An r.e. degree a ≠ 0, 0' is called strongly noncappable if it has no inf with any incomparable r.e. degree. We show the existence of a high strongly noncappable degree.

In lieu of an abstract, here is a brief excerpt of the content:KARL ASCHENBRENNER, 19x 1-1988 Karl Aschenbrenner was born in Bison, Kansas, on November 20, 1911. He received the A. B. degree from Reed College in 1934 and his graduate degrees at Berkeley (M. A., 1938; Ph.D., 194o). After two years as an instructor at Reed College, he served in the U.S. Naval Reserve (Lieutenant in Meteorology ) from 1943 to 1946. From 1946 to 1948, he taught in (...) the Department of Speech at Berkeley and thereafter in the Department of Philosophy until his retirement in 1978. His teaching was devoted mainly to aesthetics and to the history of philosophy, most notably his course on Kant. For many years he was active as a trustee of the American Society for Aesthetics, and from 1961 as a member of the Journal's founding executive committee and, after incorporation, of the Board of Directors. Karl's first two years of attachment to theJournal coincided with service as chairman of the Department of Philosophy. This conjunction enabled him to be extraordinarily helpful in dealing with problems of bringing the Journal to birth--problems of funding, editorial appointments, publication policies, and business arrangements with the University of California Press. He welcomed the opportunity offered the Philosophy Department of collaborating in the publishing venture recommended by a special committee of the American Philosophical Association in 1958. The recognition early won by the Journal for its articles and reviews answered to his hope and work for success. At the annual meeting of the Board of Directors in San Francisco in 1987, the twenty-fifth birthday of the Journal was celebrated as was his twenty-seven years of diligent care for theJournafs excellence. Karl was a regular contributor to the philosophy series published by the University of California prior to three books issued by D. Reidel: The Concepts ofValue(1971), The ConceptsofCriticism(1974) and AnalysisofAppraisiveCharacterization (1983). He received Guggenheim, Fulbright, and NEH fellowships. Despite a physically disabling stroke in 1979, he continued his trips to Budapest which he began in 1972. He was concerned to study a non-IndoEuropean language spoken by people of European culture and had selected the Magyar tongue spoken in Hungary. He learned the language to test theories he advanced about appraisive concepts. He discovered in the structure of Magyar a mode of valuing embodied in verb usage differing significantly [333] 334 from the special appraisive vocabularies of English and German. Besides his lectures in Hungary, he responded to invitations to lecture received from universities in England, Austria, Poland, Bulgaria, and Romania. Shortly after his return to Budapest on his eleventh trip, he died of a massive stroke on July 4, 1988. He is buried there in a city he loved, especially for its music. He is survived by Marie, his wife of fifty-one years, and three children: Lisabeth, an attorney in Los Angeles; Peter, a judge in Fairbanks; and John, a composer in New York. E. W. STRONG... (shrink)

We show that for every nontrivial r.e. wtt-degree a, there are r.e. wtt-degrees b and c incomparable to a such that the infimum of a and b exists but the infimum of a and c fails to exist. This shows in particular that there are no strongly noncappable r.e. wtt-degrees, in contrast to the situation in the r.e. Turing degrees.

We prove that there exists a noncappable enumeration degree strictly below 0' e.

We prove that there exists a nonzero recursively enumerable Turing degree possessing a strong minimal cover.

We prove that there exists a nonzero recursively enumerable Turing degree possessing a strong minimal cover.

We establish two theorems concerning strongly compact cardinals and universal indestructibility for degrees of supercompactness. In the first theorem, we show that universal indestructibility for degrees of supercompactness in the presence of a strongly compact cardinal is consistent with the existence of a proper class of measurable cardinals. In the second theorem, we show that universal indestructibility for degrees of supercompactness is consistent in the presence of two non-supercompact strongly compact cardinals, each of which (...) exhibits a significant amount of indestructibility for its strong compactness. (shrink)

We prove, relative to suitable hypotheses, that it is consistent for there to be unboundedly many measurable cardinals each of which possesses a large degree of strong compactness, and that it is consistent to assume that the least measurable is partially strongly compact and that the second measurable is strongly compact. These results partially answer questions of Magidor on the relationship of strong compactness to measurability.

A strong degree of categoricity is a Turing degree [Formula: see text] such that there is a computable structure [Formula: see text] that is [Formula: see text]-computably categorical (there is a [Formula: see text]-computable isomorphism between any two computable copies of [Formula: see text]), and such that there exist two computable copies of [Formula: see text] between which every isomorphism computes [Formula: see text]. The question of whether every [Formula: see text] degree is a strong degree of categoricity has been (...) of interest since the first paper on this subject. We answer the question in the affirmative, by constructing an example. (shrink)

$\eta $ -representations are a way of coding sets in computable linear orders that were first introduced by Fellner in his thesis. Limitwise monotonic functions have been used to characterize the sets with $\eta $ -representations, and give characterizations for several variations of $\eta $ -representations. The one exception is the class of sets with strong $\eta $ -representations, the only class where the order type of the representation is unique.We introduce the notion of a connected approximation of a set, (...) a variation on $\Sigma ^0_2$ approximations. We use connected approximations to give a characterization of the many-one degrees of sets with strong $\eta $ -representations as well new characterizations of the variations of $\eta $ -representations with known characterizations. (shrink)

We show that any partial order with a Σ3 enumeration can be effectively embedded into any partial order obtained by imposing a strong reducibility such as ≤tt on the c. e. sets. As a consequence, we obtain that the partial orders that result from imposing a strong reducibility on the sets in a level of the Ershov hiearchy below ω + 1 are co-embeddable.

In this paper, we improve a result of Seetapun and prove that above any nonzero, incomplete recursively enumerable degree a, there is a high2 r.e. degree c>ac>a witnessing that a is locally noncappable . Theorem 1.1 provides a scheme of obtaining high2 nonboundings , as all known high2 nonboundings, such as high2 degrees bounding no minimal pairs, high2 plus-cuppings, etc.

A computable structure $\mathcal {A}$ is $\mathbf {x}$-computably categorical for some Turing degree $\mathbf {x}$ if for every computable structure $\mathcal {B}\cong\mathcal {A}$ there is an isomorphism $f:\mathcal {B}\to\mathcal {A}$ with $f\leq_{T}\mathbf {x}$. A degree $\mathbf {x}$ is a degree of categoricity if there is a computable structure $\mathcal {A}$ such that $\mathcal {A}$ is $\mathbf {x}$-computably categorical, and for all $\mathbf {y}$, if $\mathcal {A}$ is $\mathbf {y}$-computably categorical, then $\mathbf {x}\leq_{T}\mathbf {y}$. We construct a $\Sigma^{0}_{2}$ set whose degree (...) is not a degree of categoricity. We also demonstrate a large class of degrees that are not degrees of categoricity by showing that every degree of a set which is 2-generic relative to some perfect tree is not a degree of categoricity. Finally, we prove that every noncomputable hyperimmune-free degree is not a degree of categoricity. (shrink)

This chapter argues that the distinction between empiricism and metaphysics is not as clear as van Fraassen would like to believe. Almost all inquiry is metaphysical to a degree, including van Fraassen's stance empiricism. Van Fraassen does not make a strong case against metaphysics, since the argument against metaphysics has to happen at the level of meta-stances — the level where one decides which stance to endorse. The chapter maintains that utilizing van Fraassen's own conception of rationality, metaphysicians are rational. (...) Empiricists should not reject all metaphysics, but just the sort of metaphysics which goes well beyond the empirical contexts that most interest them. (shrink)

We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear ordering. Countable $\Pi _{1}^{0}$ subsets of 2ω and Kolmogorov complexity play a major role in the proof.

A Turing degreedis the degree of categoricity of a computable structure${\cal S}$ifdis the least degree capable of computing isomorphisms among arbitrary computable copies of${\cal S}$. A degreedis the strong degree of categoricity of${\cal S}$ifdis the degree of categoricity of${\cal S}$, and there are computable copies${\cal A}$and${\cal B}$of${\cal S}$such that every isomorphism from${\cal A}$onto${\cal B}$computesd. In this paper, we build a c.e. degreedand a computable rigid structure${\cal M}$such thatdis the degree of categoricity of${\cal M}$, butdis not the strong degree of categoricity (...) of${\cal M}$. This solves the open problem of Fokina, Kalimullin, and Miller [13].For a computable structure${\cal S}$, we introduce the notion of the spectral dimension of${\cal S}$, which gives a quantitative characteristic of the degree of categoricity of${\cal S}$. We prove that for a nonzero natural numberN, there is a computable rigid structure${\cal M}$such that$0\prime$is the degree of categoricity of${\cal M}$, and the spectral dimension of${\cal M}$is equal toN. (shrink)

Important examples of $\Pi^0_1$ classes of functions $f \in {}^\omega\omega$ are the classes of sets (elements of ω 2) which separate a given pair of disjoint r.e. sets: ${\mathsf S}_2(A_0, A_1) := \{f \in{}^\omega2 : (\forall i < 2)(\forall x \in A_i)f(x) \neq i\}$ . A wider class consists of the classes of functions f ∈ ω k which in a generalized sense separate a k-tuple of r.e. sets (not necessarily pairwise disjoint) for each k ∈ ω: ${\mathsf S}_k(A_0,\ldots,A_k-1) := (...) \{f \in {}^\omega k : (\forall i < k) (\forall x \in A_i) f(x) \neq i\}$ . We study the structure of the Medvedev degrees of such classes and show that the set of degrees realized depends strongly on both k and the extent to which the r.e. sets intersect. Let ${\mathcal S}^m_k$ denote the Medvedev degrees of those ${\mathsf S}_k(A_0,\ldots,A_{k-1})$ such that no m + 1 sets among A 0,...,A k-1 have a nonempty intersection. It is shown that each ${\mathcal S}^m_k$ is an upper semi-lattice but not a lattice. The degree of the set of k-ary diagonally nonrecursive functions $\mathsf{DNR}_k$ is the greatest element of ${\mathcal S}^1_k$ . If 2 ≤ l < k, then 0 M is the only degree in ${\mathcal S}^1_l$ which is below a member of ${\mathcal S}^1_k$ . Each ${\mathcal S}^m_k$ is densely ordered and has the splitting property and the same holds for the lattice ${\mathcal L}^m_k$ it generates. The elements of ${\mathcal S}^m_k$ are exactly the joins of elements of ${\mathcal S}^1_i$ for $\lceil{k \over m}\rceil \leq i \leq k$. (shrink)

In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension for multi-valued functions on represented spaces. We call the corresponding equivalence classes Weihrauch degrees and we show that the corresponding partial order induces a lower semi-lattice. It turns out that parallelization is a closure operator for this semi-lattice and that the parallelized Weihrauch degrees even form a lattice into which the Medvedev lattice and the Turing degrees can (...) be embedded. The importance of Weihrauch degrees is based on the fact that multi-valued functions on represented spaces can be considered as realizers of mathematical theorems in a very natural way and studying the Weihrauch reductions between theorems in this sense means to ask which theorems can be transformed continuously or computably into each other. As crucial corner points of this classification scheme the limited principle of omniscience LPO, the lesser limited principle of omniscience LLPO and their parallelizations are studied. It is proved that parallelized LLPO is equivalent to Weak Kőnig's Lemma and hence to the Hahn—Banach Theorem in this new and very strong sense. We call a multi-valued function weakly computable if it is reducible to the Weihrauch degree of parallelized LLPO and we present a new proof, based on a computational version of Kleene's ternary logic, that the class of weakly computable operations is closed under composition. Moreover, weakly computable operations on computable metric spaces are characterized as operations that admit upper semi-computable compact-valued selectors and it is proved that any single-valued weakly computable operation is already computable in the ordinary sense. (shrink)

This paper combines various structures representing degrees of belief, degrees of disbelief, and degrees of non-belief (degrees of expectations) into a unified whole. The representation uses relations of comparative necessity and possibility, as well as non-probabilistic functions assigning numerical values of necessity and possibility. We define all-encompassing necessity structures which have weak expectations (mere hypotheses, guesses, conjectures, etc.) occupying the lowest ranks and very strong, ineradicable ('a priori') beliefs occupying the highest ranks. Structurally, there are no (...) differences from the top to the bottom. I argue that belief is a vague notion, and that thresholds for belief, if there are any, are context-dependent. (shrink)

In this paper, we give a characterization of the strong degrees of categoricity of computable structures greater or equal to [Formula: see text]. They are precisely the treeable degrees — the least degrees of paths through computable trees — that compute [Formula: see text]. As a corollary, we obtain several new examples of degrees of categoricity. Among them we show that every degree [Formula: see text] with [Formula: see text] for [Formula: see text] a computable ordinal (...) greater than [Formula: see text] is the strong degree of categoricity of a rigid structure. Using quite different techniques we show that every degree [Formula: see text] with [Formula: see text] is the strong degree of categoricity of a structure. Together with the above example this answers a question of Csima and Ng. To complete the picture we show that there is a degree [Formula: see text] with [Formula: see text] that is not the degree of categoricity of a rigid structure. (shrink)

We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of categoricity is${\rm{\Delta }}_\alpha ^0 $-complete for someα. To prove this, we extend Montalbán’sη-system framework to deal with limit ordinals in a more general way. We also show that, for any fixed computable structure, there is an ordinalαand a cone in the Turing degrees such that the (...) exact complexity of computing an isomorphism between the given structure and another copy${\cal B}$in the cone is a c.e. degree in${\rm{\Delta }}_\alpha ^0\left$. In each of our theorems the cone in question is clearly described in the beginning of the proof, so it is easy to see how the theorems can be viewed as general theorems with certain effectiveness conditions. (shrink)

This paper explores a notion of “the strong version” of a sentential logic S, initially defined in terms of the notion of a Leibniz filter, and shown to coincide with the logic determined by the matrices of S whose filter is the least S-filter in the algebra of the matrix. The paper makes a general study of this notion, which appears to unify under an abstract framework the relationships between many pairs of logics in the literature. The paradigmatic examples are (...) the local and the global consequences associated with a normal modal logic, and the logics preserving degrees of truth and preserving truth associated with certain substructural and many-valued logics. For protoalgebraic logics the results in the paper coincide with those obtained by two of the authors in 2001, so the main novelty of the approach is its suitability for all kinds of logics. The paper also studies three kinds of definability of the Leibniz filters, and their consequences for the determination of the strong version. In a second part of the paper several case studies are developed, comprising positive modal logic, Dunn–Belnap’s four-valued logic, the large family of substructural logics, and some relevance logics. (shrink)

In this paper we argue that reflection on the patterns of practical concern that agents like us exhibit strongly suggests that the same person relation comes in continuous degrees rather than being an all or nothing matter. We call this the SP-degree thesis. Though the SP-degree thesis is consistent with a range of views about personal-identity, we argue that combining desire-first approaches to personal-identity with the SP-degree thesis better explains our patterns of practical concern, and hence gives us (...) reason to endorse such an approach. We then argue that the combination of the SP-degree thesis and the desire-first approach are best modelled by a stage-theoretic view of persistence according to which temporal counterpart relations are non-symmetric relations that come in continuous degrees. Ultimately, we think that the overall appeal of this package of views provides reason to accept the package: reasons that outstrip the reasons we have to endorse any particular member of the package. (shrink)

Epistemic deontology maintains that our beliefs and degrees of belief are open to deontic evaluations—evaluations of what we ought to believe or may not believe. Some philosophers endorse strong internalist versions of epistemic deontology on which agents can always access what determines the deontic status of their beliefs and degrees of belief. This paper articulates a new challenge for strong internalist versions of epistemic deontology. Any version of epistemic deontology must face William Alston’s argument. Alston combined a broadly (...) voluntarist conception of responsibility, on which ought implies can, with doxastic involuntarism, the position that our beliefs are not under our control. Together, those views imply that epistemic deontology is false. A promising response to Alston’s argument is to embrace a compatibilist account of control—specifically a reason-responsive version of compatibilism—and use it to criticism his doxastic involuntarism. I argue that while reason-responsive compatibilism about control does undermine Alston’s argument, it comes at a cost. Specifically, it is inconsistent with strong internalist versions of epistemic deontology. The surprising upshot is that so long as we retain a voluntarist conception of responsibility, we have reason for rejecting strong internalist versions of epistemic deontology. (shrink)

We investigate strong versions of enumeration reducibility, the most important one being s-reducibility. We prove that every countable distributive lattice is embeddable into the local structure $L(\mathfrak D_s)$ of the s-degrees. However, $L(\mathfrak D_s)$ is not distributive. We show that on $\Delta^{0}_{2}$ sets s-reducibility coincides with its finite branch version; the same holds of e-reducibility. We prove some density results for $L(\mathfrak D_s)$ . In particular $L(\mathfrak D_s)$ is upwards dense. Among the results about reducibilities that are stronger than (...) s-reducibility, we show that the structure of the $\Delta^{0}_{2}$ bs-degrees is dense. Many of these results on s-reducibility yield interesting corollaries for Q-reducibility as well. (shrink)

In this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation of first order logic and the strong logics ω-logic and β-logic, isolating two facets of absoluteness, namely, generic invariance and faithfulness. It turns out that absoluteness is relative in the sense that stronger background assumptions secure greater degrees of absoluteness. Our aim is to investigate the hierarchies of strong logics of first and second order that are generically (...) invariant and faithful against the backdrop of the strongest large cardinal hypotheses. We show that there is a close correspondence between the two hierarchies and we characterize the strongest logic in each hierarchy. On the first-order side, this leads to a new presentation of Woodin's Ω-logic. On the second-order side, we compare the strongest logic with full second-order logic and argue that the comparison lends support to Quine's claim that second-order logic is really set theory in sheep's clothing. (shrink)

Motivated by the seeming structure of the sciences, metaphysical emergence combines broadly synchronic dependence coupled with some degree of ontological and causal autonomy. Reflecting the diverse, frequently incompatible interpretations of the notions of dependence and autonomy, however, accounts of emergence diverge into a bewildering variety. Here I argue that much of this apparent diversity is superficial. I first argue, by attention to the problem of higher-level causation, that two and only two strategies for addressing this problem accommodate the genuine emergence (...) of special science entities. These strategies in turn suggest two distinct schema for metaphysical emergence---'Weak' and 'Strong' emergence, respectively. Each schema imposes a condition on the powers of entities taken to be emergent: Strong emergence requires that higher-level features have more token powers than their dependence base features, whereas Weak emergence requires that higher-level features have a proper subset of the token powers of their dependence base features. Importantly, the notion of “power” at issue here is metaphysically neutral, primarily reflecting commitment just to the plausible thesis that what causes an entity may bring about are associated with how the entity is---that is, with its features. (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)

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)

The computable Lipschitz reducibility was introduced by Downey, Hirschfeldt and LaForte under the name of strong weak truth-table reducibility [6]). This reducibility measures both the relative randomness and the relative computational power of real numbers. This paper proves that the computable Lipschitz degrees of computably enumerable sets are not dense. An immediate corollary is that the Solovay degrees of strongly c.e. reals are not dense. There are similarities to Barmpalias and Lewis’ proof that the identity bounded Turing (...) degrees of c.e. sets are not dense [2]), however the problem for the computable Lipschitz degrees is more complex. (shrink)

The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz type paradoxes”. The logic we define, PŁ4, is a strong paraconsistent and paracomplete 4-valued modal logic free from this type of paradoxes. PŁ4 is determined by the degree of truth-preserving consequence relation defined on the ordered set of values of a modification of the matrix MŁ characteristic for the logic Ł. On the other hand, PŁ4 (...) is a rich logic in which a number of connectives can be defined. It also has a simple bivalent semantics of the Belnap–Dunn type. (shrink)

We review the current knowledge concerning strong jump-traceability. We cover the known results relating strong jump-traceability to randomness, and those relating it to degree theory. We also discuss the techniques used in working with strongly jump-traceable sets. We end with a section of open questions.

Background: Double degrees in nursing and midwifery have evolved in Australia as a proposed solution to possible impending shortages of qualified midwives in the healthcare workforce. The double degree is seen as a more acceptable option in non-metropolitan areas in particular. Concern has been expressed however, about dilution of midwifery philosophy and graduates opportunities in respect of future clinical practice. Aim: This study aimed to provide a better understanding of motivations and intentions of students who undertake the Bachelor of (...) Nursing Science/Bachelor of Midwifery double degree. Methods: A cross-sectional survey design was employed at four universities that offered double degrees in nursing and midwifery in three states of Australia. Students enrolled in first and fourth year of a double degree and graduates of a double degree were invited to complete an online survey comprised of Likertscales and items requiring free text responses. Quantitative data was analysed using SPSS and thematic analysis was used to analyse the qualitative data. Findings: Participants indicated a clear preference for midwifery as a career with this preference increasing for each cohort at each stage of study. Discussion: Primary reasons for selecting a double degree were perceived increased opportunity for employment and use of nursing skills to enhance midwifery practice in a population with growing co-morbidities. A strong identification with midwifery philosophy and identity was also demonstrated.Conclusion: An understanding of motivations and career intentions of students undertaking double degree studies can inform future program development and workforce planning. (shrink)

Located at the intersection of philosophy of cognitive science and philosophy of biology, this thesis aims to provide a novel approach to understanding the strong continuity between life and mind. This thesis applies the Free Energy Framework, predictive processing and the conceptual apparatus from ecological psychology to reveal different manners in which the organizational processes and principles underlying life have been enriched so as to result in cognitive processes. By using these anticipatory cognitive frameworks this thesis unveils different forms of (...) cognition at work in surprising places and considers how such expressions of cognition are ultimately driven by various forms of environmental complexity. Importing the concepts of affordances, environmental information and perceptual medium from ecological psychology into predictive processing and the Free Energy Framework, an empirically grounded account of cognition as an anticipatory process that allows living systems to adapt to various degrees of uncertainty in their environments at distinct and yet overlapping timescales is argued for. In doing so, this thesis attempts to identify both the explanatory limits of ecological coupling accounts of perception and action, and the possible environmental conditions under which the predictive brain evolved from its decentralized non-neural predecessors as a solution to uncertainty. In contributing to a novel approach to constraining the mind, the various concepts deployed in both philosophy and cognitive science are sharpened, furthering the current debate on what cognition is and how it is related to life. (shrink)

We investigate various strong notions of rigidity for Souslin trees, separating them under ♢ into a hierarchy. Applying our methods to the automorphism tower problem in group theory, we show under ♢ that there is a group whose automorphism tower is highly malleable by forcing.

This paper explores a notion of “the strong version” of a sentential logic S, initially defined in terms of the notion of a Leibniz filter, and shown to coincide with the logic determined by the matrices of S whose filter is the least S-filter in the algebra of the matrix. The paper makes a general study of this notion, which appears to unify under an abstract framework the relationships between many pairs of logics in the literature. The paradigmatic examples are (...) the local and the global consequences associated with a normal modal logic, and the logics preserving degrees of truth and preserving truth associated with certain substructural and many-valued logics. For protoalgebraic logics the results in the paper coincide with those obtained by two of the authors in 2001, so the main novelty of the approach is its suitability for all kinds of logics. The paper also studies three kinds of definability of the Leibniz filters, and their consequences for the determination of the strong version. In a second part of the paper several case studies are developed, comprising positive modal logic, Dunn–Belnap’s four-valued logic, the large family of substructural logics, and some relevance logics. (shrink)

According to the predictive coding theory of psychosis, hallucinations and delusions are explained by an overweighing of high-level prior expectations relative to sensory information that leads to false perceptions of meaningful signals. However, it is currently unclear whether the hypothesized overweighing of priors represents a pervasive alteration that extends to the visual modality and takes already effect at early automatic processing stages. Here, we addressed these questions by studying visual perception of socially meaningful stimuli in healthy individuals with varying (...) class='Hi'>degrees of psychosis proneness. In a first task, we quantified participants’ prior for detecting faces in visual noise using a Bayesian decision model. In a second task, we measured participants’ prior for detecting direct gaze stimuli that were rendered invisible by continuous flash suppression. We found that the prior for detecting faces in noise correlated with hallucination proneness as well as delusion proneness. The prior for detecting invisible direct gaze was significantly associated with hallucination proneness but not conclusively with delusion proneness. Our results provide evidence for the idea that overly strong high-level priors for automatically detecting socially meaningful stimuli might constitute a processing alteration in psychosis. (shrink)

In Eth. Nic. V 8, Aristotle provides a classification of damages an agent may do, establishing degrees of culpability. In doing so, Aristotle recalls what he said about voluntary and involuntary actions in the preceding books about voluntary and involuntary actions. In this paper, I defend the thesis according to which the Eudemian account on voluntariness is consistent with the classification of damages Aristotle provides in Eth. Nic. V 8, arguing that one of Aristotle’s concerns in dealing with voluntariness (...) is the legal practices of his time, which we can regard as strongly linked to his discussion on moral responsibility. Thereby, I challenge David Charles’ view that the account of voluntariness featured in the book on justice differs both from the Nicomachean account and the Eudemian one. (shrink)

In this paper we first give a variant of a theorem of Jockusch–Lewis– Remmel on existence of a computable, degree-preserving homeomorphism between a bounded strong ${\Pi^0_2}$ class and a bounded ${\Pi^0_1}$ class in 2 ω . Namely, we show that for mathematically common and interesting topological spaces, such as computably presented ${\mathbb{R}^n}$ , we can obtain a similar result where the homeomorphism is in fact the identity mapping. Second, we apply this finding to give a new, priority-free proof of existence (...) of a tree of shadow points computable in 0′. (shrink)