Tenenbaum and Griffiths (2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (1987) and Tversky’s (1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that generalisation as a Bayesian inference should be seen as (...) a complement to, instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (shrink)

An important problem with machine learning is that when label number n>2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory (...) consists of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic. (shrink)

The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace (...) of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart. (shrink)

It is often claimed that the greatest value of the Bayesian framework in cognitive science consists in its unifying power. Several Bayesian cognitive scientists assume that unification is obviously linked to explanatory power. But this link is not obvious, as unification in science is a heterogeneous notion, which may have little to do with explanation. While a crucial feature of most adequate explanations in cognitive science is that they reveal aspects of the causal mechanism that produces the phenomenon (...) to be explained, the kind of unification afforded by the Bayesian framework to cognitive science does not necessarily reveal aspects of a mechanism. Bayesian unification, nonetheless, can place fruitful constraints on causal–mechanical explanation. 1 Introduction2 What a Great Many Phenomena Bayesian Decision Theory Can Model3 The Case of Information Integration4 How Do Bayesian Models Unify?5 Bayesian Unification: What Constraints Are There on Mechanistic Explanation?5.1 Unification constrains mechanism discovery5.2 Unification constrains the identification of relevant mechanistic factors5.3 Unification constrains confirmation of competitive mechanistic models6 ConclusionAppendix. (shrink)

Shepard’s (1987) universal law of generalisation (ULG) illustrates that an invariant gradient of generalisation across species and across stimuli conditions can be obtained by mapping the probability of a generalisation response onto the representations of similarity between individual stimuli. Tenenbaum and Griffiths (2001) Bayesian account of generalisation expands ULG towards generalisation from multiple examples. Though the Bayesian model starts from Shepard’s account it refrains from any commitment to the notion of psychological similarity to explain categorisation. This chapter presents (...) the conceptual spaces theory (Gärdenfors 2000, 2014) as a mediator between Shepard’s and Tenenbaum & Griffiths’ conflicting views on the role of psychological similarity for a successful model of categorisation. It suggests that the conceptual spaces theory can help to improve the Bayesian model while finding an explanatory role for psychological similarity. (shrink)

We criticise Shepard's notions of “invariance” and “universality,” and the incorporation of Shepard's work on inference into the general framework of his paper. We then criticise Tenenbaum and Griffiths' account of Shepard (1987b), including the attributed likelihood function, and the assumption of “weak sampling.” Finally, we endorse Barlow's suggestion that minimum message length (MML) theory has useful things to say about the Bayesian inference problems discussed by Shepard and Tenenbaum and Griffiths. [Barlow; Shepard; Tenenbaum & Griffiths].

Information was a frequently used concept in many fields of investigation. However, this concept is still not really understood, when it is referred for instance to consciousness and its informational structure. In this paper it is followed the concept of information from philosophical to physics perspective, showing especially how this concept could be extended to matter in general and to the living in particular, as a result of the intimate interaction between matter and information, the human body appearing as (...) a bipolar informed-matter structure. It is detailed on this way how this concept could be referred to consciousness, and an informational modeling of consciousness as an informational system of the human body is presented. Based on the anatomic architecture of the organism and on the inference of the specific information concepts, it is shown that the informational system of the human body could be described by seven informational subsystems, which are reflected in consciousness as corresponding cognitive centers. These results are able to explain the main properties of consciousness, both the cognitive and extra-cognitive properties of the mind, like that observed during the near-death experiences and other similar phenomena. Moreover, the results of such a modeling are compared with the existing empirical concepts and models on the energetic architecture of the organism, showing their relevance for the understanding of consciousness. (shrink)

Probability updating via Bayes' rule often entails extensive informational and computational requirements. In consequence, relatively few practical applications of Bayesian adaptive control techniques have been attempted. This paper discusses an alternative approach to adaptive control, Bayesian in spirit, which shifts attention from the updating of probability distributions via transitional probability assessments to the direct updating of the criterion function, itself, via transitional utility assessments. Results are illustrated in terms of an adaptive reinvestment two-armed bandit problem.

This paper outlines new work in cross-cultural psychology largely drawn from Nisbett, Choi, and Smith (Cognition, 65, 15–32, 1997); Nisbett, Peng, Choi, & Norenzayan, Psychological Review, 108(2), 291–310, 2001; Nisbett, The Geography of Thought: How Asians and Westerners Think Differently...and Why. New York: Free Press 2003), Ji, Zhang and Nisbett (Journal of Personality and Social Psychology, 87(1), 57–65, 2004), Norenzayan (2000) and Peng (Naive Dialecticism and its Effects on Reasoning and Judgement about Contradiction. University of Michigan, Ann Arbor, Michigan 1997) (...) Peng and Nisbett (Cross-Cultural Similarities and Differences in the Understanding of Physical Causality. Paper presented at the Science and Culture: Proceedings of the Seventh Interdisciplinary Conference on Science and Culture, Frankfort, K. Y. 1996), and Peng, Ames, & Knowles (Culture and Human Inference: Perspectives from three traditions. In: D. Matsumoto (Ed.), Handbook of Cross-Cultural Psychology (pp. 1–2). Oxford: Oxford University Press 2000). The paper argues that the findings on cultural influences on inference-making have implications for teaching and education generally, and specifically for the debate on conceptions and misconceptions of Asian students studying in western tertiary institutions around the world. The position defended is that, while there seems to be compelling empirical evidence for intercultural differences in thought patterns, these patterns are, for the most part, insignificant in everyday exchanges, though language and culture might subtlety modulate our inference-making at the margins. Linguistic determinism however is not defended. Nonetheless, the evidence provides food for thought, and it needs to inform the recent debates about international students studying overseas. (shrink)

We argue in Roche and Sober (2013) that explanatoriness is evidentially irrelevant in that Pr(H | O&EXPL) = Pr(H | O), where H is a hypothesis, O is an observation, and EXPL is the proposition that if H and O were true, then H would explain O. This is a “screening-off” thesis. Here we clarify that thesis, reply to criticisms advanced by Lange (2017), consider alternative formulations of Inference to the Best Explanation, discuss a strengthened screening-off thesis, and consider how (...) it bears on the claim that unification is evidentially relevant. (shrink)

I argue against the skeptical epistemological view exemplified by the Groarkes that “all theories of informal argument must face the regress problem.” It is true that in our theoretical representations of reasoning, infinite regresses of self-justification regularly and inadvertently arise with respect to each of the RSA criteria for argument cogency (the premises are to be relevant, sufficient, and acceptable). But they arise needlessly, by confusing an RSA criterion with argument content, usually premise material.

Philosophers interested in the theoretical consequences of predictive processing often assume that predictive processing is an inferentialist and representationalist theory of cognition. More specifically, they assume that predictive processing revolves around approximated Bayesian inferences drawn by inverting a generative model. Generative models, in turn, are said to be structural representations: representational vehicles that represent their targets by being structurally similar to them. Here, I challenge this assumption, claiming that, at present, it lacks an adequate justification. I examine the only (...) argument offered to establish that generative models are structural representations, and argue that it does not substantiate the desired conclusion. Having so done, I consider a number of alternative arguments aimed at showing that the relevant structural similarity obtains, and argue that all these arguments are unconvincing for a variety of reasons. I then conclude the paper by briefly highlighting three themes that might be relevant for further investigation on the matter. (shrink)

Politics is rife with motivated cognition. People do not dispassionately engage with the evidence when they form political beliefs; they interpret it selectively, generating justifications for their desired conclusions and reasons why contrary evidence should be ignored. Moreover, research shows that epistemic ability (e.g. intelligence and familiarity with evidence) is correlated with motivated cognition. Bjørn Hallsson has pointed out that this raises a puzzle for the epistemology of disagreement. On the one hand, we typically think that epistemic ability in an (...) interlocutor gives us reason to downgrade our belief upon learning that we disagree. On the other hand, if our interlocutor is under the sway of motivated cognition, then we have reason to discount his opinion. In this paper, I argue that Hallsson's puzzle is solved by adopting a Bayesian approach to disagreement. If an interlocutor is under the sway of motivated cognition, his disagreement should not affect our beliefs--no matter his ability. Because we implicitly and to high accuracy know his beliefs before he reveals them to us, disagreement provides us with no new information on which to conditionalize. I advance a model which accommodates the motivated cognition dynamic and other key epistemic features of disagreement. (shrink)

When we compare the influences of two causes on an outcome, if the conclusion from every group is against that from the conflation, we think there is Simpson’s Paradox. The Existing Causal Inference Theory (ECIT) can make the overall conclusion consistent with the grouping conclusion by removing the confounder’s influence to eliminate the paradox. The ECIT uses relative risk difference Pd = max(0, (R − 1)/R) (R denotes the risk ratio) as the probability of causation. In contrast, Philosopher Fitelson uses (...) confirmation measure D (posterior probability minus prior probability) to measure the strength of causation. Fitelson concludes that from the perspective of Bayesian confirmation, we should directly accept the overall conclusion without considering the paradox. The author proposed a Bayesian confirmation measure b* similar to Pd before. To overcome the contradiction between the ECIT and Bayesian confirmation, the author uses the semantic information method with the minimum cross-entropy criterion to deduce causal confirmation measure Cc = (R − 1)/max(R, 1). Cc is like Pd but has normalizing property (between −1 and 1) and cause symmetry. It especially fits cases where a cause restrains an outcome, such as the COVID-19 vaccine controlling the infection. Some examples (about kidney stone treatments and COVID-19) reveal that Pd and Cc are more reasonable than D; Cc is more useful than Pd. (shrink)

When we compare the influences of two causes on an outcome, if the conclusion from every group is against that from the conflation, we think there is Simpson’s Paradox. The Existing Causal Inference Theory (ECIT) can make the overall conclusion consistent with the grouping conclusion by removing the confounder’s influence to eliminate the paradox. The ECIT uses relative risk difference Pd = max(0, (R − 1)/R) (R denotes the risk ratio) as the probability of causation. In contrast, Philosopher Fitelson uses (...) confirmation measure D (posterior probability minus prior probability) to measure the strength of causation. Fitelson concludes that from the perspective of Bayesian confirmation, we should directly accept the overall conclusion without considering the paradox. The author proposed a Bayesian confirmation measure b* similar to Pd before. To overcome the contradiction between the ECIT and Bayesian confirmation, the author uses the semantic information method with the minimum cross-entropy criterion to deduce causal confirmation measure Cc = (R − 1)/max(R, 1). Cc is like Pd but has normalizing property (between −1 and 1) and cause symmetry. It especially fits cases where a cause restrains an outcome, such as the COVID-19 vaccine controlling the infection. Some examples (about kidney stone treatments and COVID-19) reveal that Pd and Cc are more reasonable than D; Cc is more useful than Pd. (shrink)

In this article, I will provide a critical overview of the form of non-deductive reasoning commonly known as “Inference to the Best Explanation” (IBE). Roughly speaking, according to IBE, we ought to infer the hypothesis that provides the best explanation of our evidence. In section 2, I survey some contemporary formulations of IBE and highlight some of its putative applications. In section 3, I distinguish IBE from C.S. Peirce’s notion of abduction. After underlining some of the essential elements of IBE, (...) the rest of the entry is organized around an examination of various problems that IBE confronts, along with some extant attempts to address these problems. In section 4, I consider the question of when a fact requires an explanation, since presumably IBE applies only in cases where some explanation is called for. In section 5, I consider the difficult question of how we ought to understand IBE in light of the fact that among philosophers, there is significant disagreement about what constitutes an explanation. In section 6, I consider different strategies for justifying the truth-conduciveness of the explanatory virtues, e.g., simplicity, unification, scope, etc., criteria which play an indispensable role in any given application of IBE. In section 7, I survey some of the most recent literature on IBE, much of which consists of investigations of the status of IBE from the standpoint of the Bayesian philosophy of science. (shrink)

To estimate causal relationships, time series econometricians must be aware of spurious correlation, a problem first mentioned by Yule (1926). To deal with this problem, one can work either with differenced series or multivariate models: VAR (VEC or VECM) models. These models usually include at least one cointegration relation. Although the Bayesian literature on VAR/VEC is quite advanced, Bauwens et al. (1999) highlighted that “the topic of selecting the cointegrating rank has not yet given very useful and convincing results”. (...) The present article applies the Full Bayesian Significance Test (FBST), especially designed to deal with sharp hypotheses, to cointegration rank selection tests in VECM time series models. It shows the FBST implementation using both simulated and available (in the literature) data sets. As illustration, standard non informative priors are used. (shrink)

Proponents of IBE claim that the ability of a hypothesis to explain a range of phenomena in a unifying way contributes to the hypothesis’s credibility in light of these phenomena. I propose a Bayesian justification of this claim that reveals a hitherto unnoticed role for explanatory unification in evaluating the plausibility of a hypothesis: considerations of explanatory unification enter into the determination of a hypothesis’s prior by affecting its ‘explanatory coherence’, that is, the extent to which the hypothesis offers (...) mutually cohesive explanations of various phenomena. (shrink)

Several philosophers and psychologists have characterized belief in conspiracy theories as a product of irrational reasoning. Proponents of conspiracy theories apparently resist revising their beliefs given disconfirming evidence and tend to believe in more than one conspiracy, even when the relevant beliefs are mutually inconsistent. In this paper, we bring leading views on conspiracy theoretic beliefs closer together by exploring their rationality under a probabilistic framework. We question the claim that the irrationality of conspiracy theoretic beliefs stems from an inadequate (...) response to disconfirming evidence and internal incoherence. Drawing analogies to Lakatosian research programs, we argue that maintaining a core conspiracy belief can be Bayes-rational when it is embedded in a network of auxiliary beliefs, which can be revised to protect the more central belief from disconfirmation. We propose that the irrationality associated with conspiracy belief lies not in a flawed updating method, but in a failure to converge toward wellconfirmed, stable belief networks in the long run. This approach not only reconciles previously disjointed views, but also points toward more specific descriptions of why agents may be prone to adopting beliefs in conspiracy theories. (shrink)

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data will (...) run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data. (shrink)

In this paper, I consider the relationship between Inference to the Best Explanation and Bayesianism, both of which are well-known accounts of the nature of scientific inference. In Sect. 2, I give a brief overview of Bayesianism and IBE. In Sect. 3, I argue that IBE in its most prominently defended forms is difficult to reconcile with Bayesianism because not all of the items that feature on popular lists of “explanatory virtues”—by means of which IBE ranks competing explanations—have confirmational import. (...) Rather, some of the items that feature on these lists are “informational virtues”—properties that do not make a hypothesis \ more probable than some competitor \ given evidence E, but that, roughly-speaking, give that hypothesis greater informative content. In Sect. 4, I consider as a response to my argument a recent version of compatibilism which argues that IBE can provide further normative constraints on the objectively correct probability function. I argue that this response does not succeed, owing to the difficulty of defending with any generality such further normative constraints. Lastly, in Sect. 5, I propose that IBE should be regarded, not as a theory of scientific inference, but rather as a theory of when we ought to “accept” H, where the acceptability of H is fixed by the goals of science and concerns whether H is worthy of commitment as research program. In this way, IBE and Bayesianism, as I will show, can be made compatible, and thus the Bayesian and the proponent of IBE can be friends. (shrink)

The aim of this study is to justify the belief that there are biological normative mechanisms that fulfill non-trivial causal roles in the explanations (as formulated by researchers) of actions and behaviors present in specific systems. One example of such mechanisms is the predictive mechanisms described and explained by predictive processing (hereinafter PP), which (1) guide actions and (2) shape causal transitions between states that have specific content and fulfillment conditions (e.g. mental states). Therefore, I am guided by a specific (...) theoretical goal associated with the need to indicate those conditions that should be met by the non-trivial theory of normative mechanisms and the specific models proposed by PP supporters. In this work, I use classical philosophical methods, such as conceptual analysis and critical reflection. I also analyze selected studies in the field of cognitive science, cognitive psychology, neurology, information theory and biology in terms of the methodology, argumentation and language used, in accordance with their theoretical importance for the issues discussed in this study. In this sense, the research presented here is interdisciplinary. My research framework is informed by the mechanistic model of explanation, which defines the necessary and sufficient conditions for explaining a given phenomenon. The research methods I chose are therefore related to the problems that I intend to solve. In the introductory chapter, “The concept of predictive processing”, I discuss the nature of PP as well as its main assumptions and theses. I also highlight the key concepts and distinctions for this research framework. Many authors argue that PP is a contemporary version of Kantianism and is exposed to objections similar to those made against the approach of Immanuel Kant. I discuss this thesis and show that it is only in a very general sense that the PP framework is neo-Kantian. Here we are not dealing with transcendental deduction nor with the application of transcendental arguments. I argue that PP is based on reverse engineering and abduction inferences. In the second part of this chapter, I respond to the objection formulated by Dan Zahavi, who directly accuses this research framework of anti-realistic consequences. I demonstrate that the position of internalism, present in the so-called conservative PP, does not imply anti-realism, and that, due to the explanatory role played in it by structural representations directed at real patterns, it is justified to claim that PP is realistic. In this way, I show that PP is a non-trivial research framework, having its subject, specific methods and its own epistemic status. Finally, I discuss positions classified as the socalled radical PP. In the chapter “Predictive processing as a Bayesian explanatory model” I justify the thesis according to which PP offers Bayesian modeling. Many researchers claim that the brain is an implemented statistical probabilistic network that is an approximation of the Bayesian 7 rule. In practice, this means that all cognitive processes are to apply Bayes' rule and can be described in terms of probability distributions. Such a solution arouses objections among many researchers and is the subject of wide criticism. The purpose of this chapter is to justify the thesis that Bayesian PP is a non-trivial research framework. For this purpose, I argue that it explains certain phenomena not only at the computational level described by David Marr, but also at the level of algorithms and implementation. Later in this chapter I demonstrate that PP is normative modeling. Proponents of the use of Bayesian models in psychology or decision theory argue that they are normative because they allow the formulation of formal rules of action that show what needs to be done to make a given action optimal. Critics of this approach emphasize that such thinking about the normativity of Bayesian modeling is unjustified and that science should shift from prescriptive to descriptive positions. In a polemic with Shira Elqayam and Jonathan Evans (2011), I show that the division they propose into prescriptivism and Bayesian descriptivism is apparent, because, as I argue, there are two forms of prescriptivism, i.e. the weak and the strong. I argue that the weak version is epistemic and can lead to anti-realism, while the strong version is ontic and allows one to justify realism in relation to Bayesian models. I argue that a weak version of prescriptivism is valid for PP. It allows us to adopt anti-realism in relation to PP. In practice, this means that you can explain phenomena using Bayes' rule. This does not, however, imply that they are Bayesian in nature. However, the full justification of realism in relation to the Bayesian PP presupposes the adoption of strong prescriptivism. This position assumes that phenomena are explained by Bayesian rule because they are Bayesian as such. If they are Bayesian in nature, then they should be explained using Bayesian modeling. This thesis will be substantiated in the chapters “Normative functions and mechanisms in the context of predictive processing” and “Normative mechanisms and actions in predictive processing”. In the chapter “The Free Energy Principle in predictive processing”, I discuss the Free Energy Principle (hereinafter FEP) formulated by Karl Friston and some of its implications. According to this principle, all biological systems (defined in terms of Markov blankets) minimize the free energy of their internal states in order to maintain homeostasis. Some researchers believe that PP is a special case of applying this principle to cognition, and that predictive mechanisms are homeostatic mechanisms that minimize free energy. The discussion of FEP is important due to the fact that some authors consider it to be important for explanatory purposes and normative. If this is the case, then FEP turns out to be crucial in explaining normative predictive mechanisms and, in general, any normative biological mechanisms. To define the explanatory possibilities of this principle, I refer to the discussion of its supporters on the issue they define as the problem of continuity and discontinuity between life and mind. A critical analysis of this discussion and the additional arguments I have formulated have allowed me to revise the explanatory ambitions of FEP. I also reject the belief that this principle is necessary to explain the nature of predictive mechanisms. I argue that the principle formulated and defended by Friston is an important research heuristic for PP analysis. 8 In the chapter “Normative functions and mechanisms in predictive processing”, I start my analyzes by formulating an answer to the question about the normative nature of homeostatic mechanisms. I demonstrate that predictive mechanisms are not homeostatic. I defend the view that a full explanation of normative mechanisms presupposes an explanation of normative functions. I discuss the most important proposals for understanding the normativity of a function, both from a systemic and teleosemantic perspective. I conclude that the non-trivial concept of a function must meet two requirements which I define as explanatory and normative. I show that none of the theories I have invoked satisfactorily meets both of these requirements. Instead, I propose a model of normativity based on Bickhard's account, but supplemented by a mechanistic perspective. I argue that a function is normative when: (1) it allows one to explain the dysfunction of a given mechanism; (2) it contributes to the maintenance of the organism's stability by shaping and limiting possible relations, processes and behaviors of a given system; and when (3) (according to the representational and predictive functions) it enables explaining the attribution of logical values of certain representations / predictions. In such an approach, a mechanism is normative when it performs certain normative functions and when it is constitutive for a specific action or behavior, despite the fact that for some reason it cannot realize it either currently or in the long-term. Such an understanding of the normativity of mechanisms presupposes the acceptance of the epistemic hypothesis. I argue that this hypothesis is not cognitively satisfactory, and therefore the ontic hypothesis should be justified, which is directly related to adopting the position of ontic prescriptivism. For this reason, referring to the mechanistic theory of scientific explanations, I formulate an ontical interpretation of the concept of a normative mechanism. According to this approach, a mechanism or a function is normative when they perform such and such causal roles in explaining certain actions and behaviors. With regard to the normative properties of predictive mechanisms and functions, this means that they are the causes of specific actions an organism carries out in the environment. In this way, I justify the necessity of accepting the ontic hypothesis and rejecting the epistemic hypothesis. The fifth chapter, “Normative mechanisms and actions in predictive processing”, is devoted to the dark room problem and the related exploration-exploitation trade-off. A dark room is the state that an agent could be in if it minimized the sum of all potential prediction errors. I demonstrate that, in accordance with the basic assumption of PP about the need for continuous and long-term minimization of prediction errors, such a state should be desirable for the agent. Is it really so? Many authors believe it is not. I argue that the test of the value of PP is the possibility of a non-trivial solution of this problem, which can be reduced to the choice between active and uncertainty-increasing exploration and safe and easily predictable exploitation. I show that the solution proposed by PP supporters present in the literature does not enable a fully satisfactory explanation of this dilemma. Then I defend the position according to which the full explanation of the normative mechanisms, and, subsequently, the solution to the dilemma of exploration and exploitation, involves reference to the existence of constraints present in the environment. The constraints 9 include elements of the environment that make a given mechanism not only causal but also normative. They are therefore key to explaining the predictive mechanisms. They do not only play the role of the context in which the mechanism is implemented, but, above all, are its constitutive component. I argue that the full explanation of the role of constraints in normative predictive mechanisms presupposes the integration of individual models of specific cognitive phenomena, because only the mechanistic integration of PP with other models allows for a non-trivial explanation of the nature of normative predictive mechanisms that would have a strong explanatory value. The explanatory monism present in many approaches to PP makes it impossible to solve the problem of the dark room. Later in this chapter, I argue that the Bayesian PP is normative not because it enables the formulation of such and such rules of action, but because the predictive mechanisms themselves are normative. They are normative because they condition the choice of such and such actions by agents. In this way, I justify the hypothesis that normative mechanisms make it possible to explain the phenomenon of agent motivation, which is crucial for solving the dark room problem. In the last part of the chapter, I formulate the hypothesis of distributed normativity, which assumes that the normative nature of certain mechanisms, functions or objects is determined by the relations into which these mechanisms, functions or objects enter. This means that what is normative (in the primary sense) is the relational structure that constitutes the normativity of specific items included in it. I suggest that this hypothesis opens up many areas of research and makes it possible to rethink many problems. In the “Conclusion”, I summarize the results of my research and indicate further research perspectives. (shrink)

This paper has two aims. First, it sets out an interpretation of the relevant logic E of relevant entailment based on the theory of situated inference. Second, it uses this interpretation, together with Anderson and Belnap’s natural deduc- tion system for E, to generalise E to a range of other systems of strict relevant implication. Routley–Meyer ternary relation semantics for these systems are produced and completeness theorems are proven. -/- .

A new trend in deep learning, represented by Mutual Information Neural Estimation (MINE) and Information Noise Contrast Estimation (InfoNCE), is emerging. In this trend, similarity functions and Estimated Mutual Information (EMI) are used as learning and objective functions. Coincidentally, EMI is essentially the same as Semantic Mutual Information (SeMI) proposed by the author 30 years ago. This paper first reviews the evolutionary histories of semantic information measures and learning functions. Then, it briefly introduces the author’s semantic information (...) G theory with the rate-fidelity function R(G) (G denotes SeMI, and R(G) extends R(D)) and its applications to multi-label learning, the maximum Mutual Information (MI) classification, and mixture models. Then it discusses how we should understand the relationship between SeMI and Shannon’s MI, two generalized entropies (fuzzy entropy and coverage entropy), Autoencoders, Gibbs distributions, and partition functions from the perspective of the R(G) function or the G theory. An important conclusion is that mixture models and Restricted Boltzmann Machines converge because SeMI is maximized, and Shannon’s MI is minimized, making information efficiency G/R close to 1. A potential opportunity is to simplify deep learning by using Gaussian channel mixture models for pre-training deep neural networks’ latent layers without considering gradients. It also discusses how the SeMI measure is used as the reward function (reflecting purposiveness) for reinforcement learning. The G theory helps interpret deep learning but is far from enough. Combining semantic information theory and deep learning will accelerate their development. (shrink)

A central concept for information retrieval is that of similarity. Although an information retrieval system is expected to return a set of documents most relevant to the query word(s), it is often described as returning a set of documents most similar to the query. The authors argue that in order to reason with similarity we need to model the concept of discriminating power. They offer a simple topological notion called resolution space that provides a rich mathematical framework for reasoning with (...) limited discriminating power, avoiding the vagueness paradox. (shrink)

This monograph is an in-depth and engaging discourse on the deeply cognitive roots of human scientific quest. The process of making scientific inferences is continuous with the day-to-day inferential activity of individuals, and is predominantly inductive in nature. Inductive inference, which is fallible, exploratory, and open-ended, is of essential relevance in our incessant efforts at making sense of a complex and uncertain world around us, and covers a vast range of cognitive activities, among which scientific exploration constitutes the pinnacle. (...) Inductive inference has a personal aspect to it, being rooted in the cognitive unconscious of individuals, which has recently been found to be of paramount importance in a wide range of complex cognitive processes. One other major aspect of the process of inference making, including the making of scientific inferences, is the role of a vast web of beliefs lodged in the human mind, as also of a huge repertoire of heuristics, that constitute an important component of ‘unconscious intelligence’. Finally, human cognitive activity is dependent in a large measure on emotions and affects, that operate mostly at an unconscious level. Of special importance in scientific inferential activity is the process of hypothesis making, which is examined in this book, along with the above aspects of inductive inference, at considerable depth. The book focuses on the inadequacy of the viewpoint of naive realism in understanding the contextual nature of scientific theories, where a cumulative progress towards an ultimate truth about Nature appears to be too simplistic a generalization. It poses a critique to the commonly perceived image of science which is seen as the last word in logic and objectivity, the latter in the double sense of being independent of individual psychological propensities and, at the same time, approaching a correct understanding of the workings of a mind-independent nature. Adopting the naturalist point of view, it examines the essential tension between the cognitive endeavours of individuals and scientific communities, immersed in belief systems and cultures, on the one hand, and the engagement with a mind-independent reality on the other. In the end, science emerges as an interpretation of nature, which is perceived by us only contextually, as successively emerging cross-sections of limited scope and extent. Successive waves of theory building in science appear as episodic and kaleidoscopic changes in perspective as certain in-built borders are crossed, rather than as a cumulative progress towards some ultimate truth. While written in an informal and conversational style, the book raises a number of deep and intriguing questions located at the interface of cognitive psychology and philosophy of science, meant for both the general lay reader and the specialist. Of particular interest is the way it explores the role of belief (aided by emotions and affects) in making the process of inductive inference possible since belief is a subtle though all-pervasive cognitive factor not adequately investigated in the current literature. (shrink)

This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both logically (...) and probabilistically. The statistical relevance of one function in determining another is put forward as a way of defining the value of information: The statistical relevance of a function F to a function G is the absolute value of the change in one's information about the value of G afforded by specifying the value of F. This theory provides normative justifications for conclusions projected by analogy from one case to another, and for generalization from an instance to a rule. The soundness of such conclusions, in either the logical or the probabilistic case, can be identified with the extent to which the corresponding criteria (determination and uniformity) actually hold for the features being related. (shrink)

It is usually accepted that deductions are non-informative and monotonic, inductions are informative and nonmonotonic, abductions create hypotheses but are epistemically irrelevant, and both deductions and inductions can’t provide new insights. In this article, I attempt to provide a more cohesive view of the subject with the following hypotheses: (1) the paradigmatic examples of deductions, such as modus ponens and hypothetical syllogism, are not inferential forms, but coherence requirements for inferences; (2) since any reasoner aims to be coherent, any inference (...) must be deductive; (3) a coherent inference is an intuitive process where the premises should be taken as sufficient evidence for the conclusion, which on its turn should be viewed as necessary evidence for the premises in some modal range; (4) inductions, properly understood, are abductions, but there are no abductions beyond the fact that in any inference the conclusion should be regarded as necessary evidence for the premises; (5) monotonicity is not only compatible with the retraction of past inferences given new information, but it is a requirement for it; (6) this explanation of inferences holds true for discovery processes, predictions and trivial inferences. (shrink)

In this article, I explore the compatibility of inference to the best explanation (IBE) with several influential models and accounts of scientific explanation. First, I explore the different conceptions of IBE and limit my discussion to two: the heuristic conception and the objective Bayesian conception. Next, I discuss five models of scientific explanation with regard to each model’s compatibility with IBE. I argue that Kitcher’s unificationist account supports IBE; Railton’s deductive–nomological–probabilistic model, Salmon’s statistical-relevance model, and van Fraassen’s erotetic (...) account are incompatible with IBE; and Salmon’s causal–mechanical model is merely consistent with IBE. In short, many influential models of scientific explanation do not support IBE. I end by outlining three possible conclusions to draw: (1) either philosophers of science or defenders of IBE have seriously misconstrued the concept of explanation, (2) philosophers of science and defenders of IBE do not use the term ‘explanation’ univocally, and (3) the ampliative conception of IBE, which is compatible with any model of scientific explanation, deserves a closer look. (shrink)

Every year, the Vietnamese people reportedly burned about 50,000 tons of joss papers, which took the form of not only bank notes, but iPhones, cars, clothes, even housekeepers, in hope of pleasing the dead. The practice was mistakenly attributed to traditional Buddhist teachings but originated in fact from China, which most Vietnamese were not aware of. In other aspects of life, there were many similar examples of Vietnamese so ready and comfortable with adding new norms, values, and beliefs, even contradictory (...) ones, to their culture. This phenomenon, dubbed “cultural additivity”, prompted us to study the co-existence, interaction, and influences among core values and norms of the Three Teachings –Confucianism, Buddhism, and Taoism–as shown through Vietnamese folktales. By applying Bayesian logistic regression, we evaluated the possibility of whether the key message of a story was dominated by a religion (dependent variables), as affected by the appearance of values and anti-values pertaining to the Three Teachings in the story (independent variables). Our main findings included the existence of the cultural additivity of Confucian and Taoist values. More specifically, empirical results showed that the interaction or addition of the values of Taoism and Confucianism in folktales together helped predict whether the key message of a story was about Confucianism, β{VT ⋅ VC} = 0.86. Meanwhile, there was no such statistical tendency for Buddhism. The results lead to a number of important implications. First, this showed the dominance of Confucianism because the fact that Confucian and Taoist values appeared together in a story led to the story’s key message dominated by Confucianism. Thus, it presented the evidence of Confucian dominance and against liberal interpretations of the concept of the Common Roots of Three Religions (“tam giáo đồng nguyên”) as religious unification or unicity. Second, the concept of “cultural additivity” could help explain many interesting socio-cultural phenomena, namely the absence of religious intolerance and extremism in the Vietnamese society, outrageous cases of sophistry in education, the low productivity in creative endeavors like science and technology, the misleading branding strategy in business. We are aware that our results are only preliminary and more studies, both theoretical and empirical, must be carried out to give a full account of the explanatory reach of “cultural additivity”. (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, (...) neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

Is more information always better? Or are there some situations in which more information can make us worse off? Good (1967) argues that expected utility maximizers should always accept more information if the information is cost-free and relevant. But Good's argument presupposes that you are certain you will update by conditionalization. If we relax this assumption and allow agents to be uncertain about updating, these agents can be rationally required to reject free and relevant information. Since there are good reasons (...) to be uncertain about updating, rationality can require you to prefer ignorance. (shrink)

In recent years, sequencing technologies have enabled the identification of a wide range of non-coding RNAs (ncRNAs). Unfortunately, annotation and integration of ncRNA data has lagged behind their identification. Given the large quantity of information being obtained in this area, there emerges an urgent need to integrate what is being discovered by a broad range of relevant communities. To this end, the Non-Coding RNA Ontology (NCRO) is being developed to provide a systematically structured and precisely defined controlled vocabulary for the (...) domain of ncRNAs, thereby facilitating the discovery, curation, analysis, exchange, and reasoning of data about structures of ncRNAs, their molecular and cellular functions, and their impacts upon phenotypes. The goal of NCRO is to serve as a common resource for annotations of diverse research in a way that will significantly enhance integrative and comparative analysis of the myriad resources currently housed in disparate sources. It is our belief that the NCRO ontology can perform an important role in the comprehensive unification of ncRNA biology and, indeed, fill a critical gap in both the Open Biological and Biomedical Ontologies (OBO) Library and the National Center for Biomedical Ontology (NCBO) BioPortal. Our initial focus is on the ontological representation of small regulatory ncRNAs, which we see as the first step in providing a resource for the annotation of data about all forms of ncRNAs. The NCRO ontology is free and open to all users. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical (...) means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem. (shrink)

The significance of and the role played by Knowledge Management (KM) is ever increasing in today's business and organizational decision-making environment. This paper attempts to underline the importance of organizing knowledge not for its own sake, but for its efficient use in organizational decision making. The tremendous explosion of knowledge resources, both electronic and conventional, within the last few decades calls for an understanding of how knowledge is organized for management of data and information. This is so for the reason (...) that they can be proficiently employed to create value and utility. This also calls for a search for 'relevance' in KM with regard to its situated nature in different contexts within which knowledge is situated, and that which nevertheless indirectly refers to its ontological scaffolding. We have devised two simple mathematical models of reference with regard to the design of the systems mostly intended for organizing knowledge in knowledge organizations for its most efficient utilization. The model specifies several unique scenarios aided by discovery of arguments related to its ontological framework within which knowledge is situated. Several contexts were drawn to draw inferences from the research study. The results bear relevance to knowledge managers who make important decisions for realization of organizational goals and objectives. (shrink)

The present PhD thesis is concerned with the question whether good reasoning requires that the subject has some cognitive grip on the relation between premises and conclusion. One consideration in favor of such a requirement goes as follows: In order for my belief-formation to be an instance of reasoning, and not merely a causally related sequence of beliefs, the process must be guided by my endorsement of a rule of reasoning. Therefore I must have justified beliefs about the relation between (...) my premises and my conclusion. -/- The rationality of a belief often depends on whether it is rightly connected to other beliefs, or more generally to other mental states —the states capable of providing a reason to holding the belief in question. For instance, some rational beliefs are connected to other beliefs by being inferred from them. It is often accepted that the connection implies that the subject in some sense ‘takes the mental states in question to be reason-providing’. But views on how exactly this is to be understood differ widely. They range from interpretations according to which ‘taking a mental state to be reason-providing’ imposes a mere causal sustaining relation between belief and reason-providing state to interpretations according to which one ‘takes a mental state to be reason-providing’ only if one believes that the state is reason-providing. The most common worry about the latter view is that it faces a vicious regress. In this thesis a different but in some respects similar interpretation of ‘taking something as reason-providing’ is given. It is argued to consist of a disposition to react in certain ways to information that challenges the reason-providing capacity of the allegedly reason-providing state. For instance, that one has inferred A from B partly consists in being disposed to suspend judgment about A if one obtains a reason to believe that B does not render A probable. The account is defended against regress-objections and the suspicion of explanatory circularity. (shrink)

Thanks to the advent of social media, large numbers of Americans believe outlandish falsehoods that have been widely debunked. Many of us have a tendency to fault the individuals who hold such beliefs. We naturally assume that the individuals who form and maintain such beliefs do so in virtue of having violated some epistemic obligation: perhaps they failed to scrutinize their sources, or failed to seek out the available competing evidence. I maintain that very many ordinary individuals who acquire outlandish (...) false beliefs thanks to their use of popular social media platforms (and other similar internet technologies) deserve little or no blame for believing these falsehoods. Such individuals would be fully blameworthy only if they had formed or maintained the relevant beliefs partly in virtue of violating some epistemic obligation and had no excuse for violating that obligation. However, the nature of these internet technologies provides excuses for violating the relevant epistemic obligations, and so individuals are excused for holding the resulting false beliefs. (shrink)

How do agents with limited cognitive capacities flourish in informationally impoverished or unexpected circumstances? Aristotle argued that human flourishing emerged from knowing about the world and our place within it. If he is right, then the virtuous processes that produce knowledge, best explain flourishing. Influenced by Aristotle, virtue epistemology defends an analysis of knowledge where beliefs are evaluated for their truth and the intellectual virtue or competences relied on in their creation. However, human flourishing may emerge from how degrees of (...) ignorance are managed in an uncertain world. Perhaps decision-making in the shadow of knowledge best explains human wellbeing—a Bayesian approach? In this dissertation I argue that a hybrid of virtue and Bayesian epistemologies explains human flourishing—what I term homeostatic epistemology. Homeostatic epistemology supposes that an agent has a rational credence p when p is the product of reliable processes aligned with the norms of probability theory; whereas an agent knows that p when a rational credence p is the product of reliable processes such that: 1) p meets some relevant threshold for belief, 2) p coheres with a satisficing set of relevant beliefs and, 3) the relevant set of beliefs is coordinated appropriately to meet the integrated aims of the agent. Homeostatic epistemology recognizes that justificatory relationships between beliefs are constantly changing to combat uncertainties and to take advantage of predictable circumstances. Contrary to holism, justification is built up and broken down across limited sets like the anabolic and catabolic processes that maintain homeostasis in the cells, organs and systems of the body. It is the coordination of choristic sets of reliably produced beliefs that create the greatest flourishing given the limitations inherent in the situated agent. (shrink)

The paper discusses this year’s Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum information (...) science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by this year’s Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview. (shrink)

The Introduction provides a historical and literary context for the examination of Albert Camus’s 1947 fictional novel, The Plague, to suggest its relevance to our own lived experiences of the 2021 Covid-19 pandemic that brought the routines and expectations of our normal, daily lives to an unprecedented halt. Details of Camus’s life and work inform our reading of the narrative that give rise to multiple interpretations as well as intriguing questions of scholarly inquiry: How realistic are the characters? Does (...) solidarity eventually triumph over isolation? Does the popular novel inspire social change or fail in its aspirations? Facing the absurdity of a similarly unwelcome and unpredictable disease, have we managed our fear of death more successfully than the citizens of Oran? An overview of authors’ contributions sets the stage for new and unique perspectives: an invitation for readers to reflect upon our communal experience of immense grief. (shrink)

I show that in our theoretical representations of argument, vicious infinite regresses of self-reference may arise with respect to each of the three usual, informal criteria of argument cogency: the premises are to be relevant, sufficient, and acceptable. They arise needlessly, by confusing a cogency criterion with argument content. The three types of regress all are structurally similar to Lewis Carroll’s famous regress, which involves quantitative extravagance with no explanatory power. Most attention is devoted to the sufficiency criterion, including its (...) relation to the view au courant that inferring necessarily involves the thinker taking her premises to support her conclusion. I contend that this view is mistaken and likewise that arguments make no such assumption or inference claim as that the premises support the conclusion. The core of the positive alternative model I propose is that there is commitment to, but not claiming, the proposition that the premises support the conclusion. (shrink)

Introduction: the neuroscientific turn in political science The observation that brains and political orders are interdependent is almost trivial. Obviously, political orders require brain processes in order to emerge and to remain in place, as these processes enable action and cognition. Conversely, every since Aristotle coined man as “by nature a political animal” (Aristotle, Pol.: 1252a 3; cf. Eth. Nic.: 1097b 11), this also suggests that the political engagements of this animal has likely consequences for its natural development, including the (...) development of its psychological functions. Given these mutual interdependencies, it is remarkable that only since the 1960s, the more general domain of ‘biopolitics’ has attracted attention though first particularly in the form of behavioral politics (Alford and Hibbing). Since then biopolitics has gained in interest, so much so that different subdomains can be identified. Indeed, a 2008 review of the field of biopolitics identified five ‘headings’ of it: “(1) the case for a ‘more biologically oriented political science’, (2) ‘biologically related’ public policy issues, (3) physiological measures of political attitudes and behaviour, (4) the influence of physiological factors on actual political behaviour, and (5) the manner in which our species’ evolutionary history has left homo sapiens genetically endowed with certain social and political behavioural tendencies” (Somit and Peterson 43). Striking is how the relation between biology and politics is taken here in a rather unidirectional way, emphasizing particularly the decisive power of biology upon politics. The reverse relation is not mentioned specifically, reflecting the field of biopolitics, perhaps until quite recently. This absence of studies of political influences on our biology may have to do with the difficulty in investigating such influences. Empirical studies in biopolitics have two foci, broadly speaking: genetics and the brain, both of which have turned out to be complex and dynamic phenomena (Alford and Hibbing). Yet the studies of genetics and brain processes have made much progress in the last few decades, thanks to the development of research instruments - like fMRI brain scanners and TMS brain stimulation instruments - and of computational tools for data analysis and the simulation of explanatory models. For the field of biopolitics it is particularly relevant that within cognitive neuroscience the study of social and political issues has witnessed an increasing interest of researchers even more recently. Indeed, aware of the enabling and mediating role of the brain regarding those issues, a truly ‘neuroscientific turn’ can be observed in the social sciences, testified for example by the emergence of the field of ‘neuropolitics’ (Connolly; Vandervalk). Developing a systematic neuropolitics or biopolitics in general is a difficult challenge because of the wealth of causal influences on and interdependencies between biological, brain, cognitive and socio-political factors. Taking a somewhat more abstract perspective, this paper focuses on the process of emerging complexity in adaptive systems, enabling those to conduct ever more complex processes. Yet, parallel to that development can be observed that such systems, or organisms, are also capable in reducing the complexity of the information they are to process. Once they’re capable of developing and adjusting such compressed and complex representations of information, those systems or organisms can handle more information faster and more efficient and adaptive, yielding important benefits to the organism in navigating its environment (Halford, Wilson and Phillips). Before focusing on the role of narrative as a cognitive strategy for such a reduction of informational complexity, I will discuss the development of stable structures and increasing complexity in dynamic systems. Such a more general perspective prepares our discussion of the structures of both narratives and politics and in doing so contributes to the explanation of their interaction. (shrink)

In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n (...) = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it. (shrink)

Simple random sampling resolutions of the raven paradox relevantly diverge from scientific practice. We develop a stratified random sampling model, yielding a better fit and apparently rehabilitating simple random sampling as a legitimate idealization. However, neither accommodates a second concern, the objection from potential bias. We develop a third model that crucially invokes causal considerations, yielding a novel resolution that handles both concerns. This approach resembles Inference to the Best Explanation (IBE) and relates the generalization’s confirmation to confirmation of an (...) associated law. We give it an objective Bayesian formalization and discuss the compatibility of Bayesianism and IBE. (shrink)

In this essay we collect and put together a number of ideas relevant to the under- standing of the phenomenon of creativity, confining our considerations mostly to the domain of cognitive psychology while we will, on a few occasions, hint at neuropsy- chological underpinnings as well. In this, we will mostly focus on creativity in science, since creativity in other domains of human endeavor have common links with scientific creativity while differing in numerous other specific respects. We begin by briefly (...) introducing a few basic notions relating to cognition, among which the notion of ‘concepts’ is of basic relevance. The myriads of concepts lodged in our mind constitute a ‘conceptual space’ of an enormously complex structure, where con- cepts are correlated by beliefs that are themselves made up of concepts and are as- sociated with emotions. The conceptual space, moreover, is perpetually in a state of dynamic evolution that is once again of a complex nature. A major component of the dynamic evolution is made up of incessant acts of inference, where an inference occurs essentially by means of a succession of correlations among concepts set up with beliefs and heuristics, the latter being beliefs of a special kind, namely, ones relatively free of emotional associations and possessed of a relatively greater degree of justification. Beliefs, along with heuristics, have been described as the ‘mind’s software’, and con- stitute important cognitive components of the self-linked psychological resources of an individual. The self is the psychological engine driving all our mental and physical activity, and is in a state of ceaseless dynamics resulting from one’s most intimate ex- periences of the world accumulating in the course of one’s journey through life. Many of our psychological resources are of a dual character, having both a self-linked and a shared character, the latter being held in common with larger groups of people and imbibed from cultural inputs. We focus on the privately held self-linked beliefs of an individual, since these are presumably of central relevance in making possible inductive inferences – ones in which there arises a fundamental need of adopting a choice or making a decision. Beliefs, decisions, and inferences, all have the common link to the self of an individual and, in this, are fundamentally analogous to free will, where all of these have an aspect of non-determinism inherent in them. Creativity involves a major restructuring of the conceptual space where a sustained inferential process eventually links remote conceptual domains, thereby opening up the possibility of a large number of new correlations between remote concepts by a cascading process. Since the process of inductive inference depends crucially on de- cisions at critical junctures of the inferential chain, it becomes necessary to examine the basic mechanism underlying the making of decisions. In the framework that we attempt to build up for the understanding of scientific creativity, this role of decision making in the inferential process assumes central relevance. With this background in place, we briefly sketch the affect theory of decisions. Affect is an innate system of response to perceptual inputs received either from the exter- nal world or from the internal physiological and psychological environment whereby a positive or negative valence gets associated with a perceptual input. Almost every sit- uation faced by an individual, even one experienced tacitly, i.e., without overt aware-ness, elicits an affective response from him, carrying a positive or negative valence that underlies all sorts of decision making, including ones carried out unconsciously in inferential processes. Referring to the process of inferential exploration of the conceptual space that gener- ates the possibility of correlations being established between remote conceptual do- mains, such exploration is guided and steered at every stage by the affect system, analogous to the way a complex computer program proceeds through junctures where the program ascertains whether specified conditions are met with by way of generating appropriate numerical values – for instance, the program takes different routes, depending on whether some particular numerical value turns out to be positive or negative. The valence generated by the affect system in the process of adoption of a choice plays a similar role which therefore is of crucial relevance in inferential processes, especially in the exploration of the conceptual space where remote domains need to be linked up – the affect system produces a response along a single value dimension, resembling a number with a sign and a magnitude. While the affect system plays a guiding role in the exploration of the conceptual space, the process of exploration itself consists of the establishment of correlations between concepts by means of beliefs and heuristics, the self-linked ones among the latter having a special role in making possible the inferential journey along alternative routes whenever the shared rules of inference become inadequate. A successful access to a remote conceptual domain, necessary for the creative solution of a standing problem or anomaly – one that could not be solved within the limited domain hitherto accessed – requires a phase of relatively slow cumulative search and then, at some stage, a rapid cascading process when a solution is in sight. Representing the conceptual space in the form of a complex network, the overall process can be likened to one of self-organized criticality commonly observed in the dynamical evolution of complex systems. In order that inferential access to remote domains may actually be possible, it is necessary that restrictions on the exploration process – necessary for setting the context in ordinary instances of inductive inference – be relaxed and a relatively free exploration in a larger conceptual terrain be made possible. This is achieved by the mind going into the default mode, where external constraints – ones imposed by shared beliefs and modes of exploration – are made inoperative. While explaining all these various aspects of the creative process, we underline the supremely important role that analogy plays in it. Broadly speaking, analogy is in the nature of a heuristic, establishing correlations between concepts. However, analo- gies are very special in that these are particularly effective in establishing correlations among remote concepts, since analogy works without regard to the contiguity of the concepts in the conceptual space. In establishing links between concepts, analogies have the power to light up entire terrains in the conceptual space when a rapid cas- cading of fresh correlations becomes possible. The creative process occurs within the mind of a single individual or of a few closely collaborating individuals, but is then continued by an entire epistemic community, eventually resulting in a conceptual revolution. Such conceptual revolutions make pos- sible the radical revision of scientific theories whereby the scope of an extant theory is broadened and a new theoretical framework makes its appearance. The emerging theory is characterized by a certain degree of incommensurability when compared with the earlier one – a feature that may appear strange at first sight. But incommen- surability does not mean incompatibility and the apparently contrary features of the relation between the successive theories may be traced to the multi-layered structureof the conceptual space where concepts are correlated not by means of single links but by multiple ones, thereby generating multiple layers of correlation, among which some are retained and some created afresh in a conceptual restructuring. We conclude with the observation that creativity occurs on all scales. Analogous to correlations being set up across domains in the conceptual space and new domains being generated, processes with similar features can occur within the confines of a domain where a new layer of inferential links may be generated, connecting up sub- domains. In this context, insight can be looked upon as an instance of creativity within the confines of a domain of a relatively limited extent. (shrink)

It is argued that two observers with the same information may rightly disagree about the probability of an event that they are both observing. This is a correct way of describing the view of a lottery outcome from the perspective of a winner and from the perspective of an observer not connected with the winner - the outcome is improbable for the winner and not improbable for the unconnected observer. This claim is both argued for and extended by developing a (...) case in which a probabilistic inference is supported for one observer and not for another, though they relevantly differ only in perspective, not in any information that they have. It is pointed out, finally, that all probabilities are in this way dependent on perspective. (shrink)

A generalized information theory is proposed as a natural extension of Shannon's information theory. It proposes that information comes from forecasts. The more precise and the more unexpected a forecast is, the more information it conveys. If subjective forecast always conforms with objective facts then the generalized information measure will be equivalent to Shannon's information measure. The generalized communication model is consistent with K. R. Popper's model of knowledge evolution. The mathematical foundations of the new information theory, the generalized communication (...) model , information measures for semantic information and sensory information, and the coding meanings of generalized entropy and generalized mutual information are introduced. Assessments and optimizations of pattern recognition, predictions, and detection with the generalized information criterion are discussed. For economization of communication, a revised version of rate-distortion theory: rate-of-keeping-precision theory, which is a theory for datum compression and also a theory for matching an objective channels with the subjective understanding of information receivers, is proposed. Applications include stock market forecasting and video image presentation. (shrink)

The five studies of this special section investigate the role of models and similar representational tools in interdisciplinarity. These studies were all written by philosophers of science, who focused on interdisciplinary episodes between disciplines and sub-disciplines ranging from physics, chemistry and biology to the computational sciences, sociology and economics. The reasons we present these divergent studies in a collective form are three. First, we want to establish model-exchange as a kind of interdisciplinary event. The five case studies, which are summarized (...) in Section 2 below, show the relevance of this kind. Arguing for the relative unity of these cases will, we hope, re-orient the current debate over interdisciplinarity so as to reflect more appropriately the importance of this kind. We discuss our view of the current state of the debate in Section 3. The evidence from these cases also helps us to develop a taxonomy of interdisciplinary model exchanges in Section 4da taxonomy, we would like to add, that might be useful for the discussion of interdisciplinary exchanges beyond the context of models and their transfer. The second reason for presenting these studies together is that they provide an important source of evidence for the philosophy of science. Over the last three decades, philosophy of science has increasingly differentiated into philosophies of various disciplines. This differentiation in our view has greatly increased our understanding of the scientific practices of the respective disciplines, including the epistemological and methodological standards and conventions on which these practices are based and by which they are evaluated. But it has also made it harder to compare these practices and standards across disciplines. The studies we present here are case studies of interdisciplinary exchange: they focus on the transfer, collaborative construction or parallel use of models and similar representational tools. They therefore provide a unique opportunity to investigate various disciplinary treatments of the same or at least similar representational tools. This allows the identification and comparison of different disciplinary practices and their underlying conventions as well as of the respective normative standards of their evaluation. By tracing the paths along which models travel between disciplines and research fields we can observe to which extent discipline-external practices associated with an adopted tool are retained or replaced by disciplineinternal practices. This generates invaluable information about both disciplinarity and interdisciplinarity. We develop this argument further in Section 5. The third reason for presenting these studies in collective form is that their philosophical analysis also has important normative implications for the notion of interdisciplinarity itself. Too often in the current (non-philosophical) discourse is interdisciplinarity cast as an exclusively integrative project: interdisciplinary exchange is often claimed to be successful only if the involved disciplines become mutually more integrated as a consequence of this process. In contrast to this, many of the cases presented here show that interdisciplinary exchange can be scientifically highly successful, even if at the end of the exchange disciplinary borders remain fully intact. Indeed, borders can be fruitfully crossed without any integration across these borders. Such considerations of divergence in scientific practices and tools offer arguments against a naïve plea for unitarian or non-pluralist versions of interdisciplinarity. Disciplinary divergences may have their justifications, and attempting exchanges that require the reduction of these divergences may consequently not be justified. We pursue this argument further in Section 6. (shrink)

The paper builds on a methodological idea from experimental philosophy and on findings from psycholinguistics, to develop and defend ordinary language analysis (OLA) as practiced in J.L. Austin’s Sense and Sensibilia. That attack on sense-datum theories of perception focuses on the argument from illusion. Through a case-study on this paradoxical argument, the present paper argues for a form of OLA which is psychologically informed, seeks to expose epistemic, rather than semantic, defects in paradoxical arguments, and is immune to the main (...) objections to ordinary language philosophising, including those arising from the semantic/pragmatics distinction: A key project in current experimental philosophy is to develop psychological explanations of philosophically relevant intuitions that help us determine what warrant thinkers have for accepting them. Psycholinguistic work on the role of stereotypes in verb-comprehension has shown that intuitive judgments can be generated by automatic cognitive processes that duplicate both semantic and pragmatic inferences and are shaped by dominant uses of words. For systematic reasons, philosophers are prone to unwittingly deviate from such dominant uses. Where this happens, they are liable to automatically infer unwarranted conclusions that strike them as intuitively compelling. OLA helps us to determine those dominant uses, to identify unwitting deviations from them, and thus to expose unwarranted intuitions – e.g., in the premises of paradoxical arguments. Ordinary language does not determine the bounds of sense but shapes our leaps of thought. The paper shows how this enables its ‘Austinian’ analysis to contribute to a novel, epistemic, resolution of philosophical paradoxes and problems. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this (...) paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)