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.

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.

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.

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 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)

The aim of the Analytic of Concepts is to derive and deduce a set of pure concepts of the understanding, the categories, which play a central role in Kant’s explanation of the possibility of synthetic a priori cognition and judgment. This chapter is structured around two questions. First, what is a pure concept of the understanding? Second, what is involved in a deduction of a pure concept of the understanding? In answering the first, we focus on how the categories differ (...) from the pure forms of sensibility and examine whether they are known only to be the pure forms of human thinking or rather the forms of discursive cognition as such. In answering the second, we draw a distinction between the application and the exemplification of the categories and use it to identify different ways of understanding Kant’s project in the Transcendental Deduction of the Categories. These questions connect because the answer to the first determines how we should understand the kind of entitlement which is to be established in the Deduction. (shrink)

Contemporary analytic philosophy is dominated by metaphilosophical naturalism, the view that philosophy ought to be continuous with science. This naturalistic turn is for a significant part due to the work of W. V. Quine. Yet, the development and the reception of Quine’s naturalism have never been systematically studied. In this paper, I examine Quine’s evolving naturalism as well as the reception of his views. Scrutinizing a large set of unpublished notes, correspondence, drafts, papers, and lectures as well as published responses (...) to Quine’s work, I show how both internal tensions and external criticisms forced him to continuously develop, rebrand, and refine his metaphilosophy before he explicitly decided to label his view ‘naturalism’ in the late 1960s. (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)

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)

Contemporary African philosophy ranges over a number of debates, positions, and theoretical traditions. It can, however, be read as its own critical tradition of hard-won methodological refinements and substantive philosophical debates common to a body of philosophical work concerned with African philosophical resources elided by coloniality and postcoloniality. In this paper I argue for an account of Analytic philosophy as a style of philosophy, and trace a congruous approach in history of African philosophy, suggesting that these should not be characterised (...) as antagonistic. I conclude by contrasting this style of philosophy with positions drawn from the work of Mogobe Ramose, arguing that the Analytic approach captures a set of questions worth pursuing in engagements with Ramose's work. (shrink)

Working in academia is challenging, even more so for those with limited resources and opportunities. Researchers around the world do not have equal working conditions. The paper presents the structure, operation method, and conceptual framework of the SM3D Portal's community coaching method, which is built to help Early Career Researchers (ECRs) and researchers in low-resource settings overcome the obstacle of inequality and start their career progress. The community coaching method is envisioned by three science philosophies (cost-effectiveness, transparency spirit, and proactive (...) attitude) and established and operated based on the Serendipity-Mindsponge-3D knowledge (SM3D) management framework (i.e., mindsponge thinking and Bayesian Mindsponge Framework analytics serve as the coaching program's foundational theory and analytical tools). The coaching method also embraces Open Science's values for lowering the cost of doing science and encouraging the trainees to be transparent, which is expected to facilitate the self-correcting mechanism of science through open data, open review, and open dialogue. Throughout the training process, members are central beneficiaries by gaining research knowledge and skills, acquiring publication as the training's product, and shifting their mindsets from “I can't do it” to “I can do it,” and at the same time transforming a mentee to be ready for a future mentor's role. The coaching method is thus one of the members, for the member, by the members. -/- • The paper provides the structure, operation method, and conceptual framework of the SM3D Portal's community coaching method, which is built to help Early Career Researchers (ECRs) and researchers in low-resource settings overcome the obstacle of inequality and start their career progress. • The paper presents three major science philosophies envisioning the establishment and operation of scholarly community coaching. • The paper employs the mindsponge theory and BMF analytics to construct a conceptual framework explaining how an environment is created to help shift members’ mindsets from “I can't do it” to “I can do it.”. (shrink)

The study aims to identify the reality of management of electronic documents and electronic archiving retirement in the Palestinian Pension Agency -analytical study, as well as to recognize the reality of the current document management system in the Palestinian Pension Agency. The study found the following results: that the reality of the current system for the management of documents in the agency is weak and suffers from many jams. Employee in the agency understand the importance and benefits of the (...) management of electronic documents system, where the application of electronic document management system provide important features and benefits most of which reduce the loss of documents between departments, illustrates the flow path, the speed, accuracy, transparency, and reduce the proportion of damage and destruction of files. Furthermore, the electronic documents system cost will be less than the cost of the current system and it will reduce the tasks assigned for the staff. The existence of a clear adoption of the agency for the policies and procedures established for the application of electronic documents management system. There are weak plans for training and developing of staff in the agency to raise their efficiency. The study found a set of recommendations, including: increased interest and awareness of the need to implement policies, mechanisms, and procedures to ensure the success of electronic document management system through benefiting from the experiences of other organizations and the private sector. The agency need to increase and develop its services for retirees in order to encourage the private sector, universities, and institutions to join the agency, and open the way for all segments of society in Gaza and West Bank and enhance its competitiveness between international social security institutions. The need to focus its attention on developing and publishing appropriate clear plans and specific goals about management of electronic documents and the agency should be committed to apply them. The need to focus on the establishment of a public management of archiving in the structure dealing with all technical operations and having competent and qualified employees in the field of electronic document management. The need to focus on the Palestinian National Archives and the follow-up with the international standards by the International Council Archives (ICA). (shrink)

Much discussion was inspired by the publication of Harvey Brown's book \textit{Physical Relativity} and the so-called dynamical approach to Special Relativity there advocated. At the center of the debate there is the question about the nature of the relation between spacetime and laws or, more specifically, between spacetime symmetries and the symmetries of laws. Originally, the relation was mainly assumed to be explanatory and the dispute expressed in terms of the arrow of explanation – whether it goes from spacetime (symmetries) (...) to (symmetries of) laws or vice-versa. Not everybody agreed with a setting that involves leaving ontology out. In a recent turn, the relation has been claimed to be analytical or definitional. In this paper I intend to examine critically this claim and propose a way to generally understand the relation between spacetime symmetries and symmetries of laws as deriving from constitutive principles. (shrink)

The ability to analyze arguments is critical for higher-level reasoning, yet previous research suggests that standard university education provides at best modest improvements in students’ analytical reasoning abilities. What techniques are most effective for cultivating these skills? Here we investigate the effectiveness of a 12-week undergraduate seminar in which students practice a software-based technique for visualizing the logical structures implicit in argumen- tative texts. Seminar students met weekly to analyze excerpts from contemporary analytic philosophy papers, completed argument visualization problem (...) sets, and received individualized feedback on a weekly basis. We found that Seminar students improved substantially more on LSAT Logical Reasoning test forms than Control students (d = .71, p < .001), suggesting that learning how to visualize arguments in the seminar led to large generalized improvements in students’ analytical reasoning skills. Moreover, blind scoring of final essays from Seminar students and Control students, drawn from a parallel lecture course, revealed large differences in favor of seminar students (d = 0.87, p = .005). Seminar students understood the arguments better, and their essays were more accurate and effectively structured. Taken together, these findings deepen our understanding of how visualizations support logical reasoning, and provide a model for improving analytical reasoning pedagogy. (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)

The paper provides an overview of the most fundamental ideas representing analytic philosophy throughout its history from the beginning of 20th century up to now. The history of analytic philosophy is divided into two stages – the early and the contemporary ones. The main distinguishing features of early analytic philosophy are using mathematical logic as a tool of stating and solving philosophical problems, and critical attitude toward ‘metaphysics’, i.e., traditional and contemporary non-analytic philosophical theories. The genesis of analytic philosophy was (...) closely related to the revolution in logic that led to the rise of mathematical logic, and it is no coincidence that some founders of analytic tradition (first of all Frege, Russell, and Carnap) were also prominent logicians. (But there were also authors and schools within early analytic philosophy whose researches were based on less formal tools such as classical logic and linguistic methods of analysis of language. Ordinary language philosophy is an example of this type of philosophy.) Using the new logic as a philosophical tool led to a huge number of new ideas and generated a new type of philosophical criticism that was implemented in a number of projects of ‘overcoming metaphysics’. These features constituted the methodological and thematic profile of early analytic philosophy. As opposed to the later, contemporary analytic philosophy cannot be characterized by a prevailing method or a set of main research topic. Its characteristic features are rather of historical, institutional, and stylistic nature. In the paper, early analytic philosophy is represented by Frege, Russell, early Wittgenstein, Vienna Circle (Schlick, Carnap etc.), and ordinary language philosophy (later Wittgenstein, Ryle, Austin, and Searle). Contemporary analytic philosophy is represented by Quine, and direct reference theory in philosophy of language (Kripke, Donnellan, Kaplan, and Putnam). (shrink)

Thomism, conceived of as the set of broad doctrines and style of thought expressed in the works of St. Thomas Aquinas and of those who follow him, first emerged in the thirteenth century. Aquinas himself was born in 1225 into a religious culture in which the dominant tradition of speculative thought was a version of Christian neoplatonism heavily influenced by St. Augustine. Early in his studies as a Dominican, however, Aquinas came under the direction of Albert the Great, who was (...) to exercise an important role in communicating his own enthusiasm for innovations in philosophical, theological and scientific thought. (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)

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)

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)

In his recent paper ‘Analyticity: An Unfinished Business in Possible-World Semantics’ (Rabinowicz 2006), Wlodek Rabinowicz takes on the task of providing a satisfactory definition of analyticity in the framework of possible-worlds semantics. As usual, what Wlodek proposes is technically well-motivated and very elegant. Moreover, his proposal does deliver an interesting analytic/synthetic distinction when applied to sentences with natural kind terms. However, the longer we thought and talked about it, the more questions we had, questions of both philosophical and technical nature. (...) Hence the idea of this little paper – for how better to honor a philosopher than by trying very hard to criticize him? After quickly running over some background in possible worlds semantics and setting out Wlodek's proposal against that background, we shall bring up and discuss our questions in sections 3 – 5. In the final section, we shall also make a stab at a different solution to the problem, making use of our own earlier idea of relational modality. (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)

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 generalize two concepts from special cases of Polish group actions to the general case. The two concepts are elementary embeddability, from model theory, and analytic sets, from the usual descriptive set theory.

Say that some things form a set just in case there is a set whose members are precisely the things in question. For instance, all the inhabitants of New York form a set. So do all the stars in the universe. And so do all the natural numbers. Under what conditions do some things form a set?