The paper argues that the phenomenon of first-order phase transitions (e.g., freezing) has features that make it a candidate to be classified as 'emergent'. However, it cannot be described either as 'weakly emergent' or 'strongly emergent'; hence it escapes categorization in terms employed in the current literature on the metaphysics of science.

This book engages with the writings of W.G. Sebald, mediated by perspectives drawn from curriculum and architecture, to explore the theme of unsettling complacency and confront difficult knowledge around trauma, discrimination and destruction. Moving beyond overly instrumentalist and reductive approaches, the authors combine disciplines in a scholarly fashion to encourage readers to stretch their understandings of currere. The chapters exemplify important, timely and complicated conversations centred on ethical response and responsibility, in order to imagine a more just and aesthetically experienced (...) world. In the analysis of bildung as human formation, the book illuminates the pertinent lessons to be learned from the works of Sebald and provokes further investigations into the questions of memory, grief, and limits of language. Through its juxtaposition of curriculum and architecture, and using the prose of Sebald as a prism, the book revitalizes questions about education and ethics, probes the unsettling of complacency, and enables conversation around difficult knowledge and ethical responsibility, as well as offering hope and resolve. An important intervention in standard approaches to understanding currere, this book provides essential context for scholars and educators with interests in the history of education, curriculum studies, cultural studies, memory studies, narrative research, Sebaldian studies, and educational philosophy. (shrink)

The Uniformly Reflexive Structure was introduced by E. G. Wagner who showed that the theory of such structures generalized much of recursive function theory. In this paper Uniformly Reflexive Structures are constructed as factor algebras of Free nonassociative algebras. Wagner's question about the existence of a model with no computable splinter ("successor set") is answered in the affirmative by the construction of a model whose only computable sets are the finite sets and their complements. Finally, for each countable Boolean (...) algebra R of subsets of a countable set which contains the finite subsets, a model is constructed with R as its family of computable sets. (shrink)

Nations with legal environments that allow indigenous entrepreneurs to create legal businesses are more likely to be peaceful and prosperous nations. In addition to focusing on the role of multinational corporations, those interested in creating peace through commerce should focus on promoting legal environments that allow indigenous entrepreneurs to create peace and prosperity. In order to illustrate the relationship between improved legal environments and conflict reduction, this article describes a case study in which increased economic freedom led to reduced (...) violence in Northern Ireland between 1975 and 2000. (shrink)

Knee proprioception deficits and neuroplasticity have been indicated following injury to the anterior cruciate ligament. Evidence is, however, scarce regarding brain response to knee proprioception tasks and the impact of ACL injury. This study aimed to identify brain regions associated with the proprioceptive sense of joint position at the knee and whether the related brain response of individuals with ACL reconstruction differed from that of asymptomatic controls. Twenty-one persons with unilateral ACL reconstruction of either the right or left knee, as (...) well as 19 controls matched for sex, age, height, weight and current activity level, performed a knee joint position sense test during simultaneous functional magnetic resonance imaging. Integrated motion capture provided real-time knee kinematics to activate test instructions, as well as accurate knee angles for JPS outcomes. Recruited brain regions during knee angle reproduction included somatosensory cortices, prefrontal cortex and insula. Neither brain response nor JPS errors differed between groups, but across groups significant correlations revealed that greater errors were associated with greater ipsilateral response in the anterior cingulate, supramarginal gyrus and insula. This is the first study to capture brain response using fMRI in relation to quantifiable knee JPS. Activated brain regions have previously been associated with sensorimotor processes, body schema and interoception. Our innovative paradigm can help to guide future research investigating brain response to lower limb proprioception. (shrink)

Much has been written recently about both the urgency and efficacy of teaching business ethics. The results of our survey of AACSB member schools confirm prior reports of similar surveys: The teaching of business ethics is indiscriminate, unorganized, and undisciplined in most North American schools of business. If universities are to be taken seriously in their efforts to create more ethical awareness and better moral decision-making skills among their graduates, they must provide a rigorous and well-developed system in which students (...) can "live ethics" instead of merely learn ethics. A system must be devised to allow students to discover and refine their own values rather than simply learning ethical theories from an intellectual point of view. After reviewing the literature on business ethics in undergraduate curricula, we make a series of recommendations to deliver experiential ethical education for business students. The recommendations include student and faculty written codes of ethics, emphasis on ethical theory within the existing required legal environment course, applied ethics in the functional area capstones using alternative learning, a discussion of employee rights and responsibilities during the curriculum capstone course, and a public service requirement for graduation. These recommendations may be implemented without substantive additional cost or programming requirements. (shrink)

In 1988 the Journal of Business Ethics published a paper by David Mathison entitled Business Ethics Cases and Decision Models: A Call for Relevancy in the Classroom. Mathison argued that the present methods of teaching business ethics may be inappropriate for MBA students. He believes that faculty are teaching at one decision-making level and that students are and will be functioning on another (lower) level. The purpose of this paper is to respond to Mathison's arguments and offer support for the (...) present methods and materials used to teach Master level ethics classes. The support includes suggested class discussion ideas and assignments. (shrink)

The situated potentials for action between material things in the world and the interactional processes thereby afforded need to be seen as not only constituting the possibility of agency, but thereby also comprising it. Eo ipso, agency must be de-fused from any local, "contained" subject and be understood as a situational property in which subjects and objects can both participate. Any technological artifact should thus be understood as a complex of agential capacities that function relative to any number of (...) social and material factors. Keeping in mind that we are co-constituted by webs of relations involving increasingly complex collections of artefacts, networks, niches, and communities of practice, our investigation will be guided by interrogating the functional potential of a thing that in the last fifteen years has seamlessly worked its way into the everyday life of millions of human agents. This "thing," the smartphone, is merely a nodal point in a highly complex network. Recognizing this massive "collective," we nevertheless want to show some of the ways in which something as seemingly mundane as a smartphone can reflexively alter the range of actions available to a cognitive agent (Latour 1994). Specifically, we hope to shed light on some of the social-cognitive consequences of technological mediation by looking at the complementary, if not mutually implied, domains of memory and knowledge. (shrink)

I argue that an adequate account of non-reductive realization must guarantee satisfaction of a certain condition on the token causal powers associated with (instances of) realized and realizing entities---namely, what I call the 'Subset Condition on Causal Powers' (first introduced in Wilson 1999). In terms of states, the condition requires that the token powers had by a realized state on a given occasion be a proper subset of the token powers had by the state that realizes it on that occasion. (...) Accounts of non-reductive realization conforming to this condition are implementing what I call 'the powers-based subset strategy'. I focus on the crucial case involving mental and brain states; the results may be generalized, as appropriate. I first situate and motivate the strategy by attention to the problem of mental causation; I make the case, in schematic terms, that implementation of the strategy makes room (contra Kim 1989, 1993, 1998, and elsewhere) for mental states to be ontologically and causally autonomous from their realizing physical states, without inducing problematic causal overdetermination, and compatible with both Physicalism and Non-reduction; and I show that several contemporary accounts of non-reductive realization (in terms of functional realization, parthood, and the determinable/determinate relation) are plausibly seen as implementing the strategy. As I also show, implementation of the powers-based strategy does not require endorsement of any particular accounts of either properties or causation---indeed, a categoricalist contingentist Humean can implement the strategy. The schematic location of the strategy in the space of available responses to the problem of mental (more generally, higher-level) causation, as well as the fact that the schema may be metaphysically instantiated, strongly suggests that the strategy is, appropriately generalized and instantiated, sufficient and moreover necessary for non-reductive realization. I go on to defend the sufficiency and necessity claims against a variety of objections, considering, along the way, how the powers-based subset strategy fares against competing accounts of purportedly non-reductive realization in terms of supervenience, token identity, and constitution. (shrink)

Some claim that Non- reductive Physicalism is an unstable position, on grounds that NRP either collapses into reductive physicalism, or expands into emergentism of a robust or ‘strong’ variety. I argue that this claim is unfounded, by attention to the notion of a degree of freedom—roughly, an independent parameter needed to characterize an entity as being in a state functionally relevant to its law-governed properties and behavior. I start by distinguishing three relations that may hold between the degrees of (...) freedom needed to characterize certain special science entities, and those needed to characterize their composing physical entities; these correspond to what I call ‘reductions’, ‘restrictions’, and ‘eliminations’ in degrees of freedom. I then argue that eliminations in degrees of freedom, in particular—when strictly fewer degrees of freedom are required to characterize certain special science entities than are required to characterize their composing physical entities—provide a basis for making sense of how certain special science entities can be both physically acceptable and ontologically irreducible to physical entities. (shrink)

Some claim that Non-reductive Physicalism is an unstable position, on grounds that NRP either collapses into reductive physicalism, or expands into emergentism of a robust or ‘strong’ variety. I argue that this claim is unfounded, by attention to the notion of a degree of freedom—roughly, an independent parameter needed to characterize an entity as being in a state functionally relevant to its law-governed properties and behavior. I start by distinguishing three relations that may hold between the degrees of freedom (...) needed to characterize certain special science entities, and those needed to characterize their composing physical entities; these correspond to what I call ‘reductions’, ‘restrictions’, and ‘eliminations’ in degrees of freedom. I then argue that eliminations in degrees of freedom, in particular—when strictly fewer degrees of freedom are required to characterize certain special science entities than are required to characterize their composing physical entities—provide a basis for making sense of how certain special science entities can be both physically acceptable and ontologically irreducible to physical entities. (shrink)

A strong reducibility relation between partial numberings is introduced which is such that the reduction function transfers exactly the numbers which are indices under the numbering to be reduced into corresponding indices of the other numbering. The degrees of partial numberings of a given set with respect to this relation form an upper semilattice.In addition, Ershov’s completion construction for total numberings is extended to the partial case: every partially numbered set can be embedded in a set which (...) results from the given set by adding one point and which is enumerated by a total and complete numbering. As is shown, the degrees of complete numberings of the extended set also form an upper semilattice. Moreover, both semilattices are isomorphic.This is not so in the case of the usual, weaker reducibility relation for partial numberings which allows the reduction function to transfer arbitrary numbers into indices. (shrink)

In the light of what appear to be clear counterexamples, I argue that Jaegwon Kim’s comparative evaluation of functional reduction and reduction via necessary identities is problematic. I trace the problem to two sources: a misplaced metaphysical assumption about the explanatory role of identities and an excessively strong and narrow criterion for successful reductive explanation. Appreciating where Kim’s critique runs astray enhances our understanding of the role of necessary identities in reductive explanation.

In 1973, Nickles identified two senses in which the term `reduction' is used to describe the relationship between physical theories: namely, the sense based on Nagel's seminal account of reduction in the sciences, and the sense that seeks to extract one physical theory as a mathematical limit of another. These two approaches have since been the focus of most literature on the subject, as evidenced by recent work of Batterman and Butterfield, among others. In this paper, I discuss (...) a third sense in which one physical theory may be said to reduce to another. This approach, which I call `dynamical systems reduction,' concerns the reduction of individual models of physical theories rather than the wholesale reduction of entire theories, and specifically reduction between models that can be formulated as dynamical systems. DS reduction is based on the requirement that there exist a function from the state space of the low-level model to that of the high-level model that satisfies certain general constraints and thereby serves to identify quantities in the low-level model that mimic the behavior of those in the high-level model - but typically only when restricted to a certain domain of parameters and states within the low-level model. I discuss the relationship of this account of reduction to the Nagelian and limit-based accounts, arguing that it is distinct from both but exhibits strong parallels with a particular version of Nagelian reduction, and that the domain restrictions employed by the DS approach may, but need not, be specified in a manner characteristic of the limit-based approach. Finally, I consider some limitations of the account of reduction that I propose and suggest ways in which it might be generalised. I offer a simple, idealised example to illustrate application of this approach; a series of more realistic case studies of DS reduction is presented in another paper. (shrink)

This paper discusses refinements of the natural ordering of them-degrees (1-degrees) of strong recursive reducibility classes. Such refinements are obtained by posing complexity conditions on the reduction function. The discussion uses the axiomatic complexity theory and is hence very general. As the main result it is proved that if the complexity measure is required to be linearly bounded (and space-like), then a natural class of refinements forms a lattice with respect to a natural ordering upon them.

Let A and B be subsets of the set of natural numbers. The well-known strong reducibilities are dened as follows: A m B i 2 B)) A 1 B i A m B and the reduction function f is one-one. where T ot denotes the set of total recursive functions. These reducibilities induce an equivalence relation of interreducibility, the equivalence classes of which are commonly called the m-degrees and the 1-degrees, respectively. The ordering of these degrees has (...) been extensively studied. In this paper the renements of the ordering of the m-degrees are studied by posing complexity conditions on the reduction func- tion. The discussion uses the axiomatic complexity theory and is hence very general. The paper is self-contained in the sense that the basic framework of the axiomatic complexity theory is brie y presented. (shrink)

Any theory of reduction that goes only so far as carried in Parts I and II does only half the job. Prima facie at least, there are cases of would-be reduction which seem torn between two conflicting intuitions. On the one side there is a strong intuition that reduction is involved, and a strongly retentive reduction at that. On the other side it seems that the concepts at one level cross-classify those at the other level, (...) so that there is no way to identify properties at one level with those at the other. There is evidence to suggest that there will be no unique mental state/neural state association that can be set up, because, e.g., many different parts of the nervous system are all capable of taking over ‘control’ of the one mental function. And it is alleged that infinitely many, worse: indefinitely many, different bio-chemo-physical states could correspond to the economic property ‘has a monetary system of economic exchange’; and similarly for the property ‘has just won a game of tennis’. Yet one doesn't want an economic system or a game of tennis to be some ghostly addition to the actual bio-chemo-physical processes and events involved. Similarly one hopes that neurophysiology allied with the rest of natural science will render human experience and behaviour explicable. (shrink)

In this article I evaluate recent attempts to illuminate the human infant cry from an evolutionary perspective. Infants are born into an uncertain parenting environment, which can range from indulgent care of offspring to infanticide. Infant cries are in large part adaptations that maintain proximity to and elicit care from caregivers. Although there is not strong evidence for acoustically distinct cry types, infant cries may function as a graded signal. During pain-induced autonomic nervous system arousal, for example, neural (...) input to the vocal cords increases cry pitch. Caregivers may use this acoustic information, together with other cues, to guide caregiving behavior. Serious pathology, on the other hand, results in chronically and severely abnormal cry acoustics. Such abnormal crying may be a proximate cause of adaptive infant maltreatment, in circumstances in which parents cut their losses and reduce or withdraw investment from infants with low survival chances. An increase in the amount of crying during the first few months of life is a human universal, and excessive crying, or colic, represents the upper end of this normal increase. Potential signal functions of excessive crying include manipulation of parents to acquire additional resources, honest signaling of need, and honest signaling of vigor. Current evidence does not strongly support any one of these hypotheses, but the evidence is most consistent with the hypothesis that excessive early infant crying is a signal of vigor that evolved to reduce the risk of a reduction or withdrawal of parental care. Key Words: colic; crying; early infant crying; honest signaling; infanticide; parental care; parent-offspring conflict; separation call; vocalization. (shrink)

La conversion de la France à une politique de « réduction des risques » , est généralement interprétée comme l’indice d’un changement de paradigme en matière de toxicomanie. Il est néanmoins possible de la voir comme une forme de réagencement politique du monde des consommations de drogues, visant à définir de nouveaux seuils, les plus bas possibles, pour l’entrée dans des dispositifs de soin et de service. L’examen des visions du monde sur lesquelles reposent ces équipements politiques, en France comme (...) dans le reste de l’Union européenne, montre d’ailleurs que la vision du monde autonomiste y compose avec d’autres, compensatoires et additives, plus anciennement implantées. C’est sans doute pourquoi on retrouve, à divers niveaux, un véritable décalage entre les mesures volontaristes liées à ces politiques publiques et les contextes dans lesquels elles sont mises en œuvre : qu’il s’agisse des promoteurs, professionnels ou amateurs, ou qu’il s’agisse des destinataires, tout le monde semble s’accommoder d’un fonctionnement minimal de ces dispositifs, vérifiant ainsi une fois de plus la force des liens faibles.The French turn to the so-called « risk reduction policy » , is generally interpreted as a shift of the paradigm of drug addiction policies. One can, nevertheless, see it as a kind of new political layout of the drug addiction field, intended to define new thresholds for one’s entering in the treatment and care devices. When we examine the worldviews which sustain these political equipments , we can see that the autonomist worldview has to come to terms with others, namely : the compensatory and additive ones. That is probably why we can see, at various levels, a real discrepancy between the strong willings supporting the actions promoted by the risk reduction policies, and the contexts in which they take place : would it be the main actors , or the beneficiaries, everyone seems to be satisfied with a minimal functioning of these devices, verifying once again the strength of the weak ties. (shrink)

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov (...) class='Hi'>function, which assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)

This paper gives the strong reduction of the combinatory calculus SCL, which was introduced as a combinatory calculus corresponding to the untyped Lambda-mu calculus. It proves the confluence of the strong reduction. By the confluence, it also proves the conservativity of the extensional equality of SCL over the combinatory calculus CL, and the consistency of SCL.

In this paper a model for barrecursion is presented. It has as a novelty that it contains discontinuous functionals. The model is based on a concept called strong majorizability. This concept is a modification of Howard's majorizability notion; see [T, p. 456].

TThis paper aims to evidence the inherently metonymic nature of co-speech gestures. Arguing that motivation in gesture involves iconicity (similarity), indexicality (contiguity), and habit (conventionality) to varying degrees, it demonstrates how a set of metonymic principles may lend a certain systematicity to experientially grounded processes of gestural abstraction and enaction. Introducing visuo-kinetic signs as an umbrella term for co-speech gestures and signed languages, the paper shows how a frame-based approach to gesture may integrate different cognitive/functional linguistic and semiotic accounts of (...) metonymy (e.g., experiential domains, frame metonymy, contiguity, and pragmatic inferencing). The guiding assumption is that gestures metonymically profile deeply embodied, routinized aspects of familiar scenes, that is, the motivating context of frames. The discussion shows how gestures may evoke frame structures exhibiting varying degrees of groundedness, complexity, and schematicity: basic physical action and object frames; more complex frames; and highly abstract, complex frame structures. It thereby provides gestural evidence for the idea that metonymy is more basic and more directly experientially grounded than metaphor and thus often feeds into correlated metaphoric processes. Furthermore, the paper offers some initial insights into how metonymy also seems to induce the emergence of schematic patterns in gesture which may result from action-based and discourse-driven processes of habituation and conventionalization. It exemplifies how these forces may engender grammaticalization of a basic physical action into a gestural marker that shows strong metonymic form reduction, decreased transitivity, and interacting pragmatic functions. Finally, addressing basic metonymic operations in signed lexemes elucidates certain similarities regarding sign constitution in gesture and sign. English and German multimodal discourse data as well as German Sign Language (DGS) are drawn upon to illustrate the theoretical points of the paper. Overall, this paper presents a unified account of metonymy’s role in underpinning forms, functions, and patterns in visuo-kinetic signs. (shrink)

Light Linear Logic (LLL) and Intuitionistic Light Affine Logic (ILAL) are logics that capture polynomial time computation. It is known that every polynomial time function can be represented by a proof of these logics via the proofs-as-programs correspondence. Furthermore, there is a reduction strategy which normalizes a given proof in polynomial time. Given the latter polynomial time “weak” normalization theorem, it is natural to ask whether a “strong” form of polynomial time normalization theorem holds or not. In (...) this paper, we introduce an untyped term calculus, called Light Affine Lambda Calculus (λLA), which corresponds to ILAL. λLA is a bi-modal λ-calculus with certain constraints, endowed with very simple reduction rules. The main property of LALC is the polynomial time strong normalization: any reduction strategy normalizes a given λLA term in a polynomial number of reduction steps, and indeed in polynomial time. Since proofs of ILAL are structurally representable by terms of λLA, we conclude that the same holds for ILAL. (shrink)

Impairments in emotional face processing are demonstrated by individuals with neurodevelopmental disorders, including autism spectrum disorder and attention-deficit/hyperactivity disorder, which is associated with altered emotion processing networks. Despite accumulating evidence of high rates of diagnostic overlap and shared symptoms between ASD and ADHD, functional connectivity underpinning emotion processing across these two neurodevelopmental disorders, compared to typical developing peers, has rarely been examined. The current study used magnetoencephalography to investigate whole-brain functional connectivity during the presentation of happy and angry faces in (...) 258 children, including ASD, ADHD and typically developing groups to determine possible differences in emotion processing. Data-driven clustering was also applied to determine whether the patterns of connectivity differed among diagnostic groups. We found reduced functional connectivity in the beta band in ASD compared to TD, and a further reduction in the ADHD group compared to the ASD and the TD groups, across emotions. A group-by-emotion interaction in the gamma frequency band was also observed. Greater connectivity to happy compared to angry faces was found in the ADHD and TD groups, while the opposite pattern was seen in ASD. Data-driven subgrouping identified two distinct subgroups: NDD-dominant and TD-dominant; these subgroups demonstrated emotion- and frequency-specific differences in connectivity. Atypicalities in specific brain networks were strongly correlated with the severity of diagnosis-specific symptoms. Functional connectivity strength in the beta network was negatively correlated with difficulties in attention; in the gamma network, functional connectivity strength to happy faces was positively correlated with adaptive behavioural functioning, but in contrast, negatively correlated to angry faces. Our findings establish atypical frequency- and emotion-specific patterns of functional connectivity between NDD and TD children. Data-driven clustering further highlights a high degree of comorbidity and symptom overlap between the ASD and ADHD children. (shrink)

A natural extension theorem for strongly continuous mappings, the morphisms in the category of apartness spaces, is proved constructively.

It has often been remarked that the metatheory of strong reduction $\succ$ , the combinatory analogue of βη-reduction ${\twoheadrightarrow_{\beta\eta}}$ in λ-calculus, is rather complicated. In particular, although the confluence of $\succ$ is an easy consequence of ${\twoheadrightarrow_{\beta\eta}}$ being confluent, no direct proof of this fact is known. Curry and Hindley’s problem, dating back to 1958, asks for a self-contained proof of the confluence of $\succ$ , one which makes no detour through λ-calculus. We answer positively to this (...) question, by extending and exploiting the technique of transitivity elimination for ‘analytic’ combinatory proof systems, which has been introduced in previous papers of ours. Indeed, a very short proof of the confluence of $\succ$ immediately follows from the main result of the present paper, namely that a certain analytic proof system G e [ $\mathbb {C}$ ] , which is equivalent to the standard proof system CL ext of Combinatory Logic with extensionality, admits effective transitivity elimination. In turn, the proof of transitivity elimination—which, by the way, we are able to provide not only for G e [ $\mathbb {C}$ ] but also, in full generality, for arbitrary analytic combinatory systems with extensionality—employs purely proof-theoretical techniques, and is entirely contained within the theory of combinators. (shrink)

Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ++ + ≤ λ, κ<κ = κ and 2κ = κ+, and η is an ordinal with κ+ ≤ η < κ++ and cf = κ+. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra equation image such that equation image, equation image for every α < η and equation image. Especially, equation image and equation image can (...) be cardinal sequences of superatomic Boolean algebras. (shrink)

We consider the logics determined by the set of all natural implicative expansions of Kleene’s strong 3-valued matrix and select the class of all logics functionally equivalent to Łukasiewicz’s 3-valued logic Ł3. The concept of a “natural implicative matrix” is based upon the notion of a “natural conditional” defined in Tomova.

We study the notion of polynomial-time relation reducibility among computable equivalence relations. We identify some benchmark equivalence relations and show that the reducibility hierarchy has a rich structure. Specifically, we embed the partial order of all polynomial-time computable sets into the polynomial-time relation reducibility hierarchy between two benchmark equivalence relations Eλ and id. In addition, we consider equivalence relations with finitely many nontrivial equivalence classes and those whose equivalence classes are all finite.

We relate two sequential models of PCF: the sequential algorithm model due to Berry and Curien and the strongly stable model due to Bucciarelli and the author. More precisely, we show that all the morphisms araising in the strongly stable model of PCF are sequential in the sense that they are the “extensional projections” of some sequential algorithms. We define a model of PCF where morphisms are “extensional” sequential algorithms and prove that any equation between PCF terms which holds in (...) this model also holds in the strongly stable model. (shrink)

Kim’s model of ‘functional reduction’ of properties is shown to fail in a class of cases from physics involving properties at different spatial levels. The diagnosis of this failure leads to a non-reductive account of the relation of micro and macro properties.

In his recent article ‘Consciousness and Reduction’, Ausonio Marras argues that functional reduction must appeal to bridge laws and thus does not represent a genuine alternative to Nagelian reduction. In response, I first argue that even if functional reduction must use bridge laws, it still represents a genuine alternative to Nagelian reduction. Further, I argue that Marras does not succeed in showing that functional reduction must use bridge laws. Introduction Nagelian Reduction, Functional (...) class='Hi'>Reduction, and Bridge Laws Marras on Functional Reduction The Logical Space of ‘Bridge Law’ Views of Reduction [RP] as an Account of Realization Conclusion CiteULike Connotea Del.icio.us What's this? (shrink)

Jaegwon Kim, and others, have recently posed a powerful challenge to both emergentism and nom-reductive physicalism by providing arguments that these positions are committed to an untenable combination of both ‘upward’ and ‘dounward’ determination. In section 1, I illuminate how the nature of the realization relation underlies such skeptical arguments However, in section 2, I suggest that such conclusions involve a confusion between the implications of physicalism and those of a related thesis the ‘Completeness of Physics' (Co?) I show that (...) the truth of CoP poses a very serious obstacle to realized properties being efficacious in a physicalist universe and suggest that abandoning CoP offers hope for defending non-reductive physicalism. I then formulate a schema for a physicalist metaphysics, in section 3, which rejects CoP. This scenario is one where microphysical properties have a few conditional powers that they contribute to individuals when they realize certain properties In such a situation, I argue, though physicalism holds true there is still plausibly both ‘upward’ and ‘downward’ determination, where the latter is crucially an underappreciated form of determination I temn 'non- causal'. Ultimately, I conclude that this metaphysical schema offers a coherent account of Strongly emergent properties that preserves the truth of NRP albeit, in a form that is purged of any commitment to CoP. Finally, in section: 4, I carefully explore which of Kim's assumptions and arguments this metaphysics undermines. (shrink)

Bodily sensations, such as pain, hunger, itches, or sexual feelings, are commonly characterized in terms of their phenomenal character. In order to account for this phenomenal character, many philosophers adopt strong representationalism. According to this view, bodily sensations are essentially and entirely determined by an intentional content related to particular conditions of the body. For example, pain would be nothing more than the representation of actual or potential tissue damage. In order to motivate and justify their view, strong (...) representationalists often appeal to the reliable causal covariance between bodily sensations and certain kinds of bodily conditions or to the corresponding biological function that these bodily sensations are supposed to fulfill. In this paper, I argue on the basis of recent empirical research that arguments from reliable causal covariance and biological function cannot motivate the introduction of corresponding intentional content. In particular, I argue that bodily sensations are caused by a heterogeneous class of physiological and psychological factors and their biological functions are too diverse to be reduced to the representation of a particular bodily condition. Responses are available to strong representationalists, but they either require substantial alterations to their core assumptions or incur a significant empirical burden. (shrink)

Functional reduction follows two familiar steps: a definition of a higher-level or special science property in terms of a functional role, then a statement describing a physical property that plays or occupies that role. But Kim (2005) adds a third step, namely, an explanation regarding how the physical property occupies the functional role. I think Kim is correct. But how is the third step satisfied? An examination of the pertinent scientific explanations reveals that the third step is best satisfied (...) by a multiple-subject, part-whole explanation, which is to say, a decomposition of the occupier’s causal capacities or relations. This is true even in cases wherein role and occupant properties are identical, for an occupier’s causal capacities are always underwritten by a part-whole explanation. As a consequence, functional reduction is transformed into a larger picture that at bottom always contains multiple layers of distinct, nonidentical properties that divide between parts and their whole systems. I call it “Part-Based Functional Reduction.” My aim is to develop this larger picture of reduction. (shrink)

Iaegwon Kim, and others, have recently posed a powerful challen,ge to both emergentism cmd ncm-reductIve physicalism lyy providing arguments that these positums are cornmitted to an untenabie combmation of both `upwarcit and 'clouniwardi determmation. In secuon 1, I illuminate how the nature of the realiza:0n relatzon underlies such sicepucal arguments However, tn secuon 2, I suggest that such conclusicrns involve a confusion between the implications of physicahsm and those of a related thesis the Vompleteness of Physics' (Co?) I show tht (...) the truth of Co? poses a very senous obstacle to realized properues beeng efficacrous in a physicalut =verse cmd sikwest that abandonmg Co? offers hope for defending non- reducuve physicalism. (shrink)

The paper sets out a new strategy for theory reduction by means of functional sub-types. This strategy is intended to get around the multiple realization objection. We use Kim's argument for token identity (ontological reductionism) based on the causal exclusion problem as starting point. We then extend ontological reductionism to epistemological reductionism (theory reduction). We show how one can distinguish within any functional type between functional sub-types. Each of these sub-types is coextensive with one type of realizer. By (...) this means, a conservative theory reduction is in principle possible, despite multiple realization. We link this account with Nagelian reduction, as well as with Kim's functional reduction. (shrink)