Consciousness is defined as cognizance about cosmic secrets in the causal level ( sookshma thala jnanam). It is the insight on the invisible and inexplicable realms of the nature of nature. It is the intuitive perception, logical analysis, perceptual synthesis and conviction on Truth within truth and beyond in its pure and primordial state which is hitherto imperceptible to normal human beings who stays in the mundane plane. In its subtle sense there is only single consciousness and all the states (...) of consciousness with other prefixed appellations should have to be attained by inner transformation happening within the progressive layers of consciousness. Awakening consciousness is really the enlightenment on the consciousnesses in progression. Soul is the seat of consciousness. This supranano cosmic biochip is the boundless mine of knowledge, intelligence, awareness, memory, understanding, wisdom, love, intuition and prescience that is confined with elemental limitations. A person elevates to the sublime state of supra consciousness when he or she evolves into transhuman energy beyond elemental limits. (shrink)

The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article (...) explains the distinction and why it has proved to be one of the great organizing themes of mathematics. (shrink)

Advocates of dynamic systems have suggested that higher mental processes are based on continuous representations. In order to evaluate this claim, we first define the concept of representation, and rigorously distinguish between discrete representations and continuous representations. We also explore two important bases of representational content. Then, we present seven arguments that discrete representations are necessary for any system that must discriminate between two or more states. It follows that higher mental processes require discrete representations. We also argue that discrete (...) representations are more influenced by conceptual role than continuous representations. We end by arguing that the presence of discrete representations in cognitive systems entails that computationalism (i.e., the view that the mind is a computational device) is true, and that cognitive science should embrace representational pluralism. (shrink)

In this field questions arise which are certainly difficult; but as I listened last time to members of the group, I felt that the main difficulty perhaps lay in determining precisely what questions we are trying to answer. I have the conviction that if we could only say clearly what the questions are, the answers to them might not appear so elusive. So I have begun with a simple list of questions about discretion which in one form or another (...) were, as it seemed to me, expressed by the group last time. I may indeed have omitted something and inserted something useless: if so, no doubt I shall be informed of this later. The central questions then seem to me to be the following: 1. What is discretion, or what is the exercise of discretion? 2. Under what conditions and why do we in fact accept or tolerate discretion in a legal system? 3. Must we accept discretion or tolerate discretion, and if so, why? 4. What values does the use of discretion menace, and what values does it maintain or promote? 5. What can be done to maximize the beneficial operation of the use of discretion and to minimize any harm that it does? (shrink)

Soul substance (jīva dravya) is ubiquitous but unseen. Driving force within each one of us, it has been, since time immemorial, a subject matter of research by philosophers, religious leaders and laity. Still, ambiguity and misconceptions prevail as regard its real nature. Some negate the existence of soul and attribute consciousness to the union of four basic substances – earth (prthvī), water (jala), fire (agni), and air (vāyu); death leads to its annihilation. Some believe it to be momentary, devoid of (...) self-existence. Still others consider it a product of illusion (māyā) or ignorance (avidyā) as all objects are manifestations of Brahma; only the one eternally undivided Brahma exists. All such conceptions are based on absolutism like: existence (bhāvaikānta) and non-existence (abhāvaikānta), non-dualism (advaita-ekānta) and separateness (prthaktva-ekānta), and permanence (nityatva-ekānta) and momentariness (ksanika-ekānta). Jaina epistemology goes beyond the superficial and examines objects of knowledge from all possible points of view. It asserts that the entity (dharmī) and its attributes (dharma) are neither absolutely dependent (āpeksika) nor absolutely independent (anāpeksika). Only an entity which has general (sāmānya – concerning the substance, dravya) and particular (viśesa – concerning the mode, paryāya) attributes can be the subject of knowledge. Substance without its modification and modification without its substance cannot be the subject of valid knowledge; only their combination can be the subject of knowledge. (shrink)

Leibniz argues against Descartes’s conception of material substance based on considerations of unity. I examine a key premise of Leibniz’s argument, what I call the Plurality Thesis—the claim that matter (i.e. extension alone) is a plurality of parts. More specifically, I engage an objection to the Plurality Thesis stemming from what I call Material Monism—the claim that the physical world is a single material substance. I argue that Leibniz can productively engage this objection based on his view that matter is (...) discrete. The discreteness of matter provides two aspects of support for the Plurality Thesis. First, it indicates that the parts of matter do not share boundaries and are, therefore, independent in an important sense. Second, it indicates that the parts of matter are determinate and are, therefore, ontologically prior to the wholes they compose. (shrink)

The use of the model of discrete/quantized space sets the focus on mathematics instead of physics. It benefits the interpretation of observed and measured phenomena at the cosmological scale size. It is an approach that simplifies the problems around the understanding of the properties of the basic quantum fields.

This article interprets the religious epistemology of the Caitanya Vaiṣṇava theologian Jīva Gosvāmin, specifically his division of perception in ‘learned’ and ‘ignorant’, to argue that ‘learned’ perception is supersensible cognitive experience shaped by learning and language. The article goes on to show that the contemporary scholarship on religious experience can learn an important lesson from Jīva’s epistemology, namely that the social construction of categories that shape religious experience need not involve ontological agnosticism with respect to the existence of objects presented (...) in it. (shrink)

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

Recently there is some new interest in understanding the physical reality behind the formalism of quantum mechanics. This paper relates the known “quantum mysteries” of QM with the properties of the underlying structure of discrete space. DOI: 10.5281/zenodo.5236617.

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some philosophers wrote Principia (...) Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. (shrink)

This paper addresses the issues related to designing and estimating the strength of solid-alloy elements in the deforming broaches of significant diameter (exceeding 150 mm) for the developed process of discrete broaching. The tool limit condition was assessed based on two strength criteria: the specific potential energy of shape change and the maximum tangent stresses. Numerical modeling using the finite element method has made it possible to derive the distribution of equivalent stresses in the tool elements and the contact stresses (...) at the surface of the contact between a solid-alloy insert and the body, which enabled the analysis of tool strength under loading. The simulation was performed under a single normal load, which ensured the versatility of the calculation for any contact pressure values. We have derived formulae to calculate the acceptable contact pressure depending on unit load. The effect of the insert protrusion height over the body on the strength of tool elements has been established. We have derived engineering dependences that determine the required magnitude of insert protrusion over the body depending on the ultimate load. An example of calculating the strength of a prefabricated deforming element in the machining of a sleeve made from gray modified cast iron of hardness HB230 has been considered. Our calculations have shown that the deforming element designed for the new technological process corresponds to the conditions of strength, provided the ratio h1/h=0.15 is maintained (where h1 is the insert height above the body, h is the insert height). The results obtained could be used in engineering calculations when designing the prefabricated tool for discrete deformation, as well as to assess the strength of prefabricated tools, such as cutters, core drills, reamers, when refining external loads. (shrink)

This paper presents a new modified quantum mechanics, Critical Complexity Quantum Mechanics, which includes a new account of wavefunction collapse. This modified quantum mechanics is shown to arise naturally from a fully discrete physics, where all physical quantities are discrete rather than continuous. I compare this theory with the spontaneous collapse theories of Ghirardi, Rimini, Weber and Pearle and discuss some implications of these theories and CCQM for a realist view of the quantum realm.

In this paper, we have tried to prove the lack of discretion by providing a logical and philosophical connection between the fundamental concept of a function in mathematics and one of Einstein's most exceptional relativity results, namely, the relativity of simultaneity. Then, by providing real examples of social experiences and philosophical interpretations of them, we propose another proof for lack of discretion.

The ancient Greek philosopher Parmenides reasoned that observable reality is created by an underlying reality. However, an invisible underlying creating reality suggests that we cannot determine its existence with the help of experimental physics. This paper describes an experiment to measure absolute motion that will show that Parmenides concept about an underlying reality is correct. This in spite of Albert Einstein’s theory of special relativity that is founded on the assumption that it is impossible to detect the absolute motion of (...) objects. (shrink)

As far as we know the scientific search for the nature of reality in Europe started about 2500 years ago in ancient Greek. It was the ancient Greek philosopher Parmenides who reasoned that observable reality is created by an underlying reality. There are indications that the ancient Greek concept of the atom was (also) related to the proposed units of the structure of the underlying creating reality of Parmenides. However, an invisible underlying creating reality suggests that we cannot determine its (...) existence with the help of experimental physics. This paper describes an experiment that will show that Parmenides concept about an underlying reality is correct. (shrink)

In this brief introduction, I shall rather reflect, from a biographer’s viewpoint, on the significance of Discretion for our understanding of the trajectory of Hart’s ideas and on the significance of his year at Harvard. I shall then move on to consider the intriguing question of why Hart did not subsequently publish or build on some of the key insights in the paper itself. Here I highlight the fact that, almost uniquely in Hart’s work, Discretion features a notable (...) emphasis on the significance of institutional factors in our understanding of the nature of legal decisionmaking; and I argue that Hart’s failure fully to develop this insight in the essay, or to build on it in his subsequent work, derives from the fact that such a development would have necessitated a diversion from the philosophical issues that were his core intellectual concern, and moreover would have presented certain dangers to his conception of legal positivism. I shall conclude by considering what contribution the essay makes to our overall interpretation and evaluation of Hart’s legal philosophy. (shrink)

We give a new argument supporting a gravitational role in quantum collapse. It is demonstrated that the discreteness of space-time, which results from the proper combination of quantum theory and general relativity, may inevitably result in the dynamical collapse of thewave function. Moreover, the minimum size of discrete space-time yields a plausible collapse criterion consistent with experiments. By assuming that the source to collapse the wave function is the inherent random motion of particles described by the wave function, we further (...) propose a concrete model of wavefunction collapse in the discrete space-time. It is shown that the model is consistent with the existing experiments and macroscopic experiences. (shrink)

Paper about the origin of the wave-particle duality.

We analyze the possible implications of spacetime discreteness for the special and general relativity and quantum theory. It is argued that the existence of a minimum size of spacetime may explain the invariance of the speed of light in special relativity and Einstein’s equivalence principle in general relativity. Moreover, the discreteness of spacetime may also result in the collapse of the wave function in quantum mechanics, which may provide a possible solution to the quantum measurement problem. These interesting results might (...) have some important implications for a complete theory of quantum gravity. (shrink)

The discrete–structural structure of the world is described. In comparison with the idea of Heraclitus about an indissoluble world, preference is given to the discrete world of Democritus. It is noted that if the discrete atoms of Democritus were simple and indivisible, the atoms of the modern world indicated in the article would possess, rather, a structural structure. The article proves the problem of how the mutual connection of mathematics and philosophy influences cognition, which creates a discrete–structural worldview. The author (...) notes that the appearance of writing, symbolic language and the depiction of the picture of the world through mathematics, led us into the sphere of discrete mathematical mathematics. (shrink)

This paper presents a theoretical study of the binary oppositions underlying the mechanisms of natural computation understood as dynamical processes on natural information morphologies. Of special interest are the oppositions of discrete vs. continuous, structure vs. process, and differentiation vs. integration. The framework used is that of computing nature, where all natural processes at different levels of organisation are computations over informational structures. The interactions at different levels of granularity/organisation in nature, and the character of the phenomena that unfold through (...) those interactions, are modeled from the perspective of an observing agent. This brings us to the movement from binary oppositions to dynamic networks built upon mutually related binary oppositions, where each node has several properties. (shrink)

The concept of discrete space can be termed as “the ex­ternal mathematical reality hypothesis”. The concept was already known among the ancient Greek philosophers (≈ 500 BC). Unfortunately the phenomenological point of view has dominated science during more than 2000 years and it is only recently that the concept of discrete space gets “tangible” attention again in philosophy and theoretical physics. Although the model de­scribes the existence of the universal conservation laws, constants and principles in a convincing way, the re­lation (...) between phenomenological reality and the geo­metrical description of discrete space is difficult to ima­gine for everyone who is only familiar with phenomeno­logical reality. The purpose of this paper is to describe some easy to imagine properties of discrete space. DOI: 10.5281/zenodo.5498120. (shrink)

The increasing use of opioid treatment agreements has prompted debate within the medical community about ethical challenges with respect to their implementation. The focus of debate is usually on the efficacy of OTAs at reducing opioid misuse, how OTAs may undermine trust between physicians and patients and the potential coercive nature of requiring patients to sign such agreements as a condition for receiving pain care. An important consideration missing from these conversations is the potential for racial bias in the current (...) way that OTAs are incorporated into clinical practice and in the amount of physician discretion that current opioid guidelines support. While the use of OTAs has become mandatory in some states for certain classes of patients, physicians are still afforded great leeway in how these OTAs are implemented in clinical practice and how their terms should be enforced. This paper uses the guidelines provided for OTA implementation by the states of Indiana and Pennsylvania as case studies in order to argue that giving physicians certain kinds of discretion may exacerbate racial health disparities. This problem cannot simply be addressed by minimising physician discretion in general, but rather by providing mechanisms to hold physicians accountable for how they treat patients on long-term opioid therapy to ensure that such treatment is equitable. There are no data in this work. (shrink)

According to Discrete Emotion Theory, a number of emotions are distinguishable on the basis of neural, physiological, behavioral and expressive features. Critics of this view emphasize the variability and context-sensitivity of emotions. This paper discusses some of these criticisms, and argues that they do not undermine the claim that emotions are discrete. This paper also presents some works in dynamical affective science, and argues that to conceive of discrete emotions as self-organizing and softly assembled patterns of various processes accounts more (...) naturally than traditional Discrete Emotion Theory for the variability and context-sensitivity of emotions. (shrink)

The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space and to the rest of reality requires, I (...) believe, that we consider how space itself relates to reality, and how other so-called "spaces" used in physics relate to reality. In chapter 2, I compare space and space-time to other spaces used in physics, such as configuration space, phase space and Hilbert space. I support what is known as the "property view" of space, opposing both the traditional views of space and space-time, substantivalism and relationism. I argue that all these spaces are property spaces. After examining the relationships of these spaces to causality, I argue that configuration space has, due to its role in quantum mechanics, a special status in the microscopic world similar to the status of position space in the macroscopic world. In chapter 3, prespace itself is considered. One way of approaching this structure is through the comparison of the prespace structure with a computational system, in particular to a cellular automaton, in which space or space-time and all other physical quantities are broken down into discrete units. I suggest that one way open for a prespace metaphysics can be found if physics is made fully discrete in this way. I suggest as a heuristic principle that the physical laws of our world are such that the computational cost of implementing those laws on an arbitrary computational system is minimized, adapting a heuristic principle of this type proposed by Feynman. In chapter 4, some of the ideas of the previous chapters are applied in an examination of the physics and metaphysics of quantum theory. I first discuss the "measurement problem" of quantum mechanics: this problem and its proposed solution are the primary subjects of chapter 4. It turns out that considering how quantum theory could be made fully discrete leads naturally to a suggestion of how standard linear quantum mechanics could be modified to give rise to a solution to the measurement problem. The computational heuristic principle reinforces the same solution. I call the modified quantum mechanics Critical Complexity Quantum Mechanics (CCQM). I compare CCQM with some of the other proposed solutions to the measurement problem, in particular the spontaneous localization model of Ghirardi, Rimini and Weber. Finally, in chapters 5 and 6, I argue that the measure of complexity of quantum mechanical states I introduce in CCQM also provides a new definition of entropy for quantum mechanics, and suggests a solution to the problem of providing an objective foundation for statistical mechanics, thermodynamics, and the arrow of time. (shrink)

Street-level bureaucrats are a fundamental part of the implementation process of any policy. This study provides an examination of the factors that shape the behavior of street-level bureaucrats at the frontlines of policy implementation. This study investigates how rebelliousness generates an impact on the discretion of street-level bureaucrats and to what extent client meaningfulness plays a moderating factor. It utilizes a survey questionnaire distributed among inspectors of the Department of Labor in the Ministry of Human Resources of Malaysia (n=241). (...) The result of this study demonstrates that rebelliousness has a negative relationship with discretion, and client meaningfulness has a direct positive correlation with discretion. However, the relationship between rebelliousness and discretion is stronger with a high level of client meaningfulness. The objective of this study is to examine street-level bureaucrat behavior through the lens of Lipsky's theory which will provide an answer to the broad question of the factors that contribute to the existence of an imperfect implementation process. This study sheds light on the importance of client meaningfulness in moderating the behavior of street-level bureaucrats while interacting with inspectees. The novelty of this study is by highlighting two main constructs that are likely contributing to the implementation process by directly and indirectly impacting bureaucrats’ discretion: rebelliousness, and client meaningfulness. (shrink)

While it is known that Euclid’s five axioms include a proposition that a line consists at least of two points, modern geometry avoid consistently any discussion on the precise definition of point, line, etc. It is our aim to clarify one of notorious question in Euclidean geometry: how many points are there in a line segment? – from discrete-cellular space (DCS) viewpoint. In retrospect, it may offer an alternative of quantum gravity, i.e. by exploring discrete gravitational theories. To elucidate our (...) propositions, in the last section we will discuss some implications of discrete cellular-space model in several areas of interest: (a) cell biology, (b) cellular computing, (c) Maxwell equations, (d) low energy fusion, and (e) cosmology modelling. (shrink)

A recently proposed model of sensory processing suggests that perceptual experience is updated in discrete steps. We show that the data advanced to support discrete perception are in fact compatible with a continuous account of perception. Physiological and psychophysical constraints, moreover, as well as our awake-primate imaging data, imply that human neuronal networks cannot support discrete updates of perceptual content at the maximal update rates consistent with phenomenology. A more comprehensive approach to understanding the physiology of perception (and experience at (...) large) is therefore called for, and we briefly outline our take on the problem. (shrink)

Our universe shows to be local and non-local. The concept is confusing because in daily live we are not aware of the non-locality of our universe. Actually, in daily live local reality seems to be quite orderly and understandable. But we don’t know why everything is in motion and all our theories in physics are still approximations of physical reality. At least that is what they supposed to be.

There are reports about human experiences of time that are not in line with Einstein’s theory of Special relativity and not in line with the rate of change of the electromagnetic field at the smallest scale size. Some psychological reports describe human experiences about the metric of time that defy physical reality as we know it. These reports question the reliability of our understanding of time.

In this essay I argue that art is able to open a new window on to reality only when art can transcend reason and the confines of language. Moreover, both logic and language have their limitations when used as tools for the creation of meaning and that art helps us overcome these inadequacies in the way it transcends — or even transgresses — the absolutes that underpin our “rational” view of the world. Lastly, the violation of the strictures of logic (...) by art is also emblematic of art’s heightened awareness of certain unique features of reality — in particular, its dynamic and fluid nature — which are not normally readily visible to a mind tied to thinking in terms only of binary truth values. (shrink)

The explanation of the existence of quantum transfer in vacuum space around celestial bodies under influence of gravitational vectors./.

Regulatory enforcement is a multifaceted phenomenon that revolves around the concept of discretion of Street-Level Bureaucrats (SLBs). Discretion can be defined as the ability to freely decide how to deliver services to the clients/public. Regulations are enforced by the decisions made by bureaucrats when they interact with clients. By combining street-level bureaucracy and responsive regulation theories, this study is set to examine how different factors shape the discretion of street-level bureaucrats. This study is built on available literature (...) pertaining to SLBs and policy implementation to provide a comprehensive understanding of regulation enforcement in Malaysia. SLBs are the Labor Inspectors responsible for the enforcement of minimum wage in Malaysia. The study’s main contribution is examining how personal characteristics, internal organizational factors, and a multidimensional enforcement style shape the discretion of bureaucrats in Malaysia. The study’s main finding highlights that Labor Inspectors in Malaysia demonstrate a range of enforcement style dimensions when enforcing the minimum wage. The novelty of this thesis highlights two primary constructs; willingness to implement and client meaningfulness, and their importance in shaping policy implementation and its effect on street-level bureaucrats' behavior. These constructs are also likely contributing to the imperfect enforcement of the minimum wage policy. Furthermore, this study demonstrates that enforcement style consists of three dimensions; legal, facilitation, and accommodation. Finally, this study's empirical finding highlights that street-level bureaucrats' discretion is influenced by various factors that ultimately define the enforcement process. (shrink)

Special issue in honour of Landon Rabern. This special issue of Discrete Mathematics is dedicated to his memory, as a tribute to his many research achievements. It contains 10 new articles written by his collaborators, friends, and colleagues that showcase his interests.

This report presents the results of a research project which examined how Polish administrative courts exercise discretionary powers when deciding cases related to business activity. When a business enterprise asks the court to review actions taken by administration, judges decide whether an administrative body has used its powers in accordance with the law. The law in this case includes both the relevant statutory regulations but also more general principles originating from other sources, such as the Constitution or European Union law. (...) It is generally accepted that in such cases courts have discretion, i.e. are able to select legal standards on which to base their judgments and to decide how to apply such standards to the case at hand. This does not mean, of course, that administrative court judges can do what they please. But, within some well-established boundaries, they can select from among various rules and principles those legal standards which apply to the case before them, interpret their meaning, and assess their importance. We aim to understand this process. (shrink)

Among the many problems facing u.s. immigration law is a crisis of discretion and judicial deference. Through two recently passed laws, the United States Congress and the President have seriously limited judicial review o f discretionary immigration decisions o f the Board ofImmigration Appeals. This Article focuses on this preclusion of judicial review of discretionary agency decisions. The Article begins with an examination ofdiscretion from a theoretical perspective, and goes on to examine areas o f immigration law in which (...) discretion was traditionally most imponant. That examination is followed by a discussion of immigration-law scholarship and critique. The Article concludes that what is needed in U.S. immigration law is greater restraint, and calls on the Judiciary to provide more oversight regarding discretionary agency decisions. (shrink)

The ancient Greek philosophers – like Parmenides – reasoned that observable reality cannot exist by itself. It has to be a creation of an underlying reality. An all-in­clusive existence that has a structure because observable reality shows structure at every scale size. Although observable reality is involved in a continuous transformation too. If our concept about the relation between phenomenological reality and the creating underlying reality is correct, the unification of the properties of phenomenological reality is part of an enveloping (...) mathematical model. DOI: 10.5281/zenodo.5457368. (shrink)

This Essay analyzes an essay by H. L. A. Hart about discretion that has never before been published, and has often been considered lost. Hart, one of the most significant legal philosophers of the twentieth century, wrote the essay at Harvard Law School in November 1956, shortly after he arrived as a visiting professor. In the essay, Hart argued that discretion is a special mode of reasoned, constrained decisionmaking that occupies a middle ground between arbitrary choice and determinate (...) rule application. Hart believed that discretion, soundly exercised, provides a principled way of coping with legal indeterminacy that is fully consistent with the rule of law. This Essay situates Hart’s paper – Discretion – in historical and intellectual context, interprets its main arguments, and assesses its significance in jurisprudential history. In the context of Hart’s work, Discretion is notable because it sketches a theory of legal reasoning in depth, with vivid examples. In the context of jurisprudential history, Discretion is significant because it sheds new light on long-overlooked historical and theoretical connections between Hart’s work and the Legal Process School, the American jurisprudential movement dominant at Harvard during Hart’s year as a visiting professor. Hart’s Discretion is part of our jurisprudential heritage, advancing our understanding of legal philosophy and its history. (shrink)

In 2001, three non-Aboriginal men in their twenties were charged with the sexual assault of a twelve year old Aboriginal girl in rural Saskatchewan. Legal proceedings lasted almost seven years and included two preliminary hearings, two jury trials, two retrials with juries, and appeals to the provincial appeal court and the Supreme Court of Canada. One accused was convicted. The case raises questions about the administration of justice in sexual assault cases in Saskatchewan. Based on observation and analysis of the (...) record, this paper: (1) examines relationships between legal errors dealing with availability of the defence of “belief in consent” and interpretation of the “all reasonable steps” provision, the need for retrials, and apprehended race-gender-age bias and discrimination; and 2) proposes incremental and systemic remedies to address the weaknesses in police, prosecutorial and judicial policy and practice highlighted by this case. (shrink)

This study considers the problem of using approximate way for realizing the neural supervisor for nonlinear multivariable systems. The Nonlinear Autoregressive-Moving Average (NARMA) model is an exact transformation of the input-output behavior of finite-dimensional nonlinear discrete time dynamical organization in a hoodlum of the equilibrium state. However, it is not convenient for intention of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate technique are used for realizing the neural supervisor to (...) overcome computational complexity. In this study, we introduce two classes of ideal which are approximations to the NARMA model and which are linear in the control input, namely NARMA-L1 and NARMA-L2. The latter fact substantially simplifies both the theoretical breakdown as well as the practical request of the controller. Extensive imitation studies have shown that the neural controller designed using the proposed approximate models perform very well and in dozens situation even better than an approximate controller designed using the exact NARMA Model. In view of their mathematical tractability as well as their fate in simulation studies, a matter is made in this study that such approximate input-output paragon warrants a detailed study in their own right. (shrink)

Outlined here is a simulation hypothesis approach that uses an expanding (the simulation clock-rate measured in units of Planck time) 4-axis hyper-sphere and mathematical particles that oscillate between an electric wave-state and a mass (unit of Planck mass per unit of Planck time) point-state. Particles are assigned a spin axis which determines the direction in which they are pulled by this (hyper-sphere pilot wave) expansion, thus all particles travel at, and only at, the velocity of expansion (the origin of $c$), (...) however only the particle point-state has definable co-ordinates within the hyper-sphere. Photons are the mechanism of information exchange, as they lack a mass state they can only travel laterally (in hypersphere co-ordinate terms) between particles and so this hypersphere expansion cannot be directly observed, relativity then becomes the mathematics of perspective translating between the absolute (hypersphere) and the relative motion (3D space) co-ordinate systems. A discrete `pixel' lattice geometry is assigned as the gravitational space. Units of $\hbar c$ `physically' link particles into orbital pairs. As these are direct particle to particle links, a gravitational force between macro objects is not required, the gravitational orbit as the sum of these individual orbiting pairs. A 14.6 billion year old hyper-sphere (the sum of Planck black-hole units) has similar parameters to the cosmic microwave background. The Casimir force is a measure of the background radiation density. (shrink)

One of the oldest questions in science and philosophy is whether reality is fundamentally discrete, or fundamentally continuous. In this short essay I show that this question should first be classified into two main categories. 1) Intrinsic existence, 2) Behavioral existence. I show that the first category should be continuous by definition, while the second category could probably be either continuous or discrete.

The proposed existence of relative time and the curvature of space – both combined into the concept of spacetime – influences the search for an adequate theoretical model that can describe the structure of space in an accurate way. The aim of building space is to develop a quantum theory of gravitation. This paper investigate the theoretical problems that have their origin in the concepts that are at the basis of phenomenological physics.

When faced with the charge that a given concept of God is contradictory, the standard move among philosophers and theologians has been to try to explain away the contradiction and show that the concept of God in question is consistent. This has to do, of course, with the Law of Non-Contradiction (LNC). Another option, which has recently generated interest among logicians and analytic philosophers of religion, is to reject such a move as unnecessary and defend what might be called the (...) contradictory God thesis. To be sure, something close to that can be found in philosophers such as Pseudo-Dionysius, Thomas Aquinas and Nicolaus de Cusa. However, it is only recently that this approach has gained momentum, certainly driven by the contemporary advance of dialetheism and glut theoretic approaches in general, and paraconsistent logic. Needless to say, a standard move among defenders of the contradictory God thesis is to reject the LNC. The argumentation, however, is seldomly framed in conceptual terms. Instead, it is mostly framed in ontological terms, as God being a contradictory entity. From this perspective, the contradictory God thesis is the thesis that God is a contradictory object. My goal in this paper is to provide a conceptual assessment of the discussion surrounding the contradictory God thesis. To achieve this, I make use of a general and hopefully non-controversial meta-theory of concepts and adopt a semantic approach rather than a metaphysical one. Within this framework, I address the following questions: What are the different ways we can understand the contradictory God thesis? What grounds are there for rejecting a contradictory concept of God? What standard moves are available to defend oneself from such criticisms and how do they relate to the LNC? What challenges do they present? As a secondary goal, the paper introduces a novel defense of the contradictory God thesis, drawing on a specific interpretation of the theology of the 16th-century Indian thinker Jīva Gosvāmī, which does not necessitate the rejection of the LNC. I term this approach ‘non-dialetheic mystical contradictory theism.’. (shrink)

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...) of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible. (shrink)

Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so (...) that ignorance of their nature is profound. (shrink)

Pańcāstikāya-samgraha or Pańcāstikāya-sāra (known briefly as Pańcāstikāya and spelled commonly as Panchastikay) is one of the four most important and popular works of Ācārya Kundakunda (circa first century B.C.), the other three being Samayasāra, Pravacanasāra and Niyamasāra. The original text is in Prakrit language and contains a total of 173 verses (gāthā). Pańcāstikāya means ‘five-substances-with-bodily-existence’ and these are: the soul (jīva), the physical-matter (pudgala), the medium-of-motion (dharma), the medium-of-rest (adharma), and the space (ākāśa). These five substances collectively constitute the universe-space (...) (loka). Outside this universe-space (loka) is the infinite non-universe-space (aloka), comprising just the pure space (ākāśa). The substance-of-time (kāla dravya) which renders assistance to all substances in their continuity of being through gradual changes is not an ‘astikāya’ since it occupies a single space-point and, therefore, does not possess the characteristic of body (kāya). Pańcāstikāya-samgraha expounds the Jaina metaphysics – the philosophy of being and knowing – including the nature of the pure soul-substance (jīvāstikāya) which is integral to the seven realities (tattva), the nine objects (padārtha), and the six substances (dravya). While the substance (dravya) never leaves its essential character of existence (sattā), it undergoes origination (utpāda), destruction (vyaya) and permanence (dhrauvya). There is inseparable association between the qualities (guņa) and the substance (dravya). The discussion relies on the ‘doctrine of conditional predication’ (syādvāda) and the ‘seven-nuance system’ (saptabhańgī), as expounded by Lord Jina. (shrink)

Ācārya Umāsvāmī’s (circa 1st century CE) Tattvārthasūtra (spelled commonly as Tattvarthsutra or Tattvarthasutra), also known as Mokşaśāstra, is the most widely read Jaina Scripture. It expounds the Jaina Doctrine, the nature of the Reality, in form of aphorisms (sūtra), in Sanskrit. Brief and to-the-point, Tattvārthasūtra delineates beautifully the essentials of all objects-of-knowledge (jñeya). Sarvārthasiddhi by Ācārya Pūjyapāda (circa 5th century CE) is the first and foremost extant commentary on Tattvārthasūtra. Sarvārthasiddhi is an exposition of the reality – the true nature (...) of substances, soul and non-soul – the knowledge of which equips one to tread the path to liberation, as expounded in Tattvārthasūtra. There is beginningless intermingling of the soul (jīva) and the non-soul (ajīva) karmic matter. Our activities (yoga) are responsible for the influx (āsrava) of the karmic matter into the soul. Actuated by passions (kaşāya) the soul takes in particles of the karmic matter; this is bondage (bandha). Obstructing fresh inflow of the karmic matter into the soul – samvara – and its subsequent separation or falling off from the soul – nirjarā – are two important steps in attaining the infallible, utterly pristine, sense-independent and infinitely blissful state of the soul, called liberation (mokşa). (shrink)