What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

While philosophers tend to consider a single type of causal history, biologists distinguish between two kinds of causal history: evolutionary history and developmental history. This essay studies the peculiarity of development as a criterion for the individuation of biological traits and its relation to form, function, and evolution. By focusing on examples involving serial homologies and genetic reprogramming, we argue that morphology (form) and function, even when supplemented with evolutionary history, are sometimes insufficient to individuate traits. Developmental mechanisms bring in (...) a novel aspect to the business of classification—identity of process-type—according to which entities are type-identical across individuals and natural kinds in virtue of the fact that they form and develop through similar processes. These considerations bear important metaphysical implications and have potential applications in several areas of philosophy. (shrink)

The indispensability argument comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA (...) can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and genuine IA, and argue that no genuine sound IA is available or easily forthcoming. We then submit that this holds also in the particularly relevant case in which indispensability is conceived as explanatory indispensability. (shrink)

Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$and on whether it (...) applies to definitions of both natural and real numbers. Our aim is to trace the origins of$FC$and to explore how different understandings of it can be faithful to Frege’s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (§1), we appropriately distinguish$AC$from$FC$(§2). We discuss six rationales which may motivate the adoption of different instances of$AC$and$FC$(§3). We turn to the possible interpretations of$FC$(§4), and advance a Semantic$FC$(§4.1), arguing that while it suits Frege’s definition of natural numbers (4.1.1), it cannot reasonably be imposed on definitions of real numbers (§4.1.2), for reasons only partly similar to those offered by Crispin Wright (§4.1.3). We then rehearse a recent exchange between Bob Hale and Vadim Batitzky to shed light on Frege’s conception of real numbers and magnitudes (§4.2). We argue that an Architectonic version of$FC$is indeed faithful to Frege’s definition of real numbers, and compatible with his views on natural ones. Finally, we consider how attributing different instances of$FC$to Frege and appreciating the role of the Architectonic$FC$can provide a more perspicuous understanding of his foundational program, by questioning common pictures of his logicism (§5). (shrink)

This volume takes cue from the idea that the thought of no philosopher can be understood without considering it as the result of a constant, lively dialogue with other thinkers, both in its internal evolution as well as in its reception, re-use, and assumption as a starting point in addressing past and present philosophical problems. In doing so, it focuses on a feature that is crucially emerging in the historiography of early modern philosophy and science, namely the complexity in the (...) production of knowledge. The book explores the applicability of this approach to a long-considered armchair philosopher, namely René Descartes, who is now more and more understood as a full-blown scientist, networker, and intellectual éminence grise rather than as the mere philosopher of the cogito, as well as the originator of different ‘Cartesianisms’ which encompassed many ideas and approaches for long captured by dichotomic historiographical categories as rationalism and empiricism, or speculative and experimental philosophy. The essays gathered in the volume aim to address the ways in which Descartes’s philosophy evolved and was progressively understood by scientists, philosophers, and intellectuals from different contexts and eras, either by considering direct interlocutors of Descartes such as Isaac Beeckman and Elisabeth of Bohemia, early modern thinkers who developed upon his ideas and on particular topics as Nicolas Malebranche or Thomas Willis, those who adapted his overall methodology in developing new systems of knowledge as Johannes Clauberg and Pierre-Sylvain Régis, and contemporary thinkers from continental and analytic traditions like Emanuele Severino and Peter Strawson. (shrink)

This essay enriches causal models capturing the propagation of prejudice, bias, and other aggregative social mechanisms, negative or positive. These explananda include the reinforcement of economic inequality, “mob-like” behavior, peer pressure, and the establishment of social norms. The stage is set by introducing various forms of redundant causation and discussing some difficulties with mainstream preemption. Next the main proposal extends current representations of aggregative social mechanisms in two respects. First, it is more nuanced, as it identifies three distinct kinds of (...) inferences: relevance of causes to effects, degree of redundancy of an effect, and the influence that causes exert on other causes. Second, it offers a quantitative—as opposed to merely qualitative—distinction between the causal contribution of preempting and preempted causes. (shrink)

This research explores the marginal stakeholder engagement and propensity to value cocreation in the fast-fashion industry by taking Generation Z consumers (GZCs) as observation unit and social networking sites (SNSs) as context of investigation. By undertaking 24 in-depth interviews with US and Italian GZCs, the study uncovers the main elements that influence their engagement generation on SNSs and highlights that at least four main paradoxes (PXs) exist in this scenario. Specifically, the interviewees reported that they do not trust those brands (...) that make them feel as marginal consumers (PX1) and that they are likely to be extremely loyal to those brands that actively take them into consideration in their activities on SNSs (PX2). In addition, although GZCs concerned about the environment, in most cases, they will buy repeatedly from fast-fashion brands for convenience reasons (PX3). Finally, social dimension of GZCs engagement appears to be influenced by their peers' preferences (PX4). This research is the first that explored GZCs by considering them under the lenses of stakeholder engagement and offering novel insights about common believes on this generation of consumers. Therefore, theoretical and managerial implications are discussed to advance current knowledge on GZCs and to help the development of new strategies to engage them on SNSs. (shrink)

Most of the existing natural language processing systems for legal texts are developed for the English language. Nevertheless, there are several application domains where multiple versions of the same documents are provided in different languages, especially inside the European Union. One notable example is given by Terms of Service (ToS). In this paper, we compare different approaches to the task of detecting potential unfair clauses in ToS across multiple languages. In particular, after developing an annotated corpus and a machine learning (...) classifier for English, we consider and compare several strategies to extend the system to other languages: building a novel corpus and training a novel machine learning system for each language, from scratch; projecting annotations across documents in different languages, to avoid the creation of novel corpora; translating training documents while keeping the original annotations; translating queries at prediction time and relying on the English system only. An extended experimental evaluation conducted on a large, original dataset indicates that the time-consuming task of re-building a novel annotated corpus for each language can often be avoided with no significant degradation in terms of performance. (shrink)

Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: A∪B holds at the current time instant w iff either B holds at w or there exists a time instant w' in the future at which B holds and such that A holds in all the time instants between the current one and ẃ. This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in (...) contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and ẃ. This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system N(LTL∇) for a linear-time logic LTL∇ endowed with the new history operator. We show that LTL∇ is equivalent to the linear temporal logic LTL with until, which follows by formalizing back and forth translations between the two logics. We also define an indirect translation from LTL∇ into LTL via temporal logics with past operators; such a result provides an upper bound to the problem of satisfiability for LTL∇ formulas. (shrink)

Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: A∪B holds at the current time instant w iff either B holds at w or there exists a time instant w' in the future at which B holds and such that A holds in all the time instants between the current one and ẃ. This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in (...) contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and ẃ. This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system N(LTL∇) for a linear-time logic LTL∇ endowed with the new history operator. We show that LTL∇ is equivalent to the linear temporal logic LTL with until, which follows by formalizing back and forth translations between the two logics. We also define an indirect translation from LTL∇ into LTL via temporal logics with past operators; such a result provides an upper bound to the problem of satisfiability for LTL∇ formulas. (shrink)

Eye movement desensitization and reprocessing therapy is a well-established therapeutic method to treat post-traumatic stress disorder. However, how EMDR exerts its therapeutic action has been studied in many types of research but still needs to be completely understood. This is in part due to limited knowledge of the neurobiological mechanisms underlying EMDR, and in part to our incomplete understanding of PTSD. In order to model PTSD, we used a biologically inspired computational model based on firing rate units, encompassing the cortex, (...) hippocampus, and amygdala. Through the modulation of its parameters, we fitted real data from patients treated with EMDR or classical exposure therapy. This allowed us to gain insights into PTSD mechanisms and to investigate how EMDR achieves trauma remission. (shrink)

The Test Your Memory is a brief self-administered, cognitive screening test, currently used in several settings. It requires minimal administrator supervision and the computation of the final test score takes approximately 2 min. We assessed the discrimination ability of the Italian version of the TYM in detecting Mild Cognitive Impairment in clinical setting. TYM-I was administered to 94 MCI patients and 134 healthy controls. The clinical diagnosis of MCI was considered as the gold standard. An extended formal neuropsychological test battery (...) was used to define MCI subtypes. Receiver Operating Characteristic analyses were conducted to find the optimal cut-off and measure discrimination ability of TYM-I in detecting MCI. TYM-I had a similar area under the curve point estimate as Mini Mental State Examination. A TYM-I score lower or equal to 36 was found to be optimal cut off to detect MCI. The TYM-I showed the highest discrimination ability among individuals aged more than 70 and high educational level. The amnestic MCI subtype patients, compared to non-amnestic MCI patients, had worse performance in recall, orientation and visuospatial abilities TYM-I subscores. The TYM-I is a valid screening test in detecting cognitive dysfunction, easily carried out in clinical practice. The TYM-I subscores may allow to identify amnestic and non-amnestic MCI subtypes. (shrink)

The investigation of visual categorization has recently been aided by the introduction of deep convolutional neural networks (CNNs), which achieve unprecedented accuracy in picture classification after extensive training. Even if the architecture of CNNs is inspired by the organization of the visual brain, the similarity between CNN and human visual processing remains unclear. Here, we investigated this issue by engaging humans and CNNs in a two‐class visual categorization task. To this end, pictures containing animals or vehicles were modified to contain (...) only low/high spatial frequency (HSF) information, or were scrambled in the phase of the spatial frequency spectrum. For all types of degradation, accuracy increased as degradation was reduced for both humans and CNNs; however, the thresholds for accurate categorization varied between humans and CNNs. More remarkable differences were observed for HSF information compared to the other two types of degradation, both in terms of overall accuracy and image‐level agreement between humans and CNNs. The difficulty with which the CNNs were shown to categorize high‐passed natural scenes was reduced by picture whitening, a procedure which is inspired by how visual systems process natural images. The results are discussed concerning the adaptation to regularities in the visual environment (scene statistics); if the visual characteristics of the environment are not learned by CNNs, their visual categorization may depend only on a subset of the visual information on which humans rely, for example, on low spatial frequency information. (shrink)

The use of writing or journaling as a tool toward healing is becoming increasingly accepted in the vernacular of healing litanies. Reference books, personal narratives, and research on the effects of writing on healing psychological discomfort are abundant. Heal Yourself with Writing, written by screenwriter Catherine Ann Jones, and published in 2013, won a Nautilus Book Award for 2014. The following review reflects a book that is a well-thought journey through the steps of intentional or focused writing for the express (...) purpose of moving from living from beliefs and thoughts that do not serve healthy wholeness or fullness of life, into living more freely and more authentically. (shrink)

This Perspective adapts the ViolEx Model, a framework validated in several clinical conditions, to better understand the role of expectations in the recovery and/or maintenance of musculoskeletal pain. Here, particular attention is given to the condition in which dysfunctional expectations are maintained despite no longer being supported by confirmatory evidence. While the ViolEx Model suggests that cognitive immunization strategies are responsible for the maintenance of dysfunctional expectations, we suggest that such phenomenon can also be understood from a Bayesian Brain perspective, (...) according to which the level of precision of the priors is the determinant factor accounting for the extent of priors’ updating. Importantly, this Perspective translates the theory behind these two frameworks into clinical suggestions. Precisely, it is argued that different strategies should be implemented when treating MSK pain patients, depending on the nature of their expectations. (shrink)

We present two eye-tracking experiments on the interpretation of sentences like “The tall girl is the only one that …,” which are ambiguous between the anaphoric and the exophoric interpretation. These interpretations differ in informativeness: in a positive context, the exophoric reading entails the anaphoric, while in a negative context the entailment pattern is reversed and the anaphoric reading is the strongest one. We tested whether adults rely on considerations about informativeness in solving the ambiguity. The results show that participants (...) interpreted one exophorically in both positive and negative contexts. Given these findings, we cast doubts on the idea that Informativeness plays a role in ambiguity resolution and proposes a Principle of Maximal Exploitation: When a context is provided, adults extend their domain of evaluation to include the whole scenario, independently from truth-conditional considerations about informativity and strength. (shrink)

Despite the recent proliferation of scientific, clinical, and narrative accounts of auditory verbal hallucinations, the phenomenology of voice hearing remains opaque and undertheorized. In this article, we outline an interdisciplinary approach to understanding hallucinatory experiences which seeks to demonstrate the value of the humanities and social sciences to advancing knowledge in clinical research and practice. We argue that an interdisciplinary approach to the phenomenology of AVH utilizes rigorous and context-appropriate methodologies to analyze a wider range of first-person accounts of AVH (...) at 3 contextual levels: cultural, social, and historical; experiential; and biographical. We go on to show that there are significant potential benefits for voice hearers, clinicians, and researchers. These include informing the development and refinement of subtypes of hallucinations within and across diagnostic categories; “front-loading” research in cognitive neuroscience; and suggesting new possibilities for therapeutic intervention. In conclusion, we argue that an interdisciplinary approach to the phenomenology of AVH can nourish the ethical core of scientific enquiry by challenging its interpretive paradigms, and offer voice hearers richer, potentially more empowering ways to make sense of their experiences. (shrink)