We give a direct mathematical proof of the Mathias-Silver theorem that every analytic set is Ramsey.

We prove that for every family I of closed subsets of a Polish space each Σ 1 1 set can be covered by countably many members of I or else contains a nonempty Π 0 2 set which cannot be covered by countably many members of I. We prove an analogous result for κ-Souslin sets and show that if A ♯ exists for any $A \subset \omega^\omega$ , then the above result is true for Σ 1 2 sets. A theorem (...) of Martin is included stating that this result is also true for weakly homogeneously Souslin sets. As an application of our results we derive from them a general form of Hurewicz's theorem due to Kechris, Louveau, and Woodin and a theorem of Feng on the open covering axiom. Also some well-known theorems on finding "big" closed sets inside of "big" Σ 1 1 and Σ 1 2 sets are consequences of our results. (shrink)

Local sentences and the formal languages they define were introduced by Ressayre in. We prove that locally finite ω‐languages and effective analytic sets have the same topological complexity: the Borel and Wadge hierarchies of the class of locally finite ω‐languages are equal to the Borel and Wadge hierarchies of the class of effective analytic sets. In particular, for each non‐null recursive ordinal there exist some ‐complete and some ‐complete locally finite ω‐languages, and the supremum of the set of (...) Borel ranks of locally finite ω‐languages is the ordinal, which is strictly greater than the first non‐recursive ordinal. This gives an answer to the question of the topological complexity of locally finite ω‐languages, which was asked by Simonnet and also by Duparc, Finkel, and Ressayre in. Moreover we show that the topological complexity of a locally finite ω‐language defined by a local sentence φ may depend on the models of the Zermelo‐Fraenkel axiomatic system. Using similar constructions as in the proof of the above results we also show that the equivalence, the inclusion, and the universality problems for locally finite ω‐languages are ‐complete, hence highly undecidable. (shrink)

We prove that if V = L then there is a $\Pi _{1}^{1}$ maximal orthogonal (i.e., mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known theorem of Preiss and Rataj [16] that no analytic set of measures can be maximal orthogonal.

We discover geometric properties of certain definable sets over non-Archimedean valued fields with analytic structures. Results include a parameterized smooth stratification theorem and the existence of a bound on the piece number of fibers for these sets. In addition, we develop a dimension theory for these sets and also for the formulas which define them.

This paper explores agenda-setting theory within digital media. It aims to evaluate changes in these paradigms due to digital platforms and their impact on mass communication theories. The discussion includes a historical overview of agenda-setting theory, grounded in foundational works and expanded by contemporary insights on user agency and information dissemination in the digital age. Using qualitative methods, the study incorporates thematic analysis, content analysis, and interviews with media professionals and users to collect comprehensive data. Key findings indicate that the (...) traditional linear flow of information from media to the public has shifted to a multidirectional exchange influenced by user-generated content and social media dynamics. The study emphasizes the need for scholars to adapt traditional media theories to the participatory nature of modern platforms. This research enhances understanding of current media ecosystems and lays the groundwork for future studies on media influence in complex digital environments. (shrink)

This article introduces an interpretative approach to the analysis of situations in computational settings called situational analytics. I outline the theoretical and methodological underpinnings of this approach, which is still under development, and show how it can be used to surface situations from large data sets derived from online platforms such as YouTube. Situational analytics extends to computationally-mediated settings a qualitative methodology developed by Adele Clarke, Situational Analysis, which uses data mapping to detect heterogeneous entities in fieldwork data to determine (...) ‘what makes a difference’ in a situation. Situational analytics scales up this methodology to analyse situations latent in computational data sets with semi-automated methods of textual and visual analysis. I discuss how this approach deviates from recent analyses of situations in computational social science, and argue that Clarke’s framework renders tractable a fundamental methodological problem that arises in this area of research: while social researchers turn to computational settings in order to analyse social life, the social processes unfolding in these envirnoments are fundamentally affected by the computational architectures in which they occur. Situational analytics offers a way to address this problematic by making a heterogeneously composed situation – involving social, technical and media elements – the unit of computational analysis. To conclude, I show how situational analytics can be applied in a case study of YouTube videos featuring intelligent vehicles and discuss how situational analysis itself needs to be elaborated if we are to come to terms with computational transformations of the situational fabric of social life. (shrink)

We study the Hardy field associated with an o-minimal expansion of the real numbers. If the set of analytic germs is dense in the Hardy field, then we can definably analytically separate sets in , and we can definably analytically approximate definable continuous unary functions. A similar statement holds for definable smooth functions.

The aim of the paper is to prove tha analytic completeness theorem for a logic LAs with two integral operators in the singular case. The case of absolute continuity was proved in [4]. MSC: 03B48, 03C70.

Motivated by results on interactive proof systems we investigate an ∃-∀hierarchy over P using word quantifiers as well as two types of set quantifiers. This hierarchy, which extends the polynomial-time hierarchy, is called the analytic polynomial-time hierarchy. It is shown that every class of this hierarchy coincides with one of the following Classes: ∑math image, Πmath image , PSPACE, ∑math image or Πmath image . This improves previous results by Orponen [6] and allows interesting comparisons with the above mentioned (...) results on inter-active proof systems. (shrink)

Descriptive set theory and computability theory are closely-related fields of logic; both are oriented around a notion of descriptive complexity. However, the two fields typically consider objects of very different sizes; computability theory is principally concerned with subsets of the naturals, while descriptive set theory is interested primarily in subsets of the reals. In this paper, we apply a generalization of computability theory, admissible recursion theory, to consider the relative complexity of notions that are of interest in descriptive set theory. (...) In particular, we examine the perfect set property, determinacy, the Baire property, and Lebesgue measurability. We demonstrate that there is a separation of descriptive complexity between the perfect set property and determinacy for analytic sets of reals; we also show that the Baire property and Lebesgue measurability are both equivalent in complexity to the property of simply being a Borel set, for $\boldsymbol {\Sigma ^{1}_{2}}$ sets of reals. (shrink)

Analytic ethics in the central period – extending from the beginning of the twentieth century to post-World War II linguistic analysis – is too often construed by historians and philosophers alike in monolithic terms as the emotivism of A. J. Ayer. In contrast, we argue that a multiplicity of ethical doctrines were developed by analytic philosophers at this time of which Ayer's emotivism was just one. Moreover, we maintain that this multiplicity of ethical doctrines was itself the result (...) of a multiplicity of conceptions of analysis and that connecting these two sets of beliefs makes for the best understanding of analytic ethics. (shrink)

An analytic cognitive style denotes a propensity to set aside highly salient intuitions when engaging in problem solving. We assess the hypothesis that an analytic cognitive style is associated with a history of questioning, altering, and rejecting supernatural claims, both religious and paranormal. In two studies, we examined associations of God beliefs, religious engagement, conventional religious beliefs and paranormal beliefs with performance measures of cognitive ability and analytic cognitive style. An analytic cognitive style negatively predicted both (...) religious and paranormal beliefs when controlling for cognitive ability as well as religious engagement, sex, age, political ideology, and education. Participants more willing to engage in analytic reasoning were less likely to endorse supernatural beliefs. Further, an association between analytic cognitive style and religious engagement was mediated by religious beliefs, suggesting that an analytic cognitive style negatively affects religious engagement via lower acceptance of conventional religious beliefs. Results for types of God belief indicate that the association between an analytic cognitive style and God beliefs is more nuanced than mere acceptance and rejection, but also includes adopting less conventional God beliefs, such as Pantheism or Deism. Our data are consistent with the idea that two people who share the same cognitive ability, education, political ideology, sex, age and level of religious engagement can acquire very different sets of beliefs about the world if they differ in their propensity to think analytically. (shrink)

We show that every analytic filter is generated by a Π 0 2 prefilter, every Σ 0 2 filter is generated by a Π 0 1 prefilter, and if $P \subseteq \mathscr{P}(\omega)$ is a Σ 0 2 prefilter then the filter generated by it is also Σ 0 2 . The last result is unique for the Borel classes, as there is a Π 0 2 -complete prefilter P such that the filter generated by it is Σ 1 1 (...) -complete. Also, no complete coanalytic filter is generated by an analytic prefilter. The proofs use König's infinity lemma, a normal form theorem for monotone analytic sets, and Wadge reductions. (shrink)

Hoover [2] proved a completeness theorem for the logic L[MATHEMATICAL SCRIPT CAPITAL A]. The aim of this paper is to prove a similar completeness theorem with respect to product measurable biprobability models for a logic Lmath image with two integral operators. We prove: If T is a ∑1 definable theory on [MATHEMATICAL SCRIPT CAPITAL A] and consistent with the axioms of Lmath image, then there is an analytic absolutely continuous biprobability model in which every sentence in T is satified.

ABSTRACT Sensory Processing Sensitivity is an individual difference that affects people’s thinking and behavior. People who are high in SPS, Highly Sensitive People, are more sensitive to stimuli and prefer to take their time in thinking through problems. This study examined the effects of SPS and analytic mind-set on ethical decision-making. Mind-Set was manipulated by instructing participants to either think thoroughly through the ethical problem or focus on finding a concrete, practical solution when solving the problems. HSPs performed better (...) in the deliberative mind-set, allowing them to solve the problem using their natural problem-solving approach. People low in SPS performed better in the implementation mind-set. Results suggest that ethics interventions should not be “one size fits all,” and should consider a person’s natural problem-solving tendencies. (shrink)

This paper offers an explanation of the maj or traditions in the logical treatment of definite descriptions as reactions to paradoxical naive definite descriptiontheory. The explanation closely parallels that of various set theories as reactions to paradoxical naive set theory. Indeed, naive set theory is derivable from naive definite description theory given an appropriate definition of set abstracts in terms of definite descriptions.

SummaryThis paper defends the philosophical importance of analyticity against the influential objections raised by W. V. Quine. It characterizes analyticity in a way that is nonepistemic, avoids Quine's objections and fits his general strictures, and explains the epistemological importance of analyticity. It also explains why even proponents of Quine's naturalized epistemology should value the epistemological importance of analyticity, in connection with questions about the correctness of their epistemic principles. Given these considerations, this paper may be regarded as having rescued analyticity (...) from the throes of suspicion and myth, as set by “Two Dogmas of Empiricism.”. (shrink)

This dissertation focuses on the topic of analyticity. The traditional concept of analyticity characterizes analytic sentences in at least two ways. On the one hand, these sentences are thought to be true in virtue only of the meaning of the expressions that constitute them. On the other hand, they are thought to be such that they can be concluded by competent speakers in an a priori fashion--that is, merely on the basis of the speakers' knowledge of the meaning of (...) the expressions contained in the sentences. In the dissertation I argue that these two ways of characterizing analyticity do not single out the same set of sentences, and that at least two different notions of meaning should be postulated to account for this fact. ;To show this I focus first on the notion of truth in virtue of meaning. I identify two ways in which a sentence can be said to be true in virtue of meaning: on the one hand, if the condition it expresses necessarily obtains; on the other hand, if semantic facts concerning the reference of the expressions that constitute it determine that it has to be true. I argue that the sets of sentences that can be said to be true in virtue of meaning according to these two criteria and the set of sentences ordinarily deemed analytically true do not coincide. ;I focus then on the second traditional criterion for analyticity--i.e., apriority. This criterion determines a set of sentences--what I call a priori acceptable sentences--that seems to coincide most closely with the set of sentences we ordinarily judge to be analytic. To account for the disparity between the extensions of this and the 'truth in virtue of meaning' criteria I propose that a distinction should be made between truth-conditional meaning--which concerns the contribution of expressions to truth-conditions--and conceptual meaning--which concerns the abilities necessary for competence in a language. I finally argue that conceptual meaning cannot always guarantee the truth of a priori acceptable sentences. (shrink)

We show that every analytic set in the Baire space which is dominating contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. We call this property of analytic sets u-regularity. However, we show that the concept of uniform tree does not suffice to characterize dominating analytic sets in general. We construct a dominating closed set with the property that for no (...) uniform tree whose branches are contained in the closed set, the set of these branches is dominating. We also show that from a Σ1n+1-rapid filter a non-u-regular Π1n-set can be constructed. Finally, we prove that ∑12-Kσ-regularity implies ∑12-u-regularity. (shrink)

Rational choice modeling originating in economics is sweeping across many areas of social science. This paper examines a popular methodological proposal for integrating formal models from game theory with more traditional narrative explanations of historical phenomena, known as “analytic narratives”. Under what conditions are we justified in thinking that an analytic narrative provides a good explanation? In this paper I criticize the existing criteria and provide a set of my own. Along the way, I address the critique of (...) analytic narratives by Jon Elster. (shrink)

David Lewis's position, often called analytic functionalism, was inspired by Ryle's analytic behaviorism, which took psychological predicates to express complex sets of behavioral dispositions. In this chapter, the author reviews some tenets of Lewis's philosophy of mind and begins with some comments on the methodology Lewis employed in his analysis of psychological terms, which has become standard in functionalist accounts across philosophy. Then, he discusses the difference between what are often called “realizer functionalism” and “role functionalism,” and argues (...) that Lewis made the wrong choice. In Lewis's argument for the identity theory, the identity of mental states with biological states follows logically from folk‐psychological definitions and broadly physical facts. A central part of folk psychology concerns the interaction of beliefs, desires, and choices. The chapter presents Lewis's often misunderstood account of intentionality. It also presents few pessimistic remarks on the prospect of analyzing phenomenal truths in terms of functional role. (shrink)

This paper provides a comprehensive survey of the literature on Analytical Marxism (AM) and analyses its relevance for social theory. AM is precisely defined and distinguished from Rational Choice Marxism (RCM). The different substantive implications of the two approaches are discussed: according to RCM, the role of Marxism in the social sciences is exhausted, whereas AM has reconstructed a set of propositions that aim to provide the foundations of a distinctive approach in social theory. The methodological debate around and within (...) AM is analysed and the shortcomings of methodological individualism and rational choice theory are stressed, raising doubts on the claim that RCM is the only scientific approach to Marx's theory. Yet, wholesale rejections on a priori methodological or exegetical grounds are questioned. A focused, immanent critique of RCM is developed, which emphasizes the lack of an adequate analysis of structural constraints and endogenous preferences in RCM models. It is argued that the analysis of endogenous preferences and structural constraints is consistent with an anti-reductionist AM approach and it may provide the outline of a fertile, distinctive research programme in explanatory social theory that builds on the core of Marxism identified by AM. (shrink)

In this dissertation, I defend a view that combines an analytic conception of a priori knowledge with a version of reliabilist platonism. Roughly put, the analytic theory is the view that our a priori knowledge can be explained by our grasp of analytic truths. Platonism is the view that there are abstract objects and those objects are partly responsible for some of our knowledge. My primary goal is to show that the hybrid account I develop solves central (...) problems that arise for the analytic view and platonism on their own. One well-known difficulty facing platonism is the following epistemological concern: given that abstracta are causally inefficacious, it is unclear how we can ever come to know anything about them. I argue that platonism on its own cannot adequately address this problem. Likewise, there is the following serious difficulty for the analytic theory: given the central role of implicit definitions for the analytic theory, if there are good reasons to doubt the unqualified success of such stipulations, it seems that the analytic theory fails to explain our a priori knowledge. I also show that this is a serious problem for the analytic theory. However, I show how a combination of the analytic theory and platonism can address both sets of difficulties: one view makes up for the shortcomings of the other. On the one hand, reliabilist platonism helps explain the success of the relevant stipulations; on the other hand, the analytic theory helps show why the causal inefficacy of abstracta is not a problem for our a priori knowledge. (shrink)

We prove that every analytic set in ω ω × ω ω with σ-bounded sections has a not σ-bounded closed free set. We show that this result is sharp. There exists a closed set with bounded sections which has no dominating analytic free set, and there exists a closed set with non-dominating sections which does not have a not σ-bounded analytic free set. Under projective determinacy analytic can be replaced in the above results by projective.

This article makes four claims. First, that the analytic/Continental split in political theory stems from an unarticulated disagreement about human nature, with analytics believing we have an innate set of mostly compatible moral and political inclinations, and Continentals seeing such things as alterable products of historical contingency. Second, that we would do better to talk of Continental-political-theory versus Rawlsian-political-philosophy, given that the former avoids arguments over principles, whilst the latter leaves genuine analytic philosophy behind. Third, that Continentals suffer (...) from a lack of such arguments, even by their own lights, whilst Rawlsians suffer from inconsistencies within the thought-patterns on which their principles depend. Fourth, that there is an alternative method – ‘normative behaviourism’ – that at least tries to move beyond the problems of both approaches, whilst sharing an idea of ‘praxis’ with the first, and an idea of deriving-principles-from-existing-judgements with the second. (shrink)

We investigate the existence of perfect homogeneous sets for analytic colorings. An analytic coloring of X is an analytic subset of [X]N, where N>1 is a natural number. We define an absolute rank function on trees representing analytic colorings, which gives an upper bound for possible cardinalities of homogeneous sets and which decides whether there exists a perfect homogeneous set. We construct universal σ-compact colorings of any prescribed rank γ<ω1. These colorings consistently contain homogeneous sets of (...) cardinality γ but they do not contain perfect homogeneous sets. As an application, we discuss the so-called defectedness coloring of subsets of Polish linear spaces. (shrink)

The present paper is a commentary on O.A. Domanov’s paper devoted to the use of modern type theory in the analysis of quantification in opaque contexts (e. g., propositional attitudes and believe reports). The article briefly mentions several recent attempts to use type theory to solve a number of philosophical problems. The paper suggests that the use of modern type theory, which has a number of significant advantages over classical logic and set theory, is a very promising direction in the (...) development of philosophical problems in the spirit of analytic philosophy. In addition, the paper indicates a number of questions on which it would be desired to receive a clarification from the author of the paper being commented. (shrink)

Recently, big data analytics have gained significant attention in healthcare industry due to generation of massive quantities of data in various forms such as electronic health records, sensors, medical imaging, and pharmaceutical details. However, the data gathered from various sources are intrinsically uncertain owing to noise, incompleteness, and inconsistency. The analysis of such huge data necessitates advanced analytical techniques using machine learning and computational intelligence for effective decision making. To handle data uncertainty in healthcare sector, this article presents a novel (...) metaheuristic rough set-based feature selection with rule-based medical data classification technique on MapReduce framework. The proposed MRSFS-RMDC technique designs a butterfly optimization algorithm for minimal rough set selection. In addition, Hadoop MapReduce is applied to process massive quantity of data. Moreover, a rule-based classification approach named Repeated Incremental Pruning for Error Reduction is used with the inclusion of a set of conditional rules. The RIPPER will scale in a linear way with the number of training records utilized and is suitable to build models with data uncertainty. The proposed MRSFS-RMDC technique is validated using benchmark dataset and the results are inspected under varying aspects. The experimental results highlighted the supremacy of the MRSFS-RMDC technique over the recent state of art methods in terms of different performance measures. The proposed methodology has achieved a higher F-score of 96.49%. (shrink)

I cannot claim to be an “Analytical Thomist” for two reasons: first, I am a practicing Jew, and Thomism is a philosophical tradition within the Roman Catholic Church. But not only do I philosophize within a different religious tradition than Thomists do, there is also the fact that my own approach to philosophy is, I think, quite different. My purpose here, however, is not to reject Analytical Thomism, or even to criticize it, but rather to enter into a dialogue with (...) it. Thus, even if I do not put the remarks that follow in the form of questions, they are intended in a sense as a set of questions addressed to those who do consider themselves to be Analytical Thomists. (shrink)

The method of analytic tableaux is employed in many introductory texts and has also been used quite extensively as a basis for automated theorem proving. In this paper, we discuss the complexity of the system as a method for refuting contradictory sets of clauses, and resolve several open questions. We discuss the three forms of analytic tableaux: clausal tableaux, generalized clausal tableaux, and binary tableaux. We resolve the relative complexity of these three forms of tableaux proofs and also (...) resolve the relative complexity of analytic tableaux versus resolution. We show that there is a quasi-polynomial simulation of tree resolution by analytic tableaux; this simulation is close to optimal, since we give a matching lower bound that is tight to within a polynomial. (shrink)

_The Concept of Analytic Contact_ presents practitioners with new ways to assist the often severely disturbed patients that come to see them in both private and institutional settings. In this book Robert Waska outlines the use of psychoanalysis as a method of engagement that can be utilised with or without the addition of multiple weekly visits and the analytic couch. The chapters in this book follow a wide spectrum of cases and clinical situations where hard to reach patients (...) are provided with the best opportunity for health and healing through the establishment of analytic contact. Divided into four parts, this book covers: the concept of analytic contact caution and reluctance concerning psychological engagement drugs, mutilation, and psychic fragmentation clinical reality, psychoanalysis and the utility of analytic contact. Analytic contact is demonstrated to be a valuable clinical approach to working analytically with a complicated group of patients in a successful manner. It will be of great interest to all practitioners in the field of psychoanalysis and psychotherapy. (shrink)

Early analytic philosophy is known for its logical rigor that seems to leave no place for non-rational sources of knowledge such as mystical experiences. The following paper shows on the example of Bertrand Russell and Ludwig Wittgen-stein that despite of this early analytic philosophy was interested in mysticism and it also shows the roots of this interest. For Russell an application of logical methods to solving philosophical puzzled was an expression of more fundamental striving – to know the (...) world as it is, sub specie aeternitatis – which is mystical in nature. In turn early Wittgenstein’s philosophy sets the limits of meaningful propositions and provides the distinction between what can be said and what can only be shown and what manifests itself in the world. The latter belongs to the realm of the mystical. (shrink)

The word ‘equality’ often requires disambiguation, which is provided by context or by an explicit modifier. For each sort of magnitude, there is at least one sense of ‘equals’ with its correlated senses of ‘is greater than’ and ‘is less than’. Given any two magnitudes of the same sort—two line segments, two plane figures, two solids, two time intervals, two temperature intervals, two amounts of money in a single currency, and the like—the one equals the other or the one is (...) greater than the other or the one is greater than the other [sc. in appropriate correlated senses of ‘equals’, ‘is greater than’ and ‘is less than’]. In case there are two or more appropriate senses of ‘equals’, the one intended is often indicated by an adverb. For example, one plane figure may be said to be equal in area to another and, in certain cases, one plane figure may be said to be equal in length to another. Each sense of ‘equality’ is tied to a specific domain and is therefore non-logical. Notice that in every cases ‘equality’ is definable in terms of ‘is greater than’ and also in terms of ‘is less than’ both of which are routinely considered domain specific, non-logical. The word ‘identity’ in the logical sense does not require disambiguation. Moreover, it is not correlated ‘is greater than’ and ‘is less than’. If it is not the case that a certain designated triangle is [sc. is identical to] an otherwise designated triangle, it is not necessary for the one to be greater than or less than the other. Moreover, if two magnitudes are equal then a unit of measure can be chosen and, no matter what unit is chosen, each magnitude is the same multiple of the unit that the other is. But identity does not require units. In this regard, congruence is like identity and unlike equality. In arithmetic, the logical concept of identity is coextensive with the arithmetic concept of equality. The logical concept of identity admits of an analytically adequate definition in terms of logical concepts: given any number x and any number y, x is y iff x has every property that y has. The arithmetical concept of equality admits of an analytically adequate definition in terms of arithmetical concepts: given any number x and any number y, x equals y iff x is neither less than nor greater than y. As Aristotle told us and as Frege retold us, just because one relation is coextensive with another is no reason to conclude that they are one. (shrink)

According to the Genuine Modal Realist, there is a plurality of possible worlds, each world nothing more than a maximally inter-related spatiotemporal sum. One advantage claimed for this position is that it offers us the resources to analyse, in a noncircular manner, the modal operators. In this paper, we argue that the prospects for such an analysis are poor. For the analysis of necessity as truth in all worlds to succeed it is not enough that no modal concepts be used (...) in the realist's account of a possible world (a fact we grant); rather, such an analysis will succeed only if the set of worlds that is postulated is complete. By appealing to plausible truths about the number of possible alien natural properties, we show that there are serious difficulties in guaranteeing that such a set exists without taking some modal concept as primitive. Accordingly, at least in its current form, Genuine Modal Realism must curtail its analytic ambitions. (shrink)