Is a human more conscious than an octopus? In the science of consciousness, it’s oftentimes assumed that some creatures (or mental states) are more conscious than others. But in recent years, a number of philosophers have argued that the notion of degrees of consciousness is conceptually confused. This paper (1) argues that the most prominent objections to degrees of consciousness are unsustainable, (2) examines the semantics of ‘more conscious than’ expressions, (3) develops an analysis of what it is for a (...) degreed property to count as degrees of consciousness, and (4) applies the analysis to various theories of consciousness. I argue that whether consciousness comes in degrees ultimately depends on which theory of consciousness turns out to be correct. But I also argue that most theories of consciousness entail that consciousness comes in degrees. (shrink)

Abstract - The aim of the study is to identify the degree of administrative transparency in the Palestinian higher educational institutions in the Gaza Strip. In the study, the researchers adopted a descriptive and analytical method. The research population consisted of administrative staff, whether academic or administrative, except for those in senior management or the university council. The study population reached 392 employees. A random sample was selected (197). The number of questionnaires recovered was (160) with a recovery rate (...) of (81.2%). The researchers used a questionnaire for the data collection and were treated using SPSS to obtain the results. The results show that there is no significant difference between male responses and female responses due to gender variable. The results also confirm that there is no significant difference between respondents' responses due to the age variable. The results also showed a significant difference between respondents' responses attributed to the university variable. There is a fundamental difference between respondents' responses attributed to the scientifically qualified variable. The results also confirmed a significant difference between respondents' responses attributed to the management level variable. The results also confirmed a significant difference between respondents' responses due to variable years of service. The research reached a number of recommendations, the most important of which is: The necessity of Palestinian universities to adhere to the application of transparency standards in all university activities. The need to benefit from regional and international experience in the application of transparency systems within universities and to examine the possibility of applying these systems in our universities. As well as the need to engage in the program of teaching transparency in universities, as it is confirmed that only five universities participated in this experiment. The importance of raising awareness among the employees of Palestinian universities to clarify the foundations of building transparency and its dimensions to represent the active supporter through workshops and seminars. (shrink)

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)

Abstract— This study aimed to identify the degree of use of the capabilities of decision-support systems in Palestinian institutions higher education, Aqsa University in Gaza - a case study. The study used a analytical descriptive approach, and the researchers used the of questionnaire tool to collect the data, the researchers using stratified random sample distributed (150) questioners to the study population and (126) was obtained back with rate of 84%. The study showed that the most important results are: that (...) senior management supports the existence of decision support systems and that there is approval by the respondents on the paragraphs of the use of the capabilities of decision support systems in general. And that there are no significant differences between the averages of the answers of respondents differences about the degree of use of decision support systems capabilities attributed to personal data. The study also concluded a series of recommendations including: increasing the adoption of the senior management decision support in their decision-making systems. And increased regulatory attention to the potential available to decision support systems directly to the senior management in the Palestinian universities in the Gaza Strip. There is an increased interest in the physical and technical possibilities available for the use of decision support systems. There is an increased interest in human potential available for the use of decision support systems. Investment of information available to universities in building the capacities of integration techniques and other information technology capabilities. The empowerment of human resources in universities and participating in making decisions concerning the construction of the capabilities of information technology. (shrink)

According to the recent Perceptual Confidence view, perceptual experiences possess not only a representational content, but also a degree of confidence in that content. The motivations for this view are partly phenomenological and partly epistemic. We discuss both the phenomenological and epistemic motivations for the view, and the resulting account of the interface between perceptual experiences and degrees of belief. We conclude that, in their present state of development, orthodox accounts of perceptual experience are still to be favoured over (...) the perceptual confidence view. (shrink)

Let us agree that everything that there is exists, and that to be, to be real, and to exist are one and the same. Does everything that there is exist to the same degree? Or do some things exist more than others? Are there gradations of being? I argue that some entities exist more than others. Moreover, many of the notions in play in contemporary metaphysical discourse, such as fundamentality, perfect naturalness, and grounding ought to be cashed out in (...) terms of degree of existence. (shrink)

Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this (...) problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for (...) Bayesian reasoning with idealized models in science. (shrink)

Here is a puzzle, which I learned from Terence Parsons in his “True Contradictions” [8]. First Degree Entailment is a logic which allows for truth value gaps as well as truth value gluts. If you are agnostic between assigning paradoxical sentences gaps and gluts, then this looks no different, in effect, from assigning them a gap value? After all, on both views you end up with a theory that doesn’t commit you to the paradoxical sentence or its negation. How (...) is the fde theory any different from the theory with gaps alone? In this paper, I will present a clear answer to this puzzle – an answer that explains how being agnostic between gaps and gluts is a genuinely different position than admitting gaps alone, by using the formal notion of a bi-theory, and showing that while such positions might agree on what is to be accepted, they differ on what is to be rejected. (shrink)

This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I (...) argue that any measure of epistemic justification is also a measure of incremental confirmation. However, the degree of epistemic justification must meet an additional condition, and all known measures of incremental confirmation fail to meet it. I describe this additional condition as well as a measure that meets it. The paper then applies the measure to the conjunction fallacy and proposes an explanation of the fallacy. (shrink)

We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set (...) of structures with degrees of categoricity is $\Pi_{1}^{1}$-complete. (shrink)

Based on the theory of dialectical structures, I review the concept of degree of justification of a partial position a proponent may hold in a controversial debate. The formal concept of degree of justification dovetails with our pre-theoretic intuitions about a thesis' strength of justification. The central claim I'm going to defend in this paper maintains that degrees of justification, as defined within the theory of dialectical structures, correlate with a proponent position's verisimilitude. I vindicate this thesis with (...) the results of simulations of controversial argumentation. (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)

Which country, politician, or policy is more of a cause of the Covid-19 pandemic death toll? Which of the two factories causally contributed more to the pollution of the nearby river? A wide-ranging portion of our everyday thought and talk, and attitudes rely on a graded notion of causation. However, it is sometimes highlighted that on most contemporary accounts, causation is on-off. Some philosophers further question the legitimacy of talk of degrees of causation and suggest that we avoid it. Some (...) hold that the notion of degrees of causation is an illusion. In this paper, I’ll argue that causation does come in degrees. (shrink)

Philosophy and Phenomenological Research, Volume 104, Issue 1, Page 19-49, January 2022.

Human freedom is in tension with nomological determinism and with statistical determinism. The goal of this paper is to answer both challenges. Four contributions are made to the free-will debate. First, we propose a classification of scientific theories based on how much freedom they allow. We take into account that indeterminism comes in different degrees and that both the laws and the auxiliary conditions can place constraints. A scientific worldview pulls towards one end of this classification, while libertarianism pulls towards (...) the other end of the spectrum. Second, inspired by Hoefer, we argue that an interval of auxiliary conditions corresponds to a region in phase space, and to a bundle of possible block universes. We thus make room for a form of non-nomological indeterminism. Third, we combine crucial elements from the works of Hoefer and List; we attempt to give a libertarian reading of this combination. On our proposal, throughout spacetime, there is a certain amount of freedom that can be interpreted as the result of agential choices. Fourth, we focus on the principle of alternative possibilities throughout and propose three ways of strengthening it. (shrink)

While many authors distinguish belief from acceptance, it seems almost universally agreed that no similar distinction can be drawn between degrees of belief, or credences, and degrees of acceptance. I challenge this assumption in this paper. Acceptance comes in degrees and acknowledging this helps to resolve problems in at least two philosophical domains. Degrees of acceptance play vital roles when we simplify our reasoning, and they ground the common ground of a conversation if we assume context probabilism, i.e., that the (...) common ground must be represented with probability spaces rather than possible worlds. (shrink)

The primary aim of this paper is to analyze the concept of degrees of causal contribution for actual events and examine the way in which it can be formally defined. This should go some way to filling out a gap in the legal and philosophical literature on causation. By adopting the conception of a cause as a necessary element of a sufficient set (the so-called NESS test) we show that the concept of degrees of causation can be given clear and (...) even empirical meaning. We then apply a game theoretical framework to derive a measure of causal contribution. Our favoured measure turns out to be a generalised version of the normalized Penrose-Banzhaf index of voting power. (shrink)

This paper explores a novel analysis of adjectives in the comparative and the positive based on the notion of a trope, rather than the notion of a degree. Tropes are particularized properties, concrete manifestations of properties in individuals. The point of departure is that a sentence like ‘John is happier than Mary’ is intuitively equivalent to ‘John’s happiness exceeds Mary’s happiness’, a sentence that expresses a simple comparison between two tropes, John’s happiness and Mary’s happiness. The analysis received particular (...) support from various parallels between adjectival constructions and corresponding adjective nominalizations which make reference to tropes. (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)

We regularly make graded normative judgements in the epistemic domain. Recent work in the literature examines degrees of justification, degrees of rationality, and degrees of assertability. This paper addresses a different dimension of the gradeability of epistemic normativity, one that has been given little attention. How should we understand degrees of epistemic criticizability? In virtue of what sorts of factors can one epistemic failing be worse than another? The paper develops a dual-factor view of degrees of epistemic criticizability. According to (...) the view, degrees of epistemic criticizability are (i) an inverse function of degrees of doxastic justification and (ii) a function of degrees of agent culpability. The paper develops an account of each factor, and explains how they should be weighted. The paper also addresses the importance of modelling degrees of epistemic criticizability in a broader context. I focus on the role that such a model can play in the ethics of epistemic criticism. (shrink)

There are many classical connections between the proof-theoretic strength of systems of arithmetic and the provable totality of recursive functions. In this paper we study the provability strength of the totality of recursive functions by investigating the degree structure induced by the relative provability order of recursive algorithms. We prove several results about this proof-theoretic degree structure using recursion-theoretic techniques such as diagonalization and the Recursion Theorem.

An essential guide to an essential book, this first anthology on Camera Lucida offers critical perspectives on Barthes's influential text. Roland Barthes's 1980 book Camera Lucida is perhaps the most influential book ever published on photography. The terms studium and punctum, coined by Barthes for two different ways of responding to photographs, are part of the standard lexicon for discussions of photography; Barthes's understanding of photographic time and the relationship he forges between photography and death have been invoked countless times (...) in photographic discourse; and the current interest in vernacular photographs and the ubiquity of subjective, even novelistic, ways of writing about photography both owe something to Barthes. Photography Degree Zero, the first anthology of writings on Camera Lucida, goes beyond the usual critical orthodoxies to offer a range of perspectives on Barthes's important book. Photography Degree Zero includes essays written soon after Barthes's book appeared as well as more recent rereadings of it, some previously unpublished. The contributors' approaches range from psychoanalytical to Buddhist ; they include a history of Barthes's writings on photography and an account of Camera Lucida and its reception; two views of the book through the lens of race; and a provocative essay by Michael Fried and two responses to it. The variety of perspectives included in Photography Degree Zero, and the focus on Camera Lucida in the context of photography rather than literature or philosophy, serve to reopen a vital conversation on Barthes's influential work. (shrink)

Defining the degree of categoricity of a computable structure ${\mathcal{M}}$ to be the least degree d for which ${\mathcal{M}}$ is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that for all n, degrees d.c.e. in and above 0 (n) can be so realized, as can the degree 0 (ω).

What propositions are rational for one to believe? With what confidence is it rational for one to believe these propositions? Answering the first of these questions requires an epistemology of beliefs, answering the second an epistemology of degrees of belief.

The primary aim of this paper is to analyze the concept of degrees of causal contribution for actual events and examine the way in which it can be formally defined. This should go some way to filling out a gap in the legal and philosophical literature on causation. By adopting the conception of a cause as a necessary element of a sufficient set (the so-called NESS test) we show that the concept of degrees of causation can be given clear and (...) even empirical meaning. We then apply a game theoretical framework to derive a measure of causal contribution. Our favoured measure turns out to be a generalised version of the normalized Penrose–Banzhaf index of voting power. (shrink)

I argue that Aristotle believes that virtue comes in degrees. After dispatching with initial concerns for the view, I argue that we should accept it because Aristotle conceives of heroic virtue as the highest degree of virtue. I support this interpretation of heroic virtue by considering and rejecting alternative readings, then showing that heroic virtue characterized as the highest degree of virtue is consistent with the doctrine of the mean.

A number of authors have noted that vagueness engenders degrees of belief, but that these degrees of belief do not behave like subjective probabilities. So should we countenance two different kinds of degree of belief: the kind arising from vagueness, and the familiar kind arising from uncertainty, which obey the laws of probability? I argue that we cannot coherently countenance two different kinds of degree of belief. Instead, I present a framework in which there is a single notion (...) of degree of belief, which in certain circumstances behaves like a subjective probability assignment and in other circumstances does not. The core idea is that one’s degree of belief in a proposition P is one’s expectation of P’s degree of truth. (shrink)

The goal of this paper is an account of the semantics and pragmatics of exclamation. I focus on two key observations: first, that sentence exclamations like Wow, John bakes delicious desserts! and exclamatives like What delicious desserts John bakes! express that a particular proposition has violated the speaker’s expectations; and second, that exclamatives are semantically restricted in a way that sentence exclamations are not. In my account of these facts, I propose a characterization of illocutionary force of exclamation, a function (...) from propositions to speech acts of exclamation. The difference in meaning between sentence exclamations and exclamatives has consequences for the type of violated expectation. I end with a comparison to some previous approaches and a tentative extension of parts of the analysis to other constructions. (shrink)

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)

Partial explanations are everywhere. That is, explanations citing causes that explain some but not all of an effect are ubiquitous across science, and these in turn rely on the notion of degree of explanation. I argue that current accounts are seriously deficient. In particular, they do not incorporate adequately the way in which a cause’s explanatory importance varies with choice of explanandum. Using influential recent contrastive theories, I develop quantitative definitions that remedy this lacuna, and relate it to existing (...) measures of degree of causation. Among other things, this reveals the precise role here of chance, as well as bearing on the relation between causal explanation and causation itself. (shrink)

We analyze the degree spectra of structures in which different types of immunity conditions are encoded. In particular, we give an example of a structure whose degree spectrum coincides with the hyperimmune degrees. As a corollary, this shows the existence of an almost computable structure of which the complement of the degree spectrum is uncountable.

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)

We show, for each computable ordinal α and degree $\alpha > {0^{\left( \alpha \right)}}$, the existence of a torsion-free abelian group with proper α th jump degree α.

It has been argued that Kants actions. However, it would be uncompromising to allow for only two possibilities: either full responsibility or none. Moreover, in the Metaphysics of Morals Kant himself claims that there can be degrees of responsibility, depending on the magnitude of the obstacles that have to be overcome when acting. I will show that this claim is consistent with Kant’s theory as a whole and thereby make transparent how degrees of responsibility are possible for Kant. The solution (...) is based on the distinction between two senses of responsibility: taking oneself to be an accountable person is an all-or-nothing affair, whereas praise- or blameworthiness for a particular action can still be a matter of degree. (shrink)

Starting from John MacFarlane's recent survey of answers to the question ‘What is assertion?’, I defend an account of assertion that draws on elements of MacFarlane's and Robert Brandom's commitment accounts, Timothy Williamson's knowledge norm account, and my own previous work on the normative status of logic. I defend the knowledge norm from recent attacks. Indicative conditionals, however, pose a problem when read along the lines of Ernest Adams' account, an account supported by much work in the psychology of reasoning. (...) Furthermore, there seems to be no place for degrees of belief in the accounts of belief and assertion given here. Degrees of belief do have a role in decision‐making, but, again, there is much evidence that the orthodox theory of subjective utility maximization is not a good description of what we do in decision‐making and, arguably, neither is it a good normative guide to how we ought to make decisions. (shrink)

We consider the Turing degrees of prime models of complete decidable theories. In particular we show that every complete decidable atomic theory has a prime model whose elementary diagram is low. We combine the construction used in the proof with other constructions to show that complete decidable atomic theories have low prime models with added properties. If we have a complete decidable atomic theory with all types of the theory computable, we show that for every degree d with 0 (...) 0, T has a d-decidable model omitting the nonprincipal types listed by L. (shrink)

We wish to give a precise formulation of the intuitive concept: The degree to which the known facts support a given hypothesis.

Schwitzgebel (2001) — henceforth 'S' — offers three examples in order to convince us that there are situations in which individuals are neither accurately describable as believing that p or failing to so believe, but are rather in 'in-between states of belief'. He then argues that there are no 'Bayesian' or representational strategies for explicating these, and proposes a dispositional account. I do not have any fundamental objection to the idea that there might be 'in-between states of belief'. What I (...) shall argue, rather, is that: (I) S does not provide a convincing argument that there really are such states; (II) S does not show, as he claims, that 'in-between states of belief' could not be accounted for in terms of degrees of belief; (III) S’s dispositional account of 'in-between states of belief' is more problematic than the 'degree of belief' alternative. (shrink)

This paper gives an explication of our intuitive notion of strength of justification in a controversial debate. It defines a thesis' degree of justification within the bipolar argumentation framework of the theory of dialectical structures as the ratio of coherently adoptable positions according to which that thesis is true over all coherently adoptable positions. Broadening this definition, the notion of conditional degree of justification, i.e.\ degree of partial entailment, is introduced. Thus defined degrees of justification correspond to (...) our pre-theoretic intuitions in the sense that supporting and defending a thesis t increases, whereas attacking it decreases, t's degree of justification. Moreover, it is shown that (conditional) degrees of justification are (conditional) probabilities. Eventually, the paper explains that it is rational to believe theses with a high degree of justification insofar as this strengthens the robustness of one's position. (shrink)

We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, \ bi-embeddable categoricity, and degrees of bi-embeddable categoricity. These notions mirror the classical notions used to study the complexity of isomorphisms between structures. We show that the notions of \ bi-embeddable categoricity and relative \ bi-embeddable categoricity coincide for equivalence structures for \. We also prove that computable equivalence structures have degree of bi-embeddable categoricity \, or \. We furthermore obtain (...) results on the index set complexity of computable equivalence structure with respect to bi-embeddability. (shrink)

A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a $\mathbf {0}'$ -computable low $_3$ compact Polish space which is not homeomorphic to a computable one, and that, for any natural number $n\geq 2$, there exists a Polish space $X_n$ such that exactly the high $_{n}$ -degrees are required to present the homeomorphism type of $X_n$. (...) Along the way we investigate the computable aspects of Čech homology groups. We also show that no compact Polish space has a least presentation with respect to Turing reducibility. (shrink)

The philosophical work of Jean-Luc Marion has opened new ways of speaking about religious convictions and experiences. In this exploration of Marion’s philosophy and theology, Christina M. Gschwandtner presents a comprehensive and critical analysis of the ideas of saturated phenomena and the phenomenology of givenness. She claims that these phenomena do not always appear in the excessive mode that Marion describes and suggests instead that we consider degrees of saturation. Gschwandtner covers major themes in Marion’s work—the historical event, art, nature, (...) love, gift and sacrifice, prayer, and the Eucharist. She works within the phenomenology of givenness, but suggests that Marion himself has not considered important aspects of his philosophy. (shrink)

Reports of the Intergovernmental Panel on Climate Change (IPCC) employ an evolving framework of calibrated language for assessing and communicating degrees of certainty in findings. A persistent challenge for this framework has been ambiguity in the relationship between multiple degree-of-certainty metrics. We aim to clarify the relationship between the likelihood and confidence metrics used in the Fifth Assessment Report (2013), with benefits for mathematical consistency among multiple findings and for usability in downstream modeling and decision analysis. We discuss how (...) our proposal meshes with current and proposed practice in IPCC uncertainty assessment. (shrink)

Two objects of valuation are said to be incommensurable if neither is better than the other, nor are they equally good. This negative, coarse-grained characterization fails to capture the nuanced structure of incommensurability. We argue that our evaluative resources are far richer than orthodoxy recognizes. We model value comparisons with the corresponding class of permissible preference orderings. Then, making use of our model, we introduce a potentially infinite set of degrees of approximation to better, worse, and equally good, which we (...) interpret as degrees of commensurability.One payoff is the solution our approach provides to a paradox in population ethics, generated by Parfit's “Continuum Argument”. Parfit imagines a sequence of populations, starting with one consisting of excellent lives and, by a sequence of apparent improvements, reaching a much larger population of lives barely worth living. What he dubs “the Repugnant Conclusion” is that the final population is better than the first. Developing Parfit's response, we argue that some of the populations in the sequence are merely almost better than their immediate predecessors. Almost better is not transitive (unlike better). We offer analogies to other ‘spectrum arguments’, Condorcet's paradox, and to developments in formal epistemology. (shrink)

What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In this paper, we seek (...) to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

In this paper we study intermediate logics between the logic G≤∼, the degree preserving companion of Gödel fuzzy logic with involution G∼ and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts G≤n∼. Although G≤∼ and G≤ are explosive w.r.t. Gödel negation ¬, they are paraconsistent w.r.t. the involutive negation ∼. We introduce the notion of saturated paraconsistency, a weaker notion than ideal paraconsistency, and we fully characterize the ideal and the saturated paraconsistent logics (...) between G≤n∼ and CPL. We also identify a large family of saturated paraconsistent logics in the family of intermediate logics for degree-preserving finite-valued Łukasiewicz logics. (shrink)