Riassunto: L’articolo di Caterina Villani intende mostrare come, per risolvere la “sfida dei concetti astratti”, all’ Embodied Cognition occorra concepire l’astrattezza da una prospettiva “multidimensionale”. Questo commento contiene due considerazioni. La prima riguarda il nesso logico tra la sfida dei concetti astratti e il cosiddetto “problema della generalizzazione”. La seconda discute alcune possibili tensioni dell’approccio multidimensionale stesso. Parole chiave: Concetti astratti; Concetti concreti; Embodied Cognition; Approccio multidimensionale; Generalizzazione Two Challenges for the Multidimensional Approach: Caterina Villani’s paper aims to show how, (...) in order to solve the “challenge of abstract concepts”, the paradigm of Embodied Cognition might have to conceive of abstractness from a “multidimensional” perspective. The present commentary includes two considerations. The first addresses the logical relationship that is supposed to hold between the challenge of abstract concepts and what is called the “generalization problem”. The second concerns possible tensions involved in the multidimensional approach itself. Keywords: Abstract Concepts; Concrete Concepts; Embidied Cognition; Multidimensional Approach; Generalization. (shrink)

Agostino Lupoli considers anew the skeptical elements in Hobbes’s Logica. At variance with Popkin’s approach, which he finds insufficient, and in the line with the late Arrigo Pacchi’s insights, which he intends to extend, he shows that the De corpore contains both more than traces of skepticism and a very engaged discussion of the thesis of Quod nihil scitur, the famous, but seldom read, book by Francis Sanchez, who taught philosophy and medicine in France in the early years of (...) seventeenth century. In line with nominalist logic, Sanchez makes a very sharp criticism of Aristotelian theory of the definition, whose ontological claims he criticizes. In accordance with this criticism is Hobbes’s strict nominalism, his tautological conception of the proposition as well as other elements in his logic. (shrink)

The young French philosopher, Maurice Blondel, was fascinated by the vinculum substantiale hypothesis proposed by the late Leibniz in his correspondence with Bartolomeo Des Bosses, a Jesuit from Collegio Romano. What did young Blondel see in this intricate hypothesis? An answer to the question can be found by making a thorough critical analysis of two manuscripts of Blondel: «Première notule» and «Nota complementare». The focal point of these texts is the substantiality of the concrete individual. Blondel compares this with some (...) passages from Aristotle's book Lambda in Metaphysics in his search for the «first substance» in its real and ontological sense. In fact, had Blondel known the twentieth century studies of book Zeta Metaphysics he could have found what he was seeking. (shrink)

Quale rapporto c'è tra una noticina di appena 30 righe e un'opera filosofica di quasi 500 pagine? A questa domanda, appassionante per chi s'interessa alla genesi delle opere del pensiero, Simone D'Agostino risponde esaminando il rapporto tra il capolavoro blondeliano del 1893, L'Action, e quella che si suole chiamare la "Première notule" del 5 novembre 1882. Il presente lavoro non è uno studio genetico del pensiero blondeliano, bensì una sua interpretazione sistematica da due punti focali e rispecchiantisi l'uno nell'altro. (...) Sotto questo aspetto, la ricerca di D'Agostino può definirsi unica nel suo genere. (shrink)

In the intellectual life of an architect, design and representation are inextricably connected terms, both in theoretical speculation and in operational practice. Indeed the drawn image is both a document of what is yet to be realized (and in this case it assumes a pre-figurative value), and a registration of what exists, in that way becoming an action purporting to document. In both cases, of course, the object – the building, already built or yet to build – will be or (...) is elsewhere, and it is made present to our eyes through drawing. The visionary action of Alberti’s lineamenti remains the focus of the designer’s entire operational life, but the new digital technologies pose unprecedented issues to the draftsman. One is autographism; yet another is the role that the illusory forms of mimetic rendition may take, relative to the objectivity of a concrete world that is increasingly removed from the field of knowledge and experience. The question remains open of how to allocate a strong linguistic identity to digital images: maybe they don’t dwell in the technological world – the same world that enables them to be realized – but, as proposed here, in the world of art. In this way, it might be possible to strengthen and to renew an old link between science and figurative expression, a link that lies, through the invention of perspective, at the very origins of the modern civilizations of the images. (shrink)

L’obiettivo del presente articolo è mostrare che, come sostentuto da Armstrong, il pensiero agostiniano si caratterizza per un’attitudine positiva nei confronti del mondo sensibile e del corpo. A tal fine, saranno analizzate le riflessioni di Agostino presenti nel primo libro del De Libero Arbitrio e nel decimo libro delle Confessioni. La presente indagine si articolerà in tre momenti. In primo luogo, esaminerò le analisi dell’Ipponate relative alla natura del peccato per mostrare che, per Agostino, agire bene è amare (...) i beni eterni. In seguito, traccerò le riflessioni agostiniane dedicate al peccato e all’ordine della natura umana per chiarire perché, per l’Ipponate, dominare le passioni è realizzare la propria natura. Infine, esaminerò le analisi agostiniane dedicate ai concetti di uti e frui per mostrare cosa l’Ipponate intenda per uso corretto dei beni temporali e per dominio della ragione sulle passioni. Sarà così possibile evidenziare che, per Agostino, contenere le passioni non significa astenersi da esse e allontanarsi dalle creature, ma utilizzare entrambe correttamente. Parole chiave: Agostino; peccato; mondo sensibile; uti; frui. (shrink)

BL-algebras are the Lindenbaum algebras for Hájek's Basic Logic, just as Boolean algebras correspond to the classical propositional calculus. The finite totally ordered BL-algebras are ordinal sums of MV-chains. We develop a natural duality, in the sense of Davey and Werner, for each subvariety generated by a finite BL-chain, and we use it to describe the injective and the weak injective members of these classes.

R. M. Friedberg demonstrated the existence of a recursive functional that agrees with no Banach-Mazur functional on the class of recursive functions. In this paper Friedberg's result is generalized to both α-recursive functionals and weak α-recursive functionals for all admissible ordinals α such that $\lambda , where α * is the Σ 1 -projectum of α and λ is the Σ 2 -cofinality of α. The theorem is also established for the metarecursive case, α = ω 1 , where α (...) * = λ = ω. (shrink)

The naïve idea of “size” for collections seems to obey both Aristotle’s Principle: “the whole is greater than its parts” and Cantor’s Principle: “1-to-1 correspondences preserve size”. Notoriously, Aristotle’s and Cantor’s principles are incompatible for infinite collections. Cantor’s theory of cardinalities weakens the former principle to “the part is not greater than the whole”, but the outcoming cardinal arithmetic is very unusual. It does not allow for inverse operations, and so there is no direct way of introducing infinitesimal numbers. Here (...) we maintain Aristotle’s principle, instead halving Cantor’s principle to “equinumerous collections are in 1–1 correspondence”. In this way we obtain a very nice arithmetic: in fact, our “numerosities” may be taken to be nonstandard integers. These numerosities appear naturally suited to sets of ordinals, but they depend, for generic sets, on a “labelling” of the universe by ordinals. The problem of finding a canonical way of attaching numerosities to all sets seems to be worth further investigation. (shrink)