Psychological construction represents an important new approach to psychological phenomena, one that has the promise to help us reconceptualize the mind both as a behavioral and as a biological system. It has so far been developed in the greatest detail for emotion, but it has important implications for how researchers approach other mental phenomena such as reasoning, memory, and language use. Its key contention is that phenomena that are characterized in (folk) psychological vocabulary are not themselves basic features of (...) the mind, but are constructed from more basic psychological operations. The framework of mechanistic explanation, currently under development in philosophy of science, can provide a useful perspective on the psychological construction approach. A central insight of the mechanistic account of explanation is that biological and psychological phenomena result from mechanisms in which component parts and operations do not individually exhibit the phenomena of interest but function together in an orchestrated and sometimes in a complex dynamical manner to generate it. While at times acknowledging the compatibility of the mechanist approach with constructionist approach (Lindquist, Wager, Kober, Bliss-Moreau, & Barrett, 2012), proponents of the constructionist approach have at other times pitched their approach as anti-mechanist. For example, Barrett (2009) claims that the psychological constructionist approach rejects machines as the primary metaphor for understanding the mind, instead favoring a recipe metaphor; constructionism also purportedly rejects the “mechanistic” picture of causation, which it portrays as linear or sequential in nature (see also Barrett, Wilson-Mendenhall, & Barsalou, in press). While some mechanistic accounts do fit this description, we will see that the mechanisms generating phenomena can be complex and dynamic, producing phenomena far less stereotypic and more adaptive than people often associate with machines. Our goal, however, is not just to render constructionism and mechanism compatible. Philosophers of science have been examining the nature of mechanistic explanation in biology with the goal of gaining new insights into the operation of science. We will identify some of the places where the mechanistic account can shed new light on the constructionist project. (shrink)

Memory perspectives on past events allegedly take one of two shapes. In field memories, we recall episodes from a first-person point of view, while in observer memories, we look at a past scene from a third-person perspective. But this mere visuospatial dichotomy faces several practical and conceptual challenges. First, this binary distinction is not exhaustive. Second, this characterization insufficiently accounts for the phenomenology of observer memories. Third, the focus on the visual aspect of memory perspective neglects emotional, agential, and self-related (...) social aspects. Fourth, the focus on the time of recall neglects the fact that visual, emotional, agential, and social aspects of perspective can also be dissociated in the original experience. In this chapter, we move away from the standard visual dichotomy. Instead, we propose that memory perspective is better understood along four lines: visual, agential, emotional, and social. Drawing on empirical research, we argue that these dimensions predict a disposition to recall a past event based on the present situation of the memorizer. This account supports seeing episodic memory as a natural kind, supported by scenario construction mechanisms and minimal memory traces. By remapping the classic distinction between field and observer perspectives along four dimensions, our proposal provides explanatory advantages and secures practical gains by enabling testable hypotheses. (shrink)

We present a formal mechanical analysis using sweeping net methods to approximate surfacing singularities of saddle maps. By constructing densified sweeping subnets for individual vertices and integrating them, we create a comprehensive approximation of singularities. This approach utilizes geometric concepts, analytical methods, and theorems that demonstrate the robustness and stability of the nets under perturbations. Through detailed proofs and visualizations, we provide a new perspective on singularities and their approximations in analytic geometry.

We advance an account that grounds cognition, specifically decision-making, in an activity all organisms as autonomous systems must perform to keep themselves viable—controlling their production mechanisms. Production mechanisms, as we characterize them, perform activities such as procuring resources from their environment, putting these resources to use to construct and repair the organism's body and moving through the environment. Given the variable nature of the environment and the continual degradation of the organism, these production mechanisms must be regulated (...) by control mechanisms that select when a production is required and how it should be carried out. To operate on production mechanisms, control mechanisms need to procure information through measurement processes and evaluate possible actions. They are making decisions. In all organisms, these decisions are made by multiple different control mechanisms that are organized not hierarchically but heterarchically. In many cases, they employ internal models of features of the environment with which the organism must deal. Cognition, in the form of decision-making, is thus fundamental to living systems which must control their production mechanisms. (shrink)

We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences. Theories carry with them their own ontology while the metaphysics may remain the same in the background. We follow a broadly Kantian tradition, distinguishing between the noumenal and phenomenal realities where the former is independent of our perception while the latter is assembled from the former by means of fragmentary bits of interpretation. Theories do not tell us how the noumenal world (...) is constituted but are conceptual constructs applying to models generated in the phenomenal world within limited contexts. -/- The ontology of quantum theory principally rests on the view that entities in the world are pervasively correlated with one another not by means of probabilities as in the case of the classical theory, but by means of probability amplitudes involving finely tuned phases characterising the oscillatory behaviour of quantum mechanical states. -/- The amplitude-dependent correlations (quantum entanglement) exist over and above the classical ones expressed in terms of probabilities. While the classical correlations are essentially local in nature, quantum correlations are shared globally in the process of environment-induced decoherence. The decoherence is an effectively random process that removes local correlations in the course of global sharing of entanglement—the removal being especially manifest in the case of systems that appear as classical ones. It is this aspect of the decoherence process that makes the so-called measurement postulate (one relating to wave function collapse) cohere with the rest of the principles of quantum theory where the latter implies a Schrodinger type time evolution of quantum mechanical systems. -/- The mathematical basis of the quantum correlations consists of the description of pure states of a system in terms of vectors in a linear vector space (a mixed state appears as an admixture of pure states with some probability distribution associated with it) and, in addition, the description of (pure) states of composite systems as vectors in the product space arising from the component sub-systems. -/- The crucial aspect of the decoherence process, of significance in the context of the apparent incompatibility of the measurement postulate with the unitary Schrodinger evolution, relates to the fact that it is almost instantaneous in the case of a classical object (one that is nevertheless amenable to a quantum description). Indeed, the decoherence time is, in all likelihood, of the order of the Planck scale, being driven by field fluctuations in the Planck regime. This points to factors of an unknown nature determining the finest details of the decoherence process since Planck scale physics remains an obscure terrain. -/- In other words, quantum theory is, to all intents and purposes, in the need of a radical revision, in keeping with the fact that all theories are defeasible and need revision as our domains of experience expand and get realigned in a complex manner. The context within which quantum theory (and quantum field theory too) is defined is set precisely by the Planck scale, across which a novel theoretical framework is likely to emerge. However, as in the case of theory revisions in general, that emerging theory will stand in an asymmetric relation of incommensurability with the present-day quantum theory, where the concepts of the latter will be comprehensible in terms of those of the former, but the converse will not hold. (shrink)

In evolutionary biology, niche construction is sometimes described as a genuine evolutionary process whereby organisms, through their activities and regulatory mechanisms, modify their environment such as to steer their own evolutionary trajectory, and that of other species. There is ongoing debate, however, on the extent to which niche construction ought to be considered a bona fide evolutionary force, on a par with natural selection. Recent formulations of the variational free-energy principle as applied to the life sciences describe (...) the properties of living systems, and their selection in evolution, in terms of variational inference. We argue that niche construction can be described using a variational approach. We propose new arguments to support the niche construction perspective, and to extend the variational approach to niche construction to current perspectives in various scientific fields. (shrink)

This paper addresses the question of how human science categories yield projectable inferences by critically examining Ron Mallon’s ‘social role’ account of human kinds. Mallon contends that human categories are projectable when a social role produces a homeostatic property cluster (HPC) kind. On this account, human categories are projectable when various social mechanisms stabilize and entrench those categories. Mallon’s analysis obscures a distinction between transitory and robust projectable inferences. I argue that the social kinds discussed by Mallon yield the (...) former, while classifications of biological kinds yield the latter. Classifications from psychiatry (‘schizophrenia,’ ‘hysteria’) are discussed as examples. (shrink)

According to psychological constructivism, emotions result from projecting folk emotion concepts onto felt affective episodes (e.g., Barrett 2017, LeDoux 2015). Moreover, while constructivists acknowledge there’s a biological dimension to emotion, they deny that emotions are (or involve) affect programs. So they also deny that emotions are natural kinds. However, the essential role constructivism gives to felt experience and folk concepts leads to an account that’s extensionally inadequate and functionally inaccurate. Moreover, biologically-oriented proposals that reject these commitments are not similarly encumbered. (...) Recognizing this has two implications: biological mechanisms are more central to emotion than constructivism allows, and the conclusion that emotions aren’t natural kinds is premature. (shrink)

In this paper, I explore the feasibility of a realistic interpretation of the quantum mechanical path integral - that is, an interpretation according to which the particle actually follows the paths that contribute to the integral. I argue that an interpretation of this sort requires spacetime to have a branching structure similar to the structures of the branching spacetimes proposed by previous authors. I point out one possible way to construct branching spacetimes of the required sort, and I ask whether (...) the resulting interpretation of quantum mechanics is empirically testable. (shrink)

Integration sustainability outcomes give attention to construction ecology in the design review of urban environments to comply with Earth’s System that is composed of integral parts of the (i.e., physical, chemical and biological components). Naturally, exchange patterns of industrial ecology have consistent and periodic cycles to preserve energy flows and materials in Earth’s System. When engineering topology is affecting internal and external processes in system networks, it postulated the valence of the first-level spatial outcome (i.e., project compatibility success). These (...) instrumentalities are dependent on relating the second-level outcome (i.e., participant security satisfaction). The construction ecology-based topology (i.e., as feedback energy system) flows from biotic and abiotic resources in the entire Earth’s ecosystems. These spatial outcomes are providing an innovation, as entails a wide range of interactions to state, regulate and feedback “topology” to flow as “interdisciplinary equilibrium” of ecosystems. The interrelation dynamics of ecosystems are performing a process in a certain location within an appropriate time for characterizing their unique structure in “equilibrium patterns”, such as biosphere and collecting a composite structure of many distributed feedback flows. These interdisciplinary systems regulate their dynamics within complex structures. These dynamic mechanisms of the ecosystem regulate physical and chemical properties to enable a gradual and prolonged incremental pattern to develop a stable structure. The engineering topology of construction ecology for integration sustainability outcomes offers an interesting tool for ecologists and engineers in the simulation paradigm as an initial form of development structure within compatible computer software. This approach argues from ecology, resource savings, static load design, financial other pragmatic reasons, while an artistic/architectural perspective, these are not decisive. The paper described an attempt to unify analytic and analogical spatial modeling in developing urban environments as a relational setting, using optimization software and applied as an example of integrated industrial ecology where the construction process is based on a topology optimization approach. (shrink)

Art museums are built to elicit a wide variety of feelings, emotions, and moods from their visitors. While these effects are primarily achieved through the artworks on display, museums commonly deploy numerous other affect-inducing resources as well, including architectural solutions, audio guides, lighting fixtures, and informational texts. Art museums can thus be regarded as spaces that are designed to influence affective experiencing through multiple structures and mechanisms. At face value, this may seem like a somewhat self-evident and trivial statement (...) to make. However, in this article, I argue that niche construction theory enables us to make several illuminating observations about the ways in which art museums are engineered to influence our feelings. To expound on this claim, I single out for discussion the Museum of Non-Objective Painting, which for its entire lifespan (1939–52)—and prior to its evolution into the Solomon R. Guggenheim Museum—was expressly organized to kindle in its visitors a special, spiritual form of aesthetic experience: a liberating feeling of cosmic rhythm and order, no less. -/- The argument will proceed as follows: In Part 1, I introduce the basics of niche construction theory and specify the sense in which I apply it to museums and aesthetic affective experiencing. In Part 2, I outline the origins and ethos of the Museum of Non-Objective Painting, after which I pin down the type of affective experience it fostered by drawing from visitors’ self-reported reactions to the artworks on display. Then, in Part 3, I use niche construction theory to explain how the Museum consciously fashioned itself, by means of various mutually supportive resources and technologies, into a fertile setting for the specified feelings. Finally, in Part 4, I extend beyond the discussed case to assess the implications of niche construction theory for a broader understanding of how art museums make us feel. In other words, by tracing the early steps of the Museum of Non-Objective Painting towards the present-day Guggenheim, I call attention to the general variation in affective niches as regards their structure, technologies, and affective aims. Overall, the article elucidates the functioning of art museums as affective niches and furthers the conceptual development of niche construction theory in aesthetics. (shrink)

We review a rough scheme of quantum mechanics using the Clifford algebra. Following the steps previously published in a paper by another author [31], we demonstrate that quantum interference arises in a Clifford algebraic formulation of quantum mechanics. In 1932 J. von Neumann showed that projection operators and, in particular, quantum density matrices can be interpreted as logical statements. In accord with a previously obtained result by V. F Orlov , in this paper we invert von Neumann’s result. Instead of (...) constructing logic from quantum mechanics , we construct quantum mechanics from an extended classical logic. It follows that the origins of the two most fundamental quantum phenomena , the indeterminism and the interference of probabilities, lie not in the traditional physics by itself but in the logical structure as realized here by the Clifford algebra. (shrink)

In the present paper I argue that the formalism of Newtonian mechanics stems directly from the general principle to be called the principle of microlevel reducibility which physical systems obey in the realm of classical physics. This principle assumes, first, that all the properties of physical systems must be determined by their states at the current moment of time, in a slogan form it is ``only the present matters to physics.'' Second, it postulates that any physical system is nothing but (...) an ensemble of structureless particles arranged in some whose interaction obeys the superposition principle. I substantiate this statement and demonstrate directly how the formalism of differential equations, the notion of forces in Newtonian mechanics, the concept of phase space and initial conditions, the principle of least actions, etc. result from the principle of microlevel reducibility. The philosophical concept of thick presentism and the introduction of two dimensional time-physical time and meta-time that are mutually independent on infinitesimal scales-are the the pivot points in these constructions. (shrink)

As the title of this essay suggests, my concern is with the issue of what are economic models. However, the goal of the paper is not to offer an in-depth study on multiple approaches to modelling in economics, but rather to overcome the dichotomical divide between conceptualizing models as isolations and constructions. This is done by introducing the idea of economic models as believable worlds, precisely descriptions of mechanisms that refer to the essentials of the modelled targets. In doing (...) so I make use of the Woodward’s (2002) conceptualization of mechanisms. It is shown that such models do not offer the perfectly true descriptions of the actual world but justified beliefs about the modelled, precisely they aim at maximizing truth and minimizing falsity in a large body of belief about the real world. The analysis throughout the paper is supported by in-depth examination of the Varian’s (1980) model of sales that is here treated as a representative way of reasoning in neoclassical economics. (shrink)

Quantum Mechanics is a fundamental physical theory about atomic-scale processes. It was built between 1920 and 1940 by the most distinguished physicists of that time. The accordance between the predictions of the theory and experimental results is remarkable. The physical interpretation of its mathematical constructs, however, raised unprecedented controversies. Ontological, semantic, and epistemic vagueness abound in the orthodox interpretations and have resulted in serious misunderstandings that are often repeated in textbooks and elsewhere. In this work, we identify, criticize, and clarify (...) the most spread ones. (shrink)

Published with great thanksgiving for Yaohushua, the living One Yahowah, "Jesus Christ." -/- In previous work, Formalizing Mechanical Analysis Using Sweeping Net Methods I, sweeping net methods have been extended to complex analysis, relying on the argument of complex functions defined on the unit circle. In this paper, we reformulate these methods purely within a real-valued and geometric framework, avoiding the use of complex analysis. By redefining the sweeping net constructs and the associated theorems using real functions and geometric interpretations (...) on the unit circle, we demonstrate how singularities and their approximations can be effectively analyzed without the need for imaginary numbers. This approach provides intuitive geometric insights and broadens the applicability of sweeping net methods in mathematical analysis. (shrink)

A traditional social scientific divide concerns the centrality of the interpretation of local understandings as opposed to attending to relatively general factors in understanding human individual and group differences. We consider one of the most common social scientific variables, race, and ask how to conceive of its causal power. We suggest that any plausible attempt to model the causal effects of such constructed social roles will involve close interplay between interpretationist and more general elements. Thus, we offer a case study (...) that one cannot offer a comprehensive model of the causal power of racial categories as social constructions without careful attention both to local meanings and more general mechanisms. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather (...) a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

In this paper, the issues of computability and constructivity in the mathematics of physics are discussed. The sorts of questions to be addressed are those which might be expressed, roughly, as: Are the mathematical foundations of our current theories unavoidably non-constructive: or, Are the laws of physics computable?

Using as case studies two early diagrams that represent mechanisms of the cell division cycle, we aim to extend prior philosophical analyses of the roles of diagrams in scientific reasoning, and specifically their role in biological reasoning. The diagrams we discuss are, in practice, integral and indispensible elements of reasoning from experimental data about the cell division cycle to mathematical models of the cycle’s molecular mechanisms. In accordance with prior analyses, the diagrams provide functional explanations of the cell (...) cycle and facilitate the construction of mathematical models of the cell cycle. But, extending beyond those analyses, we show how diagrams facilitate the construction of mathematical models, and we argue that the diagrams permit nomological explanations of the cell cycle. We further argue that what makes diagrams integral and indispensible for explanation and model construction is their nature as locality aids: they group together information that is to be used together in a way that sentential representations do not. (shrink)

This chapter focuses on the psychological mechanisms behind the construction of preference, especially the actual processes used by humans when they make decisions in their everyday lives or in business situations. The chapter uses cognitive psychological techniques to break down these processes and set them in their social context. When attributes are compatible with the response scale, they are assigned greater weight because they are most easily mapped onto the response. For instance, when subjects are asked to set (...) a price for a gamble this task is compatible with the information about the gamble payoff, which is also expressed in monetary values (e.g., dollars). Conversely, when the task requires a choice the payoff information is not easily mapped onto the response anymore and loses some of its salience. In fact, Slovic, Griffin, and Tversky (1990) could show that using non-monetary outcomes attenuates preference reversals when no compatibility between the pricing task and the outcome attribute was possible. An assumption of the compatibility effect is that response modes compatible with specific characteristics of the options (e.g., payoffs) draw attention to them. One of the main themes that has emerged from behavioral decision research during the past decades is the view that people's preferences are often constructed—not merely revealed—in the process of elicitation (see e.g. Slovic). This conception is derived in part from studies demonstrating that normatively equivalent methods of elicitation often give rise to systematically different responses. These "preference reversals" violate the principle of procedure invariance fundamental to theories of rational choice and raise difficult questions about the nature of human values. If different elicitation procedures produce different orderings of options, how can preferences be defined and in what sense do they exist? Describing and explaining such failures of invariance will require choice models of far greater complexity than the traditional models -/- . (shrink)

In the introduction I argue that the basic element (or primitive) for constructing the physical universe is "displacement from a prior level", and the basic structure is "a sequence of such displacements" (summarized as postulates 1 and 2). The displacements are then defined as one-dimensional objects with a direction (postulate 3). The relations between these displacements are stated in postulate 4. In section 2 we discuss basic consequences of the postulates, and in section 3 we use the postulates to derive (...) a (3+1)-dimensional structure, interpreted as ordinary space and time. We then derive further properties of space --- isotropy, homogeneity, and a rapid early expansion (i.e. inflation). Time, comporting with experience, is shown to be a one-dimensional stream --- with a direction. In section 4 we associate energy with the displacements, and find that the same factors that construct ordinary space (and make it isotropic and homogeneous) also smear the locations of entities/particles across that space --- thereby providing a mechanism/explanation for that iconic and enigmatic aspect of quantum mechanics. We also determine that there must be a continual, uniformly-distributed stream of (non-zero-point) energy coming into the system that constructs new space (i.e. dark energy). The streaming natures of both time and dark energy are shown to have the same basic cause: the processes that input dark energy into the system, and that construct time, are themselves independent of time --- and so they are continual processes. Further consequences follow from the model, including an explanation for why the presence of energy affects space and time, and why quantum vacuum energy is an exception to this rule (i.e. does not gravitate) --- thereby eliminating the cosmological constant problem. A key benefit of the model is that it liberates us from always having to think about the construction of the universe in terms of spatio-temporal relations and evolution (e.g. the big bang model), which is problematic because presumably (and as we will indeed see) space and time are products of the fundamental construction process, not things that govern it. (shrink)

Genesis of the early quantum theory represented by Planck’s 1897-1906 papers is considered. It is shown that the first quantum theoretical schemes were constructed as crossbreed ones composed from ideal models and laws of Maxwellian electrodynamics, Newtonian mechanics, statistical mechanics and thermodynamics. Ludwig Boltzmann’s ideas and technique appeared to be crucial. Deriving black-body radiation law Max Planck had to take the experimental evidence into account. It forced him not to deduce from phenomena but to use more theory instead. The experiments (...) forced Planck to apply the statistical technique to radiation in increasing portions. Planck’s theories in no way were generalizations of existing experimental results. They represented the stages of an ambitious programme of Maxwellian electrodynamics and statistical mechanics reconciliation. (shrink)

The purpose of this article is to establish a connection between modelling practices and interpretive approaches in quantum mechanics, taking as a starting point the literature on scientific representation. Different types of modalities play different roles in scientific representation. I postulate that the way theoretical structures are interpreted in this respect affects the way models are constructed. In quantum mechanics, this would be the case in particular of initial conditions and observables. I examine two formulations of quantum mechanics, the standard (...) wave-function formulation and the consistent histories formulation, and show that they correspond to opposite stances, which confirms my approach. Finally, I examine possible strategies for deciding between these stances. (shrink)

The main algebraic foundations of quantum mechanics are quickly reviewed. They have been suggested since the birth of this theory till up to last years. They are the following ones: Heisenberg-Born- Jordan’s (1925), Weyl’s (1928), Dirac’s (1930), von Neumann’s (1936), Segal’s (1947), T.F. Jordan’s (1986), Morchio and Strocchi’s (2009) and Buchholz and Fregenhagen’s (2019). Four cases are stressed: 1) the misinterpretation of Dirac’s algebraic foundation; 2) von Neumann’s ‘conversion’ from the analytic approach of Hilbert space to the algebraic approach of (...) the rings of operators; 3) Morchio and Strocchi’s improving Dirac’s analogy between commutators and Poisson Brackets into an exact equivalence; 4) the recent foundation of quantum mechanics upon the algebra of perturbations. Some considerations on alternating theoretical importance of the algebraic approach in the history of QM are offered. The level of formalism has increased from the mere introduction of matrices to group theory and C*-algebras but has not led to a definition of the foundations of physics; in particular, an algebraic formulation of QM organized as a problem-based theory and an exclusive use of constructive mathematics is still to be discovered. (shrink)

Abstract: This study focused on comparative assessment of the implementation of quality assurance mechanisms in educational management programme of federal and state universities in south-east, Nigeria. Four research questions and four null hypotheses guided the study. The study was carried out in the eight government-owned (3 federal and 5 state) universities in south-east that run educational management programme. The study adopted a survey research design on a population of eight heads of department. A 44-item researcher constructed questionnaire was used (...) to rate the implementation of quality assurance mechanisms as it relates to; moderation of examination, in-service professional development programmes, mock accreditation exercise, and infrastructural facilities. The instrument was validated by three experts, while a grand reliability index of 0.84 was obtained using crombach alpha reliability coefficient. Mean scores were used to answer the four research questions while t-test was used to test the four null hypotheses at 0.05 level of significance. The major findings of the study indicated that both federal and state universities in south-east implement the four mechanisms for quality assurance in educational management programme to a little extent. Though they both have implemented it to a little extent, the federal universities seem to record better implementation of these mechanisms compared to the state universities. This is supported by the outcome of research questions 3 & 4 as well as hypotheses 3 & 4. It was recommended among others that the National Universities Commission (NUC) should lay more emphasis on the state universities during the usual general/main accreditation exercise of institutions. This will reduce the differences that may exist in standard. Conclusions, implications and limitations of the study were made as well as suggestions for further studies. (shrink)

Plastic waste accumulation in the environment due to huge volumes of plastic waste produced daily with no effective disposal method and waste management have raised public awareness to look for an alternative to replace the current disposal techniques. Waste utilisation or plastic recycling has been regarded as an excellent method to reduce the abundant amount of plastic waste as well as minimising the environmental impacts. In this article, a total of 163 previous studies between 2012 and 2021 had been reviewed (...) to discuss the utilisation of different types of plastic waste as aggregate in construction materials. This paper evaluates on the use of plastic as aggregate in terms of the physical, mechanical and durability properties of the construction materials as well as the environmental and cost analyses. It was found that the mechanical and durability properties of produced materials were altered after the addition of plastic as aggregates; however, the materials are still fulfilling the requirement of construction materials. Besides, a general SWOT analysis to highlight the advantages and disadvantages of plastic waste utilisation was also conducted. -/- . (shrink)

The goal of the current chapter is to discuss how counterfactual thinking serves a more general sense-making function and to delineate the mechanisms by which this may occur. To demonstrate the meaning as sense-making function of counterfactual thinking, we (Lindberg & Markman, 2012) selected a historical event that was likely to be compelling to most student participants, yet not one with which most students would be familiar. This allowed for the manipulation of event details for the purpose of examining (...) underlying cognitive mechanisms believed to influence the sense-making process. Two sets of studies were conducted. The current work lends further support for the sense-making function of counterfactual thinking. (shrink)

We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...) be labelled a finitary, evidence-based, `agnostic' perspective and argue that Brouwerian atheism is merely a restricted perspective within the finitary agnostic perspective, whilst Hilbertian theism contradicts the finitary agnostic perspective. -/- We then consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary, evidence-based, definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways. -/- We show that the two definitions correspond to two distinctly different---not necessarily evidence-based but complementary---assignments of satisfaction and truth to the compound formulas of PA over N. -/- We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both the complementary interpretations; and conclude some unsuspected constructive consequences of such complementarity for the foundations of mathematics, logic, philosophy, and the physical sciences. -/- . (shrink)

Bas van Fraassen endorses both common-sense realism — the view, roughly, that the ordinary macroscopic objects that we take to exist actually do exist — and constructive empiricism — the view, roughly, that the aim of science is truth about the observable world. But what happens if common-sense realism and science come into conflict? I argue that it is reasonable to think that they could come into conflict, by giving some motivation for a mental monist solution to the measurement problem (...) of quantum mechanics. I then consider whether, in a situation where science favors the mental monist interpretation, van Fraassen would want to give up common-sense realism or would want to give up science. (shrink)

This paper constructs a model of metaphysical indeterminacy that can accommodate a kind of ‘deep’ worldly indeterminacy that arguably arises in quantum mechanics via the Kochen-Specker theorem, and that is incompatible with prominent theories of metaphysical indeterminacy such as that in Barnes and Williams (2011). We construct a variant of Barnes and Williams's theory that avoids this problem. Our version builds on situation semantics and uses incomplete, local situations rather than possible worlds to build a model. We evaluate the resulting (...) theory and contrast it with similar alternatives, concluding that our model successfully captures deep indeterminacy. (shrink)

The discrepancy between individual women and the stereotypes attributed to the group as a ‎whole has become progressively greater and more explicit over the course of history. The stereotypes remain the same age-old ‎allegations whilst the ‎developments in the occupations of women and the traits they have opportunity to express have increased the distance between women and those ascribed traits. Stereotypes’ abstention from revision in light of contrary evidence constitutes an epistemic paradox for it entails conflict between the stereotypical knowledge (...) and empirical evidence, as well as between the stereotypical knowledge and other empirical knowledges. This paradox of stubbornness also raises the question as to the epistemic source of stereotypes. For, people at young ages encounter evidence which should have formed a more complex knowledge regarding women rather than the pervasive stereotypical knowledge. It is this extremity of absurdness of stereotypes regarding women that is utile to understanding stereotypes as a whole. The epistemic paradox that is engrained in all stereotypes is exposed uncompromisingly by this group. The paradox cannot be dismissed with excuses of having a small basis of evidence, such as may be said regarding other social groups with which one may have had minimal or no contact. Thus, stereotypes of women provide a limit case to understanding the epistemology of this paradoxical form of knowledge. The traits and epistemic phenomena which render stereotypes epistemically puzzling and intriguing is the relationship between knowledges. Stereotypical knowledge regarding women as a group conflict with one’s experience-founded knowledges of particular women, deeming the corporate body of knowledge incoherent. Quine’s theory of knowledge, with its holistic empirical approach endorsing conceptual schemes, provides fertile ground for this analysis. The novelty in his account is his establishment of the criteria of coherency, which shifts the focal point of epistemic inquiry away from the adequacy of individual knowledges with empirical evidence to the intra-knowledge relationships themselves. In his empiricism, Quine rather examines the interactions between knowledges and the overarching coherence of the body of knowledge as a holistic unit. Quine creates place in his account for mechanism which provide for the epistemic incongruences of stubbornness and conflict found between stereotypical knowledges and empirical evidence. These very mechanisms are what this paper requests to examine. Quine, ultimately, formulates knowledge as a collectively held fabric consisting of relations and of posits – socially constructed mechanisms which are empirically-irreducible and implemented pragmatically for the organisation of empirical evidence. According to Quine, the fabric formation is a conceptual scheme sourced in social heritage. People are bestowed with an eclectic framework of ‎knowledge to pragmatically merge between an inherited, collective conceptual scheme and the personally experienced empirical evidence. This paper will delve into Quine’s fabric of knowledge, its relations, and inner-mechanisms. The finding of stereotypes to be an age-old posit entrenched pragmatically – thus stubbornly – in the collective conceptual scheme, will explain the epistemic paradoxes they entail and offer insight to their revision in light of empiric reality and its women. (shrink)

We describe a new approach to understanding the functioning of the nervous system, unifying previous ideas of Josephson and Hauser, Baas, and Brooks. Its basis consists in analysing the total developmental process into basic components of development, whose corresponding mechanisms (skill constructors) are organised together into a coherent total system.

I characterize Bishop's constructive mathematics as an alternative to classical mathematics, which makes use of the actual infinity. From the history an accurate investigation of past physical theories I obtianed some ones - mainly Lazare Carnot's mechanics and Sadi Carnot's thermodynamics - which are alternative to the dominant theories - e.g. Newtopn's mechanics. The way to link together mathematics to theoretical physics is generalized and some general considerations, in particualr on the geoemtry in theoretical physics, are obtained.that.

Ever since the early days of quantum mechanics it has been suggested that consciousness could be linked to the collapse of the wave function. However, no detailed account of such an interplay is usually provided. In this paper we present an objective collapse model where the collapse operator depends on integrated information, which has been argued to measure consciousness. By doing so, we construct an empirically adequate scheme in which superpositions of conscious states are dynamically suppressed. Unlike other proposals in (...) which “consciousness causes the collapse of the wave function,” our model is fully consistent with a materialistic view of the world and does not require the postulation of entities suspicious of laying outside of the quantum realm. (shrink)

Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable properties of (...) energy numbers in the context of symmetry groups, non-standard fields, fractional calculus, and non-Euclidean geometries. By employing νE as the central element, our framework resolves conventional zero-related sin- gularities and computational anomalies, offering a novel perspective that bridges advanced mathematical theories with practical applications in physics, computational algorithms, and topological transforma- tions. This work paves the way for future research to experimentally validate these formulations and explore potential applications in advanced physics, quantum mechanics, and beyond. (shrink)

Autism Spectrum Condition presents a challenge to social and relational accounts of the self, precisely because it is broadly seen as a disorder impacting social relationships. Many influential theories argue that social deficits and impairments of the self are the core problems in ASC. Predictive processing approaches address these based on general purpose neurocognitive mechanisms that are expressed atypically. Here we use the High, Inflexible Precision of Prediction Errors in Autism approach in the context of cultural niche construction (...) to explain atypicalities of the relational self, specifically its minimal, extended, and intersubjective aspects. We contend that the social self in ASC should not be seen as impaired, but rather as an outcome of atypical niche construction. We unpack the scientific, ethical, and practical consequences of this view, and discuss implications for how the challenges that autistic persons face should be approached. (shrink)

FROM THE HISTORY OF PHYSICS TO THE DISCOVERY OF THE FOUNDATIONS OF PHYSICS By Antonino Drago, formerly at Naples University “Federico II”, Italy – drago@unina,.it (Size : 391.800 bytes 75,400 words) The book summarizes a half a century author’s work on the foundations of physics. For the forst time is established a level of discourse on theoretical physics which at the same time is philosophical in nature (kinds of infinity, kinds of organization) and formal (kinds of mathematics, kinds of logic). (...) This double side of the two dichotomies assures a deep comprehension of theoretical physics by avoiding both a purely philosophical analysis and a purely formal analysis, each manifestly insufficient for representing all the aspects of theoretical physics. Among the many formulations of a physical theory, e.g. Mechanics, also Mach(1) recognized technical differences only, Instead my suggestion is to consider their differences as revealing the characteristic features of their foundations. No more radical differences may exist than those concerning both their kinds of Mathematics and their kinds of Logic. As a fact, after the 20th Century within each of these sciences there exist two antagonist foundations, within Mathematics either the classical one or the constructive one(2); within Mathematical Logic either the classical logic or the intuitionist one(3). Let us take Mechanics as an instance. Being the choices of the Newton’s formulation respectively the actual infinity of the differential equations relying on the infinitesimals and the classical logic, a formulation based on the alternative choices is Lazare Carnot’s,(4) whose mathematics is no more than algebraic-trigonometric and the logic is the intuitionist one, because this formulation makes use of doubly negated propositions, whose corresponding affirmative propositions are idealistic or false; i.e. in these cases the law of double negation fails, as in intuitionist logic occurs. By considering these two dichotomies as the foundations of the physical theories, each couple of choices upon them fashions one out four models of scientific theory, which are baptized through the authors of their most representative theories: Newtonian, Carnotian, Lagrangian, Descartesian. In correspondence four versions of the principle of inertia are recognized, as suggested by respectively: Descartes. Lazare Carnot, Enriques and Cavalieri.(5) All that suggests that the four models of scientific theory may be graphically represented as a compass orientating our minds amid the so numerous physical theories. By taking these dichotomies as interpretative categories, a new interpretative history of Physics including both classical and modern physics results according to a quadrilinear development. The birth of modern physics is characterized by the two theories - Einstein’s paper on special relativity and Einstein’s first paper on quanta - whose choices are the alternative ones to those of the previously dominant physical theory, Newtonian mechanics: in the latter paper Einstein i) declares the dichotomy on the kinds of mathematics (“Introduction”) and then he chooses the discrete mathematics; ii) by using doubly negated propositions he organizes his theory in an alternative way to the deductive-axiomatic one.(6) Moreover, a new history of Philosophy of knowledge results. Kant’s first two a priori transcendental categories represent the physical interpretation of the two choices out of the four pairs of choices on the two dichotomies, i.e. the choices of the dominant theory of mechanics, Newton’s. Hegel’s dialectic was a misleading attempt of anticipating the subsequent intuitionist logic. The book starts by a comparison of different formulations of thermodynamics in order to recognize the first dichotomy on the kind of organization. In chapter 2 the dichotomy on the kind of infinity is recognized through a comparison of Newrton’s mechanics and Lazare Carnot’s. A quickly history of the other classical physical theories is illustrated in chapter 3; it results a foundational conflict between the last two theories, and hence a conflict between their opposite couples of choices. The two main theories of modern physics, special realtivity and quantum mechanics confirm the foundational role played by the two dichotomies which gives reason for the radical change in the history of theoretical physics. Indeed, the opposition of the two main pairs of choices gives reason of the crisis in theoretical physics in the early 1900s. As a global result, the book represents the first interpretation of the entire history of Physics, both classical and modern; This fact proves that the four models of scientific theories can works as a compass (that of the front cover) suggesting a direction among the many physical theories. This new history of physics leads to re-visit both Koyré’s and Kuhn’s historiographies. Their interpretative categories are interpreted and explained through the two dichotomies so that it is possible to suggest à la Koyré categories based on the alternative choices theories to Newton’s as the suitable categories for interpreting the alternative theories to Newton’s mechanics. All that suggests a new interpretation of the crucial step in the history of Western philosophy of knowledge, i.e. the passage from Leibniz to Kant: Leibniz’s suggestion of the two labyrinths of human minds may be seen as a close anticipation of the two above dichotomies. Kant applied them in order to construct the well-known four cosmological proofs, which however he misinterpreted as leading to contradictions, instead to tow different methods of investigation corresponding to the two different kinds of logic.(7) Bibliography 1. Mach E. (1883), Die Mechanik, Leipzig: Brockhaus, Chap. IV, Sect. III. 2. Bishop E. (1967), Constructive Analysis, New York: Mc Graw-Hill. 3. Heyting A. (1962), Intuitionism. An Introduction, Amsterdam: North-Holland. 4. L. Carnot (1783), Essai on the Machines en général, Defay, Dijion (Enlish translation: Springer, Berlin, 2020). Drago A. (2004), “A new appraisal of old formulations of mechanics”, Am. J. Phys., 72(3), pp. 407-9. 5. Vella M.R. (2007), “Le quattro versioni del principio di inerzia”, in M. Leone et al. (eds.), L’eredità di Fermi, Majorana e altri Temi. Napoli: ESI, pp. 147-151. 6. Drago A. (2014), “The emergence of two options from Einstein°s first paper on Quanta”, in Pisano R., Capecchi D., Lukesova A. (eds.), Physics, Astronomy and Engineering. Critical Problems in the History of Science and Society, Scientia Socialis P., Siauliai, 2013, pp. 227-234. 7. This and all in the above points are illustrated by the book Drago A. (2017), Dalla Storia della Fisica ai Fondamenti della Scienza, Roma: Aracne. (shrink)

This paper shows that several live philosophical and scientific hypotheses – including the holographic principle and multiverse theory in quantum physics, and eternalism and mind-body dualism in philosophy – jointly imply an audacious new theory of free will. This new theory, "Libertarian Compatibilism", holds that the physical world is an eternally existing array of two-dimensional information – a vast number of possible pasts, presents, and futures – and the mind a nonphysical entity or set of properties that "read" that physical (...) information off to subjective conscious awareness (in much the same way that a song written on an ordinary compact-disc is only played when read by an outside medium, i.e. a CD-player). According to this theory, every possible physical “timeline” in the multiverse may be fully physically deterministic or physically-causally closed but each person’s consciousness still entirely free to choose, ex nihilo, outside of the physical order, which physically-closed timeline is experienced by conscious observers. Although Libertarian Compatibilism is admittedly fantastic, I show that it not only follows from several live scientific and philosophical hypotheses, I also show that it (A) is a far more explanatorily powerful model of quantum mechanics than more traditional interpretations (e.g. the Copenhagen, Everett, and Bohmian interpretations), (B) makes determinate, testable empirical predictions in quantum theory, and finally, (C) predicts and explains the very existence of a number of philosophical debates and positions in the philosophy of mind, time, personal identity, and free will. First, I show that whereas traditional interpretations of quantum mechanics are all philosophically problematic and roughly as ontologically “extravagant” as Libertarian Compatibilism – in that they all posit “unseen” processes – Libertarian Compatibilism is nearly identical in structure to the only working simulation that human beings have ever constructed capable of reproducing (and so explaining) every general feature of quantum mechanics we perceive: namely, massive-multiplayer-online-roleplaying videogames (or MMORPGs). Although I am not the first to suggest that our world is akin to a computer simulation, I show that existing MMORPGs (online simulations we have already created) actually reproduce every general feature of quantum mechanics within their simulated-world reference-frames. Second, I show that existing MMORPGs also replicate (and so explain) many philosophical problems we face in the philosophy of mind, time, personal identity, and free will – all while conforming to the Libertarian Compatibilist model of reality. -/- I conclude, as such, that as fantastic and metaphysically extravagant as Libertarian Compatibilism may initially seem, it may well be true. It explains a number of features of our reality that no other physical or metaphysical theory does. (shrink)

This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the set of observables of a physical system, be it classical or quantum, is described by a Jordan-Lie algebra. From the geometric point of view, the space of states of any system is described by a uniform Poisson space with transition probability. Both these structures (...) are here perceived as formal translations of the fundamental twofold role of properties in Mechanics: they are at the same time quantities and transformations. The question becomes then to understand the precise articulation between these two roles. The analysis will show that Quantum Mechanics can be thought as distinguishing itself from Classical Mechanics by a compatibility condition between properties-as-quantities and properties-as-transformations. -/- Moreover, this dissertation shows the existence of a tension between a certain "abstract way" of conceiving mathematical structures, used in the practice of mathematical physics, and the necessary capacity to specify particular states or observables. It then becomes important to understand how, within the formalism, one can construct a labelling scheme. The “Chase for Individuation” is the analysis of different mathematical techniques which attempt to overcome this tension. In particular, we discuss how group theory furnishes a partial solution. (shrink)

Can the neo-Aristotelian uphold a pluralist substance ontology while taking seriously the recent arguments in favour of monism based on quantum holism and other arguments from quantum mechanics? In this article, Jonathan Schaffer’s priority monism will be the main target. It will be argued that the case from quantum mechanics in favour of priority monism does face some challenges. Moreover, if the neo-Aristotelian is willing to consider alternative ways to understand ‘substance’, there may yet be hope for a pluralist substance (...) ontology. A speculative case for such an ontology will be constructed based on primitive incompatibility. (shrink)

Experimental activity is traditionally identified with testing the empirical implications or numerical simulations of models against data. In critical reaction to the ‘tribunal view’ on experiments, this essay will show the constructive contribution of experimental activity to the processes of modeling and simulating. Based on the analysis of a case in fluid mechanics, it will focus specifically on two aspects. The first is the controversial specification of the conditions in which the data are to be obtained. The second is conceptual (...) clarification, with a redefinition of concepts central to the understanding of the phenomenon and the conditions of its occurrence. (shrink)

Extensive scientific, philosophical and artistic activities were carried out in the Islamic World’s various science and civilization centers during the early Middle Ages. In these centers, noteworthy works of mathematics, astronomy, geography, medicine, pharmacology, optics, botany, chemistry and other fields of science, which would later determine improvement paths for these fields, were created. Abu al-Izz Ismail ibn al-Razzaz al-Jazari (12th-13th centuries), was a magnificent Muslim scientist known for his work named The Book of Knowledge of Ingenious Mechanical Devices (Kitab fi (...) ma‘rifati’l-hiyal al-handasiyya) and he was born in geography where many scientists were trained. He contributed to the development of science and civilization, the joint legacy of humanity and demonstrated his true capability and success in the field of ilm al-hiyal (the scientific field which addresses the information and practices regarding mechanical technology and engineering in Islamic science history). From this perspective, it is evident that al-Jazari had a wide field of interest, made his mark in the age he lived in with his brave and innovative ideas, and was a wise engineer. al-Jazari’s detailed descriptions and explanations of water clocks, oil lamp clocks and water pumping machines, as well as their construction, were astounding. In addition, al-Jazari’s studies on metal casting techniques, cone valves, wheel balance and the real-world use of aspiration tubes are important in contemporary engineering studies. When all these are considered, it becomes clear that his designation as the “Leonardo da Vinci of the Islamic World” is not a coincidence. Many studies on al-Jazari’s scientific legacy have been conducted in various parts of the world. There are various manuscripts of his aforementioned book. Based on these manuscripts, the work has been -fully or partially- translated into many languages, including Turkish. The German and English translations served as a basis for studies on al-Jazari in other languages. In recent years, studies conducted on al-Jazari in Türkiye (books, articles, domestic and international symposiums, congresses etc.) have demonstrated his brilliance and competence as a scientist. Furthermore, studies on al-Jazari are still ongoing in Türkiye. As for Russia, the scientific legacy of the scientists raised in the Islamic World such as Avicenna, al-Farabi, Abu Bakr al-Razi, Abu Rayhan al-Biruni, Abu al-Qasim al-Zahrawi, Muhammad ibn Musa al-Khwarizmi, al-Battani, al-Kashi, Abd al-Rahman al-Khazini, Nasir al-Din al-Tusi was researched within the scope of a special plan and program. Depending on the relevant studies, al-Jazari and his work drew attention as well. A small portion of the aforementioned Russian studies is known in Türkiye. It is safe to assume that al-Jazari studies in Russia are virtually unknown in Türkiye. The present study primarily aims to contribute to the literature on the scientific legacy of al-Jazari, a Middle Age Islamic scientist best known for his famous work in the mechanical field. More specifically, the present study aims to: 1) to identify the studies on al-Jazari in Russia, and in the former USSR countries, where academic studies are still in Russian after the Soviet Union period, to create a chronological biography and to set forth their compilation; in other words, to create a bibliography which includes Russian studies on al-Jazari; 2) to provide information on the structure and content of the studies in question, to detect the methodological issues encountered in these works, and make solution recommendations to solve these issues; 3) to contribute to continuing and future studies in Türkiye on al-Jazari in terms of source and material index. In conclusion, it should be stated that comparative reading was conducted centered on The Book of Knowledge of Ingenious Mechanical Devices (Kitab fi ma‘rifati’l-hiyal al-handasiyya). It should also be noted that Russian popular internet publications (which are not based on academic research and are created/reproduced for commercial and personal purposes) were excluded from the assessment. (shrink)

The article presents the results of our observations on syntactic, semantic and plot peculiarities of oral language activity, we find it justified to consider the above mentioned parameters as identification criteria for discovering characterological differences of Ukrainian-speaking and Russian-speaking objects of contact profiling. It describes the connection between mechanisms of psychological defenses as the character structural components, and agentive and non-agentive speech constructions, internal and external predicates. Localized and described plots of oral narratives inherent to representatives of different character (...) types. (shrink)

In their Introduction to Logic, Copi and Cohen suggest that students construct a formal proof by "working backwards from the conclusion by looking for some statement or statements from which it can be deduced and then trying to deduce those intermediate statements from the premises. What follows is an elaboration of this suggestion. I describe an almost mechanical procedure for determining from which statement(s) the conclusion can be deduced and the rules by which the required inferences can be made. This (...) method is designed to forestall the quandary in which many beginners find themselves: not knowing how to get started. (shrink)

Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...) verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic---classically accepted as the foundation of all our mathematical Languages---is verifiably complete in the above sense. We show how some paradoxical concepts of Quantum mechanics can, then, be expressed, and interpreted, naturally under a constructive definition of mathematical truth. (shrink)

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

Perceptual neuroscience has identified mechanisms of perceptual grouping which account for the ways in which visual sensitivity to ordered structure and regularities expresses itself, in behavior and in the brain. The need to actively construct order, notably representations of objects in depth, is mandated as soon as visual signals reach the retina, given the occlusion of retinal signals by retinal veins and other retinal elements or blur. Multiple stages of neural processing transform fragmented signals into visual key representations of (...) 3D scenes that can be used to control effective behaviors. Since our survival depends on our ability to pick up order in the physical world, and since we conceive the physical world as an ordered one, our perception must somehow be sensitive to order. The articles from this collection illustrate how texture dissimilarity, boundary completion, surface filling-in, and figure-ground segregation generate perceptual order. (shrink)