This paper exhibits a general and uniform method to prove axiomatic completeness for certain modal fixpoint logics. Given a set Γ of modal formulas of the form γ, where x occurs only positively in γ, we obtain the flat modal fixpoint language by adding to the language of polymodal logic a connective γ for each γΓ. The term γ is meant to be interpreted as the least fixed point of the functional interpretation of the term γ. We consider the following (...) problem: given Γ, construct an axiom system which is sound and complete with respect to the concrete interpretation of the language on Kripke structures. We prove two results that solve this problem.First, let be the logic obtained from the basic polymodal by adding a Kozen–Park style fixpoint axiom and a least fixpoint rule, for each fixpoint connective γ. Provided that each indexing formula γ satisfies a certain syntactic criterion, we prove this axiom system to be complete.Second, addressing the general case, we prove the soundness and completeness of an extension of . This extension is obtained via an effective procedure that, given an indexing formula γ as input, returns a finite set of axioms and derivation rules for γ, of size bounded by the length of γ. Thus the axiom system is finite whenever Γ is finite. (shrink)

A μ-algebra is a model of a first-order theory that is an extension of the theory of bounded lattices, that comes with pairs of terms where μx.f is axiomatized as the least prefixed point of f, whose axioms are equations or equational implications.Standard μ-algebras are complete meaning that their lattice reduct is a complete lattice. We prove that any nontrivial quasivariety of μ-algebras contains a μ-algebra that has no embedding into a complete μ-algebra.We then focus on modal μ-algebras, i.e. algebraic (...) models of the propositional modal μ-calculus. We prove that free modal μ-algebras satisfy a condition–reminiscent of Whitman’s condition for free lattices–which allows us to prove that modal operators are adjoints on free modal μ-algebras, least prefixed points of Σ1-operations satisfy the constructive relation μx.f=logical and operatorn≥0fn. These properties imply the following statement: the MacNeille–Dedekind completion of a free modal μ-algebra is a complete modal μ-algebra and moreover the canonical embedding preserves all the operations in the class image of the fixed point alternation hierarchy. (shrink)

Parity games are combinatorial representations of closed Boolean μ-terms. By adding to them draw positions, they have been organized by Arnold and Santocanale [3] and [27] into a μ-calculus whose standard interpretation is over the class of all complete lattices. As done by Berwanger et al. [8] and [9] for the propositional modal μ-calculus, it is possible to classify parity games into levels of a hierarchy according to the number of fixed-point variables. We ask whether this hierarchy collapses w.r.t. (...) the standard interpretation. We answer this question negatively by providing, for each n≥1, a parity game Gn with these properties: it unravels to a μ-term built up with n fixed-point variables, it is not semantically equivalent to any game with strictly less than n−2 fixed-point variables. (shrink)

In this paper we compare the strategies applied by two successful biological components of the ecosystem, the viruses and the human beings, to interact with the environment. Viruses have had and still exert deep and vast actions on the ecosystem especially at the genome level of most of its biotic components. We discuss on the importance of the human being as contraptions maker in particular of robots, hence of machines capable of automatically carrying out complex series of actions. Beside the (...) relevance of designing and assembling these contraptions, it is of basic importance the goal for which they are assembled and future scenarios of their possible impact on the ecosystem. We can’t procrastinate the development and implementation of a highly inspired and stringent “ethical code” for human beings and humanoid robots because it will be a crucial aspect for the wellbeing of the mankind and of the entire ecosystem. (shrink)

The article deals with some implications of radical uncertainty for participatory democracy, and more precisely for Participatory Technology Assessment. Two main forms of PTA are discussed. One is aimed at involving lay citizens and highlighting public opinion. The other is addressed to stakeholder groups and organisations, not only in terms of interest mediation but also of inclusion of their insight into a problem. Radical uncertainty makes 'intractable' many environmental and technological issues and brings into question traditional and new approaches to (...) policymaking. Its consequences are explored from the viewpoint of new science, deliberative democracy, and network governance. Radical uncertainty calls for a rethinking of the aims of public deliberation, and a reinterpretation of the divide between opinion- and position-oriented PTA. To look for a public opinion, understood as a shared principled view, can prove misleading, as can thinking of stakeholder participatory arrangements in the usual way. When facts and values overlap, and are deeply controversial, the only opportunity for mutual understanding may be to look for practical, 'local' answers, based on different positional insights. Moreover, radical uncertainty also affects interest determination and pursuit, and may enhance the opportunity of joint, inclusive, non-strategic issue definition and solution-devising. This vision of public deliberation is consistent with the idea of network governance. However, fragmentation can affect the effectiveness and legitimacy of participatory policies. Trying to handle fragmentation from the top, as many suggest, is unlikely to be successful. A more promising endeavour is to foster deliberative settings which, although positioned at the level of 'local' and often contingent networks and commonalities, are open to include 'Otherness' – other contexts, other problem definitions, other concerns. (shrink)

The first part of this paper aims to highlight the analogies between Schutz’s vision of the natural attitude and Wittgenstein’s vision of a phenomenon that concerns the same problematic field, i.e. certainty, the belief of common sense that is free of all doubt, that the world “out there” is as it appears, absolutely real. These certainties form the basis, the foundation of language games and therefore of knowledge in general and in its entirety. This foundation is unfounded and yet indispensable. (...) The second part of the paper examines an important topic analysed by Wittgenstein, related to the aforementioned problem: the language transposition of pre-predicative, pre-reflective and non-propositional certainties, the cornerstones of which are “hinge propositions”, whose hybrid nature can be identified in the shift from empirical propositions to grammatical rules. (shrink)

Simple assumptions represent a decisive reason to prefer one theory to another in everyday scientific praxis. But this praxis has little philosophical justification, since there exist many notions of simplicity, and those that can be defined precisely strongly depend on the language in which the theory is formulated. The language dependence is a natural feature—to some extent—but it is also believed to be a fatal problem, because, according to a common general argument, the simplicity of a theory is always trivial (...) in a suitably chosen language. But, this trivialization argument is typically either applied to toy-models of scientific theories or applied with little regard for the empirical content of the theory. This paper shows that the trivialization argument fails, when one considers realistic theories and requires their empirical content to be preserved . In fact, the concepts that enable a very simple formulation, are not necessarily measurable, in general. Moreover, the inspection of a theory describing a chaotic billiard shows that precisely those concepts that naturally make the theory extremely simple are provably not measurable. This suggests that—whenever a theory possesses sufficiently complex consequences—the constraint of measurability prevents too simple formulations in any language. This explains why the scientists often regard their assessments of simplicity as largely unambiguous. In order to reveal a cultural bias in the scientists’ assessment, one should explicitly identify different characterizations of simplicity of the assumptions that lead to different theory selections. General arguments are not sufficient. (shrink)

The relentless exploitation of the earth's resources and technologys boundless growth are a matter of urgent concern. When did this race towards the limitless begin? The Greeks, who shaped the basis of Western thinking, lived in mortal fear of humanity's hidden hunger for the infinite and referred to it as hubris, the one true sin in their moral code. Whoever desired or possessed too much was implacably punished by nemesis, yet the Greeks themselves were to pioneer an unprecedented level of (...) ambition that began to reverse that tabu. If it is true that no culture can truly repudiate its origins, and that gods who are no longer potent can vanish but still leave behind a body of myth which coninues to live and assert itself in modernized garb, then our concern with the limits of growth reflects something more than an awareness of new technological problems - it also brings to light a psychic wound a a feeling of guilt which are infinitely more ancient. (shrink)

Game-based approaches are emerging in many fields, such as education, social sciences, marketing and government. Most studies debate its role in consolidating learning, guided by both internal and external rewards. These approaches are also being applied in rehabilitation, where patients must undergo a re-learning process of motor gestures after an injury to a body structure. In physiotherapy, much importance is given to analytical-functional movement aspects, but less to the recovery of the complete experience, including motivation, perception, and emotional experience of (...) the patient during the process. The aim of this narrative review is to investigate the role of subjective experience in the application of gamification in physiotherapy, considering the added value it provides to recovery by involving neural structures, not just motor functions. By analyzing the most investigated aspects in using gamification in rehabilitation, we will outline the primary methods of investigation into the engagement and emotions involved in the process. Through a selection of scientific articles found on main databases, we identified articles investigating the patient’s experience. The analysis of these articles was based on aspects related to the recovery of movement, the technology used, as well as the methods of investigation and collection of qualitative data regarding the emotions and perceptions of patients during the gamification experience. The results are divided into two primary topics. Overall, this review supports the idea that gamification could represent a rehabilitation approach integrating physiotherapy, more suitable for the final stages of recovery, such as returning to work or sports. (shrink)

Luigi Giussani, a high school religion teacher throughout the 1950s and 1960s, grounded his teachings in the vast body of experience to be found in Christianity's two-thousand-year history. He told his students, “I'm not here to make you adopt the ideas I will give you as your own, but to teach you a method for judging the things I will say.” Throughout his life, education was one of Giussani's primary intellectual interests. He believed that effective education required an adequate (...) background in the Christian tradition, presented within a lived experience that underscored the capacity of the faith to answer universal questions. What he proposed was a process that allowed one to sift through tradition, critically examining it and comparing it against the ultimate criteria for judgment: the desires of the heart. In Giussani's view, the primary concern was to “educate the human heart as God made it.” In The Risk of Education he states that fear leads students to associate this process of criticism with negativity or doubt. Yet, without an education in criticism, students cannot develop conviction. At a time when young people are abandoning the church and questioning the value of faith, Giussani's method of judging and verifying Christianity as an experience seems a necessary intervention. In The Risk of Education he argues that, ultimately, education and the Christian message reveal themselves through human freedom. (shrink)

The point of view advocated, in the last ten years, by quantum probability about the foundations of quantum mechanics, is based on the investigation of the mathematical consequences of a deep and elementary idea developed by the founding fathers of quantum mechanics and accepted nowadays as a truism by most physicists, namely: one should be careful when applying the rules derived from the experience of macroscopic physics to experiments which are mutually incompatible in the sense of quantum mechanics.

_Abstract_: In this paper, I will examine the Goldstein-Cassirer approach to neuropathology to determine its current potential for yielding valuable insights. To this end, I will reconstruct the philosophical and theoretical underpinnings of such a standpoint in the first four sections. What will emerge is that it entails a definition of pathology as the loss of balance in the adaption of human beings to the environment, leading to a lack of proclivity to categorical behaviour and symbolic performances. Furthermore, we will (...) see that there are behavioural alterations which are not related to the locus of lesions. In the fifth section, I will compare and contrast the holistic stances with current research in neuropsychology. The sixth section is dedicated to conclusive remarks. _Keywords_: Psychopathology; Neuropathology; Ernst Cassirer; Kurt Goldstein; Holism _ La mente ordinatrice. La concezione di Goldstein e Cassirer della neuropatologia e la sua rilevanza oggi _ _Riassunto_: In questo articolo intendo analizzare l’approccio Goldstein-Cassirer alla neuropatologia per comprendere se esso può rivelarsi ancora utile alla luce delle ricerche attuali. A tal fine, ne ricostruirò le basi filosofiche e teoriche nei primi tre paragrafi. Scopriremo che esso implica una definizione di patologia come perdita di equilibrio nell’adattamento degli esseri umani all’ambiente, a seguito della quale viene a mancare la naturale tendenza verso il “comportamento categoriale” e le prestazioni simboliche. Vedremo, inoltre, che vi sono alterazioni del comportamento non collegabili al sito delle lesioni. Nel quinto paragrafo, metterò a confronto le istanze olistiche con le ricerche contemporanee nel campo della neuropsicologia. Il sesto paragrafo contiene le considerazioni conclusive. _Parole chiave_: Psicopatologia; Neuropatologia; Ernst Cassirer; Kurt Goldstein; Olismo. (shrink)

Gli emarginati diventano protagonisti di una storia alternativa all'epica cavalleresca e aristocratica.

La piega critica del realismo filosofico di Tommaso rivela una realtà inaferrabile dischiudendo al soggetto nuove possibilità conoscitive, che ci restituiscono un Tommaso un po' meno tomista.

Una proposta di lettura ";trascendentalista"; del ";De ente"; di Tommaso d'Aquino. Il venir meno dei presupposti per fondare un rapporto forte tra discorso e realtà.

1. Critica de capire e altri scritti. 2. Scritti kantiani. 3. L'analitica trascendentale. 4. Il problema della scienza e il giudizio storico.

Nel mio articolo propongo una lettura dei §§ 79-84 della Critica del Giudizio, parte della sezione Metodologia del Giudizio teleologico. Dapprima mi interrogo sul significato di una Methodenlehre del Giudizio teleologico, che rintraccio in un’attività metariflessiva del Giudizio; procedo poi ad una lettura analitica del testo nelle sue varie articolazioni, nella quale passo in rassegna le questioni attinenti alla specificità dello statuto epistemologico della teleologia, alla possibile convivenza tra finalismo e meccanicismo nella scienza della natura, all’origine della vita, allo scopo (...) ultimo della natura e allo scopo finale della creazione; approdo, infine, ad un’interpretazione per cui l’intera teleologia rationis humanae, che si estende dalla teleologia naturale alla teleologia morale passando per l’antropologia e per la filosofia della storia, viene in questa sezione riarticolata intorno ad un nuovo fulcro concettuale di livello trascendentale, che può garantire l’effettivo collegamento tra queste diverse parti della filosofia proprio perché esso non si esercita in forma di dominio legislativo, ma in forma di riflessione sul molteplice empirico e sulla causalità teleologica propria dell’uomo. (shrink)

In the following paper, the author will try to test the meaning of the transcendental approach in respect of the inner changes implied by the idea of quantum gravity. He will firstly describe the basic methodological Kant’s aim, viz. the grounding of a meta-science of physics as the a priori corpus of physical knowledge. After that, he will take into account the problematic physical and philosophical relationship between the theory of relativity and the quantum mechanics; in showing how the elementary (...) ontological and epistemological assumptions of experience result to be changed within them, he will also show the further modifications occurred in the development of the loop quantum gravity. He will particularly focus on the tough problem of the relationship space-matter, in order to settle the decisive question about the possibility of keeping a transcendental approach in the light of quantum gravity. He will positively answer by recalling Cassirer’s theory of the invariants of experience, although he will also add some problematic issues arising from the new physical context. (shrink)

The paper surveys the possibility of keeping a neo-Kantian approach in the face of Loop Quantum Gravity. Together with a preliminary analysis of Cassirer’s re-interpretation of Kantian philosophy that allowed him to harmonize the a priori cognitions with the theory of relativity and quantum mechanics, it will focus on the distinction between constitutive and regulativea priori. In this way, the paper will suggest that despite Rovelli’s refutation of Kant’s interpretation of space and time, he seems, at least implicitly, to hold (...) to a couple of neo-Kantian assumptions: the usage of constitutivea priori principlessuch as granularity, indeterminism and partially relation, and the claim for functionalism as a rule in ordering the ‘appearances’. (shrink)

Following the murder of George Floyd, the Black Lives Matter-movement (BLM) took to the streets to protest against institutional racism. In these protests, one could often hear the slogan “No Justice, No Peace”. Drawing on legal theory, speech act theory and phenomenology, this article investigates what kind of justice and peace are called upon and how the slogan functions as a claim addressed to the legal order. First, the article shows that the rule of law provides a comprehensive normative framework (...) to evaluate what went wrong during the arrest of George Floyd. Second, the article maintains that the slogan should be understood as a passionate utterance in the sense of Stanley Cavell. Finally, drawing on a responsive phenomenology of legal order inspired by the work of Bernhard Waldenfels, the article concludes that the slogan is an extraordinary claim questioning the legal order, showing its contingent origins. (shrink)