In 1957, Gödel proved that completeness for intuitionistic predicate logic HPL implies forms of Markov's Principle, MP. The result first appeared, with Kreisel's refinements and elaborations, in Kreisel. Featuring large in the Gödel-Kreisel proofs are applications of the axiom of dependent choice, DC. Also in play is a form of Herbrand's Theorem, one allowing a reduction of HPL derivations for negated prenex formulae to derivations of negations of conjunctions of suitable instances. First, we here show how to deduce Gödel's (...) results by alternative means, ones arguably more elementary than those of Kreisel. We avoid DC and Herbrand's Theorem by marshalling simple facts about negative translations and Markov's Rule. Second, the theorems of Gödel and Kreisel are commonly interpreted as demonstrating the unprovability of completeness for HPL, if means of proof are confined within strictly intuitionistic metamathematics. In the closing section, we assay some doubts about such interpretations. (shrink)

We develop a truism of commonsense psychology that perception and action constitute the boundaries of the mind. We do so however not on the basis of commonsense psychology, but by using the notion of a Markov blanket originally employed to describe the topological properties of causal networks. We employ the Markov blanket formalism to propose precise criteria for demarcating the boundaries of the mind that unlike other rival candidates for “marks of the cognitive” avoids begging the question in (...) the extended mind debate. Our criteria imply that the boundary of the mind is nested and multiscale sometimes extending beyond the individual agent to incorporate items located in the environment. Chalmers has used commonsense psychology to develop what he sees as the most serious challenge to the view that minds sometimes extend into the world. He has argued that perception and action should be thought of as interfaces that separate minds from their surrounding environment. In a series of recent papers Hohwy has defended a similar claim using the Markov blanket formalism. We use the Markov blanket formalism to show how both of their objections to the extended mind fail. (shrink)

A generalization of Ehrenfest''s urn model is suggested. This will allow usto treat a wide class of stochastic processes describing the changes ofmicroscopic objects. These processes are homogeneous Markov chains. Thegeneralization proposed is presented as an abstract conditional (relative)probability theory. The probability axioms of such a theory and some simpleadditional conditions, yield both transition probabilities and equilibriumdistributions. The resulting theory interpreted in terms of particles andsingle-particle states, leads to the usual formulae of quantum and classicalstatistical mechanics; in terms of (...) chromosomes and allelic types, it allowsthe deduction of many genetical models including the Ewens sampling formula;in terms of agents'' strategies, it gives a justification of the ``herdbehaviour'''' typical of a population of heterogeneous economic agents. (shrink)

The aim of the present paper is to give a purely probabilistic account for the approach to equilibrium of classical and quantum gas. The probability function used is classical. The probabilistic dynamics describes the evolution of the state of the gas due to unary and binary collisions. A state change amounts to a destruction in a state and the creation in another state. Transitions probabilities are splittled into destructions terms, denoting the random choice of the colliding particle(s), and creation terms, (...) describing the allocation of the same particle(s) on the final state(s). While the destruction term is the same for all types of particles, the creation one depends upon a parameter bound to the interpraticle correlation. The transition probabilities give rise to a homogeneous Markov chain. The equilibrium distributions satisfy the principle of detailed balance. Relaxation times depend upon the interparticle correlation. Relationships with the Ehrenfest urn model, Brillouin unified method, ensemble interpretation, and quantum H-theorem are considered too. (shrink)

Beth models of analysis are used in model theoretic proofs of the disjunction and (numerical) existence property. By glueing strings of models one obtains a model that combines the properties of the given models. The method asks for a common generalization of Kripke and Beth models. The proof is carried out in intuitionistic analysis plus Markov's Principle. The main new feature is the external use of intuitionistic principles to prove their own preservation under glueing.

We present a multiscale integrationist interpretation of the boundaries of cognitive systems, using the Markov blanket formalism of the variational free energy principle. This interpretation is intended as a corrective for the philosophical debate over internalist and externalist interpretations of cognitive boundaries; we stake out a compromise position. We first survey key principles of new radical views of cognition. We then describe an internalist interpretation premised on the Markov blanket formalism. Having reviewed these accounts, we develop our positive (...) multiscale account. We argue that the statistical seclusion of internal from external states of the system—entailed by the existence of a Markov boundary—can coexist happily with the multiscale integration of the system through its dynamics. Our approach does not privilege any given boundary, nor does it argue that all boundaries are equally prescient. We argue that the relevant boundaries of cognition depend on the level being characterised and the explanatory interests that guide investigation. We approach the issue of how and where to draw the boundaries of cognitive systems through a multiscale ontology of cognitive systems, which offers a multidisciplinary research heuristic for cognitive science. (shrink)

Let S be a deductive system such that S-derivability (⊦s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and ⊦s, it follows constructively that the K-completeness of ⊦s implies MP(S), a form of Markov's Principle. If ⊦s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if ⊦s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when ⊦s is (...) many-one complete, MP(S) implies the usual Markov's Principle MP. An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implies MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP. These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Godel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article. (shrink)

An application of probabilistic, stimulus-response learning theory to game-like small group situations. The theory is axiomatic, precise, and quantitative; and is deductively fruitful. There is a running comparison of the predictive success of the stimulus-response theory and game theory. The authors claim to have demonstrated "in empirical detail and with quantitative accuracy" that "the social situation, qua social, does not require the introduction of new concepts" beyond those of stimulus-response learning theory. --N. D. B. Jr.

This paper aims to provide a theoretical framework for explaining the subjective character of pain experience in terms of what we will call ‘embodied predictive processing’. The predictive processing (PP) theory is a family of views that take perception, action, emotion and cognition to all work together in the service of prediction error minimisation. In this paper we propose an embodied perspective on the PP theory we call the ‘embodied predictive processing (EPP) theory. The EPP theory proposes to explain pain (...) in terms of processes distributed across the whole body. The prediction error minimising system that generates pain experience comprises the immune system, the endocrine system, and the autonomic system in continuous causal interaction with pathways spread across the whole neural axis. We will argue that these systems function in a coordinated and coherent manner as a single complex adaptive system to maintain homeostasis. This system, which we refer to as the neural-endocrine-immune (NEI) system, maintains homeostasis through the process of prediction error minimisation. We go on to propose a view of the NEI ensemble as a multiscale nesting of Markov blankets that integrates the smallest scale of the cell to the largest scale of the embodied person in pain. We set out to show how the EPP theory can make sense of how pain experience could be neurobiologically constituted. We take it to be a constraint on the adequacy of a scientific explanation of subjectivity of pain experience that it makes it intelligible how pain can simultaneously be a local sensing of the body, and, at the same time, a more global, all-encompassing attitude towards the environment. Our aim in what follows is to show how the EPP theory can meet this constraint. (shrink)

Open peer commentary on the article “A Moving Boundary, a Plastic Core: A Contribution to the Third Wave of Extended-Mind Research” by Timotej Prosen. Abstract: We argue that the free-energy principle (FEP) can indeed be used to articulate a conception of the boundaries of cognitive systems that meets the desiderata of third-wave extended-mind research. We point out that Markov blankets under the FEP definitionally constitute the means through which internal and external states are coupled, and so do not isolate (...) systems from their environment. We argue that the nested, multiscale boundaries of the FEP formulation are indeed plastic and open to re-negotiation. Finally, we appeal to the formulation of niche construction under the FEP to argue that the extension of cognitive boundaries in this formulation is both synchronic and diachronic. (shrink)

This paper separates conditional parameter estima- tion, which consistently raises test set accuracy on statistical NLP tasks, from conditional model struc- tures, such as the conditional Markov model used for maximum-entropy tagging, which tend to lower accuracy. Error analysis on part-of-speech tagging shows that the actual tagging errors made by the conditionally structured model derive not only from label bias, but also from other ways in which the independence assumptions of the conditional model structure are unsuited to linguistic sequences. (...) The paper presents new word-sense disambiguation and POS tagging experiments, and integrates apparently conflicting reports from other recent work. (shrink)

Modern empirical macroeconomic models, known as structural autoregressions (SVARs) are dynamic models that typically claim to represent a causal order among contemporaneously valued variables and to merely represent non-structural (reduced-form) co-occurence between lagged variables and contemporaneous variables. The strategy is held to meet the minimal requirements for identifying the residual errors in particular equations in the model with independent, though otherwise not directly observable, exogenous causes (“shocks”) that ultimately account for change in the model. In nonstationary models, such shocks accumulate (...) so that variables have discernible trends. Econometricians have conceived of variables that trend in sympathy with each other (so-called “cointegrated variables”) as sharing one or more of these unobserved trends as a common cause. It is possible for estimates of the values of both the otherwise unobservable individual shocks and the otherwise unobservable common trends to be backed-out of cointegrated systems of equations. The issue addressed in this paper is whether and in what circumstances these values can be regarded as observations of real entities rather than merely artifacts of the representation of variables in the model. The issue is related, on the one hand, to practical methodological problems in the use of SVARs for policy analysis—e.g., does it make sense to estimate of shocks or trends in one model and then use them as measures of variables in a conceptually distinct model? The issue is also related to debates in the philosophical analysis of causation—particularly, whether we are entitled, as assumed by the developers of Bayes-net approaches, to rely on the causal Markov condition (a generalization of Reichenbach’s common-cause condition) or whether cointegration generates a practical example of Nancy Cartwright’s “byproducts” objection to the causal Markov condition. (shrink)

In this article, we extend the Bayesian nonparametric regression method Gaussian Process Regression to the analysis of longitudinal panel data. We call this new approach Gaussian Process Panel Modeling (GPPM). GPPM provides great flexibility because of the large number of models it can represent. It allows classical statistical inference as well as machine learning inspired predictive modeling. GPPM offers frequentist and Bayesian inference without the need to resort to Markov chain Monte Carlo-based approximations, which makes the approach exact and (...) fast. GPPMs are defined using the kernel-language, which can express many traditional modeling approaches for longitudinal data, such as linear structural equation models, multilevel models, or state-space models but also various commonly used machine learning approaches. As a result, GPPM is uniquely able to represent hybrid models combining traditional parametric longitudinal models and nonparametric machine learning models. In the present paper, we introduce GPPM and illustrate its utility through theoretical arguments as well as simulated and empirical data. (shrink)

The free energy principle is sometimes put forward as accounting for biological self-organization and cognition. It states that for a system to maintain non-equilibrium steady-state with its environment it can be described as minimising its free energy. It is said to be entirely scale-free, applying to anything from particles to organisms, and interactive machines, spanning from the abiotic to the biotic. Because the FEP is so general in its application, one might wonder whether this framework can capture anything specific to (...) biology. We take steps to correct for this here. We first explicate the worry, taking pebbles as examples of an abiotic system, and then discuss to what extent the FEP can distinguish its dynamics from an organism’s. We articulate the notion of ‘autonomy as precarious operational closure’ from the enactive literature, and investigate how it can be unpacked within the FEP. This enables the FEP to delineate between the abiotic and the biotic; avoiding the pebble worry that keeps it out of touch with the living systems we encounter in the world. (shrink)

We present a novel algorithm for the fast computation of PageRank, a hyperlink-based estimate of the “importance” of Web pages. The original PageRank algorithm uses the Power Method to compute successive iterates that converge to the principal eigenvector of the Markov matrix representing the Web link graph. The algorithm presented here, called Quadratic Extrapolation, accelerates the convergence of the Power Method by periodically subtracting off estimates of the nonprincipal eigenvectors from the current iterate of the Power Method. In Quadratic (...) Extrapolation, we take advantage of the fact that the first eigenvalue of a Markov matrix is known to be 1 to compute the nonprincipal eigenvectors using successive iterates of the Power Method. Empirically, we show that using Quadratic Extrapolation speeds up PageRank computation by 50- 300% on a Web graph of 80 million nodes, with minimal overhead. (shrink)

Beth models of analysis are used in model theoretic proofs of the disjunction and existence property. By glueing strings of models one obtains a model that combines the properties of the given models. The method asks for a common generalization of Kripke and Beth models. The proof is carried out in intuitionistic analysis plus Markov's Principle. The main new feature is the external use of intuitionistic principles to prove their own preservation under glueing.

We present four new change detection methods that create an automated change map from a probability map. In this case, the probability map was derived from a 3D model. The primary application of interest is aerial photographic applications, where the appearance, disappearance or change in position of small objects of a selectable class (e.g., cars) must be detected at a high success rate in spite of variations in magnification, lighting and background across the image. The methods rely on an earlier (...) derivation of a probability map. We describe the theory of the four methods, namely Bernoulli variables, Markov Random Fields, connected change, and relaxation-based segmentation, evaluate and compare their performance experimentally on a set probability maps derived from aerial photographs. (shrink)

Markovic draws upon the Zagreb school of Marx-interpretation, as well as on the data of the historical development of socialism in Yugoslavia in his attempt to develop a critical social theory. He constantly opposes the use of Marxian theory as an ideological orthodoxy simply legitimating political practice. And he points out how Marxian social thought may be a means of critically comprehending social processes, as well as a self-critical theory developing in relation to the historical data at whose evaluation it (...) is directed. Markovic insists that critical social theory must take as its subject matter a range of data comprised of contemporary phenomena, the history of such phenomena, and the human evaluations and aspirations which the historical situation engenders. This points up the importance of a theory of man for a critical social theory. Only an adequate theory of man enables social theory to comprehend and evaluate the goals arising from specific social processes. Markovic outlines elements of such a theory of man, as discoverable in Marx. With these guiding ideas, he examines specific themes such as economics and human values, technology, politics as a professional institution, and revolution. Markovic’s examinations valuably illustrate a balanced Marxian approach to social questions. It is argued, for example, that technological innovations must be analyzed in relation both to the concrete economic processes of given societies, and to the human needs operative in those societies. Markovic draws upon the Yugoslav experience to show the concrete nature of such an analysis. The viability of the professional political institution is discussed, with reference to specific productive relations in societies, and the political possibilities thereof. And in the context of a distinction between political and social revolution, he writes with sensitivity and discernment on the concept of revolution in Marx. Problematically, the precise status of a theory of man in a social theory of the Marxian variety remains unanswered herein. But the work stands as highly useful to those interested in non-ideological developments of Marxian social theory.—M.J.D. (shrink)

Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-conditional independence of features. This feature independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model that incorporates varying degrees of prior belief in class-conditional independence, learns whether or not independence holds, (...) and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments—designed using optimal experimental design principles—were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-conditional independence, before adapting to the true environmental structure. Class-conditional independence may be a strong and useful default assumption in category learning tasks. (shrink)

The target article “Thinking Through Other Minds” (TTOM) offered an account of the distinctively human capacity to acquire cultural knowledge, norms, and practices. To this end, we leveraged recent ideas from theoretical neurobiology to understand the human mind in social and cultural contexts. Our aim was bothsynthetic– building an integrative model adequate to account for key features of cultural learning and adaptation; andprescriptive– showing how the tools developed to explain brain dynamics can be applied to the emergence of social and (...) cultural ecologies of mind. In this reply to commentators, we address key issues, including: (1) refining the concept of culture to show how TTOM and the free-energy principle (FEP) can capture essential elements of human adaptation and functioning; (2) addressing cognition as an embodied, enactive, affective process involving cultural affordances; (3) clarifying the significance of the FEP formalism related to entropy minimization, Bayesian inference, Markov blankets, and enactivist views; (4) developing empirical tests and applications of the TTOM model; (5) incorporating cultural diversity and context at the level of intra-cultural variation, individual differences, and the transition to digital niches; and (6) considering some implications for psychiatry. The commentators’ critiques and suggestions point to useful refinements and applications of the model. In ongoing collaborations, we are exploring how to augment the theory with affective valence, take into account individual differences and historicity, and apply the model to specific domains including epistemic bias. (shrink)

We present a population density and moment-based description of the stochastic dynamics of domain $${\text{Ca}}^{2+}$$ -mediated inactivation of L-type $${\text{Ca}}^{2+}$$ channels. Our approach accounts for the effect of heterogeneity of local $${\text{Ca}}^{2+}$$ signals on whole cell $${\text{Ca}}^{2+}$$ currents; however, in contrast with prior work, e.g., Sherman et al. :985–995, 1990), we do not assume that $${\text{Ca}}^{2+}$$ domain formation and collapse are fast compared to channel gating. We demonstrate the population density and moment-based modeling approaches using a 12-state Markov chain (...) model of an L-type $${\text{Ca}}^{2+}$$ channel introduced by Greenstein and Winslow :2918–2945, 2002). Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell $${\text{Ca}}^{2+}$$ current that agrees with the traditional approach when domain dynamics are fast. We analyze the voltage-dependence of $${\text{Ca}}^{2+}$$ inactivation that may occur via slow heterogeneous domain [ $${\text{Ca}}^{2+}$$ ]. Next, we find that when channel permeability is held constant, $${\text{Ca}}^{2+}$$ -mediated inactivation of L-type channels increases as the domain time constant increases, because a slow domain collapse rate leads to increased mean domain [ $${\text{Ca}}^{2+}$$ ] near open channels; conversely, when the maximum domain [ $${\text{Ca}}^{2+}$$ ] is held constant, inactivation decreases as the domain time constant increases. Comparison of simulation results using population densities and moment equations confirms the computational efficiency of the moment-based approach, and enables the validation of two distinct methods of truncating and closing the open system of moment equations. In general, a slow domain time constant requires higher order moment truncation for agreement between moment-based and population density simulations. (shrink)

The aim of the paper is to relate Bell’s notion of local causality to the Causal Markov Condition. To this end, first a framework, called local physical theory, will be introduced integrating spatiotemporal and probabilistic entities and the notions of local causality and Markovity will be defined. Then, illustrated in a simple stochastic model, it will be shown how a discrete local physical theory transforms into a Bayesian network and how the Causal Markov Condition arises as a special (...) case of Bell’s local causality and Markovity. (shrink)

Woodward present an argument for the Causal Markov Condition (CMC) on the basis of a principle they dub ‘modularity’ ([1999, 2004]). I show that the conclusion of their argument is not in fact the CMC but a substantially weaker proposition. In addition, I show that their argument is invalid and trace this invalidity to two features of modularity, namely, that it is stated in terms of pairwise independence and ‘arrow-breaking’ interventions. Hausman & Woodward's argument can be rendered valid through (...) a reformulation of modularity, but it is doubtful that the argument so revised provides any substantially new insight regarding the basis of the CMC. Introduction The CMC versus Hausman & Woodward's conclusion Hausman & Woodward's argument Modularity and independent error terms Conclusion Appendix: D-separation. (shrink)

Based on the understanding of the term rhetoric that transcends the notion of literary genre, this book offers new answers to the questions of the provenance and the role of the main rhetorical strategies in Lucretius' De rerum natura.

1. Linguistique et critique des textesParmi les questions posées par l’étude des manuscrits et l’établissement des textes, il y a des problèmes d’attribution de fragments anonymes, des problèmes de reconnaissance d’interpolations dues à certains copistes, et plus généralement, de reconnaissance de scripteurs différents dans un corpus donné. Il s’agit donc, tantôt de rapprocher d’un corpus ou d’un scripteur connus un fragment inconnu, tantôt de déceler dans un corpus donné, un ou plusieurs pas..

The present study aims to identify contextual and psychological factors of proneness to radicalization and violent extremism operationalized through the Militant Extremist Mindset scale consisting of three distinct aspects: Proviolence, Vile World beliefs, and trust in Divine Power. A community sample of 271 high school students from Belgrade and Sandžak regions in Serbia completed: a 24-item MEM scale; contextual measures including a 6-item scale of family dysfunction and a 4-item composite measure capturing exposure to a harsh school environment and peer (...) abuse ; psychological measures including the 9-item Right-Wing Authoritarianism scale, the 5-item Social Dominance Orientation scale, and the 20-item UCLA Loneliness scale. A path analysis was conducted with contextual factors on the first and psychological factors on the second level of the model predicting the three factors of MEM. LON was positively predicted by FDys and HSE, SDO by HSE only, while RWA was positively predicted by FDys only. Contextual and psychological factors accounted for 27% of the variance in PV, 15% of the variance in VW, and 31% of the variance in DP. Obtained findings reveal a complex interplay of contextual and psychological drivers in the prediction of different aspects of RVE and build upon existing knowledge on risk factors associated with RVE. (shrink)

In this paper we argue that predictive processing (PP) theory cannot account for the phenomenon of affect-biased attention prioritized attention to stimuli that are affectively salient because of their associations with reward or punishment. Specifically, the PP hypothesis that selective attention can be analyzed in terms of the optimization of precision expectations cannot accommodate affect-biased attention; affectively salient stimuli can capture our attention even when precision expectations are low. We review the prospects of three recent attempts to accommodate affect with (...) tools internal to PP theory: Miller and Clark’s (2018) embodied inference; Seth’s (2013) interoceptive inference; and Joffily and Coricelli’s (2013) rate of change of free energy. In each case we argue that the account does not resolve the challenge from affect-biased attention. For this reason, we conclude that prediction error minimization is not sufficient to explain all mental phenomena, contrary to the claim that the PP framework provides a unified theory of all mental phenomena or the brain ‘s cognitive functioning. Nevertheless, we suggest that empirical investigation of the interaction between affective salience and precision expectations should prove helpful in understanding the limits of PP theory, and may provide new directions for the application of a Bayesian perspective to perception. (shrink)

This study described the relationships between academic class and student moral sensitivity and reasoning and between curriculum design components for ethics education and student moral sensitivity and reasoning. The data were collected from freshman (n = 506) and senior students (n = 440) in eight baccalaureate nursing programs in South Korea by survey; the survey consisted of the Korean Moral Sensitivity Questionnaire and the Korean Defining Issues Test. The results showed that moral sensitivity scores in patient-oriented care and conflict were (...) higher in senior students than in freshman students. Furthermore, more hours of ethics content were associated with higher principled thinking scores of senior students. Nursing education in South Korea may have an impact on developing student moral sensitivity. Planned ethics content in nursing curricula is necessary to improve moral sensitivity and moral reasoning of students. (shrink)