In [5], Metakides and Nerode introduced the study of recursively enumerable substructures of a recursively presented structure. The main line of study presented in [5] is to examine the effective content of certain algebraic structures. In [6], Metakides and Nerode studied the lattice of r.e. subspaces of a recursively presented vector space. This lattice was later studied by Kalantari, Remmel, Retzlaff and Shore. Similar studies have been done by Metakides and Nerode [7] for algebraically closed fields, by Remmel [10] for (...) Boolean algebras and by Metakides and Remmel [8] and [9] for orderings. Kalantari and Retzlaff [4] introduced and studied the lattice of r.e. subsets of a recursively presented topological space. Kalantari and Retzlaff consideredX, a topological space with ⊿, a countable basis. This basis is coded into integers and with the help of this coding, r.e. subsets ofωgive rise to r.e. subsets ofX. The notion of “recursiveness” of a topological space is the natural next step which gives rise to the question of what should be the “degree” of an r.e. open subset ofX? It turns out that any r.e. open set partitions ⊿; into four sets whose Turing degrees become central in answering the question raised above.In this paper we show that the degrees of the elements of the partition of ⊿ imposed by an r.e. open set can be “controlled independently” in a sense to be made precise in the body of the paper. In [4], Kalantari and Retzlaff showed that givenAany r.e. set andany r.e. open subset ofX, there exists an r.e. open set ℋ which is a subset ofand is dense in and in whichAis coded. This shows that modulo a nowhere dense set, an r.e. open set can become as complicated as desired. After giving the general technical and notational machinery in §1, and giving the particulars of our needs in §2, in §3 we prove that the set ℋ described above could be made to be precisely of degree ofA. We then go on and establish various results on the mentioned partitioning of ⊿. One of the surprising results is that there are r.e. open sets such that every element of partitioning of ⊿ is of a different degree. Since the exact wording of the results uses the technical definitions of these partitioning elements, we do not summarize the results here and ask the reader to examine §3 after browsing through §§1 and 2. (shrink)

This paper investigates gaps in degree phrases with too, as in John is too rich [for the monastery to hire ___ ]. We present two curious restrictions on such gapped degree phrases. First, the gaps must ordinarily be anteceded by the subject of the associated gradable adjective. Second, when embedded under intensional verbs, gapped degree phrases are ordinarily restricted to surface scope, unlike their counterparts without gaps. Just as puzzlingly, we show that these restrictions are lifted when (...) there is overt wh-movement in the main clause, revealing a striking similarity between the distribution of gapped degree phrases and so-called parasitic gap constructions. These findings, we argue, suggest that the theory of parasitic gaps needs to accommodate gapped degree phrases. Specifically, they argue that parasitic constituents are null operator structures—and under the right conditions need not be accompanied by matrix wh-movement. (shrink)

Degree readings of size adjectives, as in big stamp-collector, cannot be explained away as merely the consequence of some extragrammatical phenomenon. Rather, this paper proposes that they actually reflect the grammatical architecture of nominal gradability. Such readings are available only for size adjectives in attributive positions, and systematically only for adjectives that predicate bigness. These restrictions can be understood as part of a broader picture of gradable NPs in which adnominal degree morphemes—often overt—play a key role, analogous to (...) their role in the extended AP. Size adjectives acquire degree readings through a degree morpheme similar to the one that licenses AP-modifying measure phrases. Its syntax gives rise to positional restrictions on the availability of these readings, and the semantics of degree measurement interacts with the scale structure of size adjectives to give rise to restrictions on the adjective itself. (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)

Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the given (...) class in a way that is effective enough to preserve the property in which we are interested. In this paper, we show how to transfer a number of computability-theoretic properties from directed graphs to structures in the following classes: symmetric, irreflexive graphs; partial orderings; lattices; rings ; integral domains of arbitrary characteristic; commutative semigroups; and 2-step nilpotent groups. This allows us to show that several theorems about degree spectra of relations on computable structures, nonpreservation of computable categoricity, and degree spectra of structures remain true when we restrict our attention to structures in any of the classes on this list. The codings we present are general enough to be viewed as establishing that the theories mentioned above are computably complete in the sense that, for a wide range of computability-theoretic nonstructure type properties, if there are any examples of structures with such properties then there are such examples that are models of each of these theories. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:September 24, 2010 (10:17 pm) C:\Users\Milt\Desktop\backup copy of Ken's G\WPData\TYPE3001\russell 30,1 032 red corrected.wpd 1 Just what exactly “separated by degree” means is a bone of contention among those playing the game. But it seems to me that if you have actually met a person Xz, then you have knowledge by acquaintance of X, whereas if you meet someone who met Xz you are separated from Xz by (...) one degree. Thus, I never met the jazz great Sun Ra, but my friend Warren Allen Smith (former head of a recording studio) worked with him on several of his albums, so I am one degree of separation from Sun Ra. russell: the Journal of Bertrand Russell Studies n.s. 30 (summer 2010): 63–7 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631 eu d’sprit “SIX DEGREES OF BERTRAND RUSSELL” Timothy J. Madigan Philosophy / St. John Fisher College Rochester, ny 14618, usa [email protected] One of the most quoted phrases in current popular culture is “six degrees of separation”. It expresses the idea that any human being is connected with any other human being by a chain of at most six acquaintances.1 While there is much debate as to whether this is literally true, it is an interesting thoughtexperiment, as well as the basis for many fun parlour games. One of these is entitled “Six Degrees of Kevin Bacon”, in which Wlm fans try to connect the aforementioned actor with any other movie star in as few links as possible. I have been thinking of launching a similar parlour game called “Six Degrees of Bertrand Russell”, in which any Wgure from the past 200 years or so could be connected with Bertie in as few steps as possible. Why Bertie rather than, say, Ludwig Wittgenstein (who after all had a stated interest in games)? For two reasons: Wrst, Russell lived to the ripe old age of 97, and thus had the time to interact with a wide variety of people; and secondly he was for most of that long life a celebrity, who rubbed elbows with all manner of individuals, many of whom were either celebrities themselves at the time or came to be celebrated later. As is often pointed out, Russell’s list of acquaintances stretched from Lenin (V.yI.) to Lennon (zJohn), from the Bloomsbury Group to the Doomsday Prophets, from William Gladstone to Harold Wilson. Russell’s grandfather, LordJohn Russell, had as a young man visited Napoleon on the island of Elba and shaken his hand. When I shake the hand of Honorary Russell Archivist Ken Blackwell, September 24, 2010 (10:17 pm) C:\Users\Milt\Desktop\backup copy of Ken's G\WPData\TYPE3001\russell 30,1 032 red corrected.wpd 64 timothy j. madigan 2 Other historical writings by Russell are discussed in Kenneth R. Stunkel, “Bertrand Russell’s Writings and ReXections on History”, Russellz 21 (2001): 129–53. who met Bertie, I often think that I am only three degrees of separation from shaking Napoleon’s hand as well. And as for Napoleonz—zwell, who knows where that hand had been? Given this strong connection to history, it is not surprising that Russell himself would write an essay entitled “How to Read and Understand History”.2 In his Autobiographyz and other works such as Portraits from Memory, Russell made it quite clear that his aristocratic and privileged background gave him access to many of the most important movers and shakers in twentieth-century politics, literature, and academia, areas in which he himself excelled. He was aware that, unlike many of his fellow philosophers, who were known only to a small coterie of fellow deep thinkers, he was an historic Wgure, one who could interact on a personal level with cabinet ministers, Nobel prize-winners in all Welds, press lords, movie stars, presidents and premiers. During the Cuban Missile Crisis, for instance, many concerned individuals tried to reach Kennedy and Khrushchev to give them advice, but Russell was one of the few outsiders whose letters actually got through, as he no doubt knew they would. For all of his concern with... (shrink)

Levin and Schnorr (independently) introduced the monotone complexity, Km(α), of a binary string α. We use monotone complexity to define the relative complexity (or relative randomness) of reals. We define a partial ordering ≤Km on 2ω by α ≤Km β iff there is a constant c such that Km(α ↾ n) ≤ Km(β ↾ n) + c for all n. The monotone degree of α is the set of all β such that α ≤Km β and β ≤Km α. (...) We show the monotone degrees contain an antichain of size 2N0, a countable dense linear ordering (of degrees of cardinality 2N0), and a minimal pair. Downey, Hirschfeldt, LaForte, Nies and others have studied a similar structure, the K -degrees, where K is the prefix-free Kolmogorov complexity. A minimal pair of K -degrees was constructed by Csima and Montalbán. Of particular interest are the noncomputable trivial reals, first constructed by Solovay. We define a real to be (Km, K)-trivial if for some constant c, Km(α ↾ n) ≤ K(n)+c for all n. It is not known whether there is a Km-minimal real, but we show that any such real must be (Km, K)-trivial. Finally, we consider the monotone degrees of the computably enumerable (c.e.) and strongly computably enumerable (s.c.e.) reals. We show there is no minimal c.e. monotone degree and that Solovay reducibility does not imply monotone reducibility on the c.e. reals. We also show the s.c.e. monotone degrees contain an infinite antichain and a countable dense linear ordering. (shrink)

A $\Pi^0_1$ class can be defined as the set of infinite paths through a computable tree. For classes $P$ and $Q$, say that $P$ is Medvedev reducible to $Q$, $P \leq_M Q$, if there is a computably continuous functional mapping $Q$ into $P$. Let $\mathcal{L}_M$ be the lattice of degrees formed by $\Pi^0_1$ subclasses of $2^\omega$ under the Medvedev reducibility. In "Non-branching degrees in the Medvedev lattice of $\Pi \sp{0}\sb{1} classes," I provided a characterization of nonbranching/branching and a classification of (...) the nonbranching degrees. In this paper, I present a similar classification of the branching degrees. In particular, $P$ is separable if there is a clopen set $C$ such that $P \cap C \neq \emptyset \neq P \cap C^c$ and $P \cap C \perp_M P \cap C^c$. By the results in the first paper, separability is an invariant of a Medvedev degree and a degree is branching if and only if it contains a separable member. Further define $P$ to be hyperseparable if, for all such $C$, $P \cap C \perp_M P \cap C^c$ and totally separable if, for all $X,Y \in P$, $X \perp_T Y$. I will show that totally separable implies hyperseparable implies separable and that the reverse implications do not hold, that is, that these are three distinct types of branching degrees. Along the way I will show some related results and present a combinatorial framework for constructing $\Pi^0_1$ classes with priority arguments. (shrink)

This paper presents a case study of the English noun amount, a word that ostensibly relies on measurement in its semantics, yet stands apart from other quantizing nouns on the basis of its existential interpretation. John ate the amount of apples that Bill ate does not mean John and Bill ate the same apples, but rather that they each ate apples in the same quantity. Amount makes reference to abstract representations of measurement, that is, to degrees. Its existential interpretation evidences (...) the fact that degrees contain information about the objects that instantiate them. Outside the domain of nominal measurement, the noun kind exhibits behavior strikingly similar to that of amount; both yield an existential interpretation. This observation motivates re-conceiving of degrees as nominalized quantity-uniform properties—the same sort of entity as kinds. Thus, the semantic machinery handling kinds also handles degrees: as nominalized properties, degrees are instantiated by objects that hold the corresponding property; when instantiated by real-world objects, degrees deliver the existential interpretation. (shrink)

We show that for every computably enumerable degree a > 0 there is an intrinsically c.e. relation on the domain of a computable structure of computable dimension 2 whose degree spectrum is { 0 , a } , thus answering a question of Goncharov and Khoussainov 55–57). We also show that this theorem remains true with α -c.e. in place of c.e. for any α∈ω∪{ω} . A modification of the proof of this result similar to what was done (...) in Hirschfeldt shows that for any α∈ω∪{ω} and any α -c.e. degrees a 0 ,…, a n there is an intrinsically α -c.e. relation on the domain of a computable structure of computable dimension n+1 whose degree spectrum is { a 0 ,…, a n } . These results also hold for m-degree spectra of relations. (shrink)

Let W be a recursively enumerable vector space over a recursive ordered field. We show the Turing equivalence of the following sets: the set of all tuples of vectors in W which are linearly dependent; the set of all tuples of vectors in W whose convex closures contain the zero vector; and the set of all pairs of tuples in W such that the convex closure of X intersects the convex closure of Y. We also form the analogous sets consisting (...) of tuples with given numbers of elements, and prove similar results on the Turing equivalence of these. (shrink)

I call anti-resemblism the thesis that independently of any contextual specification there is no determinate fact of the matter about the comparative overall similarity of things. Anti-resemblism plays crucial roles in the philosophy of David Lewis. For instance, Lewis has argued that his counterpart theory is anti-essentialist on the grounds that counterpart relations are relations of comparative overall similarity and that anti-resemblism is true. After Lewis committed himself to a form of realism about natural properties he maintained that (...) anti-resemblism is true about the relations of overall similarity that enter his counterpart theory and his analysis of counterfactuals. However, in this article I argue that Lewis’s account of degrees of naturalness for properties combined with his modal realism entails that anti-resemblism is false. The Lewisian must amend Lewis’s system if she aims to benefit from the alleged virtues of anti-resemblism. I consider two ways of amending it, neither of which is a free lunch. (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)

Leveraging a massive dataset of over 400 million potential matches between single heterosexuals on a leading mobile dating application we were able to identify numerous characteristics of effective matching. Effective matching is defined as the exchange of contact information with the intent to meet in person. The characteristics of effective match include alignment of psychological traits (i.e. extroversion), physical traits (i.e. height), personal choices (i.e., the relationship type they desired), and shared experiences. For nearly all characteristics, the more similar the (...) individuals were the higher the likelihood of them finding each other desirable and opting to meet in person. The only exception was introversion, where introverts rarely had an effective match with other introverts. Additionally, we investigated the preliminary stages of the choice process. We looked at the consistency between the choice of men/women, the time it took users to make these binary choices and the tendency of yes/no decisions. We used a biologically-inspired choice model to estimate the time allotted to a decision and could predict the decision and response time with nearly 60% accuracy. Given that people make their initial selection within no more than 11 seconds and ultimately converge to a partner who shares numerous attributes with them, we suggest that users are less selective in their early preferences and gradually converge to clusters with high degree of similarity in characteristics during their conversation. (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)

An investigation of language use in news stories about collisions involving vehicles and nonhuman animals in the wild reveals that reports of bird-airplane collisions tend to focus on the safety of the humans involved, even to the point of constructing the bird as a projectile, rather than a victim. Reports of land vehicles and boats colliding with larger nonhuman animals tend to demonstrate a greater concern for nonhuman participants, attributing greater responsibility to humans for the collisions, although they are more (...) dangerous to humans. Although similar patterns are found in news reports in several languages and in several English-speaking countries, anthropocentrism alone does not fully explain the patterns in journalists’ choice of expressions and structures in these news stories. (shrink)

There are at least two traditional conceptions of numerical degree of similarity. According to the first, the degree of dissimilarity between two particulars is their distance apart in a metric space. According to the second, the degree of similarity between two particulars is a function of the number of (sparse) properties they have in common and not in common. This paper argues that these two conceptions are logically independent, but philosophically inconsonant.

Human interaction has two principle functions: building and maintaining relationships with others and exchanging information. The function of building and maintaining relationships with others relates to interpersonal coordination; this behavior pattern is expected to predict the outcome of social relationships, such as between therapists and patients. It is unclear, however, whether the exchange of information is associated with interpersonal coordination. In the present study, we tested a hypothesis of whether body movement synchrony occurs in a natural conversation and whether this (...) synchrony has a positive correlation with the degree of information exchange. Fifty participants were engaged in a conversation task; each had different roles in the conversation. We measured their body movements during this conversation using an optical motion capture system. Similar to methods that can be found in previous research, we calculated body movements and quantified their synchrony applying the methods previously reported that automatically quantified their body movements. Moreover, we determined the participants’ degree of information exchange concerning the conversation using a questionnaire. We observed that the body movement synchrony of pairs who talked with each other was significantly higher than that of pairs who did not talk with each other, and that this synchrony was positively associated with the degree of information exchange. These results suggest that body movement synchrony predicted information exchange. (shrink)

For [Formula: see text], the coarse similarity class of A, denoted by [Formula: see text], is the set of all [Formula: see text] such that the symmetric difference of A and B has asymptotic density 0. There is a natural metric [Formula: see text] on the space [Formula: see text] of coarse similarity classes defined by letting [Formula: see text] be the upper density of the symmetric difference of A and B. We study the metric space of coarse (...) similarity classes under this metric, and show in particular that between any two distinct points in this space there are continuum many geodesic paths. We also study subspaces of the form [Formula: see text] where [Formula: see text] is closed under Turing equivalence, and show that there is a tight connection between topological properties of such a space and computability-theoretic properties of [Formula: see text]. We then define a distance between Turing degrees based on Hausdorff distance in the metric space [Formula: see text]. We adapt a proof of Monin to show that the Hausdorff distances between Turing degrees that occur are exactly 0, [Formula: see text], and 1, and study which of these values occur most frequently in the senses of Lebesgue measure and Baire category. We define a degree a to be attractive if the class of all degrees at distance [Formula: see text] from a has measure 1, and dispersive otherwise. In particular, we study the distribution of attractive and dispersive degrees. We also study some properties of the metric space of Turing degrees under this Hausdorff distance, in particular the question of which countable metric spaces are isometrically embeddable in it, giving a graph-theoretic sufficient condition for embeddability. Motivated by a couple of issues arising in the above work, we also study the computability-theoretic and reverse-mathematical aspects of a Ramsey-theoretic theorem due to Mycielski, which in particular implies that there is a perfect set whose elements are mutually 1-random, as well as a perfect set whose elements are mutually 1-generic. Finally, we study the completeness of [Formula: see text] from the perspectives of computability theory and reverse mathematics. (shrink)

Why is it good to be less, rather than more incoherent? Julia Staffel, in her excellent book “Unsettled Thoughts,” answers this question by showing that if your credences are incoherent, then there is some way of nudging them toward coherence that is guaranteed to make them more accurate and reduce the extent to which they are Dutch-bookable. This seems to show that such a nudge toward coherence makes them better fit to play their key epistemic and practical roles: representing the (...) world and guiding action. In this paper, I argue that Staffel’s strategy needs a small tweak. While she identifies appropriate measures of epistemic value, she does not identify appropriate measures of practical value. Staffel measures practical value using Dutchbookability scores. But credences have practical value in virtue of recommending actions that produce as much utility as possible. And while susceptibility to a Dutch book is a surefire sign that one’s credences are needlessly bad at this task, one’s degree of Dutch-bookability is not itself a good measure of how well they recommend practically valuable actions. Strictly proper scoring rules, I argue, are the right tools for measuring both epistemic and practical value. I show that we can rerun Staffel’s strategy swapping in strictly proper scoring rules for Dutch-bookability measures. So long as one’s epistemic scoring rule and practical scoring rule are “sufficiently similar,” there is some way of nudging incoherent credences toward coherence that is guaranteed to yield more of both types of value. (shrink)

Background: Responsibility is an important component of the professional values and core competencies for bachelor degree nursing students and has relationships with nursing education and professionalization. It is important for providing safe and high-quality care to the clients for the present and future performance of student. But there is no clear and operational definition of this concept for bachelor degree nursing students; however, there are extensive contents and debates about the definitions, attributes, domains and boundaries of responsibility in (...) nursing and non-nursing literature. Objective: To examine the concept of responsibility among bachelor degree nursing students using the evolutionary approach to concept analysis. Methods: A total of 75 articles published between 1990 and 2016 and related to the concept of responsibility were selected from seven databases and considered for concept analysis based on Rogers’ evolutionary approach. Ethical considerations: Throughout all stages of data collection, analysis and reporting, accuracy and bailment were respected. Findings: Responsibility is a procedural, spectral, dynamic and complex concept. The attributes of the concept are smart thinking, appropriate managerial behaviours, appropriate communicational behaviours, situational self-mandatory and task-orientation behaviours. Personal, educational and professional factors lead to the emergence of the responsible behaviours among bachelor degree nursing students. The emergence of such behaviours facilitates the learning and education process, ensures nursing profession life and promotes clients and community health level. Responsibility has some effects on nursing students. Discussion: This concept had been changed over time since 1990–2016. There are similarities and differences in the elements of this concept in disciplines of nursing and other educational disciplines. Conclusion: The analysis of this concept can help to develop educational or managerial theories, design instruments for better identification and evaluation of responsible behaviours among bachelor degree nursing students, develop strategies for enhancing the responsibility and improve the safety and quality of nursing care in the community and healthcare system. (shrink)

Similarity profiled association mining from time stamped transaction databases is an important topic of research relatively less addressed in the field of temporal data mining. Mining temporal patterns from these time series databases requires choosing and applying similarity measure for similarity computations and subsequently pruning temporal patterns. This research proposes a novel z-space based interest measure named as Krishna Sudarsana for time-stamped transaction databases by extending interest measure Srihass proposed in previous research. Krishna Sudarsana is designed by (...) using the product based fuzzy Gaussian membership function and performs similarity computations in z-space to determine the similarity degree between any two temporal patterns. The interest measure is designed by considering z-values between z = 0 and z = 3.09. Applying the Krishna Sudarsana requires moving the threshold value given by user to a different transformation space which is a defined as a function of standard deviation. In addition to proposing interest measure, new expressions for standard deviation and equivalent z-space threshold are derived for similarity computations. For experimental evaluation, we considered Naïve, Sequential and Spamine algorithms that applies Euclidean distance function and compared performance of these three approaches to Z-Spamine algorithm that uses Krishna Sudarsana by choosing various test cases. Experiment results proved the performance of the proposed approach is better to Sequential approach that uses snapshot database scan strategy and Spamine approach that uses lattice based database scan strategy. (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 universities of Oxford and Cambridge had developed different attitudes towards the award of honorary degrees through the early and middle decades of the twentieth century. Recently, both have adopted a similar cautious and apolitical stance. This essay describes the role of honorary degrees in the production and reproduction of their cultural and intellectual authority of these two ancient universities.

This research investigates the development of analogy: In particular, we wish to study the development of systematicity in analogy. Systematicity refers to the mapping of systems of mutually constraining relations, such as causal chains or chains of implication. A preference for systematic mappings is a central aspect of analogical processing in adults (Gentner, 1980, 1983). This research asks two questions: Does systematicity make analogical mapping easier? And, if so, when, developmentally, do children become able to utilize systematicity?Children aged 5–7 and (...) 8–10 acted out stories with toy characters. Then they were asked to act out the same stories with new characters. Two variables were manipulated: systematicity, or the degree of explicit causal structure in the original stories, and the transparency of the object‐mappings. Transparency was manipulated by varying the similarity between the original characters and the corresponding new characters: it was included in order to vary the difficulty of the transfer task. If children can utilize systematicity, then their transfer accuracy should be greater for systematic stories.The results show: (1) As expected, transparency strongly influenced transfer accuracy (for both age groups, transfer accuracy dropped sharply as the object correspondences became less transparent); and (2) for the older group, there was also a strong effect of systematicity and an interaction between the two variables. Given a systematic story, 9‐year‐olds could transfer it accurately regardless of the transparency of the object correspondence. (shrink)

There is a rich literature about the temporal conjunctions before/after, but at the time I gave the talk that underlies this paper I was not aware of any analysis of the temporal comparatives früher/später ‘earlier/later’, which may be used to express similar states of affairs, but are constructed differently.2 Recently I got acquainted with the del Prete’s thesis about It. prima/dopo, which analyses prima as a comparative and dopo as a preposition.3 This is the only paper known to me that (...) goes into the same direction as the following proposal. Del Prete’s analysis is very different from mine and I must leave the discussion of his theory to another occasion. The semantics of before/after is notoriously controversial and the semantics of the related adjectives is therefore interesting in itself. A study of the adjectives gains additional interest from the fact that they are entirely differently constructed: they are degree adjectives and have a comparative, an equative and a positive variant. I will study each of them. (shrink)

Smarandache (1995) defined the notion of neutrosophic sets, which is a generalization of Zadeh's fuzzy set and Atanassov's intuitionistic fuzzy set. In this paper, we first develop some similarity measures of neutrosophic sets. We will present a method to calculate the distance between neutrosophic sets (NS) on the basis of the Hausdorff distance. Then we will use this distance to generate a new similarity measure to calculate the degree of similarity between NS. Finally we will prove (...) some properties of the proposed similarity measures. (shrink)

The first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic structure of bounded degree is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). This result is shown to be optimal since we also present a string automatic structure of bounded degree whose first-order theory is hard for 2EXPSPACE. We (...) prove similar results also for tree automatic structures. These findings close the gaps left open in [28] by improving both the lower and the upper bounds. (shrink)

Sierpinski networks are networks of fractal nature having several applications in computer science, music, chemistry, and mathematics. These networks are commonly used in chaos, fractals, recursive sequences, and complex systems. In this article, we compute various connectivity polynomials such as M -polynomial, Zagreb polynomials, and forgotten polynomial of generalized Sierpinski networks S k n and recover some well-known degree-based topological indices from these. We also compute the most general Zagreb index known as α, β -Zagreb index and several other (...) general indices of similar nature for this network. Our results are the natural generalizations of already available results for particular classes of such type of networks. (shrink)

In this dissertation I argue that universal attributes are the metaphysical ground of similarity, and that the ultimate reason embracing realism is that an explanation of similarity must posit the existence of universals. Other arguments for the existence of universals are ultimately motivated by the desire to explain phenomena, such as laws of nature, general predication, and general knowledge, that seem to depend on similarity. ;This work is structured on metaphilosophical principles of Lawrence Lombard and Lawrence Powers. (...) Within this framework I defend principles for assigning weights to theoretical values such as ontological economy, explanatory power, and accordance with commonsense beliefs, and develop a realist semantic position that I use to interpret and defend an argument for the existence of universals from premises that include a simple similarity statement. ;Attributions of similarity to objects are often made with respect to kind-determining attributes or with respect to determinable attributes. I provide a realist se mantic account of such attributions, including an account of attributions of degrees of similarity. While our ways of speaking and thinking about similarities can be explained using a realist approach, nominalist theories cannot explain this central aspect of our experience. Also, nominalist theories require sweeping rejections of commonsense claims. I argue that the ontological economy of the most plausible nominalist theories is not as great as is often supposed. Thus, if we can make sense of the concept of a universal, we should accept realism. ;Because the role of universals as the ground of similarity is the ultimate motivation for positing the existence of universals, the concept of a universal is essentially associated with that role. I support this view of universals by defending a criterion of identity for universals formulated in terms of their role in grounding similarities, and disproving alternative realist criteria of identity for universals. For example, I show that Armstrong is unsuccessful in his attempt to base a criterion of identity for universals on the causal roles of universals. By providing a criterion of identity of universals, in terms of their role in grounding similarities, the essential nature of universals is demonstrated. (shrink)

In the study of the arithmetic degrees the $\omega \text {-REA}$ sets play a role analogous to the role the r.e. degrees play in the study of the Turing degrees. However, much less is known about the arithmetic degrees and the role of the $\omega \text {-REA}$ sets in that structure than about the Turing degrees. Indeed, even basic questions such as the existence of an $\omega \text {-REA}$ set of minimal arithmetic degree are open. This paper makes progress (...) on this question by demonstrating that some promising approaches inspired by the analogy with the r.e. sets fail to show that no $\omega \text {-REA}$ set is arithmetically minimal. Finally, it constructs a $\prod ^0_{2}$ singleton of minimal arithmetic degree. Not only is this a result of considerable interest in its own right, constructions of $\prod ^0_{2}$ singletons often pave the way for constructions of $\omega \text {-REA}$ sets with similar properties. Along the way, a number of interesting results relating arithmetic reducibility and rates of growth are established. (shrink)

The notion of scientific representation plays a central role in current debates on modeling in the sciences. One or maybe the major epistemic virtue of successful models is their capacity to adequately represent specific phenomena or target systems. According to similarity views of scientific representation, models should be similar to their corresponding targets in order to represent them. In this paper, Suárez’s arguments against similarity views of representation will be scrutinized. The upshot is that the intuition that scientific (...) representation involves similarity is not refuted by the arguments. The arguments do not make the case for the strong claim that similarity between vehicles and targets is neither necessary nor sufficient for scientific representation. Especially, one claim that a similarity view wants to uphold, still, is the following thesis: only if a vehicle is similar to a target in relevant respects and to a specific degree of similarity then the vehicle is a scientific representation of that target. (shrink)

Ordinarily, we take moral responsibility to come in degrees. Despite this commonplace, theories of moral responsibility have focused on the minimum threshold conditions under which agents are morally responsible. But this cannot account for our practices of holding agents to be more or less responsible. In this paper we remedy this omission. More specifically, we extend an account of reasons-responsiveness due to John Martin Fischer and Mark Ravizza according to which an agent is morally responsible only if she is appropriately (...) receptive to and reactive to reasons for action. Building on this, we claim that the degree to which an agent is responsible will depend on the degree to which she is able to recognize and react to reasons. To analyze this, we appeal to relations of comparative similarity between possible worlds, arguing that the degree to which an agent is reasons-reactive depends on the nearest possible world in which given sufficient reason to do otherwise, she does so. Similarly, we argue that the degree to which an agent is reasons-receptive will depend on the intelligibility of her patterned recognition of reasons. By extending an account of reasons-responsiveness in these ways, we are able to rationalize our practice of judging people to be more or less responsible. (shrink)

Given the success of the formal approach, within contemporary epistemology, to understanding degreed belief, some philosophers have recently considered its extension to the challenge of understanding intention. According to them, (1) intentions can also admit of degrees, as beliefs do, and (2) these degreed states are all governed by the norms of the probability calculus, such that the rational norms for belief and for intention exhibit certain structural similarity. This paper, however, raises some worries about (2). It considers two (...) schemes for representing degreed intention, and casts some doubt on applying probabilistic norms to degreed intention on each scheme. And it argues that the norms of Intention–Belief Consistency and Enkrasia cannot plausibly be turned into norms prescribing a simple correspondence relation between one’s degrees of belief and intention. The results suggest a potential structural discrepancy between the norms of theoretical and practical rationality—at least for degreed belief and intention. This potential discrepancy not only raises interesting questions about the intention–belief relation and rational norms for degreed intention. It also poses a new challenge for intention-based expressivism about normative judgment and cognitivism about practical rationality. (shrink)

Examines the dialogues from Plato's early and middle periods and illustrates the similarities and differences between Plators"s concept of craft knowledge and ...

We investigate computability theoretic and topological properties of spaces of orders on computable orderable groups. A left order on a group G is a linear order of the domain of G, which is left-invariant under the group operation. Right orders and bi-orders are defined similarly. In particular, we study groups for which the spaces of left orders are homeomorphic to the Cantor set, and their Turing degree spectra contain certain upper cones of degrees. Our approach unifies and extends Sikora’s (...) [28] investigation of orders on groups in topology and Solomon’s [31] investigation of these orders in computable algebra. Furthermore, we establish that a computable free group Fn of rank n>1 has a bi-order in every Turing degree. (shrink)

A standing question in consciousness science is whether consciousness arises gradually or in a sudden way. This empirical question is connected to a metaphysical one, concerning the kind of property that consciousness is, i.e., graded or categorical. Recently, Lee (2022) suggested that settling this question requires deciding which theory of consciousness is true. Applying an insight from Wiese (2020), this chapter pursues a way of approximating answers by examining properties that are necessary for consciousness, which consciousness must have regardless of (...) which theory turns out true in the end. One such property is attention. This chapter suggests that attention is connected to consciousness in such a way that a graded view of the former brings support for a graded view of the latter. To this effect, evidence is discussed that degrees of attention are reflected in several acknowledged dimensions of consciousness. The upshot of this view is that the transition from unconscious information processing to conscious experience is gradual and is a function of degree of attention. (shrink)

Plausibility models are Kripke models that agents use to reason about knowledge and belief, both of themselves and of each other. Such models are used to interpret the notions of conditional belief, degrees of belief, and safe belief. The logic of conditional belief contains that modality and also the knowledge modality, and similarly for the logic of degrees of belief and the logic of safe belief. With respect to these logics, plausibility models may contain too much information. A proper notion (...) of bisimulation is required that characterises them. We define that notion of bisimulation and prove the required characterisations: on the class of image-finite and preimage-finite models, two pointed Kripke models are modally equivalent in either of the three logics, if and only if they are bisimilar. As a result, the information content of such a model can be similarly expressed in the logic of conditional belief, or the logic of degrees of belief, or that of safe belief. This, we found a surprising result. Still, that does not mean that the logics are equally expressive: the logics of conditional and degrees of belief are incomparable, the logics of degrees of belief and safe belief are incomparable, while the logic of safe belief is more expressive than the logic of conditional belief. In view of the result on bisimulation characterisation, this is an equally surprising result. We hope our insights may contribute to the growing community of formal epistemology and on the relation between qualitative and quantitative modelling. (shrink)

We show that the Π 4 -theory of the partial order of recursively enumerable weak truth-table degrees is undecidable, and give a new proof of the similar fact for r.e. T-degrees. This is accomplished by introducing a new coding scheme which consists in defining the class of finite bipartite graphs with parameters.

Whilst the topic of representations is one of the key topics in philosophy of mind, it has only occasionally been noted that representations and representational features may be gradual. Apart from vague allusions, little has been said on what representational gradation amounts to and why it could be explanatorily useful. The aim of this paper is to provide a novel take on gradation of representational features within the neuroscientific framework of predictive processing. More specifically, we provide a gradual account of (...) two features of structural representations: structural similarity and decoupling. We argue that structural similarity can be analysed in terms of two dimensions: number of preserved relations and state space granularity. Both dimensions can take on different values and hence render structural similarity gradual. We further argue that decoupling is gradual in two ways. First, we show that different brain areas are involved in decoupled cognitive processes to a greater or lesser degree depending on the cause (internal or external) of their activity. Second, and more importantly, we show that the degree of decoupling can be further regulated in some brain areas through precision weighting of prediction error. We lastly argue that gradation of decoupling (via precision weighting) and gradation of structural similarity (via state space granularity) are conducive to behavioural success. (shrink)

Ambos-Spies, K. and R.A. Shore, Undecidability and 1-types in the recursively enumerable degrees, Annals of Pure and Applied Logic 63 3–37. We show that the theory of the partial ordering of recursively enumerable Turing degrees is undecidable and has uncountably many 1-types. In contrast to the original proof of the former which used a very complicated O''' argument our proof proceeds by a much simpler infinite injury argument. Moreover, it combines with the permitting technique to get similar results for any (...) ideal of the r.e. degrees. (shrink)

The presence of premises expressing comparison is a problem for the Aristotelian theory of the dialectical method, first because there is no general theory of comparison in the Organon and secondly because along with propositions on the opposition and inflexion of the terms, comparative statements seem to fall outside the explicit description which Aristotle gives of possible premises. The purpose of this paper is to offer a synthetic theory of comparisons according to Aristotle’s Topics, in an attempt both to supply (...) the aforementioned absence and to highlight the importance of the second problem. There are three main types of premises on the more, the less and the similar: some comparing the degree of possession of a predicate, others comparing the plausibility of a predication and finally, others expressing an analogy. Once expounded the very marked differences that occur between these three classes of propositions, the paper analyses the various kinds of argumentation based on comparative premises and offers a formalization of its logical laws. The complexity of this theory and the volume of topoi involved in the comparisons show the magnitude of a problem that has not been sufficiently studied. (shrink)

The explanation of a child's discriminate responses to his environment turns on ascribing to the child a perceptual discrimination which counts certain things as more similar to one another than to some other thing. As Quine forcefully puts it:If an individual is to learn at all, differences in degree of similarity must be implicit in his learning pattern. Otherwise any response, if reinforced, would be conditioned equally and indiscriminately to any and every future episode, all these being equally (...) similar.Now for those determined to cleave to behaviourist canons, the problem is to use ‘perceptual similarity’ in explaining the subject's discriminating responses in a way which does not imply the existence of mental states and entities. What this really means is that the behaviourist must reconstruct the notion of ‘perceptual similarity', purifying it of its mentalistic dimension. So long as physicalism is a reasonable position, and while we are awaiting and abetting the neurophysiological millennium, the behaviourist's project is of significant moment. Now in Word and Object Quine does not seriously attempt to provide behavioural criteria for a subject's perceiving similarities, and he provisionally permits himself the mentalistic idiom he avows finally to eschew. (shrink)

This paper addresses the issue of the moral status of non-human animals, or the question whether sentient animals are morally considerable. The arguments for and against the moral status of animals are discussed, above all the argument from marginal cases. It is argued that sentient animals have moral status based on their having interests in their experiential well-being, but that there are degrees of moral status. Two interest-based approaches are presented and discussed: DeGrazia’s view that sentient animals have interests in (...) continuing to live, and that their interests should be granted moral weight; and McMahan’s TRIA which similarly postulates that animals have interests and that in a given situation we should compare the human and animal interests at stake. Finally, the paper concludes that the anthropocentric approach to animal ethics should be abandoned in favour of the biocentric ethics. (shrink)