Cantor’s theory of cardinal numbers offers a way to generalize arithmetic from finite sets to infinite sets using the notion of one-to-one association between two sets. As is well known, all countable infinite sets have the same ‘size’ in this account, namely that of the cardinality of the natural numbers. However, throughout the history of reflections on infinity another powerful intuition has played a major role: if a collectionAis properly included in a collectionBthen the ‘size’ ofAshould be less than the (...) ‘size’ ofB(part–whole principle). This second intuition was not developed mathematically in a satisfactory way until quite recently. In this article I begin by reviewing the contributions of some thinkers who argued in favor of the assignment of different sizes to infinite collections of natural numbers (Thabit ibn Qurra, Grosseteste, Maignan, Bolzano). Then, I review some recent mathematical developments that generalize the part–whole principle to infinite sets in a coherent fashion (Katz, Benci, Di Nasso, Forti). Finally, I show how these new developments are important for a proper evaluation of a number of positions in philosophy of mathematics which argue either for the inevitability of the Cantorian notion of infinite number (Gödel) or for the rational nature of the Cantorian generalization as opposed to that, based on the part–whole principle, envisaged by Bolzano (Kitcher). (shrink)

Quine is one of the most influential of contemporary philosophers, whose work has ranged broadly across a great number of topics and issues in a career spanning some fifty years. In this collection a group of distinguished philosophers offer a sustained critical evaluation of the full range of Quine's writings. Amongst the topics addressed are interpretation, epistemology, ontology, modality, and mathematical truth. This collection will certainly influence all future discussion of Quine. The contributors include: George Boolos, H-N. Castaneda, Donald Davidson, (...) Umberto Eco, Dagfinn Follesdal, James Higginbotham, Charles Parsons, Hilary Putnam, Barry Stroud, and Bas van Fraassen. However, Quine is given the last word, responding to the essays in the final contribution. (shrink)

Can we build endogenous expectations about the locus of occurrence of a target without being able to describe them? Participants performed cue–target detection tasks with different proportions of valid and invalid trials, without being informed of these proportions, and demonstrated typical endogenous effects. About half were subsequently able to correctly describe the cue–target relationships . However, even non-verbalizer participants showed endogenous orienting with peripheral cues , not depending solely on practice . Explicit instructions did not bring about dramatic advantages in (...) performance .With central symbolic cues, only verbalizers showed reliable endogenous effects . We concluded that endogenous orienting with peripheral cues can occur independently of participants developing explicit hypotheses about the cue–target relationships. (shrink)

In this article I describe and evaluate the debate that surrounds the proper interpretation of Tarski’s account of logical consequence given in his classic 1936 article ‘On the concept of logical consequence’. In the late 1980s Etchemendy argued that the familiar model theoretic account of logical consequence is not to be found in Tarski’s original article. Whereas the contemporary account of logical consequence is a variable‐domain conception – in that it calls for a reinterpretation of the domain of variation of (...) the quantifiers when evaluating logical consequence –, no such reinterpretation is found in Tarski’s original account, which was rather based on a ‘fixed‐domain’ conception. Etchemendy’s claims have sparked a debate on Tarski’s conception of logical consequence with important contributions by, among others, Bach, Bays, Corcoran, Gómez‐Torrente, Mancosu, Ray, Sagüillo, and Sher. (shrink)

Ever since the early decades of this century, there have emerged a number of competing schools of ecology that have attempted to weave the concepts underlying natural resource management and natural-historical traditions into a formal theoretical framework. It was widely believed that the discovery of the fundamental mechanisms underlying ecological phenomena would allow ecologists to articulate mathematically rigorous statements whose validity was not predicated on contingent factors. The formulation of such statements would elevate ecology to the standing of a rigorous (...) scientific discipline on a par with physics. However, there was no agreement as to the fundamental units of ecology. Systems ecologists sought to identify the fundamental organization that tied the physical and biological components of ecosystems into an irreducible unit: the ecosystem was their fundamental unit. Population ecologists sought, instead, to identify the biological mechanisms regulating the abundance and distribution of plant and animal species: to these ecologists, the individual organism was the fundamental unit of ecology, and the physical environment was nothing more than a stage upon which the play of individuals in perennial competition took place. As Joel Hagen has pointed out, the two schools were thus dividied by fundamentally different and irreconcilable assumptions about the nature of ecosystems.Notwithstanding these divisive efforts to elevate the image of ecology, the discipline remained in the shadows of American academia until the mid-1960s, when systems ecologists succeeded in projecting ecology onto the national scene. They did so by seeking closer involvement with practical problems: they argued before Congress that their approach to the theoretical problems of ecology was uniquely suited to the solution of the impending “environmental crisis.” With the establishment of the International Biological Program, they succeeded in attracting unprecedented levels of funding for systems ecology research. Theoretical population ecologists, on the other hand, found themselves consigned to the outer regions of this new institutional landscape. The systems ecologists' successful capture of the limelight and the purse brought the divisions between them and population ecologists into sharper relief — hence the hardening of the division of ecology observed by Hagen.45I have argued that the population biologist Richard Levins, prompted by these institutional developments, sought to challenge the social position of systems ecology, and to assert the intellectual priority of theoretical population ecology. He attempted to do so by articulating a nontrivial and rather carefully thought out classification of ecological models that led to the disqualification of systems analysis as a legitimate approach to the study of ecological phenomena. I have suggested that — ultimately —Levins's case against systems analysis in ecology rested on the view that an aspiration to realism and prediction was incompatible with an interest in theoretical issues, a concern that he equated with the search for generality. He sought to reinforce this argument by exploiting the fact that systems ecologists had staked their future on the provision of technical solutions to the problems of the “environmental crisis”: he associated systems ecologists' aspiration to realism and precision with a concern for practical issues, trading on the widely accepted view that practical imperatives are incompatible with the aims of scientific inquiry.46 These are plausible, but nonetheless questionable, claims which have now become an integral part of ecological knowledge. And finally, I hope to have shown how even the most abstract levels of scientific argument are shaped by political considerations, and how discussions of the conceptual development of modern ecology might benefit from a greater consideration of its historical and social dimensions.47. (shrink)

In the lively discussions on Galileo's laws of motion after the Pisan's death, we observe what might be called a new “Galilean affair.” That is, a trial brought against his new science of motion mainly by French and Italian Jesuits with the substantial adherence of M. Mersenne. This new trail was originated by Gassendi's presentation of Galileo's de motu not simply as a perfectly coherent doctrine, but also as a convincing argument in favor of the truth of Copernicanism.

Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.

In Umberto Eco's semiotics, the encyclopedia is a multidimensional space of semiosis. It is a complex system of shared knowledge that governs the production and interpretation of signs inside communicative contexts. Every semiotic act involves the elements that form the encyclopedia. By means of several examples and comparisons with different semiotic theories, my paper aims to show how semiosis is governed by semantic categorizations, pragmatic rules, and narrative frames that the encyclopedia articulates and makes operative for interpreters and producers of (...) signs. (shrink)

We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact relation. A similar characterization is proved with respect to Boolean algebras and distributive lattices with weak contact, not necessarily additive, nor overlap.

In the lively discussions on Galileo's laws of motion after the Pisan's death, we observe what might be called a new “Galilean affair.” That is, a trial brought against his new science of motion mainly by French and Italian Jesuits with the substantial adherence of M. Mersenne. This new trail was originated by Gassendi's presentation of Galileo's de motu not simply as a perfectly coherent doctrine, but also as a convincing argument in favor of the truth of Copernicanism.

In this study some typical aspects of human behavior are reconsidered in a new evolutionary perspective. Firstly, a theoretical paradigm is introduced, according to which animals show a natural propensity to maintain behavior far beyond the time when the triggering motivation has been removed;, these drifting conducts are defined as Vestigial Drifting Drives or. Such a paradigm is then applied to those human attitudes that once conferred an adaptive advantage on our species but have now become dysfunctional within the framework (...) of the current ecological crisis. In this context, human beings are considered the repository of VDDs that may play out as evolutionary threats. This thesis is supported by many examples and references that, hopefully, could stimulate scientific debate and further research in evolutionary anthropology, psychology, and related disciplines. (shrink)

The two theories of pancreatic enzyme secretion, those of exocytosis and transmembrane flow, are described. Data thought to support the theory of transmembrane flow of single molecules from pancreatic acinar cells are first reviewed, and the conditions which could allow these data to be explained by the theory of exocytosis of enzyme quanta, i.e. secretory granules, are then discussed.The evidence suggesting short‐term modulation of the composition of pancreatic juice is also considered, and its possible explanations at the organ and cellular (...) level are discussed, in the light of suggested theories on enzyme secretion pathways. (shrink)

This paper aims to foster an interdisciplinary dialogue between Ricoeur’s phenomenological- hermeneutical thought and human geography, in particular with respect to the issue of landscape interpretation. The connection draws on the idea that landscapes and lived spaces can be read as texts, not unfamiliar to human geography and semiotics from 1980s onward. In the first part of the paper I will briefly expound some theories of landscape which make use of the metaphors “landscape as cultural image” and “landscape as text” (...) in human and cultural geography. Then, I will discuss the main contribution of Ricoeur to the issue of space. The philosopher already envisioned a possible application of his “threefold mimesis” of Time and Narrative to architectural spaces. In the conclusion, I will propose to rejuvenate the geographical metaphor of “landscape as text” by introducing a possible application of the Ricoeurian notion of “meaningful action as text” to landscape. (shrink)

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we (...) calculate a canonical characteristic fomula H of S (char(S)) so that ⊢G ∼ H → (∼S) and ⊢GL-LIN ∼ H, and the complexity σ of ∼ H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of ∼ H with H = char(S) and σ(∼ H) = d(S, G). (shrink)

We present a sequent calculus for extensional mereology. It extends the classical first-order sequent calculus with identity by rules of inference corresponding to well-known mereological axioms. Structural rules, including cut, are admissible.

We will discuss a mathematical proof found in Wittgenstein’s Nachlass, a constructive version of Euler’s proof of the infinity of prime numbers. Although it does not amount to much, this proof allows us to see that Wittgenstein had at least some mathematical skills. At the very last, the proof shows that Wittgenstein was concerned with mathematical practice and it also gives further evidence in support of the claim that, after all, he held a constructivist stance, at least during the transitional (...) period of his thought (1929-33). (shrink)

The homeopathic principle of similitude is not based on the principle of vaccination but on the more general principle of inversion of effects, a widespread medical phenomenon. Based on the systemic networks which play an important role in response to stress, this principle concerns the reorganization of regulation systems, through a coherent response to the medicine. This model is backed by a large number of published studies from our laboratory and others, by toxicological evidence such as the emerging fields of (...) ‘hormesis’, of neuropharmacology, and of systems biology. The immune system is just one example of the possible application of this law of similitude, which constitutes the true ‘heart’ of the homeopathic idea, and again ethically justifies the attempt to apply it to experimental pharmacology. (shrink)

This issue of Itinera aims to address the connections between architecture and the performing arts in its various aspects and from multiple points of view. The growing emphasis on the performative character of artistic practices, namely, their ability to involve spectators directly and pervasively (Dixon 2007), imbues the relationship between architecture, the performing arts, and the spectator’s experience. The sharing of the scenic space by spectators and performers is essential for the co-production of a common energy which operates as a (...) “transforming force” and thereby opens up the shared experience of discovering oneself and the other as a union of the body and the mind (Fischer-Lichte 2004). (shrink)