The complexity of current social and environmental grand challenges generates many conflicts and tensions at the individual, organization and/or systems levels. Paradox theory has emerged as a promising way to approach such a complexity of corporate sustainability going beyond the instrumental business-case perspective and achieving superior sustainability performance. However, the fuzziness in the empirical use of the concept of “paradox” and the absence of a systems perspective limits its potential. In this paper, we perform a systematic review and content analysis (...) of the empirical literature related to paradox and sustainability, offering a useful guide for researchers who intend to adopt the concept of “paradox” empirically. Our analysis provides a comprehensive account of the uses of the construct - which allows the categorization of the literature into three distinct research streams: 1) paradoxical tensions, 2) paradoxical frame/thinking, and 3) paradoxical actions/strategies - and a comprehensive overview of the findings that emerge in each of the three. Further, by adopting a system perspective, we propose a theoretical framework that considers possible interconnections across the identified paradoxical meanings and different levels of analysis (individual, organizational, systems) and discuss key research gaps emerging. Finally, we reflect on the role a clear notion of paradox can have in supporting business ethics scholars in developing a more “immanent” evaluation of corporate sustainability, overcoming the current instrumental view. (shrink)

For the Critical Theory tradition of the Frankfurt School, rationalisation is a central concept that refers to the socio-cultural closure of capitalist modernity due to the proliferation of technical, ‘instrumental’ rationality at the expense of some form of political reason. This picture of rationalisation, however, hinges on a separation of technology and politics that is both empirically and philosophically problematic. This article aims to re-conceptualise the rationalisation thesis through a survey of research from science and technology studies and the conceptual (...) framework of Niklas Luhmann's systems theory. It argues that rationalisation indeed exhibits a logic of closure, namely the ‘operational closure’ of sociotechnical systems of measurement, but that this closure in fact produces the historical logics of technical reason and, paradoxically, also generates spaces of critical-political openness. This opens up the theoretical and practical opportunity of connecting the politically just to the technically efficient. (shrink)

We explore the developmental paradox of false belief understanding. This paradox follows from the claim that young infants already have an understanding of false belief, despite the fact that they consistently fail the elicited-response false belief task. First, we argue that recent proposals to solve this paradox are unsatisfactory because they (i) try to give a full explanation of false belief understanding in terms of a single system, (ii) fail to provide psychological concepts that are sufficiently fine-grained to capture (...) the cognitive requirements for the various manifestations of false belief understanding, and (iii) ignore questions about system interaction. Second, we present a dual-system solution to the developmental paradox of false belief understanding that combines a layered model of perspective taking with an inhibition-selection-representation mechanism that operates on different levels. We discuss recent experimental findings that shed light on the interaction between these two systems, and suggest a number of directions for future research. (shrink)

Artificial intelligence systems have been widely applied to various contexts, including high-stake decision processes in healthcare, banking, and judicial systems. Some developed AI models fail to offer a fair output for specific minority groups, sparking comprehensive discussions about AI fairness. We argue that the development of AI systems is marked by a central paradox: the less participation one stakeholder has within the AI system’s life cycle, the more influence they have over the way the system will function. This (...) means that the impact on the fairness of the system is in the hands of those who are less impacted by it. However, most of the existing works ignore how different aspects of AI fairness are dynamically and adaptively affected by different stages of AI system development. To this end, we present a use case to discuss fairness in the development of corporate wellness programs using smart wearables and AI algorithms to analyze data. The four key stakeholders throughout this type of AI system development process are presented. These stakeholders are called service designer, algorithm designer, system deployer, and end-user. We identify three core aspects of AI fairness, namely, contextual fairness, model fairness, and device fairness. We propose a relative contribution of the four stakeholders to the three aspects of fairness. Furthermore, we propose the boundaries and interactions between the four roles, from which we make our conclusion about the possible unfairness in such an AI developing process. (shrink)

It is often said that in a purely formal perspective, intuitionistic logic has no obvious advantage to deal with the liar-type paradoxes. In this paper, we will argue that the standard intuitionistic natural deduction systems are vulnerable to the liar-type paradoxes in the sense that the acceptance of the liar-type sentences results in inference to absurdity (⊥). The result shows that the restriction of the Double Negation Elimination (DNE) fails to block the inference to ⊥. It is, however, not the (...) problem of the intuitionistic approaches to the liar-type paradoxes but the lack of expressive power of the standard intuitionistic natural deduction system. We introduce a meta-level negation for a given system and a meta-level absurdity, ⋏, to the intuitionistic system. We shall show that in the system, the inference to ⊥ is not given without the assumption that the system is complete. Moreover, we consider the Double Meta-Level Negation Elimination rules (DMNE) which implicitly assume the completeness of the system. Then, the restriction of DMNE can rule out the inference to ⊥. (shrink)

$${{{\mathcal {F}}}}$$ -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘ $$\ldots $$ affirms the falsity of $$\ldots $$ ’ among them. The possible existence of non-referential sentences was also considered. To model the sets of all the (...) sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of $$\mathcal{F}$$ -systems. We showed the relation between local conglomerates and admissible sets of arguments and argued about the usefulness of the concept for the argumentation theory. (shrink)

In 1953, Jerzy Kalinowski published his paper on the logic of normative sentences. The paper is recognized as one of the first publications on the formal system of deontic logic. The aim of this paper is to present a tableau system for Kalinowski’s deontic logic and to discuss some of the topics related to the paradoxes of deontic logic.

This article aims at introducing the relation between the use of CCTV systems in urban spaces and social control. More specifically, its purpose is to problematize and reaffirm the use of the theoretical background of the panopticon in order to interpret such a relation. In CCTV studies, as a consequence of literal interpretations, as well as the existence of a hegemony in ethnographic studies carried out in control rooms, the theoretical use of the panopticon is then questioned. In this article, (...) based on an ethnographic study conducted in the public spaces surveilled by a CCTV system in a Brazilian city, it can be concluded that the effects of social control through surveillance are paradoxical. The indifferent way in which citizens deal with surveillance, or even the lack of awareness of it, imposes limits to the interpretation of the system as a tool of social control. Thus, the use of the panopticon becomes problematic. However, this research has shown how the presence of cameras in public spaces makes it conducive for a state of control in the form of a network whose project would be a mythical and homogeneous ordering of the spaces. The importance of the interpretation of Jeremy Bentham’s panopticon by Michel Foucault is then reaffirmed, that is, panopticism as a trend of normalization and moralization of the public spaces. (shrink)

Typical approaches to resolving the sorites paradox attempt to show, in one way or another, that the sorites argument is not paradoxical after all. However, if one can show that the sorites is not really paradoxical, the task remains of explaining why it appears to be a paradox. Our approach begins by addressing the appearance of paradox and then explores what this means for the paradox itself. We examine the sorites from the perspective of the various brain systems that are (...) intuitively comfortable with the key features of the premises of the sorites argument. We suggest that the explicit and implicit cognitive systems are separately responsible for the initial plausibility of the categorical and inductive premises. The appearance of paradox is a function of our brain’s architecture and arises from the conflicting interactions of neurologically distinct systems. (shrink)

Provided you start from suitable intuitions, it is easy enough to construct a whole range of arguments any or all of which might be called “the paradox of deontology.” Suppose you think that the role of agency is to bring about goodness, and that it's good to observe deontological constraints. Then it will follow that you should bring about the observing of deontological constraints. And if in some particular context the way to bring about such observings is via a breach (...) of one or more deontological constraints, so be it. Or suppose, more strongly, that you think that the role of agency is to bring about maximal goodness, and that the keeping of the maximum number of deontological constraints is a crucial part of maximal goodness. Then it will follow that you should bring this about. And again, if the route to doing this sometimes runs via the breaching of one or more deontological constraints, so be it. For a non-consequentialist, the way to challenge this supposed paradox is simply to deny that the role of agency is to bring about goodness. This is true because not all reasons are future-directed: some reasons arise from the past or the present, or arise without any time-index. Kant sees this way out of the paradox, and takes it. So far, so good. But Kant goes further, into more complex and strictly Kantian moves against consequentialism; and it is less clear that this further is better. (shrink)

The Gibbs' Paradox is commonly explained by invoking some type of "principle of indistinguishability," which asserts that the interchange of identical particles is not a real physical event, i.e., is operationally meaningless. However, if this principle is to provide a satisfactory resolution of the Paradox, it must be operationally possible to determine whether, in fact, two given systems are identical or not. That is, the assertion that the Gibbs' Paradox is resolvable by an indistinguishability principle actually is an assertion that (...) we can in principle possess a complete set of effective procedures for determining the identity or non-identity of arbitrary physical systems. We show that, in rather general situations, an assertion of this type is not well founded. It is further pointed out that a failure to recognize an incomplete set of "sameness criteria" can lead to serious blunders in physics and in biology. (shrink)

The phenomenon of the paradoxes of the largest remainders methods has been studied by numerous authors. Nevertheless, the examples presented in their studies do not deal with the case where a party’s possible additional votes can directly lead to a loss in the party’s number of representatives. This paradox, which can be called the no-show apportionment paradox, has not previously been mentioned in the literature. It is based on the assumption that a voter’s favourite party may lose a seat if (...) the voter votes honestly but get more seats if he or she abstains. The article gives simple examples illustrating the no-show paradox in a party-list proportional representation electoral system using the quota method of apportionment. In these situations it would be better for the party if some of their voters abstained, otherwise it would lose one or more seats. (shrink)

Identity and democracy and, more particularly, national identity and deliberative democracy account for a controversial relationship. However, from a classical deliberative democratic point of view, the controversy over who is the ‘we’ that needs to stand together in contemporary complex societies settled with the constitution of modern states. In this sense, the main contribution of this paper is twofold. On the one hand, I rebut the analytical appropriateness and conceptual coherence of Habermas’ discursive approach to democracy for the case of (...) plurinational societies in contemporary constitutional democracies. A discussion of a test case – Catalonia – demonstrates that this inadequacy renders incoherent the deliberative model regarding one of its most fundamental premises: the equal weight of the principles of law and the principle of democracy. On the other hand, I sustain that the challenge is not about identity but democracy, and more particularly, about the role deliberative democracy is called to play when controversy challenges whether the people of a state do conform to a single people or not. More concretely, I explore the opportunities offered by the systemic turn to sustain a more realistic approach to deliberative democracy regarding its capacity to steer society towards integration in the context of the system of public deliberation. (shrink)

As computational systems burgeon with advancing artificial intelligence (AI), the deterministic frameworks underlying them face novel challenges, especially when interfacing with self-modifying code. The Executioner Paradox, introduced herein, exemplifies such a challenge where a deterministic Executioner Machine (EM) grapples with self-aware and self-modifying code. This unveils a self-referential dilemma, highlighting a gap in current deterministic computational frameworks when faced with self-evolving code. In this article, the Executioner Paradox is proposed, highlighting the nuanced interactions between deterministic decision-making and self-aware code, and (...) the ensuing challenges. This article advocates for a re-evaluation of existing deterministic frameworks, emphasizing the need for adaptive decision-making mechanisms in computational systems. By dissecting the Executioner Paradox, the aim is to foster a robust discussion on evolving deterministic frameworks to accommodate the dynamic nature of self-modifying code, thereby contributing a forward-looking lens to the discourse on computational systems amidst advancing AI. (shrink)

Professor Kainz offers, in the comparatively brief space of just over 100 pages, a very rich series of observations, analyses, interpretations, and suggestions concerning the nature of paradox in the history of philosophy, dialectic as a form of thought involving paradox, and system in Hegel. The over-all tone of the work is tentative, suggestive, inviting us to travel along some particular paths of speculation as to the nature of paradox and its connection with dialectic, not arguing for a definitive (...) analysis of either. Nevertheless there are also some compact summaries of the structure of the Phenomenology which clearly presupposed much painstaking interpretive labor. (shrink)

The paper presents a paradoxical feature of computational systems that suggests that computationalism cannot explain symbol grounding. If the mind is a digital computer, as computationalism claims, then it can be computing either over meaningful symbols or over meaningless symbols. If it is computing over meaningful symbols its functioning presupposes the existence of meaningful symbols in the system, i.e. it implies semantic nativism. If the mind is computing over meaningless symbols, no intentional cognitive processes are available prior to symbol (...) grounding. In this case, no symbol grounding could take place since any grounding presupposes intentional cognitive processes. So, whether computing in the mind is over meaningless or over meaningful symbols, computationalism implies semantic nativism. (shrink)

The fundamental issue of Kainz’s “contemporary reconstruction of the Hegelian problematic” is the relationship of three factors: paradox, dialectic, and system. More specifically, “might it not be the case that dialectic, paradox, and system are necessarily interrelated, so that, for example, a dialectic without paradox would be suspect, and philosophically significant dialectical paradoxes might be optimally presented in a system”? The issue is complicated by the fact that these three not only have multiple meanings, but are - (...) despite significant interrelationships - separable. From examples of their different combinations in the history of philosophy, “it would seem that almost any combination of the three factors is possible, and/or actually achieved”. This point is illustrated by Nicolas of Cusa, Kant’s “Transcendental Dialectic,” Marx and Engels, Kierkegaard, Nietzsche, Bradley, and Derrida. (shrink)

This book undertakes a critical analysis of some central problems in Hegel scholarship.

Parrondo's paradox, in which losing strategies can be combined to produce winning outcomes, has received much attention in mathematics and the physical sciences; a plethora of exciting applications has also been found in biology at an astounding pace. In this review paper, the authors examine a large range of recent developments of Parrondo's paradox in biology, across ecology and evolution, genetics, social and behavioral systems, cellular processes, and disease. Intriguing connections between numerous works are identified and analyzed, culminating in an (...) emergent pattern of nested recurrent mechanics that appear to span the entire biological gamut, from the smallest of spatial and temporal scales to the largest—from the subcellular to the complete biosphere. In analyzing the macro perspective, the pivotal role that the paradox plays in the shaping of biological life becomes apparent, and its identity as a potential universal principle underlying biological diversity and persistence is uncovered. Directions for future research are also discussed in light of this new perspective. (shrink)

This essay analyses the Historical Evolution of Hong Kong, from the colonial period to the return to China sovereignty in 1997, according to the political philosophy of Socialism with Chinese Characteristics, and the principle “one country, two systems”, which means that Hong Kong is part of China and enjoys a high degree of autonomy, except in foreign and defence policy, as stipulated by the Basic Law of The Hong Kong Administrative Region of the People’s Republic of China. The political (...) class='Hi'>system implemented in HKSAR corresponds to the matrix of the People’s Republic of China, but its economic base and legal system remained untouched in essence; an extreme model of liberal capitalism, deregulated and functioning on the margins of international law, with deep social inequalities, millions of new poor (workers and students in a situation of necessity) and a serious problem of access to housing. This essay analyses the political nature of the conflict around the extraction laws, distinguishing internal causes, and external interferences. At least, this essay analyses the system of political representation of HKSAR, the government program to overcome crisis and the new legislation after crisis. Keywords: history, one country, two systems, paradox, HKSAR, fallacies. (shrink)

The ancient puzzle of the Liar was shown by Tarski to be a genuine paradox or antinomy. I show, analogously, that certain puzzles of contemporary game theory are genuinely paradoxical, i.e., certain very plausible principles of rationality, which are in fact presupposed by game theorists, are inconsistent as naively formulated. ;I use Godel theory to construct three versions of this new paradox, in which the role of 'true' in the Liar paradox is played, respectively, by 'provable', 'self-evident', and 'justifiable'. I (...) also construct in modal operator logic a paradox involving reflexive empirical reasoning. Unlike the paradox of the Liar, the paradox of reflexive reasoning does not depend on self-reference. ;I consider various solutions to the Liar paradox and evaluate how well these solutions cope with the paradox of reflexive reasoning. I then formalize the solution to the paradoxes which I favor: the indexical-hierarchical approach, first sketched out by Charles Parsons and Tyler Burge. In this solution, occurrences of the predicate 'true' in sentence-tokens are contextually relativized to levels of a hierarchy. Drawing also on some brief remarks of Bertrand Russell and Charles Parsons, I develop an account of the kind of schematic generality needed for this theory to be statable. ;Finally, I demonstrate that the principles shown to be paradoxical are in fact presupposed by contemporary game theorists in their reliance on the notion of common knowledge or, more precisely, mutual belief. I create novel analyses of and corresponding solutions to several recalcitrant puzzles within game theory, including the "chain-store paradox". (shrink)

The notion of choice and its individualistic underpinnings is fundamentally inconsistent with the collectivist NHS ethosIn both the policy1 and academic2 literatures, the issue of extending patient choice in the UK National Health Service is currently a much discussed issue. From December 2005—for example, general practitioners will be required to offer patients needing elective surgery the choice of five providers at the point of referral.1 Choice is often thought of as an intrinsically good thing; that is, that people value choice (...) in and of itself.3 A probable underlying reason for this belief is that choice is tied in with the notion of individual autonomy, or freedom, a concept that looms large in ethical theories of the good. Beauchamp and Childress—for example, classified respect for …. (shrink)

Vieles deutet darauf hin, dass das 21. Jahrhundert die Epoche des Gehirns werden könnte - samt einer wissenschaftlichen und kulturellen Revolution. Die anstehenden Veränderungen im Zusammenhang mit Künstlicher Intelligenz und der aufstrebenden Weltanschauung des Transhumanismus werfen die grundsätzliche Frage auf, ob ein System in der Lage ist, sich selbst zu durchschauen. In einer essayistischen Aufschlüsselung dieser Problematik widmet sich Herbert M. Hurka der Selbstthematisierung des Gehirns und zeigt: Mit jeder Äußerung, gleich in welchem Medium, betreibt das Gehirn in einer (...) selbstreferentiellen Schleife immer auch aktiv seine Selbsterforschung - und bleibt dabei als Subjekt der Erkenntnis immer auch ihr Objekt. (shrink)

The fundamental issue of Kainz’s “contemporary reconstruction of the Hegelian problematic” is the relationship of three factors: paradox, dialectic, and system. More specifically, “might it not be the case that dialectic, paradox, and system are necessarily interrelated, so that, for example, a dialectic without paradox would be suspect, and philosophically significant dialectical paradoxes might be optimally presented in a system”? The issue is complicated by the fact that these three not only have multiple meanings, but are - (...) despite significant interrelationships - separable. From examples of their different combinations in the history of philosophy, “it would seem that almost any combination of the three factors is possible, and/or actually achieved”. This point is illustrated by Nicolas of Cusa, Kant’s “Transcendental Dialectic,” Marx and Engels, Kierkegaard, Nietzsche, Bradley, and Derrida. (shrink)

Identity and democracy and, more particularly, national identity and deliberative democracy account for a controversial relationship. However, from a classical deliberative democratic point of view, the controversy over who is the ‘we’ that needs to stand together in contemporary complex societies settled with the constitution of modern states. In this sense, the main contribution of this paper is twofold. On the one hand, I rebut the analytical appropriateness and conceptual coherence of Habermas’ discursive approach to democracy for the case of (...) plurinational societies in contemporary constitutional democracies. A discussion of a test case – Catalonia – demonstrates that this inadequacy renders incoherent the deliberative model regarding one of its most fundamental premises: the equal weight of the principles of law and the principle of democracy. On the other hand, I sustain that the challenge is not about identity but democracy, and more particularly, about the role deliberative democracy is called to play when controversy challenges whether the people of a state do conform to a single people or not. More concretely, I explore the opportunities offered by the systemic turn to sustain a more realistic approach to deliberative democracy regarding its capacity to steer society towards integration in the context of the system of public deliberation. (shrink)

The logic BN4 was defined by R.T. Brady as a four-valued extension of Routley and Meyer’s basic logic B. The system EF4 is defined as a companion to BN4 to represent the four-valued system of implication. The system Ł was defined by J. Łukasiewicz and it is a four-valued modal logic that validates what is known as strong Łukasiewicz-type modal paradoxes. The systems EF4-M and EF4-Ł are defined as alternatives to Ł without modal paradoxes. This paper aims (...) to define a Belnap-Dunn semantics for EF4, EF4-M and EF4-Ł. It is shown that EF4, EF4-M and EF4-Ł are strongly sound and complete w.r.t. their respective semantics and that EF4-M and EF4-Ł are free from strong Łukasiewicz-type modal paradoxes. (shrink)

– The paradoxes of analysis and identity each consist of a pair of statements sharing the same referents, but differing in their informativeness properties. Carnap employs a different solution for each of these paradoxes. Church, Davidson, and others have maintained that the two paradoxes can, and should, be resolved by a single method, viz. one based on the Fregean distinction between sense and reference.The present paper argues that Carnap's solution for the paradox of analysis is unsatisfactory on several counts, but (...) primary among these is that Carnap is driven to hold that no semantic distinction can be drawn between the informativeness properties occurring in this paradox. Nevertheless, the paper shows how the required distinction can be formulated within the general framework of Carnap's extensional‐intensional system of semantics, and that such a distinction provides a single solution for both paradoxes. (shrink)

This paper examines the paradoxical transparency involved in training machine-learning models. Existing literature typically critiques the opacity of machine-learning models such as neural networks or collaborative filtering, a type of critique that parallels the black-box critique in technology studies. Accordingly, people in power may leverage the models’ opacity to justify a biased result without subjecting the technical operations to public scrutiny, in what Dan McQuillan metaphorically depicts as an “algorithmic state of exception”. This paper attempts to differentiate the black-box abstraction (...) that wraps around complex computational systems from the opacity of machine-learning models. It contends that the degree of asymmetry in knowledge is greater in the former than the latter. In the case of software systems, software codes are difficult to understand as only software experts with sufficient domain knowledge are equipped to formulate a sound critique. In contrast, the meanings of trained parameters in a machine-learning model are obscure even to the data scientists who configure and train the model. Hence, the asymmetry of knowledge lies only in how data examples are collected, the choice and configuration of machine-learning models, and the specification of features in model design. Under the trend of algorithmic decision-making proliferating with machine-learning heuristics, the paper contends that the more symmetric distribution of knowledge in machine learning could lead to a more transparent production process if proper policies are in place. (shrink)

There is no shortage of pedagogical theories from the tradition formal methods of instruction to the free-play methods of unschooling. A sharp shift in education and instruction models took place with the introduction of critical pedagogy. The focus was no longer on the authority of the teacher and the submissive, passive approach taken by the learner, but rather on the engagement between the two. Still, even when critical pedagogy is utilized in a formal model of education something is missing from (...) the system—experiential learning. Although the unschooling method has been criticized it does provide the benefit of experiential learning. This paper explores the nature of education and evaluates models and theories of pedagogy with the conclusion that a paradoxical approach in which there is a merger between the formal guidelines set by traditional educational models and the experiential learning methods of unschooling approach best prepares learners for the world and to be engaged citizens. Although what, precisely, this paradoxical system would entail is not discussed in this paper, it opens the door for further discussion on the topic and for consideration of the theories which have attempted to do exactly this and improve upon them going forward. (shrink)

Although the chinampa agriculture in Mexico City is considered an historical sustainable farming system,there have been few studies on its current status. This paper assesses the relationship between agroecological factors and socioeconomic strategies by analyzing urban forces, regional employment, and environmental concerns. Despite ecological deterioration caused by the urban expansion of Mexico City, the economic viability of this agricultural system is still based on the efficient use of farming technologies and resources management strategies that tend to maintain levels (...) of productivity in horticulture and floriculture. The chinampa agriculture generates high income and employment for families and other local residents. This agroecosystem depends on the relationship between the economic priorities and agricultural criteria of farmers. We suggest that urban development, economic growth, and resource management in the chinampa region of Mexico City coincide with ecosystem processes, biological human needs, agronomic productivity, economic viability, and sociocultural values. By evaluating these factors, we provide some useful insights on the importance of this traditional agriculture within a sustainable development context. (shrink)

The paradox of phase transitions raises the problem of how to reconcile the fact that we see phase transitions happen in concrete, finite systems around us, with the fact that our best theories—i.e. statistical-mechanical theories of phase transitions—tell us that phase transitions occur only in infinite systems. In this paper we aim to clarify to which extent this paradox is relative to the mathematical framework which is used in these theories, i.e. classical mathematics. To this aim, we will explore the (...) philosophical consequences of adopting constructive instead of classical mathematics in a statistical-mechanical theory of phase transitions. It will be shown that constructive mathematics forces certain ‘de-idealizations’ of such theories: talk of actually infinite systems is meaningless, there are no discontinuous functions, and—in a sense which will be clarified—constructive real numbers reflect our imperfect methods of determining the values of physical quantities. As such, so it will be argued, constructive mathematics offers a means to gain insight in the idealizations introduced in classical theories and the philosophical issues surrounding them. (shrink)

Classical logic, of first or higher order, is extended with sentential operators and quantifiers, interpreted substitutionally over unrestricted substitution class. Operators mark a single layered, consistent metalanguage. Self-reference, arising from substitutional quantification over sentences, allows to express paradoxes which, unlike contradictions, do not lead to explosion. Semantics of the resulting language, using semi-kernels of digraphs, is non-explosive yet two-valued and has classical semantics as a special case for clasically consistent theories. A complete reasoning is obtained by extending LK with two (...) rules for sentential quantifiers. Adding (cut) yields a complete system for the explosive semantics. (shrink)

We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion operator and give (...) its complete axiomatization. This logic is a sub-logic of statements in which the semantic predicates become internalized (for instance, counterparts of Tarski’s definitions and T-schemata become tautologies). Examples of analysis of self-referential paradoxes are given and the approach is compared to the alternative ones. (shrink)

The purpose of this study is to investigate the relationship between a firm’s strategy and consumers’ decisions in the presence of the paradox of choice and sharing personal information. The paradox of choice implies that having too many choices does not necessarily ensure happiness and sometimes having less is more. A new model is constructed introducing a factor of information sharing into the model of a previous study that embedded the paradox of choice only (Kinjo and Ebina in AI Soc (...) 30(2):291–297, 2015). A key feature of the model is its disutility function. It is demonstrated that if the sign of the cross derivative of the function is positive (negative) at the optimum, there is a positive (negative) correlation between the degree of sharing personal information chosen by the consumers and the number of products offered by the firm in its recommendation systems. It is also numerically indicated that the profit function of the firm becomes convex or concave depending on the shape of the disutility function. These results suggest that firms should carefully investigate the shape of the disutility function, under the paradox of choice and sharing personal information. (shrink)

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends (...) classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)

Scriven’s paradox of predictability arises from the combination of two ideas: first, that everything in a deterministic universe is, in principle, predictable; second, that it is possible to create a system that falsifies any prediction that is made of it. Recently, the paradox has been used by Rummens and Cuypers to argue that there is a fundamental difference between embedded and external predictors; and by Ismael to argue against a governing conception of laws. The present paper defends a new (...) diagnosis of the roots of the paradox. First, it is argued that the unpredictability has to be understood in the light of Turing’s famous results about computability, in particular his proof that there is no solution to the ‘halting problem.’ This allows us to see that previous analyses of the paradox were either mistaken or not fully adequate. Second, the sense of paradox that nevertheless remains is traced to the idea that rational behaviour is not dependent on contingent environmental circumstances: that it is always up to us to engage in activities such as rational prediction or rational belief. The paradox of predictability teaches us that this idea, natural though it may be, is mistaken. (shrink)

Rawls’ theory of justice is paradoxical, for it requires a society to aim directly to maximize the basic goods received by the least advantaged even if directly aiming is self-defeating. Rawls’ reasons for rejecting capitalist systems commit him to holding that a society must not merely maximize the goods received by the least advantaged, but must do so via specific institutions. By Rawls’ own premises, in the long run directly aiming to satisfy the difference principle is contrary to the interests (...) of the poor, though it is meant to aid them. -/- . (shrink)