Chaitin’s incompleteness result related to random reals and the halting probability has been advertised as the ultimate and the strongest possible version of the incompleteness and undecidability theorems. It is argued that such claims are exaggerations.

There are writers in both metaphysics and algorithmic information theory (AIT) who seem to think that the latter could provide a formal theory of the former. This paper is intended as a step in that direction. It demonstrates how AIT might be used to define basic metaphysical notions such as *object* and *property* for a simple, idealized world. The extent to which these definitions capture intuitions about the metaphysics of the simple world, times the extent to (...) which we think the simple world is analogous to our own, will determine a lower bound for basing a metaphysics for *our* world on AIT. (shrink)

Argumentation theory underwent a significant development in the Fifties and Sixties: its revival is usually connected to Perelman's criticism of formal logic and the development of informal logic. Interestingly enough it was during this period that Artificial Intelligence was developed, which defended the following thesis (from now on referred to as the AI-thesis): human reasoning can be emulated by machines. The paper suggests a reconstruction of the opposition between formal and informal logic as a move against a premise of (...) an argument for the AI-thesis, and suggests making a distinction between a broad and a narrow notion of algorithm that might be used to reformulate the question as a foundational problem for argumentation theory. (shrink)

In Darwin’s Dangerous Idea, Daniel Dennett claims that evolution is algorithmic. On Dennett’s analysis, evolutionary processes are trivially algorithmic because he assumes that all natural processes are algorithmic. I will argue that there are more robust ways to understand algorithmic processes that make the claim that evolution is algorithmic empirical and not conceptual. While laws of nature can be seen as compression algorithms of information about the world, it does not follow logically that they (...) are implemented as algorithms by physical processes. For that to be true, the processes have to be part of computational systems. The basic difference between mere simulation and real computing is having proper causal structure. I will show what kind of requirements this poses for natural evolutionary processes if they are to be computational. (shrink)

The mind-body problem is analyzed in a physicalist perspective. By combining the concepts of emergence and algorithmic information theory in a thought experiment employing a basic nonlinear process, it is argued that epistemically strongly emergent properties may develop in a physical system. A comparison with the significantly more complex neural network of the brain shows that also consciousness is epistemically emergent in a strong sense. Thus reductionist understanding of consciousness appears not possible; the mind-body problem does not (...) have a reductionist solution. The ontologically emergent character of consciousness is then identified from a combinatorial analysis relating to system limits set by quantum mechanics, implying that consciousness is fundamentally irreducible to low-level phenomena. In the perspective of a modified definition of free will, the character of the physical interactions of the brain's neural system is subsequently studied. As an ontologically open system, it is asserted that its future states are undeterminable in principle. We argue that this leads to freedom of the will. (shrink)

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as the length of the shortest program producing it [1]. The second, Shannon information, takes events as belonging to ensembles and quantifies the information resulting from observing the given event in terms of the number of alternate events that have been ruled (...) out [2]. The third, statistical learning theory, has introduced measures of capacity that control (in part) the expected risk of classifiers [3]. These capacities quantify the expectations regarding future data that learning algorithms embed into classifiers. Solomonoff and Hutter have applied algorithmic information to prove remarkable results on universal induction. Shannon information provides the mathematical foundation for communication and coding theory. However, both approaches have shortcomings. Algorithmic information is not computable, severely limiting its practical usefulness. Shannon information refers to ensembles rather than actual events: it makes no sense to compute the Shannon information of a single string – or rather, there are many answers to this question depending on how a related ensemble is constructed. Although there are asymptotic results linking algorithmic and Shannon information, it is unsatisfying that there is such a large gap – a difference in kind – between the two measures. This note describes a new method of quantifying information, effective information, that links algorithmic information to Shannon information, and also links both to capacities arising in statistical learning theory [4, 5]. After introducing the measure, we show that it provides a non-universal analog of Kolmogorov complexity. We then apply it to derive basic capacities in statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. A nice byproduct of our approach is an interpretation of the explanatory power of a learning algorithm in terms of the number of hypotheses it falsifies [6], counted in two different ways for the two capacities. We also discuss how effective information relates to information gain, Shannon and mutual information. (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)

This paper investigates the seeming incompatibility of reductionism and non-reductionism in the context of complexity sciences. I review algorithmic information theory for this purpose. I offer two physical metaphors to form a better understanding of algorithmic complexity, and I briefly discuss its advantages, shortcomings and applications. Then, I revisit the non-reductionist approaches in philosophy of mind which are often arguments from ignorance to counter physicalism. A new approach called mild non-reductionism is proposed which reconciliates the necessities (...) of acknowledging irreducibility found in complex systems, and maintaining physicalism. (shrink)

An information recovery problem is the problem of constructing a proposition containing the information dropped in going from a given premise to a given conclusion that folIows. The proposition(s) to beconstructed can be required to satisfy other conditions as well, e.g. being independent of the conclusion, or being “informationally unconnected” with the conclusion, or some other condition dictated by the context. This paper discusses various types of such problems, it presents techniques and principles useful in solving them, and (...) it develops algorithmic methods for certain classes of such problems. The results are then applied to classical number theory, in particular, to questions concerning possible refinements of the 1931 Gödel Axiom Set, e.g. whether any of its axioms can be analyzed into “informational atoms”. Two propositions are “informationally unconnected” [with each other] if no informative (nontautological) consequence of one also follows from the other. A proposition is an “informational atom” if it is informative but no information can be dropped from it without rendering it uninformative (tautological). Presentation, employment, and investigation of these two new concepts are prominent features of this paper. (shrink)

The main objective of this dissertation is to philosophically assess how the use of informational concepts in the field of classical thermostatistical physics has historically evolved from the late 1940s to the present day. I will first analyze in depth the main notions that form the conceptual basis on which 'informational physics' historically unfolded, encompassing (i) different entropy, probability and information notions, (ii) their multiple interpretative variations, and (iii) the formal, numerical and semantic-interpretative relationships among them. In the following, (...) I will assess the history of informational thermophysics during the second half of the twentieth century. Firstly, I analyse the intellectual factors that gave rise to this current in the late forties (i.e., popularization of Shannon's theory, interest in a naturalized epistemology of science, etc.), then study its consolidation in the Brillouinian and Jaynesian programs, and finally claim how Carnap (1977) and his disciples tried to criticize this tendency within the scientific community. Then, I evaluate how informational physics became a predominant intellectual current in the scientific community in the nineties, made possible by the convergence of Jaynesianism and Brillouinism in proposals such as that of Tribus and McIrvine (1971) or Bekenstein (1973) and the application of algorithmic information theory into the thermophysical domain. As a sign of its radicality at this historical stage, I explore the main proposals to include information as part of our physical reality, such as Wheeler’s (1990), Stonier’s (1990) or Landauer’s (1991), detailing the main philosophical arguments (e.g., Timpson, 2013; Lombardi et al. 2016a) against those inflationary attitudes towards information. Following this historical assessment, I systematically analyze whether the descriptive exploitation of informational concepts has historically contributed to providing us with knowledge of thermophysical reality via (i) explaining thermal processes such as equilibrium approximation, (ii) advantageously predicting thermal phenomena, or (iii) enabling understanding of thermal property such as thermodynamic entropy. I argue that these epistemic shortcomings would make it impossible to draw ontological conclusions in a justified way about the physical nature of information. In conclusion, I will argue that the historical exploitation of informational concepts has not contributed significantly to the epistemic progress of thermophysics. This would lead to characterize informational proposals as 'degenerate science' (à la Lakatos 1978a) regarding classical thermostatistical physics or as theoretically underdeveloped regarding the study of the cognitive dynamics of scientists in this physical domain. (shrink)

"Complexity" is a catchword of certain extremely popular and rapidly developing interdisciplinary new sciences, often called accordingly the sciences of complexity. It is often closely associated with another notably popular but ambiguous word, "information"; information, in turn, may be justly called the central new concept in the whole 20th century science. Moreover, the notion of information is regularly coupled with a key concept of thermodynamics, viz. entropy. And like this was not enough it is quite usual to (...) add one more at present extraordinarily popular notion, namely chaos, and wed it with the abovementioned concepts. It is my aim in this paper to critically analyse this conceptual mess from a logical and philosophical point of view concentrating on the concepts of complexity and information and the question concerning the true relation between them. (shrink)

According to a recent survey by the HR Research Institute, as the presence of artificial intelligence (AI) becomes increasingly common in the workplace, HR professionals are worried that the use of recruitment algorithms will lead to a “dehumanization” of the hiring process. Our main goals in this paper are threefold: i) to bring attention to this neglected issue, ii) to clarify what exactly this concern about dehumanization might amount to, and iii) to sketch an argument for why dehumanizing the hiring (...) process is ethically suspect. After distinguishing the use of the term “dehumanization” in this context (i.e., removing the human presence) from its more common meaning in the interdisciplinary field of dehumanization studies (i.e., conceiving of other humans as subhuman), we argue that the use of hiring algorithms may negatively impact the employee-employer relationship. We argue that there are good independent reasons to accept a substantive employee-employer relationship, as well as an applicant-employer relationship, both of which are consistent with a stakeholder theory of corporate obligations. We further argue that dehumanizing the hiring process may negatively impact these relationships because of the difference between the values of human recruiters and the values embedded in recruitment algorithms. Drawing on Nguyen’s (2021) critique of how Twitter “gamifies communication”, we argue that replacing human recruiters with algorithms imports artificial values into the hiring process. We close by briefly considering some ways to potentially mitigate the problems posed by recruitment algorithms, along with the possibility that some difficult trade-offs will need to be made. (shrink)

It is often said that the best system account of laws needs supplementing with a theory of perfectly natural properties. The ‘strength’ and ‘simplicity’ of a system is language-relative and without a fixed vocabulary it is impossible to compare rival systems. Recently a number of philosophers have attempted to reformulate the BSA in an effort to avoid commitment to natural properties. I assess these proposals and argue that they are problematic as they stand. Nonetheless, I agree with their aim, (...) and show that if simplicity is interpreted as ‘compression’, algorithmic information theory provides a framework for system comparison without the need for natural properties. (shrink)

Perhaps nowhere better than, "On the Names of God," can readers discern Laclau's appreciation of theology, specifically, negative theology, and the radical potencies of political theology. // It is Laclau's close attention to Eckhart and Dionysius in this essay that reveals a core theological strategy to be learned by populist reasons or social logics and applied in politics or democracies to come. // This mode of algorithmically informed negative political theology is not mathematically inert. It aspires to relate a fraction (...) or ratio to a series ... It strains to reduce the decided determinateness of such seriality ever condemned to the naive metaphysics of bad infinity. // It is worth considering that it is the specific 'number' of Dionysius in differential identification with an ineffable god (and, as such, a singular becoming between theology and numbers) that is floating in at least two dimensions [of signification] (be it political Demand on the horizontal dimension or theological Desire on [a] floating dimension) that cannot but *perform the link that relinks* names of god with any political life, populist reason, social justice, or radical democracy straining toward peace. (shrink)

Synthetic biology aims at reconstructing life to put to the test the limits of our understanding. It is based on premises similar to those which permitted invention of computers, where a machine, which reproduces over time, runs a program, which replicates. The underlying heuristics explored here is that an authentic category of reality, information, must be coupled with the standard categories, matter, energy, space and time to account for what life is. The use of this still elusive category permits (...) us to interact with reality via construction of self-consistent models producing predictions which can be instantiated into experiments. While the present theory of information has much to say about the program, with the creative properties of recursivity at its heart, we almost entirely lack a theory of the information supporting the machine. We suggest that the program of life codes for processes meant to trap information which comes from the context provided by the environment of the machine. (shrink)

This article investigates religious ideals persistent in the datafication of information society. Its nodal point is Thomas Bayes, after whom Laplace names the primal probability algorithm. It reconsiders their mathematical innovations with Laplace's providential deism and Bayes' singular theological treatise. Conceptions of divine justice one finds among probability theorists play no small part in the algorithmic data-mining and microtargeting of Cambridge Analytica. Theological traces within mathematical computation are emphasized as the vantage over large numbers shifts to weights beyond (...) enumeration in probability theory. Collateral secularizations of predestination and theodicy emerge as probability optimizes into Bayesian prediction and machine learning. The paper revisits the semiotics and theism of Peirce and a given beyond the probable in Whitehead to recontextualize the critiques of providence by Agamben and Foucault. It reconsiders datafication problems alongside Nietzschean valuations. Religiosity likely remains encoded within the very algorithms presumed purified by technoscientific secularity or mathematical dispassion. (shrink)

Despite recent breakthroughs in the field of artificial intelligence (AI) – or more specifically machine learning (ML) algorithms for object recognition and natural language processing – it seems to be the majority view that current AI approaches are still no real match for natural intelligence (NI). More importantly, philosophers have collected a long catalogue of features which imply that NI works differently from current AI not only in a gradual sense, but in a more substantial way: NI is closely related (...) to consciousness, intentionality and experiential features like qualia (the subjective contents of mental states)1 and allows for understanding (e.g., taking insight into causal relationships instead of ‘blindly’ relying on correlations), as well as aesthetical and ethical judgement beyond what we can put into (explicit or data-induced implicit) rules to program machines with. Additionally, Psychologists find NI to range from unconscious psychological processes to focused information processing, and from embodied and implicit cognition to ‘true’ agency and creativity. NI thus seems to transcend any neurobiological functionalism by operating on ‘bits of meaning’ instead of information in the sense of data, quite unlike both the ‘good old fashioned’, symbolic AI of the past, as well as the current wave of deep neural network based, ‘sub-symbolic’ AI, which both share the idea of thinking as (only) information processing: In symbolic AI, the name explicitly references to its formal system based, i.e. essentially rule-based, nature, but also sub-symbolic AI is (implicitly) rule-based, only now via globally parametrized, nested functions. In the following I propose an alternative view of NI as information processing plus ‘bundle pushing’, discuss an example which illustrates how bundle pushing can cut information processing short,and suggest first ideas for scientific experiments in neuro-biology and information theory as further investigations. (shrink)

The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be (...) good measure of the strength of the theory. I exhibit certain strong counterexamples and establish conclusively that the received view is false. Moreover, I show that the limiting constants provided by the theorem do not in any way reflect the power of formalized theories, but that the values of these constants are actually determined by the chosen coding of Turing machines, and are thus quite accidental. (shrink)

This article comprehensively examines how information processing relates to attention and consciousness. We argue that no current theoretical framework investigating consciousness has a satisfactory and holistic account of their informational relationship. Our key theoretical contribution is showing how the dissociation between consciousness and attention must be understood in informational terms in order to make the debate scientifically sound. No current theories clarify the difference between attention and consciousness in terms of information. We conclude with two proposals to advance (...) the debate. First, neurobiological homeostatic processes need to be more explicitly associated with conscious information processing, since information processed through attention is algorithmic, rather than being homeostatic. Second, to understand subjectivity in informational terms, we must define information uniqueness in consciousness (e.g., irreproducible information, biologically encrypted information). These approaches could help cognitive scientists better understand conflicting accounts of the neural correlates of consciousness and work toward a more unified theoretical framework. (shrink)

The common use of Shannon’s information, specified for the needs of telecommunications, gives rise to many misunderstandings outside of this context. (e.g. in conceptions of such well-known theorists as C.F. Weizsäcker and J. A. Wheeler). This article shows that the terms of the general definition of information meet the structural information, and Shannon’s information is a special case of it. Similarly, complexity is misunderstood today as exemplified by the concepts of reputable computer scientists, such as S. (...) Lloyd, S. Wolfram and J. Schmidhuber. These theorists use an algorithmic definition of complexity and the so-called logical depth, neither of which meets the intuitive criterion of complexity. Hence, their misconceptions of beauty, art and the universe. It will be shown that the intuitive criterion is met by Abstract Complexity Definition. This definition also fulfils the criterion for a general complexity definition, as it defines complexity of the most general/abstract structure of our reality, that is, binary structure. It also explains such fundamental issues of information theory as the information–energy relationship and the value of information, which are still discussed and need to be clarified. (shrink)

When agents insert technological systems into their decision-making processes, they can obscure moral responsibility for the results. This can give rise to a distinct moral wrong, which we call “agency laundering.” At root, agency laundering involves obfuscating one’s moral responsibility by enlisting a technology or process to take some action and letting it forestall others from demanding an account for bad outcomes that result. We argue that the concept of agency laundering helps in understanding important moral problems in a number (...) of recent cases involving automated, or algorithmic, decision-systems. We apply our conception of agency laundering to a series of examples, including Facebook’s automated advertising suggestions, Uber’s driver interfaces, algorithmic evaluation of K-12 teachers, and risk assessment in criminal sentencing. We distinguish agency laundering from several other critiques of information technology, including the so-called “responsibility gap,” “bias laundering,” and masking. (shrink)

A platitude that took hold with Kuhn is that there can be several equally good ways of balancing theoretical virtues for theory choice. Okasha recently modelled theory choice using technical apparatus from the domain of social choice: famously, Arrow showed that no method of social choice can jointly satisfy four desiderata, and each of the desiderata in social choice has an analogue in theory choice. Okasha suggested that one can avoid the Arrow analogue for theory choice (...) by employing a strategy used by Sen in social choice, namely, to enhance the information made available to the choice algorithms. I argue here that, despite Okasha’s claims to the contrary, the information-enhancing strategy is not compelling in the domain of theory choice. (shrink)

Review of "Exploring Randomness" (200) and "The Unknowable" (1999) by Gregory Chaitin.

Richard Dawkins has popularized an argument that he thinks sound for showing that there is almost certainly no God. It rests on the assumptions (1) that complex and statistically improbable things are more difficult to explain than those that are not and (2) that an explanatory mechanism must show how this complexity can be built up from simpler means. But what justifies claims about the designer’s own complexity? One comes to a different understanding of order and of simplicity when one (...) considers the psychological counterpart of information. In assessing his treatment of biological organisms as either self-programmed machines or algorithms, I show how self-generated organized complexity does not fit well with our knowledge of abduction and of information theory as applied to genetics. I also review some philosophical proposals for explaining how the complexity of the world could be externally controlled if one wanted to uphold a traditional understanding of divine simplicity. (shrink)

This article synthesizes the current theoretical attempts to understand human-machine interactions and introduces seven premises to understand our emerging dynamics with increasingly competent, pervasive, and instantly accessible algorithms. The hope that these seven premises can build toward a social theory of human-AI cocreation. The focus on human-AI cocreation is intended to emphasize two factors. First, is the fact that our machine learning systems are socialized. Second, is the coevolving nature of human mind and AI systems as smart devices form (...) an indispensable part of our cognitive scaffolds, thus, shaping how we perceive the world and ourselves. The seven premises include: primacy of social structures; human’s desire for freedom and autonomy; AI systems will form inseparable parts of our cognitive/affective scaffolds and can change our self-understanding; philosophy and humanistic foundations on human flourishing as a guide to human-AI interaction; mindsponge information-filtering process; acculturative process of how values change and emerge from human-AI interaction; overlapping Venn diagram of the human-human, human-nature, and human-machine interactions. This article concludes with a discussion on human agency in our entanglements with socialized machines and the illusoriness of the Cartesian agent view of the mind. (shrink)

The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum in-variance and the non-locality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. Quantum (...) in-variance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. A set-theory corollary is the curious in-variance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for it to be able to be obtained. Quantum in-variance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum in-variance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. The non-locality of quantum information unifies the exact position of any space-time point of a smooth trajectory and the common possibility of all space-time points due to a quantum leap. This is deduced from quantum in-variance. Epistemology involves the relation of ordering and thus a generalized kind of information, quantum one, to explain the special features of the cognition in quantum mechanics. (shrink)

Mind-body problemet analyseras i ett reduktionistiskt perspektiv. Genom att kombinera emergensbegreppet med algoritmisk informationsteori visas i ett tankeexperiment att ett starkt epistemiskt emergent system kan konstrueras utifrån en relativt enkel, ickelinjär process. En jämförelse med hjärnans avsevärt mer komplexa neurala nätverk visar att även medvetandet kan karakteriseras som starkt epistemiskt emergent. Därmed är reduktionistisk förståelse av medvetandet inte möjlig; mind-body problemet har alltså inte en reduktionistisk lösning. Medvetandets ontologiskt emergenta karaktär kan därefter konstateras utifrån en kombinatorisk analys; det är därmed (...) principiellt oreducerbart till lägre-nivå-fenomen. I perspektivet av en modifierad definition av fri vilja diskuteras den fysiska växelverkan som äger rum i hjärnans neurala system. Trots att enskilda neurala lägre-nivå-processer är deterministiska, kan globala processer visas vara icke- deterministiska i ontologisk mening. Vi argumenterar för att detta leder till viljans frihet. (shrink)

Let f(1)=2, f(2)=4, and let f(n+1)=f(n)! for every integer n≥2. Edmund Landau's conjecture states that the set P(n^2+1) of primes of the form n^2+1 is infinite. Landau's conjecture implies the following unproven statement Φ: card(P(n^2+1))<ω ⇒ P(n^2+1)⊆[2,f(7)]. Let B denote the system of equations: {x_j!=x_k: i,k∈{1,...,9}}∪{x_i⋅x_j=x_k: i,j,k∈{1,...,9}}. The system of equations {x_1!=x_1, x_1 \cdot x_1=x_2, x_2!=x_3, x_3!=x_4, x_4!=x_5, x_5!=x_6, x_6!=x_7, x_7!=x_8, x_8!=x_9} has exactly two solutions in positive integers x_1,...,x_9, namely (1,...,1) and (f(1),...,f(9)). No known system S⊆B with a finite (...) number of solutions in positive integers x_1,...,x_9 has a solution (x_1,...,x_9)∈(N\{0})^9 satisfying max(x_1,...,x_9)>f(9). For every known system S⊆B, if the finiteness/infiniteness of the set {(x_1,...,x_9)∈(N\{0})^9: (x_1,...,x_9) solves S} is unknown, then the statement ∃ x_1,...,x_9∈N\{0} ((x_1,...,x_9) solves S)∧(max(x_1,...,x_9)>f(9)) remains unproven. Let Λ denote the statement: if the system of equations {x_2!=x_3, x_3!=x_4, x_5!=x_6, x_8!=x_9, x_1 \cdot x_1=x_2, x_3 \cdot x_5=x_6, x_4 \cdot x_8=x_9, x_5 \cdot x_7=x_8} has at most finitely many solutions in positive integers x_1,...,x_9, then each such solution (x_1,...,x_9) satisfies x_1,...,x_9≤f(9). The statement Λ is equivalent to the statement Φ. It heuristically justifies the statement Φ . This justification does not yield the finiteness/infiniteness of P(n^2+1). We present a new heuristic argument for the infiniteness of P(n^2+1), which is not based on the statement Φ. Algorithms always terminate. We explain the distinction between existing algorithms (i.e. algorithms whose existence is provable in ZFC) and known algorithms (i.e. algorithms whose definition is constructive and currently known). Assuming that the infiniteness of a set X⊆N is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. *** (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) No known algorithm with no input returns the logical value of the statement card(X)=ω. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. *** Conditions (2)-(5) hold for X=P(n^2+1). The statement Φ implies Condition (1) for X=P(n^2+1). The set X={n∈N: the interval [-1,n] contains more than 29.5+\frac{11!}{3n+1}⋅sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. 501893∈X. Condition (1) holds with n=501893. card(X∩[0,501893])=159827. X∩[501894,∞)= {n∈N: the interval [-1,n] contains at least 30 primes of the form k!+1}. We present a table that shows satisfiable conjunctions of the form #(Condition 1) ∧ (Condition 2) ∧ #(Condition 3) ∧ (Condition 4) ∧ #(Condition 5), where # denotes the negation ¬ or the absence of any symbol. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove this assumption. (shrink)

A "patternist" approach to explanation seeks to formalize unificationism using notions from algorithmic information theory. Among other advantages, this account provides both a rigorous sense of how data can admit multiple explanations, and a rigorous sense of how some of those explanations can conjoin, while others compete.

This paper deals with Gärdenfors’ theory of conceptual spaces. Let \({\mathcal {S}}\) be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes \(\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}\) be given. Our main result is the construction of a classification algorithm. That is, given an element \({\tilde{A}}\in \mathcal {S},\) our algorithm classifies it into the conceptual field determined by one of the given prototypes \(\tilde{P}_i.\) The construction of our algorithm uses some physical (...) analogies and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space \(\mathcal {S}\) is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

The Kolmogorov-Sinai entropy is a fairly exotic mathematical concept which has recently aroused some interest on the philosophers’ part. The most salient trait of this concept is its working as a junction between such diverse ambits as statistical mechanics, information theory and algorithm theory. In this paper I argue that, in order to understand this very special feature of the Kolmogorov-Sinai entropy, is essential to reconstruct its genealogy. Somewhat surprisingly, this story takes us as far back as (...) the beginning of celestial mechanics and through some of the most exciting developments of mathematical physics of the 19th century. (shrink)

Complexity is a relatively new field of study that is still heavily influenced by philosophy. However, with the advent of modern computing, it has become easier to conduct thorough investigations of complex systems using computational simulations. Despite significant progress, there remain certain characteristics of complex systems that are difficult to comprehend. To better understand these features, information can be applied using simple models of complex systems. The concepts of Shannon's information theory, Kolgomorov complexity, and logical depth are (...) helpful in this regard. Computational mathematical models based on recursive processes, recursive functions, and information in functions offer new insights into complexity by exploring its connection with irreversibility and the loss of information. Through these models, it is possible to see complexity as a transformation of input information through algorithmic computation, with time, logical depth, and information loss serving as key factors in understanding the process. (shrink)

The Turing machine halting problem can be explained by several factors, including arithmetic logic irreversibility and memory erasure, which contribute to computational uncertainty due to information loss during computation. Essentially, this means that an algorithm can only preserve information about an input, rather than generate new information. This uncertainty arises from characteristics such as arithmetic logical irreversibility, Landauer's principle, and memory erasure, which ultimately lead to a loss of information and an increase in entropy. To measure (...) this uncertainty and loss of information, the concept of arithmetic logical entropy can be used. The Turing machine and its equivalent, general recursive functions can be understood through the λ calculus and the Turing/Church thesis. However, there are certain recursive functions that cannot be fully understood or predicted by other algorithms due to the loss of information during logical-arithmetic operations. In other words, the behaviour of these functions cannot be completely determined at every stage of the computation due to a lack of information in their definition. While there are some cases where the behaviour of recursive functions is highly predictable, the lack of information in most cases makes it impossible for algorithms to determine if a program will halt or not. This inability to predict the outcome of the computation is the essence of the halting problem of the Turing machine. Even in cases where more information is available about the program, it is still difficult to determine with certainty if the program will halt or not. This also highlights the importance of the Turing oracle machine, which introduces information from outside the computation to compensate for the lack of information and ultimately decide the result of the computation. (shrink)

The first decade of this century has seen the nascency of the first mathematical theory of general artificial intelligence. This theory of Universal Artificial Intelligence (UAI) has made significant contributions to many theoretical, philosophical, and practical AI questions. In a series of papers culminating in book (Hutter, 2005), an exciting sound and complete mathematical model for a super intelligent agent (AIXI) has been developed and rigorously analyzed. While nowadays most AI researchers avoid discussing intelligence, the award-winning PhD thesis (...) (Legg, 2008) provided the philosophical embedding and investigated the UAI-based universal measure of rational intelligence, which is formal, objective and non-anthropocentric. Recently, effective approximations of AIXI have been derived and experimentally investigated in JAIR paper (Veness et al. 2011). This practical breakthrough has resulted in some impressive applications, finally muting earlier critique that UAI is only a theory. For the first time, without providing any domain knowledge, the same agent is able to self-adapt to a diverse range of interactive environments. For instance, AIXI is able to learn from scratch to play TicTacToe, Pacman, Kuhn Poker, and other games by trial and error, without even providing the rules of the games. These achievements give new hope that the grand goal of Artificial General Intelligence is not elusive. This article provides an informal overview of UAI in context. It attempts to gently introduce a very theoretical, formal, and mathematical subject, and discusses philosophical and technical ingredients, traits of intelligence, some social questions, and the past and future of UAI. (shrink)

I argue for patternism, a new answer to the question of when some objects compose a whole. None of the standard principles of composition comfortably capture our natural judgments, such as that my cat exists and my table exists, but there is nothing wholly composed of them. Patternism holds, very roughly, that some things compose a whole whenever together they form a “real pattern”. Plausibly we are inclined to acknowledge the existence of my cat and my table but not of (...) their fusion, because the first two have a kind of internal organizational coherence that their putative fusion lacks. Kolmogorov complexity theory supplies the needed rigorous sense of “internal organizational coherence”. (shrink)

Applying the concepts of Kolmogorov-Chaitin complexity and Turing’s uncomputability from the computability and algorithmic information theories to the irreducible and incomputable randomness of quantum mechanics, a novel argument for the existence of God is presented. Concepts of ‘transintelligence’ and ‘transcausality’ are introduced, and from them, it is posited that our universe must be epistemologically and ontologically an open universe. The proposed idea also proffers a new perspective on the nonlocal nature and the infamous wave-function-collapse problem of quantum mechanics.

We information-theoretically reformulate two measures of capacity from statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. We show these capacity measures count the number of hypotheses about a dataset that a learning algorithm falsifies when it finds the classifier in its repertoire minimizing empirical risk. It then follows from that the future performance of predictors on unseen data is controlled in part by how many hypotheses the learner falsifies. As a corollary we show that empirical VC-entropy quantifies (...) the message length of the true hypothesis in the optimal code of a particular probability distribution, the so-called actual repertoire. (shrink)

As historically acknowledged in the Reasoning about Actions and Change community, intuitiveness of a logical domain description cannot be fully automated. Moreover, like any other logical theory, action theories may also evolve, and thus knowledge engineers need revision methods to help in accommodating new incoming information about the behavior of actions in an adequate manner. The present work is about changing action domain descriptions in multimodal logic. Its contribution is threefold: first we revisit the semantics of action (...) class='Hi'>theory contraction proposed in previous work, giving more robust operators that express minimal change based on a notion of distance between Kripke-models. Second we give algorithms for syntactical action theory contraction and establish their correctness with respect to our semantics for those action theories that satisfy a principle of modularity investigated in previous work. Since modularity can be ensured for every action theory and, as we show here, needs to be computed at most once during the evolution of a domain description, it does not represent a limitation at all to the method here studied. Finally we state AGM-like postulates for action theory contraction and assess the behavior of our operators with respect to them. Moreover, we also address the revision counterpart of action theory change, showing that it benefits from our semantics for contraction. (shrink)

Bedau's influential (1997) account analyzes weak emergence in terms of the non-derivability of a system’s macrostates from its microstates except by simulation. I offer an improved version of Bedau’s account of weak emergence in light of insights from information theory. Non-derivability alone does not guarantee that a system’s macrostates are weakly emergent. Rather, it is non-derivability plus the algorithmic compressibility of the system’s macrostates that makes them weakly emergent. I argue that the resulting information-theoretic picture provides (...) a metaphysical account of weak emergence rather than a merely epistemic one. (shrink)

The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. (...) The role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

How do conventions of communication emerge? How do sounds or gestures take on a semantic meaning, and how do pragmatic conventions emerge regarding the passing of adequate, reliable, and relevant information? My colleagues and I have attempted in earlier work to extend spatialized game theory to questions of semantics. Agent-based simulations indicate that simple signaling systems emerge fairly naturally on the basis of individual information maximization in environments of wandering food sources and predators. Simple signaling emerges by (...) means of any of various forms of updating on the behavior of immediate neighbors: imitation, localized genetic algorithms, and partial training in neural nets. Here the goal is to apply similar techniques to questions of pragmatics. The motivating idea is the same: the idea that important aspects of pragmatics, like important aspects of semantics, may fall out as a natural results of information maximization in informational networks. The attempt below is to simulate fundamental elements of the Gricean picture: in particular, to show within networks of very simple agents the emergence of behavior in accord with the Gricean maxims. What these simulations suggest is that important features of pragmatics, like important aspects of semantics, don't have to be added in a theory of informational networks. They come for free. (shrink)

In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms (...) that guarantee that every state can be diagonalized. The first axiom is Causality, which ensures that the marginal of a bipartite state is well defined. Then, Purity Preservation states that the set of pure transformations is closed under composition. The third axiom is Purification, which allows to assign a pure state to the composition of a system with its environment. Finally, we introduce the axiom of Pure Sharpness, stating that for every system there exists at least one pure effect occurring with unit probability on some state. For theories satisfying our four axioms, we show a constructive algorithm for diagonalizing every given state. The diagonalization result allows us to formulate a majorization criterion that captures the convertibility of states in the operational resource theory of purity, where random reversible transformations are regarded as free operations. (shrink)

Contemporary philosophy and theoretical psychology are dominated by an acceptance of content-externalism: the view that the contents of one's mental states are constitutively, as opposed to causally, dependent on facts about the external world. In the present work, it is shown that content-externalism involves a failure to distinguish between semantics and pre-semantics---between, on the one hand, the literal meanings of expressions and, on the other hand, the information that one must exploit in order to ascertain their literal meanings. It (...) is further shown that, given the falsity of content-externalism, the falsity of the Computational Theory of Mind (CTM) follows. It is also shown that CTM involves a misunderstanding of terms such as "computation," "syntax," "algorithm," and "formal truth." Novel analyses of the concepts expressed by these terms are put forth. These analyses yield clear, intuition-friendly, and extensionally correct answers to the questions "what are propositions?, "what is it for a proposition to be true?", and "what are the logical and psychological differences between conceptual (propositional) and non-conceptual (non-propositional) content?" Naively taking literal meaning to be in lockstep with cognitive content, Burge, Salmon, Falvey, and other semantic externalists have wrongly taken Kripke's correct semantic views to justify drastic and otherwise contraindicated revisions of commonsense. (Salmon: What is non-existent exists; at a given time, one can rationally accept a proposition and its negation. Burge: Somebody who is having a thought may be psychologically indistinguishable from somebody who is thinking nothing. Falvey: somebody who rightly believes himself to be thinking about water is psychologically indistinguishable from somebody who wrongly thinks himself to be doing so and who, indeed, isn't thinking about anything.) Given a few truisms concerning the differences between thought-borne and sentence-borne information, the data is easily modeled without conceding any legitimacy to any one of these rationality-dismantling atrocities. (It thus turns out, ironically, that no one has done more to undermine Kripke's correct semantic points than Kripke's own followers!). (shrink)

Purpose – In the last half-century, individual sensory neurons have been bestowed with characteristics of the whole human being, such as behavior and its oft-presumed precursor, consciousness. This anthropomorphization is pervasive in the literature. It is also absurd, given what we know about neurons, and it needs to be abolished. This study aims to first understand how it happened, and hence why it persists. Design/methodology/approach – The peer-reviewed sensory-neurophysiology literature extends to hundreds (perhaps thousands) of papers. Here, more than 90 (...) mainstream papers were scrutinized. Findings – Anthropomorphization arose because single neurons were cast as “observers” who “identify”, “categorize”, “recognize”, “distinguish” or “discriminate” the stimuli, using math-based algorithms that reduce (“decode”) the stimulus-evoked spike trains to the particular stimuli inferred to elicit them. Without “decoding”, there is supposedly no perception. However, “decoding” is both unnecessary and unconfirmed. The neuronal “observer” in fact consists of the laboratory staff and the greater society that supports them. In anthropomorphization, the neuron becomes the collective. Research limitations/implications – Anthropomorphization underlies the widespread application to neurons Information Theory and Signal Detection Theory, making both approaches incorrect. Practical implications – A great deal of time, money and effort has been wasted on anthropomorphic Reductionist approaches to understanding perception and consciousness. Those resources should be diverted into more-fruitful approaches. Originality/value – A long-overdue scrutiny of sensory-neuroscience literature reveals that anthropomorphization, a form of Reductionism that involves the presumption of single-neuron consciousness, has run amok in neuroscience. Consciousness is more likely to be an emergent property of the brain. (shrink)

The 20th Century is the starting point for the most ambitious attempts to extrapolate human life into artificial systems. Norbert Wiener’s Cybernetics, Claude Shannon’s Information Theory, John von Neumann’s Cellular Automata, Universal Constructor to the Turing Test, Artificial Intelligence to Maturana and Varela’s Autopoietic Organization, all shared the goal of understanding in what sense humans resemble a machine. This scientific and technological movement has embraced all disciplines without exceptions, not only mathematics and physics but also biology, sociology, psychology, (...) economics etc. New terms were developed, such as “information”, “organization”, “entropy”, “communication”, “encryption”, “computation” and “algorithmics” to mention a few, all which had an enormous impact on artificial systems. Our work follows this historical track but with a reversed order of priorities. Instead of deducing a reduced group of human acts into an artificial environment, we deduce the human aspects of machines by extrapolating algorithmic methodologies into everyday life acts. The present informational theories were insufficiently powered to achieve this objective without developing a new theoretical approach. Hence, our research is directed towards an expansion of the current informational theories. (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)

Informational theories of semantic content have been recently gaining prominence in the debate on the notion of mental representation. In this paper we examine new-wave informational theories which have a special focus on cognitive science. In particular, we argue that these theories face four important difficulties: they do not fully solve the problem of error, fall prey to the wrong distality attribution problem, have serious difficulties accounting for ambiguous and redundant representations and fail to deliver a metasemantic theory of (...) representation. Furthermore, we argue that these difficulties derive from their exclusive reliance on the notion of information, so we suggest that pure informational accounts should be complemented with functional approaches. (shrink)

Integrated Information Theory (IIT) identifies consciousness with having a maximum amount of integrated information. But a thing’s having the maximum amount of anything cannot be intrinsic to it, for that depends on how that thing compares to certain other things. IIT’s consciousness, then, is not intrinsic. A mereological argument elaborates this consequence: IIT implies that one physical system can be conscious while a physical duplicate of it is not conscious. Thus, by a common and reasonable conception of (...) intrinsicality, IIT’s consciousness is not intrinsic. It is then argued that to avoid the implication that consciousness is not intrinsic, IIT must abandon its Exclusion Postulate, which prohibits overlapping conscious systems. Indeed, theories of consciousness that attribute consciousness to physical systems, should embrace the view that some conscious systems overlap. A discussion of the admittedly counterintuitive nature of this solution, along with some medical and neuroscientific realities that would seem to support it, is included. (shrink)

Leibniz said that the universe, if God-created, would exist at a unique, conjoint, physical maximum: Of all possible worlds, it would be richest in phenomena, but its richness would arise from the simplest physical laws and initial conditions. Using concepts of ‘‘variety’’ and algorithmic informational complexity, Leibniz’ claim can be reframed as a testable theory. This theory predicts that the laws and conditions of the actual universe should be simpler, and the universe richer in phenomena, than the (...) presence of observers would require. Tegmark has shown that inhabitants of an infinite multiverse would likely observe simple laws and conditions, but also phenomenal richness just great enough to explain their existence. Empirical observations fit the claim of divine choice better than the claim of an infinite multiverse. The future of the universe, including its future information-processing capacity, is predicted to be endless. -/- . (shrink)

In 1948, Claude Shannon introduced his version of a concept that was core to Norbert Wiener's cybernetics, namely, information theory. Shannon's formalisms include a physical framework, namely a general communication system having six unique elements. Under this framework, Shannon information theory offers two particularly useful statistics, channel capacity and information transmitted. Remarkably, hundreds of neuroscience laboratories subsequently reported such numbers. But how (and why) did neuroscientists adapt a communications-engineering framework? Surprisingly, the literature offers no clear (...) answers. To therefore first answer "how", 115 authoritative peer-reviewed papers, proceedings, books and book chapters were scrutinized for neuroscientists' characterizations of the elements of Shannon's general communication system. Evidently, many neuroscientists attempted no identification of the system's elements. Others identified only a few of Shannon's system's elements. Indeed, the available neuroscience interpretations show a stunning incoherence, both within and across studies. The interpretational gamut implies hundreds, perhaps thousands, of different possible neuronal versions of Shannon's general communication system. The obvious lack of a definitive, credible interpretation makes neuroscience calculations of channel capacity and information transmitted meaningless. To now answer why Shannon's system was ever adapted for neuroscience, three common features of the neuroscience literature were examined: ignorance of the role of the observer, the presumption of "decoding" of neuronal voltage-spike trains, and the pursuit of ingrained analogies such as information, computation, and machine. Each of these factors facilitated a plethora of interpretations of Shannon's system elements. Finally, let us not ignore the impact of these "informational misadventures" on society at large. It is the same impact as scientific fraud. (shrink)