The philosophical analysis of mathematical explanations concerns itself with two different, although connected, areas of investigation. The first area addresses the problem of whether mathematics can play an explanatory role in the natural and social sciences. The second deals with the problem of whether mathematical explanations occur within mathematics itself. Accordingly, this entry surveys the contributions to both areas, it shows their relevance to the history of philosophy and science, it articulates their connection, and points to the philosophical pay-offs to (...) be expected by deepening our understanding of the topic. (shrink)

An algebraization of the notion of topology has been proposed more than 70 years ago in a classical paper by McKinsey and Tarski, leading to an area of research still active today, with connections to algebra, geometry, logic and many applications, in particular, to modal logics. In McKinsey and Tarski’s setting the model theoretical notion of homomorphism does not correspond to the notion of continuity. We notice that the two notions correspond if instead we consider a preorder relation \( \sqsubseteq (...) \) defined by \(a \sqsubseteq b\) if _a_ is contained in the topological closure of _b_, for _a_, _b_ subsets of some topological space. A _specialization poset_ is a partially ordered set endowed with a further coarser preorder relation \( \sqsubseteq \). We show that every specialization poset can be embedded in the specialization poset naturally associated to some topological space, where the order relation corresponds to set-theoretical inclusion. Specialization semilattices are defined in an analogous way and the corresponding embedding theorem is proved. Specialization semilattices have the amalgamation property. Some basic topological facts and notions are recovered in this apparently very weak setting. The interest of these structures arises from the fact that they also occur in many rather disparate contexts, even far removed from topology. (shrink)

Learning to perceive is faced with a classical paradox: if understanding is required for perception, how can we learn to perceive something new, something we do not yet understand? According to the sensorimotor approach, perception involves mastery of regular sensorimotor co-variations that depend on the agent and the environment, also known as the “laws” of sensorimotor contingencies (SMCs). In this sense, perception involves enacting relevant sensorimotor skills in each situation. It is important for this proposal that such skills can be (...) learned and refined with experience and yet up to this date, the sensorimotor approach has had no explicit theory of perceptual learning. The situation is made more complex if we acknowledge the open-ended nature of human learning. In this paper we propose Piaget’s theory of equilibration as a potential candidate to fulfill this role. This theory highlights the importance of intrinsic sensorimotor norms, in terms of the closure of sensorimotor schemes. It also explains how the equilibration of a sensorimotor organization faced with novelty or breakdowns proceeds by re-shaping pre-existing structures in coupling with dynamical regularities of the world. This way learning to perceive is guided by the equilibration of emerging forms of skillful coping with the world. We demonstrate the compatibility between Piaget’s theory and the sensorimotor approach by providing a dynamical formalization of equilibration to give an explicit micro-genetic account of sensorimotor learning and, by extension, of how we learn to perceive. This allows us to draw important lessons in the form of general principles for open-ended sensorimotor learning, including the need for an intrinsic normative evaluation by the agent itself. We also explore implications of our micro-genetic account at the personal level. (shrink)

Martin Heidegger and Emanuele Severino reflected on the meaning of technology more than anyone else in the twentieth century. Their philosophies are irreconcilable. They converge on this simple recognition and its implications: techno‐science dominates our time. But they disagree even on the interpretation of this domination. Exploring this disagreement will help us understand the leading dynamics of our civilization. Therefore, the intention in this paper is to unveil, for English speakers, the value of Severino’s philosophy in relation to Heidegger and (...) the meaning technology. We will see that, ultimately, their disagreement concerns the originary truth of Being and has repercussions on how they conceptualize technology and the possibility of redemption from it. Heidegger indicated the letting‐be of beings in their freedom as the possible path beyond technology. Severino saw Heidegger’s indication as destined to remain trapped in technology itself. If we understand why this was so – from Severino’s point of view – this may open a new path for us: the path of day, the path that may truly lead beyond technology. The aim of this paper is, finally, to indicate one reason why delving into Severino’s works is truly worthwhile: if it is possible for the truth to unveil itself beyond willing – where Heidegger couldn’t see – then Severino’s works may the place where this possibility appears in coherent conceptual form. (shrink)

Il presente intervento costituisce soltanto un breve introduzione, come richiamo delle ragioni che hanno portato a questo Exploratory Workshop, nel ricordo delle riunioni che lo hanno preceduto sino all’incontro qui a Bologna il 15 febbraio 2011 e a quello di Nijmegen nell’autunno del 2011.1 Non si tratta infatti di un convegno conclusivo ma soltanto di una tappa del cammino che il gruppo di lavoro si era prefisso. Il tema formulato dall’inizio era quello di studiare il formarsi delle identità collettive e (...) dei modelli di vita nel mondo rimasto fedele alla Chiesa di Roma, nel periodo della Riforma e della frattura religiosa sino al definirsi definitivo degli schieramenti confessionali: “Pluralism and Identity.. (shrink)

It is usually maintained that a subject with manifestly contradictory beliefs is irrational. How can we account, then, for the intuitive rationality of dialetheists, who believe that some manifest contradictions are true? My paper aims to answer this question. Its ultimate goal is to determine a characterization of (or rather a constraint for) rational belief approvable by both the theorists of Dialetheism and its opponents. In order to achieve this goal, a two-step strategy will be adopted. First, a characterization of (...) rational belief applicable to non-dialetheist believers will be determined; this characterization will involve the semantic apparatus of Nathan Salmon’s Millian Russellianism but will get rid of the problematic and obscure notion of mode of presentation (guise in his own terminology), replacing it with a couple of novel devices, belief subsystems and cognitive coordination. Second, using ideas from Graham Priest, the leading proponent of Dialetheism, such a characterization will be modified, so as to devise a new one able to account for the intuitive rationality of both dialetheist and non-dialetheist believers. (shrink)

In the sentence “Tom sits,” the name distinguishes Tom from anyone else, whereas the predicate assimilates Tom, Theaetetus, and anyone else to whom the predicate applies. The name marks out its bearer and the predicate groups together what it applies to. On that ground, his name is used to trace back Tom, and the predi- cate is used to describe and classify what it applies to. In both cases, the semantic link is a direct link between expressions and particulars. Here, (...) I will explore the workings of predicative names along the direction just hinted at. The analysis of predication has been less central to philosophical investigation than that of referen- tial expressions. Some problems have concerned the unity of the sentence—what makes us understand “The baby cries” as a sentence rather than a list of words? Other problems have been what a predicate was taken to stand for, properties and relations, and the understanding of either at the ontological level. If a predicate refers to a property or a relation, yet predication, which is central to our understand- ing of predicates, applies it to one or more particulars. On the background hinted at, these problems might be differently viewed. (shrink)

Il volume, frutto della rielaborazione della tesi di dottorato, costituisce una retrospettiva sull'antropologia filosofica moderna attraverso due dei suoi massimi esponenti. Più specificamente mostra come la mitologia, la filosofia della storia e del linguaggio, la concezione vichiana dell'uomo abbiano avuto come costante punto di riferimento la psicologia d'impostazione cartesiana di Malebranche.

In the literature on the Moral Limits of the Markets, Kant’s moral philosophy is often employed to assess the amoral or immoral nature of the commercial sphere. Markets and morality are antipodes since the instrumentality of market transactions excludes or undermines moral values. The kingdom of ends, where everything has either a price or a dignity, closes the door to market logic. The present paper challenges this view, which is also endorsed by business ethics authors advocating for Moral Purism. I (...) will show that Kant imagined a market within the Kingdom of Ends where everyone pursues their own aims while assisting others in pursuing theirs. This model, built on the universalization of the maxim of mutual assistance and the duty of honoring the spirit of mutually beneficial contracts, can be employed to judge the morality of real (empirical) market transactions. (shrink)

The evidence of the phenomenon for which, in galaxies, the gravitating mass is distributed differently than the luminous mass, increases as new data become available. Furthermore, this discrepancy is well structured and it depends on the magnitude and the compactness of the galaxy and on the radius, in units of its luminous size \, where the measure is performed. For the disk systems with \ all this leads to an amazing scenario, revealed by the investigation of individual and coadded rotation (...) curves, according to which, the circular velocity follows, from their centers out to their virial radii, an universal profile \\) function only of the properties of the luminous mass component. Moreover, from the Universal Rotation Curve, so as from many individual high quality RCs, we discover that, in the innermost regions of galaxies, the DM halo density profiles are very shallow. Finally, the disk mass, the central halo density and its core radius, come out all related to each other and to two properties of the distribution of light in galaxies: the luminosity and the compactness. This phenomenology, being absent in the simplest \ Cosmology scenario, poses serious challenges to the latter or, alternatively, it requires a substantial and tuned involvement of baryons in the formation of the galactic halos. On the other side, the URC helps to explain the two-accelerations relationship found by McGaugh et al., in terms of only well known astrophysical processes, acting in a standard DM halos + luminous disks scenario. (shrink)

Recent developments in generalized probability theory have renewed a debate about whether regularity (i.e., the constraint that only logical contradictions get assigned probability 0) should be a necessary feature of both chances and credences. Crucial to this debate, however, are some mathematical facts regarding the interplay between the existence of regular generalized probability measures and various cardinality assumptions. We improve on several known results in the literature regarding the existence of regular generalized probability measures. In particular, we give necessary and (...) sufficient conditions for the existence of regular generalized probability measures defined on the whole powerset of any sample space. (shrink)

This article explores the concept of landscape through the lens of performativity, challenging the traditional visual-centric understanding rooted in Western art and culture but without denying the visual and representational character of landscape. It examines the evolution of landscape representation, from its origins in linear perspective and Cartesian dualism to contemporary approaches that integrate performative practices. The analysis highlights the dialectical tension between visual representation and immersive, multisensory experiences, arguing for a more integrated view that acknowledges the performative aspects of (...) the visual. By re-evaluating the role of distance, vision, and representation, the article advocates for a nuanced understanding of landscape that balances the visual with embodied practices, ultimately proposing that landscape should be seen as a dynamic interplay between seeing and performing. (shrink)

This essay investigates the influence of the films of David Lynch on David Foster Wallace’s major novel Infinite Jest. It is organized in two sections. Section one illustrates Wallace’s views on what real art should be, as they are expressed in his two famous “manifestos,” and proceeds to read the essay “David Lynch Keeps His Head” in relation to the manifestos in order to demonstrate that Lynch’s influence on Wallace’s thought has not yet been fully grasped. Section two delves into (...) Infinite Jest to examine textual proof of the Wallace-Lynch connection, both in content and form. Content-wise, convergences are proven to permeate both authors’ interest in theories of consciousness, typified in themes such as: psychoanalysis, especially the Oedipus Complex; self-deception; the Sartrean “look;” the corporeal subject and the phenomenological distinction between objective body and lived body. Form-wise, the following narrative items are mapped: Lynch’s surrealism, recognizable in paradigmatic scenes from Infinite Jest; the character-idea, as both authors embody abstract ideas in characters; and a formal commitment to “an anti-teleological spirit.” Finally, the analysis takes into consideration Lynch’s films produced prior or during the writing of Infinite Jest, and exclusively those Wallace expressed direct admiration for, namely: Eraserhead (1977), The Elephant Man (1980), Blue Velvet (1986), and Lost Highway (1997). (shrink)

Speaker’s meaning is the act at the core of meaning shift, where meaning can be the very act or its output. What are its conditions, which intentions direct it? What’s its mechanics? I will give a first answer to the first question. Then, I will discuss the mechanics of speaker’s meaning, as well as meaningful links different from speaker’s meaning. This will bring me to surmise a second answer to the first question. Along the way, I will compare the act (...) of meaning with other acts. In closing, I will try a limited elucidation of the notion of intention, which I use throughout. On these issues there is the conspicuous tradition of studies, originating from the late Paul Grice, to confront us with. Rather naturally, I will move from it. But I am interested in the notion of speaker’s meaning and its place in an analysis of meaning, and not in that tradition as such. The notion of speaker’s meaning, I think, is relevant even for those who do not subscribe to a Gricean approach to meaning, as I don’t. (shrink)

Italian Abstract: Mosca, Ruffini ed Einaudi vennero da molti riconosciuti come “Maestri di libertà”, soprattutto in virtù della loro strenua difesa della libertà durante il consolidamento del regime fascista. In questo articolo miro a ricostruire l’idea di libertà che emerse nelle loro riflessioni in quel torno di tempo. Mostrerò come, al di là delle differenze tra la loro riflessione politica, giuridica ed economica, l’idea di libertà si sostanzi nell’intreccio tra le istituzioni fondamentali del liberalismo ottocentesco: mercato e società civile, opinione (...) pubblica e diritti di libertà. -/- English Abstract: Mosca, Ruffini and Einaudi were variously identified as "Masters of Freedom", particularly in light of their strong defense of freedom during the consolidation of the fascist regime. In this article I aim to reconstruct the idea of freedom that emerged in their reflections during that period. I will show how, beyond the differences between their political, legal and economic approach, the idea of freedom is entailed in the intertwining between the fundamental institutions of nineteenth-century liberalism: market and civil society, public opinion and rights of freedom. (shrink)