William Dembski claims to have established a decision process to determine when highly unlikely events observed in the natural world are due to Intelligent Design. This article argues that, as no implementable randomness test is superior to a universal Martin-Löf test, this test should be used to replace Dembski's decision process. Furthermore, Dembski's decision process is flawed, as natural explanations are eliminated before chance. Dembski also introduces a fourth law of thermodynamics, his “law of conservation of information,” to argue (...) that information cannot increase by natural processes. However, this article, using algorithmic information theory, shows that this law is no more than the second law of thermodynamics. The article concludes that any discussions on the possibilities of design interventions in nature should be articulated in terms of the algorithmic information theory approach to randomness and its robust decision process. (shrink)

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.

We present a critical discussion of the claim (most forcefully propounded by Chaitin) that algorithmic information theory sheds new light on Godel's first incompleteness theorem.

Although algorithmic information theory provides a measure of the information content of string of characters, problems of noise and noncomputability emerge. However, if pattern in a noisy string is recognized by reference to a set of similar strings, this article shows that a compressed algorithmic description of a noisy string is possible and illustrates this with some simple examples. The article also shows that algorithmic information theory can quantify the information in (...) complex organized systems where pattern is nested within pattern. (shrink)

Turing machine An idealized computing device attached to a tape, each square of which is capable of holding a symbol. We write a program (a nite binary string) on the tape, and start the machine. If the machine halts with string o written at a designated place on the tape.

Hi everybody! It's a great pleasure for me to be back here at the new, improved Santa Fe Institute in this spectacular location. I guess this is my fourth visit and it's always very stimulating, so I'm always very happy to visit you guys. I'd like to tell you what I've been up to lately. First of all, let me say what algorithmic information theory is good for, before telling you about the new version of it I've (...) got. (shrink)

clusions are only probably correct. On the other hand, algorithmic information theory provides a precise mathematical definition of the notion of random or patternless sequence. In this paper we shall describe conditions under which if the sequence of coin tosses in the Solovay– Strassen and Miller–Rabin algorithms is replaced by a sequence of heads and tails that is of maximal algorithmic information content, i.e., has maximal algorithmic randomness, then one obtains an error-free test for (...) primality. These results are only of theoretical interest, since it is a manifestation of the G¨ odel incompleteness phenomenon that it is impossible to “certify” a sequence to be random by means of a proof, even though most sequences have this property. Thus by using certified random sequences one can in principle, but not in practice, convert probabilistic tests for primality into deterministic ones. (shrink)

We provide some examples showing how game-theoretic arguments can be used in computability theory and algorithmic information theory: unique numbering theorem (Friedberg), the gap between conditional complexity and total conditional complexity, Epstein–Levin theorem and some (yet unpublished) result of Muchnik and Vyugin.

We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and wherethey are fundamentally different. We discuss and relate the basicnotions of both theories: Shannon entropy, Kolmogorov complexity, Shannon mutual informationand Kolmogorov (``algorithmic'') mutual information. We explainhow universal coding may be viewed as a middle ground betweenthe two theories. We consider Shannon's rate distortion theory, whichquantifies useful (in a certain sense) information.We use the communication of (...) information as our guiding motif, and we explain howit relates to sequential question-answer sessions. (shrink)

Review by: Jan Reimann The Bulletin of Symbolic Logic, Volume 19, Issue 3, Page 397-399, September 2013.

The Shannon information function (H) has been extensively used in ecology as a statistic of species diversity. Yet, the use of Shannon diversity index has also been criticized, mainly because of its ambiguous ecological interpretation and because of its relatively great sensitivity to the relative abundances of species in the community. In my opinion, the major shortcoming of the traditional perspective (on the possible relation of species diversity with information theory) is that species need for an external (...) receiver (the scientist or ecologist) to exist and transmit information. Because organisms are self-catalized replicating structures that can transmit genotypic information to offspring, it should be evident that any single species has two possible states or alternatives: to be or not to be. In other words, species have no need for an external receiver since they are their own receivers. Therefore, the amount of biological information (at the species scale) in a community with one only species would be species, and not bits as in the traditional perspective. Moreover, species diversity appears to be a monotonic increasing function of (or S) when all species are equally probable (S being species richness), and not a function of as in the traditional perspective. To avoid the noted shortcoming, we could use 2H (instead of H) for calculating species diversity and species evenness (= 2H/S). However, owing to the relatively great sensitivity of H to the relative abundances of species in the community, the value of species dominance (= 1 − 2H/S) is unreasonably high when differences between dominant and subordinate species are considerable, thereby lowering the value of species evenness and diversity. This unsatisfactory behaviour is even more evident for Simpson index and related algorithms. I propose the use of other statistics for a better analysis of community structure, their relationship being: species evenness + species dominance = 1; species diversity × species uniformity = 1; and species diversity = species richness × species evenness. (shrink)

While it is legitimate to study ideas and concepts related to information in their broadest sense, that formal approaches properly belong in specific contexts is a fact that is too often ignored. That their use outside these contexts amounts to misuse or imprecise use cannot and should not be overlooked. This paper presents a framework based on algorithmic information theory for discussing concepts of relevance to information in philosophical contexts. Special attention will be paid to (...) the intersection of syntactic and semantic variants and connections. (shrink)

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)

We survey concepts at the frontier of research connecting artificial, animal, and human cognition to computation and information processing—from the Turing test to Searle’s Chinese room argument, from integrated information theory to computational and algorithmic complexity. We start by arguing that passing the Turing test is a trivial computational problem and that its pragmatic difficulty sheds light on the computational nature of the human mind more than it does on the challenge of artificial intelligence. We then (...) review our proposed algorithmic information-theoretic measures for quantifying and characterizing cognition in various forms. These are capable of accounting for known biases in human behavior, thus vindicating a computational algorithmic view of cognition as first suggested by Turing, but this time rooted in the concept of algorithmic probability, which in turn is based on computational universality while being independent of computational model, and which has the virtue of being predictive and testable as a model theory of cognitive behavior. (shrink)

This paper studies the information of big data in the digital publishing industry chain and adopts advanced algorithms for its fusion calculation. The basic theory of digital publishing ecological chain is dissected, the construction requirements, construction methods, and construction paths of digital publishing ecological chain are analysed, and feasible construction measures are proposed. It also defines the connotation of the fusion of knowledge services between publishing institutions and libraries in the digital era; then analyses the characteristics and principles (...) of the fusion of knowledge services between publishing institutions and libraries in the digital era; and finally sorts out the theoretical foundations such as synergy theory, information integration service theory, and game theory. Meanwhile, this paper also studies the flow of digital publishing resources and empirically analyses the eco-efficiency of digital publishing eco-chain by using metabolic network analysis, population analysis, and life cycle analysis, and it finds the eco-efficiency problems of the existing e-book eco-chain from its analysis. Finally, the imbalance in the digital publishing ecological chain and its hazards are analysed, and specific regulation and optimization measures are proposed. The research in this paper makes up for the deficiencies of related studies and can well solve the problems that exist in the previous and provide theoretical support for the healthy development of digital publishing enterprises. (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)

Machine learning algorithms pervade contemporary society. They are integral to social institutions, inform processes of governance, and animate the mundane technologies of daily life. Consistently, the outcomes of machine learning reflect, reproduce, and amplify structural inequalities. The field of fair machine learning has emerged in response, developing mathematical techniques that increase fairness based on anti-classification, classification parity, and calibration standards. In practice, these computational correctives invariably fall short, operating from an algorithmic idealism that does not, and cannot, address systemic, (...) Intersectional stratifications. Taking present fair machine learning methods as our point of departure, we suggest instead the notion and practice of algorithmic reparation. Rooted in theories of Intersectionality, reparative algorithms name, unmask, and undo allocative and representational harms as they materialize in sociotechnical form. We propose algorithmic reparation as a foundation for building, evaluating, adjusting, and when necessary, omitting and eradicating machine learning systems. (shrink)

Introduction -- Algorithms, programs, procedures, and abstract automata -- Functioning of algorithms and automata, computation, and operations with algorithms and automata -- Basic postulates and axioms for algorithms -- Power of algorithms and classes of algorithms: comparison and evaluation -- Computing, accepting, and deciding modes of algorithms and programs -- Problems that people solve and related properties of algorithms -- Boundaries for algorithms and computation -- Software and hardware verification and testing -- Conclusion.

According to a traditional view, scientific laws and theories constitute algorithmic compressions of empirical data sets collected from observations and measurements. This article defends the thesis that, to the contrary, empirical data sets are algorithmically incompressible. The reason is that individual data points are determined partly by perturbations, or causal factors that cannot be reduced to any pattern. If empirical data sets are incompressible, then they exhibit maximal algorithmic complexity, maximal entropy and zero redundancy. They are therefore maximally (...) efficient carriers of information about the world. Since, on algorithmic information theory, a string is algorithmically random just if it is incompressible, the thesis entails that empirical data sets consist of algorithmically random strings of digits. Rather than constituting compressions of empirical data, scientific laws and theories pick out patterns that data sets exhibit with a certain noise.Author Keywords: Algorithmic randomness; Compression; Empirical data; Information; Law; Pattern. (shrink)

According to a traditional view, scientific laws and theories constitute algorithmic compressions of empirical data sets collected from observations and measurements. This article defends the thesis that, to the contrary, empirical data sets are algorithmically incompressible. The reason is that individual data points are determined partly by perturbations, or causal factors that cannot be reduced to any pattern. If empirical data sets are incompressible, then they exhibit maximal algorithmic complexity, maximal entropy and zero redundancy. They are therefore maximally (...) efficient carriers of information about the world. Since, on algorithmic information theory, a string is algorithmically random just if it is incompressible, the thesis entails that empirical data sets consist of algorithmically random strings of digits. Rather than constituting compressions of empirical data, scientific laws and theories pick out patterns that data sets exhibit with a certain noise. (shrink)

On the basis of ecological footprint theory and tourism ecological footprint theory, the sustainable development indexes such as ecological footprint, ecological carrying capacity, ecological deficit, and ecological surplus of the research area were calculated and the long-term change pattern of each index was analyzed. This paper shows that the ecological footprint of the research area increases year by year, but the ecological footprint is always smaller than the ecological carrying capacity, indicating that the area is still in the (...) state of sustainable development. However, the per capita ecological surplus shows a decreasing trend year by year, indicating that the sustainable development of the region is getting worse. This paper proposes a reordering method of tourist attractions based on heterogeneous information fusion, and realizes the retrieval and reordering of tourist attractions based on user query and fusion of heterogeneous information, so as to help users make travel decisions. In view of the shortage of tourism commercial websites to passively provide scenic spot information, this paper puts forward a scenic spot retrieval method based on query words to enable users to obtain scenic spot information according to their needs, and constructs a tourist consumer data analysis system. The preprocessing methods and methods adopted by the data preprocessing module are analyzed in detail, and the algorithms used in the travel route analysis and consumer spending ability analysis are described in detail. The data of tourism consumers are analyzed by this system, and the results are evaluated. (shrink)

This paper contributes to debates over algorithmic discrimination with particular attention to structural theories of racism and the problem of “proxy discrimination”—discriminatory effects that arise even when an algorithm has no information about socially sensitive characteristics such as race. Structural theories emphasize the ways that unequal power structures contribute to the subordination of marginalized groups: these theories thus understand racism in ways that go beyond individual choices and bad intentions. Our question is, how should a structural understanding of (...) racism and oppression inform our understanding of algorithmic discrimination and its associated norms? Some responses to the problem of proxy discrimination focus on fairness as a form of “parity,” aiming to equalize metrics between individuals or groups—looking, for example, for equal rates of accurate and inaccurate predictions between one group and another. We argue that from the perspective of structural theories, fairness-as-parity is inapt in the algorithmic context; instead, we should be considering social impact—whether a use of an algorithm perpetuates or mitigates existing social stratification. Our contribution thus offers a new understanding of what algorithmic racial discrimination is. (shrink)

The LNCS series reports state-of-the-art results in computer science research, development, and education, at a high level and in both printed and electronic form. Enjoying tight cooperation with the R&D community, with numerous individuals, as well as with prestigious Organizations and societies, LNCS has grown into the most comprehensive computer science research forum available. The scope of LNCS, including its subseries LNAI and LNBI, spans the whole range of computer science and information technology including interdisciplinary topics in a variety (...) of application fields. In Parallel to the printed book, each new volume is published electronically in LNCS Online. (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)

The purpose of the study is to investigate the features of the algorithm for forming the stock portfolio of investors using the theory of fuzzy sets, taking into account a priori uncertain input information and market dynamics. The scientific novelty of the article lies in the application of a relatively new fuzzy-multiple apparatus and the theory of fuzzy sets to the formation of the stock portfolio of investors. From a practical point of view, the proposed fuzzy model (...) makes it possible to predict not only the structure and expected return of a portfolio of securities, similarly to the application of the classical portfolio theory, but also to obtain the values of the lower and upper boundaries of the return on securities, which will allow the investor to form a more complete picture of the structure of the portfolio in the future. As a result, it was found that the use of classical statistical approaches for the formation of a stock portfolio of investors will not allow obtaining a reliable and accurate result, since traditional methods do not take into account the uncertainty factors of events in the stock market. To level information asymmetry and eliminate risks of uncertainty, it is advisable to apply the theory of fuzzy logic. (shrink)

Combining testimonial reports from independent and partially reliable information sources is an important epistemological problem of uncertain reasoning. Within the framework of Dempster–Shafer theory, we propose a general model of partially reliable sources, which includes several previously known results as special cases. The paper reproduces these results on the basis of a comprehensive model taxonomy. This gives a number of new insights and thereby contributes to a better understanding of this important application of reasoning with uncertain and incomplete (...) information. (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)

There has been considerable debate in the literature about the relative merits of information processing versus dynamical approaches to understanding cognitive processes. In this article, we explore the relationship between these two styles of explanation using a model agent evolved to solve a relational categorization task. Specifically, we separately analyze the operation of this agent using the mathematical tools of information theory and dynamical systems theory. Information-theoretic analysis reveals how task-relevant information flows through the (...) system to be combined into a categorization decision. Dynamical analysis reveals the key geometrical and temporal interrelationships underlying the categorization decision. Finally, we propose a framework for directly relating these two different styles of explanation and discuss the possible implications of our analysis for some of the ongoing debates in cognitive science. (shrink)

Platform companies use techniques of algorithmic management to control their users. Though digital marketplaces vary in their use of these techniques, few studies have asked why. This question is theoretically consequential. Economic sociology has traditionally focused on the embedded activities of market actors to explain competitive and valuation dynamics in markets. But restrictive platforms can leave little autonomy to market actors. Whether or not the analytical focus on their interactions makes sense thus depends on how restrictive the platform is, (...) turning the question into a first order analytical concern. The paper argues that we can explain why platforms adopt more and less restrictive architectures by focusing on the design logic that informs their construction. Platforms treat markets as search algorithms that blend software computation with human interactions. If the algorithm requires actors to follow narrow scripts of behavior, the platform should become more restrictive. This depends on the need for centralized computation, the degree to which required inputs can be standardized, and the misalignment of interests between users. The paper discusses how these criteria can be mobilized to explain the architectures of four illustrative cases. (shrink)

To formalize the human judgment of rhythm complexity, we used five measures from information theory and algorithmic complexity to measure the complexity of 48 artificially generated rhythmic sequences. We compared these measurements to human prediction accuracy and easiness judgments obtained from a listening experiment, in which 32 participants guessed the last beat of each sequence. We also investigated the modulating effects of musical expertise and general pattern identification ability. Entropy rate and Kolmogorov complexity were correlated with prediction (...) accuracy, and highly correlated with easiness judgments. A logistic regression showed main effects of musical training, entropy rate, and Kolmogorov complexity, and an interaction between musical training and both entropy rate and Kolmogorov complexity. These results indicate that information-theoretic concepts capture some salient features of the human judgment of rhythm complexity, and they confirm the influence of musical expertise on complexity judgments. (shrink)

I will propose the notion that the universe is digital, not as a claim about what the universe is made of but rather about the way it unfolds. Central to the argument will be the concepts of symmetry breaking and algorithmic probability, which will be used as tools to compare the way patterns are distributed in our world to the way patterns are distributed in a simulated digital one. These concepts will provide a framework for a discussion of the (...) informational nature of reality. I will argue that if the universe were analog, then the world would likely be random, making it largely incomprehensible. The digital model has, however, an inherent beauty in its imposition of an upper limit and in the convergence in computational power to a maximal level of sophistication. Even if deterministic, that it is digital doesnít mean that the world is trivial or predictable, but rather that it is built up from operations that at the lowest scale are very simple but that at a higher scale look complex and even random, though only in appearance. (shrink)

As a discipline distinct from ecology, conservation biology emerged in the 1980s as a rigorous science focused on protecting biodiversity. Two algorithmic breakthroughs in information processing made this possible: place-prioritization algorithms and geographical information systems. They provided defensible, data-driven methods for designing reserves to conserve biodiversity that obviated the need for largely intuitive and highly problematic appeals to ecological theory at the time. But the scientific basis of these achievements and whether they constitute genuine scientific progress (...) has been criticized. We counter by pointing out important inaccuracies about the science and rejecting the apparent theory-first focus. More broadly, the case study reveals significant limitations of the predominant epistemic-semantic conceptions of scientific progress and the considerable merits of pragmatic, practically-oriented accounts. (shrink)

The information-theoretic point of view proposed by Leibniz in 1686 and developed by algorithmic information theory (AIT) suggests that mathematics and physics are not that different. This will be a first-person account of some doubts and speculations about the nature of mathematics that I have entertained for the past three decades, and which have now been incorporated in a digital philosophy paradigm shift that is sweeping across the sciences.

As a discipline distinct from ecology, conservation biology emerged in the 1980s as a rigorous science focused on protecting biodiversity. Two algorithmic breakthroughs in information processing made this possible: place-prioritization algorithms and geographical information systems. They provided defensible, data-driven methods for designing reserves to conserve biodiversity that obviated the need for largely intuitive and highly problematic appeals to ecological theory at the time. But the scientific basis of these achievements and whether they constitute genuine scientific progress (...) has been criticized. We counter by pointing out important inaccuracies about the science and rejecting the apparent theory-first focus. More broadly, the case study reveals significant limitations of the predominant epistemic-semantic conceptions of scientific progress and the considerable merits of pragmatic, practically-oriented accounts. (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)

A growing body of empirical evidence suggests the existence of a Paradox of Choice, whereby a larger choice set leads to a lower expected payoff to the decisionmaker. These empirical findings contradict traditional choice-theoretic results in microeconomics and even social psychology, suggesting profound yet unexplained aspects of choice settings/behavior. The Paradox remains largely as a theoretically-rootless empirical phenomenon. We neither understand the mechanisms and conditions that generate it, nor whether the Paradox stems from choice behavior, choice setting, or both. We (...) present a general search model of consumer choice under incomplete information to examine the theoretical existence and conditions for the Paradox. The model departs from traditional microeconomic choice theory in assuming no “cognitive free lunches.” Search and evaluative efforts require time, focus, and opportunity cost in the model, as in real life. The model shows that conditions for Paradox readily exist, diminishing returns to potential value of the choice in choice set size is a necessary condition for a Paradox outcome, that a Paradox outcome can occur with or without a “choice overload” response by the decisionmaker, and that avoidance of a Paradox outcome is an impossibility in some choice settings (primitive to setting regardless of choice behavior). Lastly, we develop a pareto-improving choice set reduction algorithm that eliminates weakly dominated choice set elements and presents the restricted choice set to the decisionmaker. As such, it is shown that the algorithm acts to treat or mitigate the Paradox of Choice, as well as to pareto-improve choice-supporting evaluation more generally. Like established AI recommender systems, the novel algorithm filters choices. In the present case, the filtering is based upon identification of weakly dominated choice set elements. (shrink)

This commentary tests a methodology proposed by Munk et al. (2022) for using failed predictions in machine learning as a method to identify ambiguous and rich cases for qualitative analysis. Using a dataset describing actions performed by fictional characters interacting with machine vision technologies in 500 artworks, movies, novels and videogames, I trained a simple machine learning algorithm (using the kNN algorithm in R) to predict whether or not an action was active or passive using only information about the (...) fictional characters. Predictable actions were generally unemotional and unambiguous activities where machine vision technologies were treated as simple tools. Unpredictable actions, that is, actions that the algorithm could not correctly predict, were more ambivalent and emotionally loaded, with more complex power relationships between characters and technologies. The results thus support Munk et al.'s theory that failed predictions can be productively used to identify rich cases for qualitative analysis. This test goes beyond simply replicating Munk et al.'s results by demonstrating that the method can be applied to a broader humanities domain, and that it does not require complex neural networks but can also work with a simpler machine learning algorithm. Further research is needed to develop an understanding of what kinds of data the method is useful for and which kinds of machine learning are most generative. To support this, the R code required to produce the results is included so the test can be replicated. The code can also be reused or adapted to test the method on other datasets. (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)

This article is both a comment on Neyland’s ‘On organizing algorithms’ and a supplementary note to our ‘The concept of algorithm as an interpretative key of modern rationality’. In the first part we discuss the concepts of algorithm and recursive function from a different perspective from that of our previous article. Our cultural reference for these concepts is once again computability theory. We give additional arguments in support of the idea that a culture informed by an algorithmic logic (...) has promoted modern rationality both in science and in society. We stress again the importance of distinguishing between algorithms applied to quantifiable entities such as space, time and value and those applied to ontological entities such as human actions. In the second case, the algorithm is applied outside its domain of definition and leads to social disaggregation. (shrink)