This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called generalized stochastic systems, collectively encompass many important kinds of stochastic processes, including Markov chains and random dynamical systems. This paper then states and proves a new theorem that establishes a precise correspondence between any generalized stochastic system and a unitarily evolving quantum system. This theorem therefore leads to (...) a new formulation of quantum theory, alongside the Hilbert-space, path-integral, and quasiprobability formulations. The theorem also provides a first-principles explanation for why quantum systems are based on the complex numbers, Hilbert spaces, linear-unitary time evolution, and the Born rule. In addition, the theorem suggests that by selecting a suitable Hilbert space, together with an appropriate choice of unitary evolution, one can simulate any generalized stochastic system on a quantum computer, thereby potentially opening up an extensive set of novel applications for quantum computing. (shrink)

This paper introduces an exact correspondence between a general class of stochastic systems and quantum theory. This correspondence provides a new framework for using Hilbert-space methods to formulate highly generic, non-Markovian types of stochastic dynamics, with potential applications throughout the sciences. This paper also uses the correspondence in the other direction to reconstruct quantum theory from physical models that consist of trajectories in configuration spaces undergoing stochastic dynamics. The correspondence thereby yields a new formulation of quantum theory, (...) alongside the Hilbert-space, path-integral, and quasiprobability formulations. In addition, this reconstruction approach opens up new ways of understanding quantum phenomena like interference, decoherence, entanglement, noncommutative observables, and wave-function collapse. (shrink)

There is a widespread attitude in epistemology that, if you know on the basis of perception, then you couldn't have been wrong as a matter of chance. Despite the apparent intuitive plausibility of this attitude, which I'll refer to here as “stochastic infallibilism”, it fundamentally misunderstands the way that human perceptual systems actually work. Perhaps the most important lesson of signal detection theory (SDT) is that our percepts are inherently subject to random error, and here I'll highlight some key (...) empirical research that underscores this point. In doing so, it becomes clear that we are in fact quite willing to attribute knowledge to S that p even when S's perceptual belief that p could have been randomly false. In short, perceptual processes can randomly fail, and perceptual knowledge is stochastically fallible. The narrow implication here is that any epistemological account that entails stochastic infallibilism, like safety, is simply untenable. More broadly, this myth of stochastic infallibilism provides a valuable illustration of the importance of integrating empirical findings into epistemological thinking. (shrink)

This thesis develops a detailed account of the emergence of for all practical purposes continuous, quasi-classical world histories from the discontinuous, stochastic micro dynamics of Minimal Bohmian Mechanics (MBM). MBM is a non-relativistic quantum theory. It results from excising the guiding equation from standard Bohmian Mechanics (BM) and reinterpreting the quantum equilibrium hypothesis as a stochastic guidance law for the random actualization of configurations of Bohmian particles. On MBM, there are no continuous trajectories linking up individual configurations. Instead, (...) individual configurations are actualized independently of each other, carving out the decoherence-induced branching structure of the universal wave function. Yet, by contrast to the Everett interpretation, branches of the universal wave function are not actualized in parallel, i.e. all at the same time. Rather, world branches, on MBM, are actualized sequentially. -/- For an introduction to MBM, the transition from BM to MBM is described, and their empirical equivalence is established. I present the conditions under which MBM can be classified as a primitive ontology (PO) theory, regarded as crucial for the acceptance of a theory as Bohmian by many proponents of BM. While rendering MBM compatible with the PO approach, it must not fall prey to the problem of communication, arising from the two-space reading of BM. -/- The issue of temporal solipsism, identified by Bell as a serious problem for his “Everett (?) theory” – the historic predecessor of MBM – is discussed. I argue that Barbour’s time capsule approach does not provide a satisfactory solution. In particular, his adopting a more than minimal psychophysical parallelism between brain processes and experience of macroscopic change is argued to be reasonable in light of our current best neuroscience, yet problematic for theories relying solely on time capsules, understood as highly structured, individual, internally static configurations. As a solution, I introduce worlds, and world histories, as key concepts in providing a link between MBM’s micro dynamics and macroscopic phenomena. Worlds, other than time capsules, are coarse-grained regions in phase- or configuration space, defined as sets of possible micro states satisfying a relation of sufficient similarity from a macroscopic perspective, with respect to a given micro state. Hence, worlds may overlap. -/- I argue that worlds thus construed are a reasonable option for replacing the disjoint macro regions of phase space, resulting from the usual way of partitioning phase space in the standard framework of Boltzmannian statistical mechanics. This move solves the issue of discontinuous change of macro variables upon the micro state crossing the boundary between different macro regions. -/- I adapt this move for MBM’s discontinuous micro dynamics in configuration space. Issues revolving around the microscopic-macroscopic distinction, particle identity, impenetrability and haecceity in light of the desideratum of particle number conservation, etc., are discussed. I provide a detailed explanation of how overlapping worlds in MBM form world histories, thereby linking up macroscopically distinct worlds. Thus, the problem of temporal solipsism is resolved in a way that is compatible with a more than minimal psychophysical parallelism. (shrink)

We describe a software system for the analysis of defined benefit actuarial plans. The system uses a recursive formulation of the actuarial stochastic processes to implement precise and efficient computations of individual and group cash flows.

Unification of natural science and social science is a centuries-old, unmitigated debate. Natural science has a chronological advantage over social science because the latter took time to include many social phenomena in its fold. History of science witnessed quite a number of efforts by social scientists to fit this discipline in a rational if not mathematical framework. On the other hand a tendency among some physicists has been observed especially since the last century to recast a number of social phenomena (...) in the mould of events taking place in physical world and governed by well-known systems and equations of physics. It necessitated the introduction of social physics as a new inter-disciplinary subject. Obviously this attempt is aimed at explaining hitherto unsolved or highly debated issues of social science. Physicists are showing special interest on problems on economics, ranging from some topics of normative economics to the movement of prices of derivatives. Statistics has been widely used in these attempts and at least two sub-disciplines of the subject, namely, stochastic process and time series analysis deserve special mention. All these research activities gave birth to another inter-disciplinary subject named as econophysics. Interestingly, global financial crisis of 2007–08 has revived the need of determination of prices of derivatives in a more accurate manner. This article adumbrates a sketch of the theoretical synthesis between physics and economics and the role played by statistics in this process. (shrink)

Optimization and Stochastic Processes Applied to Economy and Finance. Textbook for the BM&F-USP (Brazilian Mercantile and Futures Exchange - University of Sao Paulo) Master's degree program in Finance.

No two individuals with the autism diagnosis are ever the same—yet many practitioners and parents can recognize signs of ASD very rapidly with the naked eye. What, then, is this phenotype of autism that shows itself across such distinct clinical presentations and heterogeneous developments? The “signs” seem notoriously slippery and resistant to the behavioral threshold categories that make up current assessment tools. Part of the problem is that cognitive and behavioral “abilities” typically are theorized as high-level disembodied and modular functions—that (...) are assessed discretely (impaired, normal, enhanced) to define a spectral syndrome. Even as biology reminds us that organic developing bodies are not made up of independent switches, we remain often seduced by the simplicity of mechanistic and cognitive models. Developmental disorders such as autism have accordingly been theorized as due to different modular dysfunctions—typically of cortical origin, i.e., failures of “theory of mind” (Baron-Cohen et al., 1985), of the “mirror neuron system” (Ramachandran and Oberman, 2006), of “weak central coherence” (Happe and Frith, 2006) or of the balance of “empathizing” and “systemizing” (Baron-Cohen, 2009), just to list a few. -/- The broad array of autonomic (Ming et al., 2005; Cheshire, 2012) and sensorimotor (Damasio and Maurer, 1978; Maurer and Damasio, 1982; Donnellan and Leary, 1995; Leary and Hill, 1996; Donnellan and Leary, 2012; Donnellan et al., 2012) differences experienced and reported by people with autism have by such theories typically been sidelined as “co-morbidities,” possibly sharing genetic causes, but rendered as incidental and decisively behaviorally irrelevant symptoms—surely disconnected from cognition. But what if the development of cortically based mental processes and autonomous control relies on the complexities and proper function of the peripheral nervous systems? Through such an “embodied” lens the heterogeneous symptoms of autism invites new interpretations. We propose here that many behavioral-level findings can be re-defined as downstream effects of how developing nervous systems attempt to cope and adapt to the challenges of having various noisy, unpredictable, and unreliable peripheral inputs. (shrink)

MỘT SỐ QUÁ TRÌNH NGẪU NHIÊN CÓ BƯỚC NHẢY -/- Hoàng Thị Phương Thảo -/- Luận án Tiến sỹ -/- TRƯỜNG ĐẠI HỌC KHOA HỌC TỰ NHIÊN ĐẠI HỌC QUỐC GIA HÀ NỘI -/- Hà Nội - 2015 .

The Generalized Poisson Distribution (GPD) adds an extra parameter to the usual Poisson distribution. This parameter induces a loss of homogeneity in the stochastic processes modeled by the distribution. Thus, the generalized distribution becomes an useful model for counting processes where the occurrence of events is not homogeneous. This model creates the need for an inferential procedure, to test for the value of this extra parameter. The FBST (Full Bayesian Significance Test) is a Bayesian hypotheses test procedure, (...) capable of providing an evidence measure on sharp hypotheses (where the dimension of the parametric space under the null hypotheses is smaller than that of the full parametric space). The goal of this work is study the empirical properties of the FBST for testing the nullity of extra parameter of the generalized Poisson distribution. Numerical experiments show a better performance of FBST with respect to the classical likelihood ratio test, and suggest that FBST is an efficient and robust tool for this application. (shrink)

The idea of new-type articles, named “Perspectives”, announced recently by some leading journals, is suggested to be approached for the controversial question of quantum mechanics interpretation. Firstly, it is revealed briefly the unsatisfactory situation of the nowadays predominant doctrine about that question. Then some basic elements of the proposed approach are presented. Those elements refer to (i) uncertainty relations, (ii) distinction between own tasks of quantum mechanics and description of quantum measurements, (iii) defects of collapse scenarios for measurements, and (iv) (...) depiction of quantum measurements as data transmission stochastic processes. The essay closes with some concluding remarks. (shrink)

Credit risk, also known as default risk, is the likelihood of a corporation losing money if a business partner defaults. If the liabilities are not met under the terms of the contract, the firm may default, resulting in the loss of the company. There is no clear way to distinguish between organizations that will default and those that will not prior to default. We can only make probabilistic estimations of the risk of default at best. There are two types of (...) credit risk default models in this regard: structural and reduced-form models. Structural models are used to calculate the likelihood of a company defaulting based on its assets and liabilities. If the market worth of a company's assets is less than the debt it owes, it will default. Reduced form models often assume an external cause of default, such as a Poisson jump process, which is driven by a stochastic process. They model default as a random event with no regard for the balance sheet of the company. This paper provides a Review of credit risk default models. (shrink)

Twenty-first century science faces a dilemma. Two of its well-verified foundation stones - relativity and quantum theory - have proven inconsistent. Resolution of the conflict has resisted improvements in experimental precision leaving some to believe that some fundamental understanding in our world-view may need modification or even radical reform. Employment of the wave-front model of electrodynamics, as a propagation process with a Markov property, may offer just such a clarification.

This is a collection of the abstracts of lectures given at the International Conference on Differential Equations, Approximations and Applications, which will be held at the old campus of the Vietnam National University at Hanoi December 10-15, 2001.

I analyze Deleuze’s concept of temporality in terms of its ontology and axiological (political and aesthetic) aspects. For Deleuze, the concept of temporality is non-monolithic, in the senses that it is modified throughout his works — the monographs, lectures, and those works that were co-authored with Félix Guattari — and that it is developed through reference to a dizzying array of concepts, thinkers, artistic works, and social phenomena. -/- I observe that Deleuze’s concept of temporality involves a complex ontology of (...) difference, which I elaborate through reference to Deleuze’s analyses of Ancient Greek and Stoic conceptualizations of time. From Plato through to Chrysippus, temporality gradually comes to be identified as a form that comprehends the variation of particulars. Deleuze modifies the ancients’ concept of time to suggest that time obtains as a form of ceaseless ontological variation. Through reference to Deleuze’s reading of Gilbert Simondon, I further suggest that Deleuze tends to conceive of temporality as an ontogenetic force which participates in the complex process of individuation. -/- A standout feature of this dissertation involves an analysis of how Deleuze’s concept of temporality is modified in his works on cinema. In Cinema 1: The Movement-Image and Cinema 2: The Time-Image, temporality comes to be characterized as something other than the measure of the movement of existents. In his detailed analyses of Bergson — in Cinema 1: The Movement-Image, Cinema 2: The Time-Image, and Bergsonism — Deleuze suggests that time involves an actualization of aspects of a virtual past as contemporaneous with the lived present. While not an outright denial of the relation of temporal succession, Deleuze’s claim implies a diminishment of this relation’s significance in an adequate elaboration of the nature of temporality. -/- Further, I observe —through reference to Deleuze’s readings of Marx, Kierkegaard, and Spinoza — that (the explicitly temporal) change of societal forms of economic organization is non-reducible to that suggested by linear evolution. The claim is that putatively discrete modes of economic organization do not enjoy temporal displacement with respect to one another. This suggests that linear evolutionary models of societal development are inadequate. This further implies that temporality is non-reducible to the relation of temporal succession. In concrete terms, societal change is characterized as immanent temporal variation. -/- Taken together, these analyses yield the conclusion that Deleuze tends to conceive of the nature of temporality as involving the ongoing realization of multiple — non-identical, sometimes contrary — aspects of a stochastic process of creation that is expressed in ontogenetic circumstances, social evolution, literary works, and filmic works. (shrink)

By means of a probabilistic mathematical model, we bring into discussion the origin of life as a stochastic process. We consider only the chance of information emergence in the proteome and genome under the ideal thermodynamic and chemical conditions. For a more realistic model, we used, as a parameter, the information amount in N. equitans genome, the simplest known nowadays, as the equivalent to the first living cell that could have emerged in primitive Earth. We estimated the probability of (...) information emergence by chance as being smaller than 10-500’000. Considering the necessary ideal conditions for information emergence, the probability of the origin of life would be even smaller. (shrink)

It has become customary to conceptualize the living cell as an intricate piece of machinery, different to a man-made machine only in terms of its superior complexity. This familiar understanding grounds the conviction that a cell's organization can be explained reductionistically, as well as the idea that its molecular pathways can be construed as deterministic circuits. The machine conception of the cell owes a great deal of its success to the methods traditionally used in molecular biology. However, the recent introduction (...) of novel experimental techniques capable of tracking individual molecules within cells in real time is leading to the rapid accumulation of data that are inconsistent with an engineering view of the cell. This paper examines four major domains of current research in which the challenges to the machine conception of the cell are particularly pronounced: cellular architecture, protein complexes, intracellular transport, and cellular behaviour. It argues that a new theoretical understanding of the cell is emerging from the study of these phenomena which emphasizes the dynamic, self-organizing nature of its constitution, the fluidity and plasticity of its components, and the stochasticity and non-linearity of its underlying processes. (shrink)

Credit risk, also known as default risk, is the likelihood of a corporation losing money if a business partner defaults. If the liabilities are not met under the terms of the contract, the firm may default, resulting in the loss of the company. There is no clear way to distinguish between organizations that will default and those that will not prior to default. We can only make probabilistic estimations of the risk of default at best. There are two types of (...) credit risk default models in this regard: structural and reduced form models. Structural models are used to calculate the likelihood of a company defaulting based on its assets and liabilities. If the market worth of a company's assets is less than the debt it owes, it will default. Reduced form models often assume an external cause of default, such as a Poisson jump process, which is driven by a stochastic process. They model default as a random event with no regard for the balance sheet of the company. This paper provides a Review of credit risk default models. (shrink)

In this article I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss’s ε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence (...) are unpromising. Despite this critique, I suggest that Werndl’s proposals are valuable because they clarify the distinction between provable and unprovable elements in arguments for observational equivalence. (shrink)

It is difficult to extract reliable criteria for causal locality from the limited ingredients found in textbook quantum theory. In the end, Bell humbly warned that his eponymous theorem was based on criteria that “should be viewed with the utmost suspicion.” Remarkably, by stepping outside the wave-function paradigm, one can reformulate quantum theory in terms of old-fashioned configuration spaces together with ‘unistochastic’ laws. These unistochastic laws take the form of directed conditional probabilities, which turn out to provide a hospitable foundation (...) for encoding microphysical causal relationships. This unistochastic reformulation provides quantum theory with a simpler and more transparent axiomatic foundation, plausibly resolves the measurement problem, and deflates various exotic claims about superposition, interference, and entanglement. Making use of this reformulation, this paper introduces a new principle of causal locality that is intended to improve on Bell's criteria, and shows directly that systems that remain at spacelike separation cannot exert causal influences on each other, according to that new principle. These results therefore lead to a general hidden-variables interpretation of quantum theory that is arguably compatible with causal locality. (shrink)

The essay offers an original view on the issues of identity and self-identification. Self-identification is being studied in the process of its implementation in different time flows. Two directions of thought (to the past and the future) which are defined according to Hameroff»s hypothesis as the bi-directional time flows, constitute the concept of a dream. Using this concept, the author explains how self-identification is realized in two time flows. The strategy of self-identification is explained using a stochastic algorithm which (...) balances the present and the future states at the same stage. The Kalman filter is used as the stochastic algorithm. (shrink)

The topic of this dissertation is the nature of linguistic competence, the capacity to understand and produce sentences of natural language. I defend the empiricist account of linguistic competence embedded in the connectionist cognitive science. This strand of cognitive science has been opposed to the traditional symbolic cognitive science, coupled with transformational-generative grammar, which was committed to nativism due to the view that human cognition, including language capacity, should be construed in terms of symbolic representations and hardwired rules. Similarly, linguistic (...) competence in this framework was regarded as being innate, rule-governed, domain-specific, and fundamentally different from performance, i.e., idiosyncrasies and factors governing linguistic behavior. I analyze state-of-the-art connectionist, deep learning models of natural language processing, most notably large language models, to see what they can tell us about linguistic competence. Deep learning is a statistical technique for the classification of patterns through which artificial intelligence researchers train artificial neural networks containing multiple layers that crunch a gargantuan amount of textual and/or visual data. I argue that these models suggest that linguistic competence should be construed as stochastic, pattern-based, and stemming from domain-general mechanisms. Moreover, I distinguish syntactic from semantic competence, and I show for each the ramifications of the endorsement of a connectionist research program as opposed to the traditional symbolic cognitive science and transformational-generative grammar. I provide a unifying front, consisting of usage-based theories, a construction grammar approach, and an embodied approach to cognition to show that the more multimodal and diverse models are in terms of architectural features and training data, the stronger the case is for the connectionist linguistic competence. I also propose to discard the competence vs. performance distinction as theoretically inferior so that a novel and integrative account of linguistic competence originating in connectionism and empiricism that I propose and defend in the dissertation could be put forward in scientific and philosophical literature. (shrink)

The monograph is an English, expanded and revised version of the book Cheshko, V. T., Ivanitskaya, L.V., & Glazko, V.I. (2018). Anthropocene. Philosophy of Biotechnology. Moscow, Course. The manuscript was completed by me on November 15, 2019. It is a study devoted to the development of the concept of a stable evolutionary human strategy as a unique phenomenon of global evolution. The name “An Evolutionary Metaphysics (Cheshko, 2012; Glazko et al., 2016). With equal rights, this study could be entitled “Biotechnology (...) as a result and factor of the evolutionary processˮ. The choice in favor of used “The Evolutionary Metaphysics of Human Enhancement Technologiesˮ was made in accordance with the basic principle of modern post-academician and human-sized science, a classic example of which is biotechnology. The “Metaphysics of Evolution” and “Evolutionary Metaphysics” concepts are used in several ways in modern philosophical discourse. In any case, the values contain a logical or associative reference to the teleological nature of the evolutionary process (Hull, 1967, 1989; Apel, 1995; Faye, 2016; Dupre, 2017; Rose, 2018, etc). In our study, the “evolutionary metaphysics” serves to denote the thesis of the rationalization and technologization of global evolution and anthropogenesis, in particular. At the same time, the postulate of an open future remains relevant in relation to the results of the evolutionary process. The theory of evolution of complex, including the humans system and algorithm for its constructing are а synthesis of evolutionary epistemology, philosophical anthropology and concrete scientific empirical basis in modern science. ln other words, natural philosophy is regaining the status bar element theoretical science in the era of technology-driven evolution. The co-evolutionary concept of 3-modal stable evolutionary strategy of Homo sapiens is developed. The concept based оn the principle of evolutionary complementarity of anthropogenesis: value of evolutionary risk and evolutionary path of human evolution are defined bу descriptive (evolutionary efficiency) and creative-teleological (evolutionary correctness) parameters simultaneously, that cannot bе instrumental reduced to others ones. Resulting volume of both parameters define the vectors of blological, social, cultural and techno-rationalistic human evolution Ьу two gear mechanism genetic and cultural co-evolution and techno-humanitarian balance. The resultant each of them сап estimated Ьу the ratio of socio-psychological predispositions of humanization / dehumanization in mentality. Explanatory model and methodology of evaluation of creatively teleological evolutionary risk component of NBIC technological complex is proposed. Integral part of the model is evolutionary semantics (time-varying semantic code, the compliance of the blological, socio-cultural and techno-rationalist adaptive modules of human stable evolutionary strategy). It is seem necessary to make three clarifications. First, logical construct, “evolutionary metaphysics” contains an internal contradiction, because it unites two alternative explanatory models. “Metaphysics”, as a subject, implies deducibility of the process from the initial general abstract principle, and, consequently, the outcome of the development of the object is uniquely determined by the initial conditions. Predicate, “evolutionary”, means stochastic mechanism of realizing the same principle by memorizing and replicating random choices in all variants of the post-Darwin paradigm. In philosophy, random choice corresponds to the category of “free will” of a reasonable agent. In evolutionary theory, the same phenomenon is reflected in the concept of “covariant replication”. Authors will attempt to synthesize both of these models in a single transdisciplinary theoretical framework. Secondly, the interpretation of the term “evolutionary (adaptive) strategyˮ is different from the classical definition. The difference is that the adaptive strategy in this context is equivalent to the survival, i.e. it includes the adaptation to the environment and the transformation (construction) of the medium in accordance with the objectives of survival. To emphasize this difference authors used verbal construction “adaptiveˮ (rather than “evolutionaryˮ) strategy as more adequate. In all other cases, the two terms may be regarded as synonymous. Thirdly, the initial two essays of this series were published in one book in 2012. Their main goal was the development of the logically consistent methodological concept of stable adaptive (evolutionary) strategy of hominines and the argumentation of its heuristic possibilities as a transdisciplinary scientific paradigm of modern anthropology. The task was to demonstrate the possibilities of the SESH concept in describing and explaining the evolutionary prospects for the interaction of social organization and technology (techno-humanitarian balance) and the associated biological and cultural mechanisms of the genesis of religion (gene-cultural co-evolution). In other words, it was related to the sphere of cultural and philosophical anthropology, i.e. to the axiological component of any theoretical constructions describing the behavior of self-organizing systems with human participation. In contrast, the present work is an attempt to introduce this concept into the sphere of biological anthropology and, consequently, its main goal is to demonstrate the possibility of verification of its main provisions by means of procedures developed by natural science, i.e. refers to the descriptive component of the same theoretical constructions. The result of this in the future should be methods for assessing, calculating and predicting the risk of loss of biological and cultural identity of a person, associated with a permanent and continuously deepening process of development of science and technology. (shrink)

Looks into evaluation of information provision probability from different sources, based on use of linguistic variables. Formation of functions appurtenant for its unclear variables provides for adoption of decisions by the decision maker, in conditions of nonprobabilistic equivocation. The development of market relations in Ukraine increases the independence and responsibility of enterprises in justifying and making management decisions that ensure their effective, competitive activities. As a result of the analysis, it is determined that the condition of economic facilities can be (...) described and determined by the decision-maker, in the presence of the necessary information. The confidence of the decision-maker in the information received is different and the decisions made have a correspondingly different level of information risk. It is important to substantiate the procedure for assessing the numerical extent of information risk in decision-making based on the information obtained in conditions of uncertainty. The use of a linguistic variable in the processing of expert data presented in the form of a matrix of binary relations of values of the membership function, which allowed to move to further processing of knowledge to support decision-making in the management of industrial, commercial, financial and other activities. As a mathematical model for estimating the numerical measure of information risk when making decisions based on the information obtained in conditions of non-stochastic uncertainty, a model has been developed to model natural language uncertainties, which differs from existing ones by formalizing knowledge taking into account uncertainty of input information. Making such a clear decision in a fuzzy environment has appropriate values of effectiveness and risk. The paper proposes all the functions and accessories of indicators of both quantitative nature and qualitative nature to bring their values in the field of definition to one scale. Then the indicator of the effectiveness of decision-making will be a measure of the clarity of the cross-section of fuzzy subsets, which correspond to the introduced indicators of information risk. The condition of economic facilities can be described and determined by the decision-maker, if the necessary information is available. Decision-making on thenumerical measure of information risk must be determined by a set of basic indicators, which can be both quantitative and qualitative in nature. Predictive values of indicators should be determined in conditions of nonstochastic uncertainty. In this case, the indicators of a quantitative nature can be determined by fuzzy triangular numbers, which implement a high level of confidence in the subjective judgments of experts. Indicators of qualitative nature should be presented in linguistic variables. The values of the indicators of qualitative nature that are predicted must be considered for all fuzzy variable terms-sets of linguistic variables introduced into consideration. For any fuzzy variable, the introduction to the consideration of a clear set of values as carriers of the α-level of its membership function allows to reduce to a single interpretation of the predicted values of indicators of quantitative and qualitative nature in terms of non-stochastic uncertainty. (shrink)

The basic idea of quantum mechanics is that the property of any system can be in a state of superposition of various possibilities. This state of superposition is also known as wave function and it evolves linearly with time in a deterministic way in accordance with the Schrodinger equation. However, when a measurement is carried out on the system to determine the value of that property, the system instantaneously transforms to one of the eigen states and thus we get only (...) a single value as outcome of the measurement. Quantum measurement problem seeks to find the cause and exact mechanism governing this transformation. In an attempt to solve the above problem, in this paper, we will first define what the wave function represents in real world and will identify the root cause behind the stochastic nature of events. Then, we will develop a model to explain the mechanism of collapse of the quantum mechanical wave function in response to a measurement. In the process of development of model, we will explain Schrodinger cat paradox and will show how Born’s rule for probability becomes a natural consequence of measurement process. (shrink)

Cognitive scientists used to deem reasoning either as a higher cognitive process based on the manipulation of abstract rules or as a higher cognitive process that is stochastic rather than involving abstract rules. I maintain that these different perspectives are closely intertwined with a theoretical and methodological endorsement of either cognitivism or connectionism. Cognitivism and connectionism represent two prevailing and opposed paradigms in cognitive science. I aim to extoll the virtues of connectionist models of enthymematic reasoning by following means: (...) via the phenomenon of creative enthymeme, viz. the inference where one cannot even articulate the missing premise, I introduce a connectionist mechanism of pattern recognition as underlying expertise; via Gestalt switch or Gestalt click, I demonstrate how differences in pattern recognition of an expert and a novice can be construed as qualitatively different, and not merely a matter of faster reasoning. (shrink)

Bell-type inequalities are proven using oversimplified probabilistic models and/or counterfactual definiteness (CFD). If setting-dependent variables describing measuring instruments are correctly introduced, none of these inequalities may be proven. In spite of this, a belief in a mysterious quantum nonlocality is not fading. Computer simulations of Bell tests allow people to study the different ways in which the experimental data might have been created. They also allow for the generation of various counterfactual experiments’ outcomes, such as repeated or simultaneous measurements performed (...) in different settings on the same “photon-pair”, and so forth. They allow for the reinforcing or relaxing of CFD compliance and/or for studying the impact of various “photon identification procedures”, mimicking those used in real experiments. Data samples consistent with quantum predictions may be generated by using a specific setting-dependent identification procedure. It reflects the active role of instruments during the measurement process. Each of the setting-dependent data samples are consistent with specific setting-dependent probabilistic models which may not be deduced using non-contextual local realistic or stochastic hidden variables. In this paper, we will be discussing the results of these simulations. Since the data samples are generated in a locally causal way, these simulations provide additional strong arguments for closing the door on quantum nonlocality. (shrink)

This survey tries to investigate the truths and deficiencies of prevalent philosophy about Uncertainty Relations (UR) and Quantum Measurements (QMS). The respective philosophy, known as being eclipsed by unfinished controversies, is revealed to be grounded on six basic precepts. But one finds that all the respective precepts are discredited by insurmountable deficiencies. So, in regard to UR, the alluded philosophy discloses oneself to be an unjustified mythology. Then UR appear either as short-lived historical conventions or as simple and limited mathematical (...) formulas, without any essential significance for physics. Such a finding reinforces the Dirac’s prediction that UR “in their present form will not survive in the physics of future”. The noted facets of UR motivate reconsiderations of associated debates on QMS. Mainly one reveals that, properly, UR have not any essential connection with genuine descriptions of QMS. For such descriptions, it is necessary that, mathematically, the quantum observables to be considered as random variables. The measuring scenarios with a single sampling, such are wave function collapse or Schrodinger’s cat thought experiment, are revealed as being useless ¨inventions. We propose to describe QMS as transmission processes for stochastic data. Note that, for existing quantum debates, the above UR–QMS revaluations, offer a few arguments for lucrative parsimony in approaches of matters. The unlucrative aspects of those debates have to be reconsidered too, probably in more or less speculative visions. (shrink)

Decision theorists widely accept a stochastic dominance principle: roughly, if a risky prospect A is at least as probable as another prospect B to result in something at least as good, then A is at least as good as B. Recently, philosophers have applied this principle even in contexts where the values of possible outcomes do not have the structure of the real numbers: this includes cases of incommensurable values and cases of infinite values. But in these contexts the (...) usual formulation of stochastic dominance is wrong. We show this with several counterexamples. Still, the motivating idea behind stochastic dominance is a good one: it is supposed to provide a way of applying dominance reasoning in the stochastic context of probability distributions. We give two new formulations of stochastic dominance that are more faithful to this guiding idea, and prove that they are equivalent. (shrink)

Nicholas Rescher’s way of understanding process philosophy reflects the ambitions of his own philosophical project and commits him to a conceptually ideal interpretation of process. Process becomes a transcendental idea of reflection that can always be predicated of our knowledge of the world and of the world qua known, but not necessarily of reality an sich. Rescher’s own taxonomy of process thinking implies that it has other variants. While Rescher’s approach to process philosophy makes it intelligible and appealing to mainstream (...) analytic philosophy, it leaves behind the more daring ideas of Bergson, James, and Whitehead, all of whom envisioned the primordial reality of process in a radical ontology of becoming. This variant of process thought can be construed as coherent and self-consistent, but not without relinquishing the correspondence theory of truth and embracing challenging ideas that bring us in close proximity to existentialism, apophatic theology, and Buddhism. (shrink)

Recently developed large language models (LLMs) perform surprisingly well in many language-related tasks, ranging from text correction or authentic chat experiences to the production of entirely new texts or even essays. It is natural to get the impression that LLMs know the meaning of natural language expressions and can use them productively. Recent scholarship, however, has questioned the validity of this impression, arguing that LLMs are ultimately incapable of understanding and producing meaningful texts. This paper develops a more optimistic view. (...) Drawing on classic externalist accounts of reference, it argues that LLMs are very likely capable of reference. Not only that: The combination of a popular externalist account of reference and recent experimental data in machine psychology even suggests that LLMs might play a role in shifting what our words refer to. (shrink)

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To (...) fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework. (shrink)

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background (...) uncertainty about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (shrink)

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that (...) entail not only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory. (shrink)

This study aimed to identify the learning and business incubation processes and their impact on developing the performance of business incubators in Gaza Strip, and the study relied on the descriptive analytical approach, and the study population consisted of all employees working in business incubators in Gaza Strip in addition to experts and consultants in incubators where their total number reached (62) individuals, and the researchers used the questionnaire as a main tool to collect data through the comprehensive survey (...) method, where (55) questionnaires were retrieved with a recovery rate of (88.7%). The results of the study showed that there is a high approval of the variables of the study, where the dimension of incubation operations came with a relative weight (84.89%), followed by the learning dimension which got a relative weight (82.50%), while the performance level of the incubators got a relative weight (80.12%) and as the study results showed There is a positive relationship statistically between the two dimensions of learning and business incubation processes and performance development in business incubators, and the linear regression analysis model showed that the main effect in improving the performance of business incubators is "after business incubation operations" while it showed weak effect after learning. The study came out with several recommendations, the most important of which is that business incubators seek to reinforce the learning process and incubation processes for business, and the need to periodically evaluate their performance, and that a more effective mechanism be designed to follow up with companies after the end of the incubation period and monitor the progress of these companies. (shrink)

I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an assignment of chance values is possible if and only if it is given by a pure state on a given algebra, your estimates for chances avoid accuracy-dominance if and only if they are given by a state on that algebra. When your estimates avoid accuracy-dominance (roughly: when you cannot guarantee that (...) other estimates would be more accurate), I say that they are sufficiently coherent. In formal epistemology and quantum foundations, the notion of rational coherence that gets more attention requires that you never allow for a sure loss (or “Dutch book”) in a given sort of betting game; I call this notion full coherence. I characterize when these two notions of rational coherence align, and I show that there is a quantum state giving estimates that are sufficiently coherent, but not fully coherent. (shrink)

Perception can’t have disjunctive content. Whereas you can think that a box is blue or red, you can’t see a box as being blue or red. Based on this fact, I develop a new problem for the ambitious predictive processing theory, on which the brain is a machine for minimizing prediction error, which approximately implements Bayesian inference. I describe a simple case of updating a disjunctive belief given perceptual experience of one of the disjuncts, in which Bayesian inference and predictive (...) coding pull in opposite directions, with the former implying that one’s confidence in the belief should increase, and the latter implying that it should decrease. Thus, predictive coding fails to approximately implement Bayesian inference across the interface between belief and perception. (shrink)

Philosophers of biology have worked extensively on how we ought best to interpret the probabilities which arise throughout evolutionary theory. In spite of this substantial work, however, much of the debate has remained persistently intractable. I offer the example of Bayesian models of divergence time estimation as a case study in how we might bring further resources from the biological literature to bear on these debates. These models offer us an example in which a number of different sources of uncertainty (...) are combined to produce an estimate for a complex, unobservable quantity. These models have been carefully analyzed in recent biological work, which has determined the relationship between these sources of uncertainty, both quantitatively and qualitatively. I suggest here that this case shows us the limitations of univocal analyses of probability in evolution, as well as the simple dichotomy between “subjective” and “objective” probabilities, and I conclude by gesturing toward ways in which we might introduce more sophisticated interpretive taxonomies of probability as a path toward advancing debates on probability in the life sciences. (shrink)

Predictive processing models of perception take issue with standard models of perception as hierarchical bottom-up processing modulated by memory and attention. The predictive framework posits that the brain generates predictions about stimuli, which are matched to the incoming signal. Mismatches between predictions and the incoming signal – so-called prediction errors – are then used to generate new and better predictions until the prediction errors have been minimized, at which point a perception arises. Predictive models hold that all bottom-up processes (...) are signals conveying prediction errors to higher areas, which respond by updating their predictions. We take issue with this claim and argue that object recognition requires bottom-up processing that cannot be understood in terms of prediction errors. Along the way, we expand on previous work casting doubt on the framework's ability to account for attention. Specifically, we argue that the type of attention that allows us to rapidly extract the gist of an object or scene presents an additional challenge to the predictive approach. We conclude by considering how the framework may be augmented to avoid these problems. (shrink)

Predictive processing (PP) accounts of perception are unique not merely in that they postulate a unity between perception and imagination. Rather, they are unique in claiming that perception should be conceptualised in terms of imagination and that the two involve an identity of neural implementation. This paper argues against this postulated unity, on both conceptual and empirical grounds. Conceptually, the manner in which PP theorists link perception and imagination belies an impoverished account of imagery as cloistered from the external world (...) in its intentionality, akin to a virtual reality, as well as endogenously generated. Yet this ignores a whole class of imagery whose intentionality is directed on the actual environment—projected mental imagery—and also ignores the fact that imagery may be triggered crossmodally in a bottom-up, stimulus-driven way. Empirically, claiming that imagery and perception share neural circuitry ignores relevant clinical results in this area. These evidence substantial perception/imagery neural dissociations, most notably in the case of aphantasia. Taken together, the arguments here suggest that PP theorists should substantially temper, if not outright abandon, their claim to a perception/imagination unity. (shrink)

A widely debated issue in contemporary metaphysics is whether the modal profile of ordinary objects has to be explained in non-modal terms (that is, Thesis 1). However, how to solve such an issue with respect to occurrences – namely, processes and events – is a question that has been largely neglected in the current metaphysical debate. The general goal of this article is to start filling this gap. As a first result of the article, we make it plausible that, (...) if Thesis 1 holds for objects, then it also holds for processes and events. Then, we develop a metaphysical account of processes derived from Fine’s (1999, 2022) suggestions, according to which a process is a variable embodiment that is manifested by different events at the different times it goes on – namely, Thesis 2. We raised the challenge from the completion of a process that asks the Finean account of processes to explain relevant modal features of processes in non-modal terms. As a second result, we argue that four initially plausible strategies for solving such a challenge fall short of solving it. As a third result, we show that the theory of variable embodiments Fine formulates for objects must differ from the theory of variable embodiments that aims to model processes. We conclude by investigating some revisions to a theory of variable embodiments that aims to model processes. (shrink)

In this paper I argue that even the most radical metaphysics of powers (such as that adopted by Mumford & Anjum, Cartwright, or Groff) are compatible with eternalism. I first offer a taxonomy of powers ontologies, and attempt to characterise the difference between moderate and radical powers ontologies – the latter are characterised by an emphasis on production and dynamicity. I consider an argument by C. Friebe to the effect that the productive character of powers is inconsistent with Eternalism and (...) find it wanting. I then elucidate the notion of dynamicity that radical powers theorists employ by making apparent their link with an ontology of irreducible processes. Finally, I respond to an argument by Donatella Donati to the effect that eternalism entails a reductive account of change which is inconsistent with process ontologies, and show that the the two are compatible. I conclude that we have no reason to think that radical powers metaphysics (and, a fortiori, every powers ontology) are not compatible with eternalism. (shrink)

We introduce the predictive processing account of body representation, according to which body representation emerges via a domain-general scheme of (long-term) prediction error minimisation. We contrast this account against one where body representation is underpinned by domain-specific systems, whose exclusive function is to track the body. We illustrate how the predictive processing account offers considerable advantages in explaining various empirical findings, and we draw out some implications for body representation research.

Monists and pluralists disagree concerning how many ordinary objects there are in a single situation. For instance, pluralists argue that a statue and the clay it is made of have different properties, and thereby are different. The standard monist’s response is to hold that there is just a single object, and that, under the description “being a statue”, this object is, e.g., aesthetically valuable, and that, under the description “being a piece of clay”, it is not aesthetically valuable. However, Fine (...) provided an ontological reading of the expression “an object under a description”: the theory of rigid embodiments. The debate between monists and pluralists reduplicates in the domain of ordinary occurrences, like walks and conferences. Specifically, they disagree whether an occurrence in progress (also called “process”) like John’s walk that is happening at tn is identical to some completed occurrence (also called “event”) like John’s walk that happened between, e.g., t1 and tn. Under the adoption of the pluralist’s position, the article aims to provide a novel theory of ordinary occurrences that develops the ontological reading of “under a description” to account for occurrences in progress and completed occurrences. As a first result, we formulate a theory according to which both occurrences in progress and completed occurrences are rigid embodiments. As a second result, we argue that the suggested theory is explanatorily powerful to the extent it solves two puzzles that we call “the Puzzle from the Completion of a Process” and “the Metaphysical-cum-Semantical Puzzle”. (shrink)

Most process theologians have rejected the creation of the world out of nothing, holding that our universe was created out of some antecedent universe. This article shows how on process grounds, and with faithfulness to much of what Whitehead had to say, process theologians can and should affirm the creation of our universe out of nothing. Standard process objections to this are refuted.

In a number of papers, Kit Fine introduced a theory of embodiment which distinguishes between rigid and variable embodiments, and has been successfully applied to clarify the ontological nature of entities whose parts may or may not vary in time. In particular, he has applied this theory to describe a process such as the erosion of a cliff, which would be a variable embodiment whose manifestations are the different states of erosion of the cliff. We find this theory very powerful, (...) and especially appropriate to capture the intuition that the same process may go on at different times. However, its formal principles have been subject to some criticisms, mainly concerning the mereological structure of a variable embodiment. Moreover, since the notion of variable embodiment is very general, simply saying that processes are variable embodiments is not enough to understand their ontological nature. To address these concerns, in this paper we proceed in two phases: first, we propose a revised version of Fine’s original theory adapted to the case of processes, which adopts a classical mereology instead of Fine’s hylomorphic mereology, and a temporalized constitution relation in place of Fine’s function of variable embodiment; second, we go deeper into the ontological nature of processes by revisiting the notions of homogeneity, intentionality, and telicity discussed in the literature, and propose an account based on ontological principles and not on semantic properties of predicates. This allows us to organize processes into a novel taxonomy based exclusively on their unity and individuation principles. (shrink)

The majority of our linguistic exchanges, such as everyday conversations, are divided into turns; one party usually talks at a time, with only relatively rare occurrences of brief overlaps in which there are two simultaneous speakers. Moreover, conversational turn-taking tends to be very fast. We typically start producing our responses before the previous turn has finished, i.e., before we are confronted with the full content of our interlocutor’s utterance. This raises interesting questions about the nature of linguistic understanding. Philosophical theories (...) typically focus on linguistic understanding characterized either as an ability to grasp the contents of utterances in a given language or as outputs of this ability—mental states of one type or another. In this paper, I supplement these theories by developing an account of the process of understanding. I argue that it enables us to capture the dynamic and temporal aspect of understanding and reconcile philosophical investigations with empirical research on language comprehension. (shrink)

Many philosophers claim that the neurocomputational framework of predictive processing entails a globally inferentialist and representationalist view of cognition. Here, I contend that this is not correct. I argue that, given the theoretical commitments these philosophers endorse, no structure within predictive processing systems can be rightfully identified as a representational vehicle. To do so, I first examine some of the theoretical commitments these philosophers share, and show that these commitments provide a set of necessary conditions the satisfaction of which allows (...) us to identify representational vehicles. Having done so, I introduce a predictive processing system capable of active inference, in the form of a simple robotic “brain”. I examine it thoroughly, and show that, given the necessary conditions highlighted above, none of its components qualifies as a representational vehicle. I then consider and allay some worries my claim could raise. I consider whether the anti-representationalist verdict thus obtained could be generalized, and provide some reasons favoring a positive answer. I further consider whether my arguments here could be blocked by allowing the same representational vehicle to possess multiple contents, and whether my arguments entail some extreme form of revisionism, answering in the negative in both cases. A quick conclusion follows. (shrink)

The iterated Prisoner’s Dilemma has become the standard model for the evolution of cooperative behavior within a community of egoistic agents, frequently cited for implications in both sociology and biology. Due primarily to the work of Axelrod (1980a, 198Ob, 1984, 1985), a strategy of tit for tat (TFT) has established a reputation as being particularly robust. Nowak and Sigmund (1992) have shown, however, that in a world of stochastic error or imperfect communication, it is not TFT that finally triumphs (...) in an ecological model based on population percentages (Axelrod and Hamilton 1981), but ‘generous tit for tat’ (GTFT), which repays cooperation with a probability of cooperation approaching 1 but forgives defection with a probability of l/3. In this paper, we consider a spatialized instantiation of the stochastic Prisoner’s Dilemma, using two-dimensional cellular automata (Wolfram, 1984, 1986; Gutowitz, 1990) to model the spatial dynamics of populations of competing strategies. The surprising result is that in the spatial model it is not GIFT but still more generous strategies that are favored. The optimal strategy within this spatial ecology appears to be a form of ‘bending over backwards’, which returns cooperation for defection with a probability of 2/3 - a rate twice as generous as GTFT. (shrink)

We begin by describing recent developments in the burgeoning discipline of applied ontology, focusing especially on the ways ontologies are providing a means for the consistent representation of scientific data. We then introduce Basic Formal Ontology (BFO), a top-level ontology that is serving as domain-neutral framework for the development of lower level ontologies in many specialist disciplines, above all in biology and medicine. BFO is a bicategorial ontology, embracing both three-dimensionalist (continuant) and four-dimensionalist (occurrent) perspectives within a single framework. We (...) examine how BFO-conformant domain ontologies can deal with the consistent representation of scientific data deriving from the measurement of processes of different types, and we outline on this basis the first steps of an approach to the classification of such processes within the BFO framework. (shrink)