It was investigated, through an empirical case study, the value of educational play and its inclusive value, by using the focus group as an educational research tool. A sample of students attending the Early Childhood Education laboratory of the three-year degree course in Education and Training Sciences of the University of Catania, participated in the study.

We offer a proof of the duality theorem for finitely presented MV-algebras and rational polyhedra, a folklore and yet fundamental result. Our approach develops first a general dual adjunction between MV-algebras and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. We then show that this dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. The duality theorem for finitely presented objects is obtained by a further specialisation. (...) Our treatment is aimed at showing exactly which parts of the basic theory of MV-algebras are needed in order to establish these results, with an eye towards future generalisations. (shrink)

This paper outlines an account of conditionals, the evidential account, which rests on the idea that a conditional is true just in case its antecedent supports its consequent. As we will show, the evidential account exhibits some distinctive logical features that deserve careful consideration. On the one hand, it departs from the material reading of ‘if then’ exactly in the way we would like it to depart from that reading. On the other, it significantly differs from the non-material accounts which (...) hinge on the Ramsey Test, advocated by Adams, Stalnaker, Lewis, and others. (shrink)

In this paper we document the developmental trajectory of the complementizer system (CP-system) in Italian by looking at the earliest spontaneous production of eleven young children, whose transcriptions are available on CHILDES. We conducted a novel corpus analysis, tracking down a number of constructions in which the clausal left-periphery is activated. First, we considered the appearance of the different complementizer particles in the CP-system, which overtly realize the three distinct functional projections ForceP, IntP, and FinP. The analysis revealed that children (...) acquiring Italian correctly use these complementizer particles already in the third year of life. Second, we looked for the simultaneous activation of different functional projections within the CP-system. We went through our corpus searching for complex sentences in which more than one constituent was moved to the left periphery. This option is allowed by the adult grammar of Italian and, as our search revealed, it is also attested in the grammar of young children. Soon after their second birthday, sequences in which a left-dislocated Topic and a Wh- element co-occur are attested, directly supporting the existence of a (high) Topic position above FocusP. Moreover, movement in general conforms to the constraints of the adult grammar, with no attested violation of obligatory inversion (a consequence of the Q-Criterion). Importantly, “why-questions” did not require inversion, much as in the adult grammar of Italian. Taken together, children's use of complementizer particles and their activation of multiple landing sites for movement show that 2-year-olds already possess a richly articulated functional structure of the CP-system, aligned to the layered adult structure. In concluding the paper, we also discuss some temporal differences between constructions activating high and low portions of the CP-system. In particular, we detect a temporal precedence for wh-questions over why-questions. Since the former activate a lower projection, this is consistent with the recently proposedGrowing Treeshypothesis, according to which the development of the CP-system proceeds stepwise. (shrink)

This paper develops a probabilistic analysis of conditionals which hinges on a quantitative measure of evidential support. In order to spell out the interpreta- tion of ‘if’ suggested, we will compare it with two more familiar interpretations, the suppositional interpretation and the strict interpretation, within a formal framework which rests on fairly uncontroversial assumptions. As it will emerge, each of the three interpretations considered exhibits specific logical features that deserve separate consideration.

The Dunning–Kruger effect focuses our attention on the notion of invisibility of ignorance, i.e., the ignorance of ignorance. Such a phenomenon is not only important for everyday life, but also, above all, for some philosophical disciplines, such as epistemology of sciences. When someone tries to understand formally the phenomenon of ignorance of ignorance, they usually end up with a nested epistemic operator highly resistant to proper regimentation. In this paper, we argue that to understand adequately the ignorance of ignorance phenomenon (...) we have to understand satisfactorily the concept of disbelief and, as we call it, the concept of “radical ignorance”. We propose also prerequisites that a notion of radical ignorance useful for the philosophy of science ought to fulfill, and we sketch a possible formalization of this notion. Finally, we propose some comments on the problem of propagation of ignorance proposed by Fine. (shrink)

One of the challenges confronted by language learners is to master the interpretation of sentences with multiple logical operators, where different interpretations depend on different scope assignments. Five-year-old children have been found to access some readings of potentially ambiguous sentences much less than adults do :73–102, 2006; Musolino, Universal Grammar and the acquisition of semantic knowledge, 1998; Musolino and Lidz, Lang Acquis 11:277–291, 2003, among many others). Recently, Gualmini et al. have shown that, by careful contextual manipulation, it is possible (...) to evoke some of the putatively unavailable interpretations from young children. Their proposal is quite general, but the focus of their work was on sentences involving nominal quantifiers and negation. The present paper extends this investigation to sentences with modal expressions. The results of our two experimental studies reveal that, in potentially ambiguous sentences with modal expressions, the kinds of contextual manipulations introduced by Gualmini and colleagues do not suffice to explain children’s initial scope interpretations. In response to the recalcitrant data, we propose a new three-stage model of the acquisition of scope relations. Most importantly, at the initial stage, child grammars make available only one interpretation of negative sentences with modal expressions. We call this the Unique Scope Assignment stage. (shrink)

Al nominalista non manca proprio nulla? La dispensabilità dell’insieme vuoto in mereologia - Quine’s commitment to nominalism has always required set theory to be replaced by an ontologically less dubious tool for the analysis of predication, one that is usually ABSTRACT Rivista di storia della filosofia, n. 1, 2009 mereological in nature, akin to the Calculus of Individuals he and Goodman developed in a seminal paper on nominalism. The problem Quine himself always acknowledged as central in any such replacement arises (...) with the mereological "translation" of numbers. I show here that Quine’s proposed translation strategy, even when successful, raises even more serious issues since it requires mereology to supply a substitute for the empty set. After proving the indispensability, given Quine’s translation, of such an entity, I demonstrate that an exact mereological replica of the empty set cannot be admitted without engendering contradictions. I conclude by discussing some paraphrases of the usual mereological axioms that prima facie might seem to be compatible with the null object and assessing their implausibility. (shrink)

This essay analyzes the work of Paolo Prodi (1932–2016), which is characterised by a constant reflection on secularisation. As a democratic Catholic, he explored the relationship between the Roman Church and the modern world starting from the Council of Trent and from the dual figure of the pope as a temporal ruler and spiritual guide. His original contribution concerned the conflict between law and conscience: a problem that led him to design a triptych of books on the foundations of the (...) western world. He was influenced not only by Verfassungsgeschichte (German constitutional history), but also by Harold Berman. If for Weber the modern world was born from the Reformation, for Berman it was the ‘Gregorian revolution’ that changed the fate of Latin Europe. For Prodi, too, the medieval conflict between canon and civil law introduced a peculiar structure in Europe that would last until the triumph of the nation states and the so-called ‘political religions’. In his three books (the first dedicated to the oath, the second to justice, the last to economics), Prodi placed at the centre of his analysis the notion of forum; the history of moral theology and casuistry and the relationship between penitence and justice. (shrink)

A famous passage in Section 64 of Frege’s Grundlagen may be seen as a justification for the truth of abstraction principles. The justification is grounded in the procedureofcontent recarvingwhich Frege describes in the passage. In this paper I argue that Frege’sprocedure of content recarving while possibly correct in the case of first-order equivalencerelations is insufficient to grant the truth of second-order abstractions. Moreover, I propose apossible way of justifying second-order abstractions by referring to the operation of contentrecarving and I show (...) that the proposal relies to a certain extent on the Basic Law V. Therefore,if we are to justify the truth of second-order abstractions by invoking the content recarvingprocedure we are committed to a special status of some instances of the Basic Law V and thusto a special status of extensions of concepts as abstract objects. (shrink)

This paper investigates the logic of reasons. Its aim is to provide an analysis of the sentences of the form ‘p is a reason for q’ that yields a coherent account of their logical properties. The idea that we will develop is that ‘p is a reason for q’ is acceptable just in case a suitably defined relation of incompatibility obtains between p and ¬q. As we will suggest, a theory of reasons based on this idea can solve three challenging (...) puzzles that concern, respectively, contraposing reasons, conflicting reasons, and supererogatory reasons, and opens a new perspective on some classical issues concerning non-deductive inferences. (shrink)

Harrigan and Spekkens, introduced the influential notion of an ontological model of operational quantum theory. Ontological models can be either “epistemic” or “ontic.” According to the two scholars, Einstein would have been one of the first to propose an epistemic interpretation of quantum mechanics. Pusey et al. showed that an epistemic interpretation of quantum theory is impossible, so implying that Einstein had been refuted. We discuss in detail Einstein’s arguments against the standard interpretation of QM, proving that there is a (...) misunderstanding in Harrigan and Spekkens’ attribution of an epistemic perspective to Einstein, whose point of view was actually statistical, but in a quasi-classical sense. (shrink)

The paper lists several editions of Euclid’s Elements in the Early Modern Age, giving for each of them the axioms and postulates employed to ground elementary mathematics.

Epistemologists and philosophers of science have often attempted to express formally the impact of a piece of evidence on the credibility of a hypothesis. In this paper we will focus on the Bayesian approach to evidential support. We will propose a new formal treatment of the notion of degree of confirmation and we will argue that it overcomes some limitations of the currently available approaches on two grounds: (i) a theoretical analysis of the confirmation relation seen as an extension of (...) logical deduction and (ii) an empirical comparison of competing measures in an experimental inquiry concerning inductive reasoning in a probabilistic setting. (shrink)

This article aims at sketching a philosophical theory of sound based on the perspective of sound designers: unique agents blurring the boundaries between engineering, music, acoustics and sound-based art. After having introduced the general framing in Section 1, focusing on a short history of the theory and practice of sound design, in Section 2 we propose a reading of sound as monad. We derive such intuition from the technology of digital sampling of audio signals, based on the decomposition of complex (...) sound waves in a number of elementary sinusoidal waves. Thus, in Section 3, we attempt at grounding the resulting “sound-atom” on Leibniz’s notion of monad, intended both as a “simple substance without parts” and as a “nucleus of forces in statu possibilitatis.” The insight is resumed and further discussed in Section 4, where we draw our conclusions by demonstrating the fitness of such framing with regards to the standpoint of sound design, while accounting for the work of sound artists Carsten Nicolai and Ryoji Ikeda. (shrink)

Is the ubiquity of contemporary popular music akin to a deliberate aggression to the hearing, making the listening experience devoid of any sense? If so, is there any strategy to morph this supposed confusion into meaningful stimuli? Relying on epistemology, we attempt at promoting the act of listening as a proper way of world-making and refer to Mark Reybrouck, Bruno Nettl, Steven Brown and Joseph Jordania—among others—to gather appropriate heuristic tools. In the last part of the essay, we advance the (...) concept of timbral quotation as an additional means to grasp meaningful cues in the timbrical richness of contemporary popular compositions. We shall sustain the particular fitness of this tool especially with regard to nowadays’ Western popular music, more and more timbre-centered rather than harmony-centered. (shrink)

The problem of artificial precision is a major objection to any theory of vagueness based on real numbers as degrees of truth. Suppose you are willing to admit that, under sufficiently specified circumstances, a predication of “is red” receives a unique, exact number from the real unit interval [0, 1]. You should then be committed to explain what is it that determines that value, settling for instance that my coat is red to degree 0.322 rather than 0.321. In this note (...) I revisit the problem in the important case of Łukasiewicz infinite-valued propositional logic that brings to the foreground the rôle of maximally consistent theories. I argue that the problem of artificial precision, as commonly conceived of in the literature, actually conflates two distinct problems of a very different nature. (shrink)

This paper outlines an account of concessive conditionals that rests on two main ideas. One is that the logical form of a sentence as used in a given context is determined by the content expressed by the sentence in that context. The other is that a coherent distinction can be drawn between a reading of ‘if’ according to which a conditional is true when its consequent holds on the supposition that its antecedent holds, and a stronger reading according to which (...) a conditional is true when its antecedent supports its consequent. As we will suggest, the logical form of concessive conditionals can be elucidated by relying on this distinction. (shrink)

In his mature works, Kuhn abandons the concept of a paradigm and becomes more interested in the analysis of the conceptual structure of scientific theories. These changes are interpreted as resulting from a ‘linguistic turn’ that Kuhn underwent sometimes around the 1980s. Much of the philosophical discussions about Kuhn’s post-‘linguistic turn’ philosophy revolves around his views on taxonomic concepts. Apart from taxonomy, however, the mature Kuhn introduces other concepts, such as conceptual networks and lexicons. This article distinguishes these three concepts (...) and shows that adopting each one of them has different impacts on Kuhn’s model of science. After distinguishing and assessing the concepts of taxonomy, network, and lexicon, it will be argued that the latter not only fits the Kuhnian model of science better, but it also helps capture the wide sense of Kuhn’s early concept of a paradigm. (shrink)

The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious probability judgements observed experimentally are typically guided by sound assessments of _confirmation_ relations, meant in terms of contemporary Bayesian confirmation theory. Our main formal (...) result is a confirmation-theoretic account of the conjunction fallacy, which is proven _robust_ (i.e., not depending on various alternative ways of measuring degrees of confirmation). The proposed analysis is shown distinct from contentions that the conjunction effect is in fact not a fallacy, and is compared with major competing explanations of the phenomenon, including earlier references to a confirmation-theoretic account. (shrink)

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty and the (...) reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma–Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information-theoretic formalism. (shrink)

Today, the concept of democracy seems inextricably linked with that of universal suffrage. But is it true? To let that anyone with a given age has the right to vote is a very good democratic practice, or would prefer to question the criteria for access to this right, perhaps to develop new systems? The current crisis of democracy in the Western world is symptomatic of a detriment of the political consciousness of the people? And yet it is very likely to (...) be admissible and that only from the mass, the large numbers, rises the better choices? In this paper I try to answer these questions, drawing from personal opinions and thoughts, which I hope will inspire questions and curiosity in those who, like me, believes that any system is always perfectible, and that its aim should be to that perfection, without fear of asking uncomfortable questions. Personally, in fact, I can accept democracy as “the worst form of government except all the others that have been tried”, to quote a famous statement by Winston Churchill. But not for that I give up, and I try other ways. Ways that are more satisfying, more fair and keep us away from the horrors that only an angry mob can do. (shrink)