The problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo-Fraenkel which is already complete with respect to the ∀*∀ class of sentences. NP-hardness and NP-completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.

As is well-known, the Bernays-Schönfinkel-Ramsey class of all prenex ∃*∀* -sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are ∈ and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability problem for (...) the BSR class is proved by following a purely semantic approach, the remaining part of the decidability result being postponed to a forthcoming paper. (shrink)

Being able to state the principles which lie deepest in the foundations of mathematics by sentences in three variables is crucially important for a satisfactory equational rendering of set theories along the lines proposed by Alfred Tarski and Steven Givant in their monograph of 1987. The main achievement of this paper is the proof that the 'kernel' set theory whose postulates are extensionality. (E), and single-element adjunction and removal. (W) and (L), cannot be axiomatized by means of three-variable sentences. This (...) highlights a sharp edge to be crossed in order to attain an 'algebraization' of Set Theory. Indeed, one easily shows that the theory which results from the said kernel by addition of the null set axiom, (N), is in its entirety expressible in three variables. (shrink)

This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth problem. (...) The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic. (shrink)

As proved recently, the satisfaction problem for all prenex formulae in the set-theoretic Bernays-Shönfinkel-Ramsey class is semi-decidable over von Neumann's cumulative hierarchy. Here that semi-decidability result is strengthened into a decidability result for the same collection of formulae.

One 1120 pages volume, with 4000 entries covering - Western philosophy: authors, schools, concepts and terminology; - religions, cultural anthropology, eastern philosophies; - Psychology and psychoanalysis; - linguistics and semiotics; - sociology and political theory.

L'A. analizza un tema fondamentale nella «querelle» sui futuri contingenti del sec. XIV, cioè il concetto di potentia absoluta di Dio. Il tema fu interpretato secondo due opposte visioni: l'interpetazione «operativa» intendeva la potentia absoluta come un potere straordinario ed «eccezionale», mentre l'interpretazione «logica», sostenuta ad esempio da Bradwardine, riteneva la potentia absoluta una mera descrizione di possibilità teoriche. L'analisi di questo problema è condotta in base alle teorie di Giovanni Buckingham e di Giovanni di Mirecourt, con riferimenti (...) alla posizione di Bradwardine, Duns Scoto, Guglielmo di Ockham e Adam Wodeham. (shrink)

1-2. Carteggio Gentile-Jaja -- 3-7. Lettere a Benedetto Croce -- 8. Carteggio Gentile-D'Ancona -- 9. Carteggio Gentile-Omodeo -- 11. Carteggio Gentile-Chiavacci -- 12. Carteggio Gentile-Pintor -- 13. Carteggio Gentile-Calogero (1926-1942) -- 14. Carteggio Gentile-Donati.

In lieu of an abstract, here is a brief excerpt of the content:Notes and Discussions AGOSTINO NIFO'S EARLY VIEWS ON IMMORTALITY Various historians of Renaissance philosophy have taken some notice of the prolific author and important philosopher of the late 15th and early 16th centuries, Agostino Nifo (1470-1538), x but no one has yet studied his writings in a methodical and exhaustive fashion. 2 He not only published philosophical works in logic, physics, psychology and metaphysics, but he also authored treatises (...) on humanist topics? Recent scholars have tended to concentrate their attention on his psychological doctrines, no doubt because he was one of the major opponents of Pietro Pomponazzi (1462-1525) during the immortality controversy.4 Nifo published his De Immortalitate Animae in 1518 as a reply to the De lmmortalitate Ardmae, On the year of Nifo)s birth, see Bruno Nardi, Saggi sull'aristotelismo padovano dal secolo xav al xvl ('Florence, 1958), p. 284, n. 8. There is contemporary evidence that he died on January 18, 1538. See Bartolommeo Capasso, "Le cronache de li antiqui ri del regno di Napoli di D. Gaspare Fuscolill0," Archivio storico per le province napoletane, I (1876), p. 538. The standard bio-bibliography still remains Pasquale Tuozzi, "Agostino Nifo 9 le sue opere," Atti e memorie della R. Accademia di Scienze, Lettere ed Arti in Padova, Nuova scrie, XX (Padua, 1904), pp. 63-86. But see also Giuseppr Tommasino, Tra umanisti e filosoft (Maddaloni, 1921), Porte I, pp. 123-147; and Edward P. Mahoney, "A Note on Agostino Nifo," Philological Quarterly (forthcoming). z See Franeeseo Fiorentino, Pietro Pomponazzi; Studi storici su la scuola bolognese e padovana del secolo xvI (Florence, 1868); Carlo Giacon, La seconda scolastica: 1 grandi commentatori di San Tommaso (Milan, 1944); Etienne Gilson, "L'affaire de l'immortalit6 de l'fime ~t Venise at* d6but du xvIe si~ele," in Umanesirno europeo e uraanesimo veneziano, ed. Vittore Branea (Florence, 1963), pp. 31-61; Miehele Giorgiantonio, "Un nostro filosofo dimentieato dcl '400 (Luea Prassicio e Agostino Nifo)," Sophia, XVI (1948), pp. 212-214 and 303-312; Bruno Nardi, Saggi sulraristotelismo padovano dal secolo x]v al xvI (Florence, 1958); idem, Sigieri di Brabante nel pensiero del Rinascimento Italiano (Rome, 1945); Giovanni di NapoH, L'immortalitd delranima nel Rinascimento ('Turin, 1963); John Herman Randall, Jr., The School of Padua and the Emergence of Modern Science (Padua, 1961); Wilhelm Risse, Die Logik der Neuzeit, I (Stuttgart, 1964); Eugenio Garin, La cultura [ilosofica del Rinascimento Italiano (Florence, 1961); idem, Storia della filosofia italiana, II (Turin, 1966). See Nifo's De Armorum Literarumque Comparatione Commentariolus (Naples, 1526); De Pulchro et Amore (Rome, 1531); De Re Aulica (Naples, 1534); and Prima Pars Opusculorum (Venice, 1535). The second of these works has been studied by Jules Houdoy, La beaut~ des femmes dans la litt#rature et darts rart du xII" au xvIe si~cle; Analyse du livre de A. Niphus du Beau et de l'amour (Paris, 1876). 4 For recent discussion of the immortality controversy, see Etienne Gilson, "Autour de Pomponazzi, ProbMmatique de l'immortalit~ de l'~me en Italic au d~but du xvIe si~.cle," Archives d'histoire doctrinale et litt~raire du moyen dge, Ann6e 1961, pp. 163-179; Giovanni di Napoli, op. cit., especially pp. 227-338; Paul Oskar Kristeller, Eight Philosophers of the Italian Renaissance (Stanford, 1964), pp. 72-90; Bruno Nardi, Studi su Pietro Pomponazzi (Florence, 1965); Martin Pine, "Pomponazzi and the Problem of 'Double Truth'," Journal ot the History of Ideas, XXIX (1968), pp. 163-176; Harold Shulsky, "Paduan Epistemology and the Doctrine of the One Mind," lournal of the History of Philosophy, VI (1968), pp. 341-361. [451] 452 HISTORY OF PHILOSOPHY (1516) of Pomponazzi, who had argued that personal immortality cannot be philosophically demonstrated, s But while these scholars correctly point out that Nifo abandoned an Averroist interpretation of Aristotle concerning the unity of the intellect and the immortality of the soul for the position which they assume to be Thomistic, they are not precise as to just when Nile made the shift.6 They have not observed that in his first two printed works, namely, the commentary on Averroes' Destructio Destructionum (1497) and the early commentary on the De Anima (1503), Nifo explicitly accepts Averroes as the... (shrink)

We propose a view of embodied representations that is alternative to both symbolic/linguistic approaches and purely sensorimotor views of cognition, and can account for procedural and declarative knowledge manipulation. In accordance with recent evidence in cognitive neuroscience and psychology, we argue that anticipatory and simulative mechanisms, which arose during evolution for action control and not for cognition, determined the first form of representational content and were exapted for increasingly sophisticated cognitive uses. In particular, procedural and declarative forms of knowledge can (...) be explained, respectively, in terms of on-line sensorimotor anticipation and off-line simulations of potential actions, which can give access to tacit knowledge and make it explicit. That is, mechanisms that evolved for the on-line prediction of the consequences of one's own actions (i.e. forward models) determine a (procedural) form of representation, and became exapted for off-line use. They can therefore be used to produce (declarative) knowledge of the world, by running a simulation of the action that would produce the relevant information. We conclude by discussing how embodied representations afford a form of internal manipulation that can be described as internalized situated action. (shrink)

This paper offers a conceptual framework which (re)integrates goal-directed control, motivational processes, and executive functions, and suggests a developmentalpathway from situated action to higher level cognition. We first illustrate a basic computational (control-theoretic) model of goal-directed action that makes use of internalmodeling. We then show that by adding the problem of selection among multiple actionalternatives motivation enters the scene, and that the basic mechanisms of executivefunctions such as inhibition, the monitoring of progresses, and working memory, arerequired for this system to (...) work. Further, we elaborate on the idea that the off-line re-enactment of anticipatory mechanisms used for action control gives rise to (embodied)mental simulations, and propose that thinking consists essentially in controlling mental simulations rather than directly controlling behavior and perceptions. We concludeby sketching an evolutionary perspective of this process, proposing that anticipationleveraged cognition, and by highlighting specific predictions of our model. (shrink)

The aims of my paper are to set out Aquinas’s arguments in favour of the thesis of God as Subsistent Being itself; set out the arguments against; and propose a fresh reading of that thesis that takes into account both Thomistic doctrine and the criticisms of it. In this way, I shall proceed as in a medieval quaestio, with arguments in favour, sed contra and respondeo.

In der Reihe werden herausragende monographische Untersuchungen und Sammelbände zu allen Aspekten der Philosophie Kants veröffentlicht, ebenso zum systematischen Verhältnis seiner Philosophie zu anderen philosophischen Ansätzen in Geschichte und Gegenwart. Veröffentlicht werden Studien, die einen innovativen Charakter haben und ausdrückliche Desiderate der Forschung erfüllen. Die Publikationen repräsentieren den aktuellsten Stand der Forschung.

Computational systems are traditionally approached from control-oriented perspectives; however, as soon as we move from centralized to decentralized computational infrastructures, direct control needs to be replaced by distributed coordination mechanisms that are on par with institutional constructs observable in human societies (contracts, agreements, enforcement mechanisms, etc.). This paper presents a formalization of Hohfeld's framework building upon a logic whose language includes primitive operators of ability and parametric deontic operators. The proposal is meant to highlight the fundamental interaction between deontic and (...) potestative concepts and contains proofs of soundness and completeness with respect to a class of relational models. (shrink)

Challenging the image of physics as dry and dusty, The Beautiful Invisible shows that this highly abstract science is in fact teeming with beautiful concepts, ...

Thomas Reid (1710–1796) presented a two-dimensional geometry of the visual field in his Inquiry into the human mind (1764), whose axioms are different from those of Euclidean plane geometry. Reid’s ‘geometry of visibles’ is the same as the geometry of the surface of the sphere, described without reference to points and lines outside the surface itself. Interpreters of Reid seem to be divided in evaluating the significance of his geometry of visibles in the history of the discovery of non-Euclidean geometries. (...) The question will be reexamined with particular attention given to his unpublished manuscripts. These include comments on Saccheri’s work and Reid’s repeated attempts to derive Euclid’s parallel postulate from the axioms of incidence. (shrink)

In this article I point out that rather than two, as is commonly thought, or indeed one, which is an old idea recently revived by some scholars, Aquinas in fact presents three main senses of being: (A1) being as actus essendi or esse or ‘present actuality’; (A2) being as (real) form or essence; (B) being as the reply to the an sit? (is there…?) question or anitas or ‘there is’ sense. Regarding the relations among these three senses of being I (...) show that: (i) the same logical treatment holds for the form (B) and (A2), since both can and need to be re-written in the form: something is so-and-so (whereas the same process cannot be applied to the A1 sense of being); (ii) the relation between the A1 and A2 senses of being is not a mere relation between distinct elements, but rather a relation among different stages of a single process, namely that between first and second actuality; (iii) the relation between the A (1 and 2) and B senses of being seems to be one of grounding, since the ‘there is’ sense seems to Aquinas to be grounded on the present actuality sense of being as an effect to its cause. (shrink)

Anticipatory looking on mindreading tasks can indicate our expectation of an agent's action. The challenge is that social situations are often more complex, involving instances where we need to track an agent's false belief to successfully identify the outcome to which an action is directed. If motor processes can guide how action goals are understood, it is conceivable— where that kind of goal ascription occurs in false-belief tasks— for motor representations to account for someone's belief-like state. Testing adults (N = (...) 42) in a real-time interactive helping scenario, we discovered that participants' early mediolateral motor activity (leftwards– rightwards leaning on balance board) foreshadowed the agent's belief-based action preparation. These results suggest fast belief-tracking can modulate motor representations generated in the course of one's interaction with an agent. While adults' leaning, and anticipatory looking, revealed the contribution of fast false-belief tracking, participants did not correct the agent's mistake in their final helping action. These discoveries suggest that adults may not necessarily use another's belief during overt social interaction or find reflecting on another's belief as being normatively relevant to one's own choice of action. Our interactive task design offers a promising way to investigate how motor and mindreading processes may be variously integrated. (shrink)

The writings of the Scottish physician and philosopher John Gregory play an important role in the modern codification of medical ethics. It is therefore appropriate to use his work as a historical example in approaching the question how elements of aesthetics were incorporated in 18th century medical ethics. The concept of a Gentleman is pivotal to the entire medical ethics of John Gregory as it provides him with the ethical source of the duty to patients. Gregory makes the trustworthiness of (...) the physician a central point of his medical ethics, and it is in this context that Gregory declares good manners as an essential moral quality of a physician. This paper delineates how good manners are ethically justified in Gregory's medical ethics and concludes with an exploration of the importance of Gregory's conception for present day reflection on the inherence of aesthetics in ethical determinations. (shrink)

This essay looks at early‐modern Venice hydroculture as a case of episteme from below. The forms of water knowledge it developed were multilayered and collective in their essence and solidly rested on a social experiential basis that was rooted in labour (especially fishing) and practices (especially water surveying and engineering). In accordance with the city's republican esprit (and correspondent political values), its episteme emerged as the encounter and negotiation between various institutions and groups: the fishermen of San Niccolò in Venice, (...) the practitioners of the water magistrature and political authorities. This essay explores the institutional settings of this water culture, seen as an instance of bottom‐up epistemic construction. It especially addresses three historical instances: firstly, a seventeenth century program to map public waters in order to block their alienation for private fish farming; secondly, water officers’ interviews with fishermen aimed to assess the state of the lagoon hydromorphology and, thirdly, fishing regulations. Venice communitarian and circular forms of knowledge production are here contrasted to an opposite paradigm, which was embodied by the Galileian mathematician and Rome courtier, Benedetto Castelli. His interactions with the Republic of Venice on water management and his approach to hydraulic problems are revealing of an elitist and abstract understanding of scientific knowledge that guided political decisions from above without taking in any consideration the opinions of the ‘vulgar’. While his science was the expression of a top‐down political epistemology, Venetian water knowledge was more egalitarian. It left room for exchange, inclusiveness and bottom‐up codification; it valued the gathering of different experiences (including the fishermen's practical knowledge of their waters) and rested on a concrete and systemic (organicist) understanding of natural‐anthropic processes. (shrink)