Let [Formula: see text] be a monster model of an arbitrary theory [Formula: see text], let [Formula: see text] be any tuple of bounded length of elements of [Formula: see text], and let [Formula: see text] be an enumeration of all elements of [Formula: see text]. By [Formula: see text] we denote the compact space of all complete types over [Formula: see text] extending [Formula: see text], and [Formula: see text] is defined analogously. Then [Formula: see text] and [Formula: see (...) text] are naturally [Formula: see text]-flows. We show that the Ellis groups of both these flows are of bounded size, providing an explicit bound on this size. Next, we prove that these Ellis groups do not depend on the choice of the monster model [Formula: see text]; thus, we say that these Ellis groups are absolute. We also study minimal left ideals of the Ellis semigroups of the flows [Formula: see text] and [Formula: see text]. We give an example of a NIP theory in which the minimal left ideals are of unbounded size. Then we show that in each of these two cases, boundedness of a minimal left ideal is an absolute property and that whenever such an ideal is bounded, then in some sense its isomorphism type is also absolute. Under the assumption that [Formula: see text] has NIP, we give characterizations of when a minimal left ideal of the Ellis semigroup of [Formula: see text] is bounded. Then we adapt the proof of Theorem 5.7 in Definably amenable NIP groups, J. Amer. Math. Soc. 31 609–641 to show that whenever such an ideal is bounded, a certain natural epimorphism 863–932]) from the Ellis group of the flow [Formula: see text] to the Kim–Pillay Galois group [Formula: see text] is an isomorphism. We also obtain some variants of these results, formulate some questions, and explain differences which occur when the flow [Formula: see text] is replaced by [Formula: see text]. (shrink)

This book enhances the understanding of the theoretical framework and leading principles of boundedness, aiming to bridge the gap between biology, artificial intelligence, and physics.

Abstract Fodor defines epistemic boundedness as a condition wherein there are epistemi?cally significant constraints on the beliefs that a mind is capable of entertaining. He discusses a type of (epistemic) boundedness wherein a hypothesis cannot be entertained because it is inexpressible in terms of the mind's stock of concepts. In addition to this semantic boundedness, I describe a number of different sources of boundedness having to do with syntactic, abductive, and implementational limitations. I also discuss the (...) similarities and differences between individual and social limitations on our epistemic possibilities. (shrink)

Fodor argues that our minds must have epistemic limitations because there must be endogenous constraints on the class of concepts we can acquire. However, his argument for the existence of these endogenous constraints is falsified by the phenomenon of the deferential acquisition of concepts. If we allow for the acquisition of concepts through deferring to experts and scientific instruments, then our conceptual capacity will be without endogenous constraints, and there will be no reason to think that our minds are epistemically (...) bounded. (shrink)

Hjorth introduced a Scott analysis for general Polish group actions, and asked whether his notion of rank satisfies a boundedness principle similar to the one of Scott rank—namely, if the orbit equivalence relation is Borel, then Hjorth ranks are bounded. We answer Hjorth’s question positively. As a corollary we prove the following conjecture of Hjorth—for every limit ordinal \, the set of elements whose orbit is of complexity less than \ is a Borel set.

In this paper we prove a boundedness theorem in the theory ID1. This answers a question asked by Feferman, for example in [3]. The background is the following.Let A[X, x] be an X-positive formula arithmetic in X. The theory ID1 is an extension of Peano arithmetic PA by the following axioms:for arbitrary formulas F; PA is a constant for the least fixed point of A[X, x]. Set-theoretically, PA can be defined by recursion on the ordinals as follows:where is the (...) first nonrecursive ordinal.Now let a ≺ b be the arithmetic relation which expresses that the recursive tree coded by a is a proper subtree of the tree coded by b, and defineThe least fixed point of Tree[X, x] is the set PTree of all well-founded recursive trees. We write W or Wα for PTree or, respectively. Since W is complete we have for all α <. If we define for each element a ∈ W its inductive norm ∣a∣ by ∣a∣≔ min{ξ: a ∈ Wξ}, then we have = {∣a∣: a ∈ W} and the elements of W can be used as codes for the ordinals less than.Assume that B[X, x] is an X-positive formula arithmetic in X with the only free variables X and x, and assume that QB is a relation that satisfiesIf we definethen we obviously have PB = IB. (shrink)

In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this purpose theorems are considered via their realizers which are operations with certain input and output data. The technical tool to express continuous or computable relations between such operations is Weihrauch reducibility and the partially ordered degree structure induced by it. We have identified certain choice (...) principles such as co-finite choice, discrete choice, interval choice, compact choice and closed choice, which are cornerstones among Weihrauch degrees and it turns out that certain core theorems in analysis can be classified naturally in this structure. In particular, we study theorems such as the Intermediate Value Theorem, the Baire Category Theorem, the Banach Inverse Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Theorem. We also explore how existing classifications of the Hahn—Banach Theorem and Weak Kőnig's Lemma fit into this picture. Well-known omniscience principles from constructive mathematics such as LPO and LLPO can also naturally be considered as Weihrauch degrees and they play an important role in our classification. Based on this we compare the results of our classification with existing classifications in constructive and reverse mathematics and we claim that in a certain sense our classification is finer and sheds some new light on the computational content of the respective theorems. Our classification scheme does not require any particular logical framework or axiomatic setting, but it can be carried out in the framework of classical mathematics using tools of topology, computability theory and computable analysis. We develop a number of separation techniques based on a new parallelization principle, on certain invariance properties of Weihrauch reducibility, on the Low Basis Theorem of Jockusch and Soare and based on the Baire Category Theorem. Finally, we present a number of metatheorems that allow to derive upper bounds for the classification of the Weihrauch degree of many theorems and we discuss the Brouwer Fixed Point Theorem as an example. (shrink)

The main theorem of this paper is: If ƒ is a partial function from ℵ 1 to ℵ 1 which is ∑ 1 1 -bounded, then there is a weakly finite primitive recursive dilator D such that for all infinite αϵdom , ƒ ⩽ D . The proof involves only elementary combinatorial constructions of trees. A generalization to ptykes is also given.

This article has two objectives: (1) to map some of the structural limitations to scientific or rational public planning; and (2) to explore the implications of this for a reconceptualization of the legitimacy of public planning. It is argued that some of the limitations to planning are inherent to the planning process in the sense that they cannot be fully mitigated through the refinement of procedures. They come to represent sources of “basic boundedness” that have to be addressed through (...) a radical reinterpretation of the policy process itself. (shrink)

We consider notions of boundedness of subsets of the natural numbers ℕ that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ℕ to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. (...) Most of the results do not require countable choice. (shrink)

We prove a strong boundedness theorem for dilators: if A ⊆ DIL is Σ 1 1 , then there is a recursive dilator D 0 such that ∀ D ∈ A.

For cardinals we let be the smallest size of a subset B of unbounded in the sense of ; that is, such that there is no function such that has size less than for all . Similarly for , the general dominating number, which is the smallest size of a subset B of such that for every there is an such that the above set has size less than . These cardinals are generalizations of the usual ones for . When (...) all three are the same regular cardinal, the relationships between them have been completely described by Cummings and Shelah. We also consider some variants of the functions, following van Douwen, in particular the version of in which B is required to consist of strictly increasing functions. Some of the main results of this paper are: (1) ; (2) for , always exists; (3) if , then ; (4) . For background see Section 1 of the paper. Several open problems are stated. (shrink)

In this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of countable Heine–Borel compactness in proofs using abstract metric structures must be carefully distinguished from an unrestricted use of countable Heine–Borel compactness.

It is argued that two different types of concept are often intermingled in discussions of Aktionsart. The most common type of classification is one of situation types, relating to the potential actualisation of a situation, although some of the definitions have to do with the actual realization of the situation. This distinction, adequately captured by the notions (a)telicity and (un)boundedness (Declerck 1989), is explored and it is shown how NPs, PPs and tense influence a sentence''s classification as (un)bounded.

Ishiharaʼs boundedness principleBD-N was introduced in Ishihara [5] and has turned out to be most useful for constructive analysis, see e.g. Ishihara [6]. It is equivalent to the statement that every sequentially continuous function from NN to N is continuous w.r.t. the usual metric topology on NN. We construct models for higher order arithmetic and intuitionistic set theory in which both every function from NN to N is sequentially continuous and in which the axiom of choice from NN to (...) N holds. Since the latter is known to be inconsistent with the statement that all functions from NN to N are continuous these models refute BD-N. (shrink)

In this paper the numerical strength of fragments of arithmetical comprehension, choice and general uniform boundedness is studied systematically. These principles are investigated relative to base systems Tnω in all finite types which are suited to formalize substantial parts of analysis but nevertheless have provably recursive functions of low growth. We reduce the use of instances of these principles in Tnω-proofs of a large class of formulas to the use of instances of certain arithmetical principles thereby determining faithfully the (...) arithmetical content of the former. This is achieved using the method of elimination of Skolem functions for monotone formulas which was introduced by the author in a previous paper.As corollaries we obtain new conservation results for fragments of analysis over fragments of arithmetic which strengthen known purely first-order conservation results.We also characterize the provably recursive functions of type 2 of the extensions of Tnω based on these fragments of arithmetical comprehension, choice and uniform boundedness. (shrink)

We deal with a restricted form WC-N' of the weak continuity principle, a version BT' of Baire's theorem, and a boundedness principle BD-N. We show, in the spirit of constructive reverse mathematics, that WC-N'. BT' + ¬LPO and BD-N + ¬LPO are equivalent in a constructive system, where LPO is the limited principle of omniscience.

In this paper we propose an ‘undisciplinary’ meeting between Elinor Ostrom and Judith Butler, with the intent to broaden the theory of the commons by discussing it as a relational politics. We use Butler’s theory of power to problematize existing visions of commons, shifting from Ostrom’s ‘bounded rationality’ to Butler’s concepts of ‘bounded selves’ and mutual vulnerability. To be bounded – as opposed to autonomous being – implies being an effect of socio-power relations and norms that are often beyond control. (...) Thus, to be a collective of bounded selves implies being mutually vulnerable in power relations which are enabling, albeit injurious. A politics of commoning is not a mere technical management of resources but a struggle to perform common livable relations. We argue that the multiple exposures which produce us are also the conditions of possibility for more just and equalitarian ‘re-commoning’ of democracies around the world. (shrink)

Working within Bishop-style constructive mathematics, we examine some of the consequences of the anti-Specker property, known to be equivalent to a version of Brouwer's fan theorem. The work is a contribution to constructive reverse mathematics.

The existing literature provides conflicting evidence of whether a collectivistic value orientation is associated with ethical or unethical behavior. To address this confusion, we integrate collectivism theory and research with prior work on social identity, moral boundedness, group morality, and moral identity to develop a model of the double-edged effects of collectivism on employee conduct. We argue that collectivism is morally bounded depending on who the other is, and thus it inhibits employees’ motivation to engage in unethical pro-self behavior, (...) yet strengthens their motivation to engage in unethical pro-organization behavior. We further predict that these effects are mediated by the psychological mechanism of organizational goal commitment and moderated by a person’s strength of moral identity. Results of three studies conducted in China and the United States and involving both field and experimental data offer strong support for our hypotheses. Theoretical and practical implications of the research are discussed. (shrink)

A fundamental aspect of human cognition is the ability to parse our constantly unfolding experience into meaningful representations of dynamic events and to communicate about these events with others. How do we communicate about events we have experienced? Influential theories of language production assume that the formulation and articulation of a linguistic message is preceded by preverbal apprehension that captures core aspects of the event. Yet the nature of these preverbal event representations and the way they are mapped onto language (...) are currently not well understood. Here, we review recent evidence on the link between event conceptualization and language, focusing on two core aspects of event representation: event roles and event boundaries. Empirical evidence in both domains shows that the cognitive representation of events aligns with the way these aspects of events are encoded in language, providing support for the presence of deep homologies between linguistic and cognitive event structure. (shrink)

Our awareness of the boundedness of the spatial sensory field—a paradigmatic structural feature of visual experience—possesses a distinctive epistemic role. Properly understood, this result undermines a widely assumed picture of how visual experience permits us to learn about the world. This paper defends an alternative picture in which visual experience provides at least two kinds of non-inferential justification for beliefs about the external world. Accommodating this justification in turn requires recognising a new way for visual experience to encode information (...) about the world. Reflection upon the epistemic contribution of sensory experience's structural features thus forces us to revise our understanding of how perception, cognition, and the world fit together. (shrink)

We prove that the boundedness theorem of generalized recursion theory can be derived from the ω-completeness theorem for number theory. This yields a proof of the boundedness theorem which does not refer to the analytical hierarchy theorem.

Cantor argued that absolute infinity is beyond mathematical comprehension. His arguments imply that the domain of mathematics cannot be grasped by mathematical means. We argue that this inability constitutes a foundational problem. For Cantor, however, the domain of mathematics does not belong to mathematics, but to theology. We thus discuss the theological significance of Cantor’s treatment of absolute infinity and show that it can be interpreted in terms of negative theology. Proceeding from this interpretation, we refer to the recent debate (...) on absolute generality and argue that the method of diagonalization constitutes a modern version of the vianegativa. On our reading, negative theology can evoke an attitude of humility with respect to the boundedness of the human condition. Along these lines, we think that the foundational problem of mathematics concerning its domain can be addressed through a methodological attitude of humility. (shrink)

Two different programmes are in the business of explicating accuracy—the truthlikeness programme and the epistemic utility programme. Both assume that truth is the goal of inquiry, and that among inquiries that fall short of realizing the goal some get closer to it than others. Truthlikeness theorists have been searching for an account of the accuracy of propositions. Epistemic utility theorists have been searching for an account of the accuracy of credal states. Both assume we can make cognitive progress in an (...) inquiry even while falling short of the target. I show that the prospects for combining these two programmes are bleak. A core accuracy principle, proximity, that is universally embraced within the truthlikeness programme turns out to be incompatible with a central principle within the epistemic utility programme, namely propriety. 1Truthlikeness and Epistemic Utility 2Inquiries 3Accuracy for Propositions 4Proximity 5Accuracy for Credal States 6Propriety 7Proximity for Credal States 8Extensionality 9Admissible Weightings 10Propriety Violates Proximity 11Possible Responses 11.1Retreat to convexity 11.2Reject boundedness 11.3Reject additivity 12The Upshot. (shrink)

Growing ecological problems have raised the need for conceptual tools dedicated to studying semiotic processes in cultural-ecological systems. Departing from both ecosemiotics and cultural semiotics, the concept of an ecosemiosphere is proposed to denote the entire complex of semiosis in an ecosystem, including the involvement of human cultural semiosis. More specifically, the ecosemiosphere is a semiotic system comprising all species and their umwelts, alongside the diverse semiotic relations (including humans with their culture) that they have in the given ecosystem, and (...) also the material supporting structures that enable the ecosemiosphere to thrive. Drawing parallels with Juri Lotman’s semiosphere concept, the ecosemiosphere is characterized by its heterogeneity, asymmetry, and boundedness. But unlike Lotman’s concept, the ecosemiosphere is not characterized by an overall boundedness, that is, by the presence of external binary boundaries and the shared identity arising from this unity. The involvement of human culture in the ecosemiosphere manifests in interspecies dialogues and semiotic engagements. We need to scrutinize what affordances and semiotic resources culture could offer to nonhuman species and how culture could, by semiotic means, raise the integrity, stability, and resiliency of the ecosystem. The ecosemiosphere is a grounded semiosphere. (shrink)

Bourrat and Griffiths :33, 2018) have recently argued that most of the evidence presented by holobiont defenders to support the thesis that holobionts are evolutionary individuals is not to the point and is not even adequate to discriminate multispecies evolutionary individuals from other multispecies assemblages that would not be considered evolutionary individuals by most holobiont defenders. They further argue that an adequate criterion to distinguish the two categories is fitness alignment, presenting the notion of fitness boundedness as a criterion (...) that allows divorcing true multispecies evolutionary individuals from other multispecies assemblages and provides an adequate criterion to single out genuine evolutionary multispecies assemblages. A consequence of their criterion is that holobionts, as conventionally defined by hologenome defenders, are not evolutionary individuals except in very rare cases, and for very specific host-symbiont associations. This paper is a critical response to Bourrat and Griffiths’ arguments and a defence of the arguments presented by holobiont defenders. Drawing upon the case of the hologenomic basis of the evolution of sanguivory in vampire bats, I argue that Bourrat and Griffiths overlook some aspects of the biological nature of the microbiome that justifies the thesis that holobionts are evolutionarily different to other multispecies assemblages. I argue that the hologenome theory of evolution should not define the hologenome as a collection of genomes, but as the sum of the host genome plus some traits of the microbiome which together constitute an evolutionary individual, a conception I refer to as the stability of traits conception of the hologenome. Based on that conception I argue that the evidence presented by holobiont defenders is to the point, and supports the thesis that holobionts are evolutionary individuals. In this sense, the paper offers an account of the holobiont that aims to foster a dialogue between hologenome advocates and hologenome critics. (shrink)

Narrative analysis is well established as a means of examining the subjective experience of those who suffer chronic illness and cancer. In a study of perceptions of the outcomes of treatment of cancer of the colon, we have been struck by the consistency with which patients record three particular observations of their subjective experience: the immediate impact of the cancer diagnosis and a persisting identification as a cancer patient, regardless of the time since treatment and of the presence or absence (...) of persistent or recurrent disease; a state of variable alienation from social familiars, expressed as an inability to communicate the nature of the experience of the illness, its diagnosis and treatment; and a persistent sense of boundedness, an awareness of limits to space, empowerment and available time. These subjectivities were experienced in varying degree by all patients in our study. Individual responses to these experiences were complex and variable. The experiences are best understood under the rubric of a category we call “liminality”. We believe that all cancer patients enter and experience liminality as a process which begins with the first manifestations of their malignancy. An initial acute phase of liminality is marked by disorientation, a sense of loss and of loss of control, and a sense of uncertainty. An adaptive, enduring phase of suspended liminality supervenes, in which each patient constructs and reconstructs meaning for their experience by means of narrative. This phase persists, probably for the rest of the cancer patient’s life. The experience of liminality is firmly grounded in the changing and experiencing body that houses both the disease and the self. Insights into the nature of the experience can be gained from the Existentialist philosophers and from the history of attitudes to death. Understanding liminality helps us to understand what it is that patients with cancer seek from the system to which they turn for help. Its explication should therefore be important for those who provide health care, those who educate health care workers and those concerned to study and use outcomes as administrative and policy making instruments. (shrink)

Introducing the ontology of theory choice -/- Economists choose theories and they choose ways of pursuing theories, and they leave others unchosen. Why do economists choose the way they do? How should economists choose? What are the objectives and what are the constraints? What should they be? The questions are both descriptive and prescriptive. -/- There are two broad classes of “criteria of choice” that have been somewhat systematically considered in the recent literature on economic methodology: (1) Empirical criteria. There (...) are several possible ways of incorporating empirical criteria in one's theory of science. The respective methodology of theory assessment may be static or dynamic, it may be deductivist or inductivist, it may include various ideas of what constitutes empirical evidence, and so on. What they all share is the general idea that scientific theories are, or are to be, checked against empirical evidence according to some rules, and that this determines the choice of theory. (2) Social criteria. Again, there are several options. The social criteria may be related to the social interests of scientists or larger social collectives, they may be based on the persuasiveness and tradition-boundedness of theories, they may involve social or moral norms, they may be derived from various costs and benefits of holding a theory in a given research community, and so on. If they involve empirical data, it is the social aspects of the data that matter. What all these views share is that scientific theories are taken to have social attributes (functions, consequences) that play or should play a major role in theory choice. (shrink)

We initiate a systematic study of the class of theories without the tree property of the second kind — NTP2. Most importantly, we show: the burden is “sub-multiplicative” in arbitrary theories ; NTP2 is equivalent to the generalized Kimʼs lemma and to the boundedness of ist-weight; the dp-rank of a type in an arbitrary theory is witnessed by mutually indiscernible sequences of realizations of the type, after adding some parameters — so the dp-rank of a 1-type in any theory (...) is always witnessed by sequences of singletons; in NTP2 theories, simple types are co-simple, characterized by the co-independence theorem, and forking between the realizations of a simple type and arbitrary elements satisfies full symmetry; a Henselian valued field of characteristic is NTP2 if and only if the residue field is NTP2 , so in particular any ultraproduct of p-adics is NTP2; adding a generic predicate to a geometric NTP2 theory preserves NTP2. (shrink)

This paper argues in favor of two claims: (a) that Scope Shifting Operations (Quantifier Raising and Quantifier Lowering) are restricted by economy considerations, and (b) that the relevant economy considerations compare syntactic derivations that end up interpretively identical. These ideas are shown to solve several puzzles having to do with the interaction of scope with VP ellipsis, coordination, and the interpretation of bare plurals. Further, the paper suggests a way of dealing with the otherwise puzzling clause-boundedness of Quantifier Raising.

Standard adaptive control is the preferred approach for stabilization and synchronization of chaotic systems when the structure of such systems is a priori known but the parameters are unknown. However, in the presence of unmodeled dynamics and/or disturbance, this approach is not effective anymore due to the drift of the parameter estimations, which eventually causes the instability of the closed-loop system. In this paper, a robustifying term, which consists of a saturation function, is used to avoid this problem. The robustifying (...) term is added to the adaptive control law. Consequently, the learning law is also modified. The boundedness of the states and the parameter estimations is rigorously and thoroughly proven by means of Lyapunov like analysis based on Barbalat’s lemma. On these new conditions, the convergence to zero cannot be achieved due to the presence of unmodeled dynamics and/or disturbance. However, it is still possible to guarantee the asymptotic convergence to a bounded zone around zero. The width of this zone can be adjusted by the designer. The performance of this robust approach is verified by numerical simulations. Although, for simplicity, this strategy is only applied to the stabilization and synchronization of Zhang system, the procedure can easily be generalized to a broad class of chaotic systems. (shrink)

The “species-as-individuals” thesis takes species, or taxa, to be individuals. On grounds of spatiotemporal boundedness, any biological entity at any level of complexity subject to evolutionary processes is an individual. From evolutionary theory flows an ontology that does not countenance universal properties shared by evolving entities. If austere nominalism were applied to evolving entities, however, nature would be reduced to a mere flow of passing events, each one a blob in space–time and hence of passing interest only. Yet if (...) there is genuine biodiversity in nature, if nature is genuinely carved into species, and taxa, then these evolutionary entities will be genuinely differentiated into specific kinds, each species being one of its kind. Given the fact that evolving entities have un-sharp boundaries, an appropriately weak, “non-essentialist” concept of natural kind has to be invoked that does not allow for strong identity conditions. The thesis of this paper is that species are not either individuals, or natural kinds. Instead, species are complex wholes (particulars, individuals) that instantiate a specific natural kind. (shrink)

Many authors have posited an “object file” system, which underlies perceptual selection and tracking of objects. Several have proposed that this system internalizes principles specifying what counts as an object and relies on them during tracking. Here I consider a popular view on which the object file system is tuned to entities that satisfy principles of three-dimensionality, cohesion, and boundedness. I argue that the evidence gathered in support of this view is consistent with a more permissive view on which (...) object files select and track according to well-known perceptual organization criteria. Further evidence supplies positive support for the permissive view. (shrink)