationship between similarity and dimensional analysis, and some of the philosophical issues involved in understanding and making use of that relationship. Discusses basics of the relationship between units, dimensions, and quantities. It explains the significance of dimensionless parameters, and explains that similarity of a physical systems is established by showing equality of a certain set of dimensionless parameters that characterizes the system behavior. Similarity is always relative -- to some system behavior. (...) Other topics discussed: generalization of the notion of similarity, the difference between relative similarity and partial similarity; how the notion of similarity in science differs from similarity as it has been discussed in recent philosophy. Philosophers' views discussed: R. Giere, N. Goodman, P. Bridgman, and B. Ellis. (shrink)

The aim of this paper is to reconstruct a modal version of the ontological argument (MOA) in a two dimensionally extended way. This modification of MOA, I argue, might respond to Tooley’s (1981) and Findlay’s (1948) prominent objections against the argument. The MOA has two distinct key premises that are criticized by Tooley and Findley. According to Tooley, the structure of the argument allows to define further properties that exclude the existence of God-like beings. Findlay, however, argues against the proof (...) in a Kantian way by claiming that the very property of necessary existence is contradictory, therefore no being can possess it. In this paper, I am going to show how Tooley and Findlay’s critique re-frame the original ontological argument debate. I will provide a comprehensive map over all possible ways of refuting the MOA. Finally, I argue that, once we apply a two dimensional framework, we are in a position to refute Findlay’s criticism. (shrink)