Search

In this paper and in its sequel, "Quantificatori generalizzati e logica del primo ordine II", I try to show that General Quantifiers (QG) are a much better formalization of natural language quantifiers than quantifiers of First order logic. First of all, general and natural language quantifiers have properties in common that first order quantifiers do not have. In the second place, there are some quantifiers in natural language that cannot be formalized in First order logic while they can be through QG theory. Furthermore, the logic form of QG is much more similar to the one of natural language quantifiers than that of first order quantifiers: QG make a clear distinction between noun phrases and predicates and do not introduce connectives which are not present in natural language sentences. Finally, some classes of quantifiers can be singled out from the point of view of QG theory that we cannot be singled out from the one of First order logic. [ABSTRACT FROM AUTHOR]

Given the traditional connection between the truth of analytic sentences and their sense, one can ask what happens to analyticity in Dummett's model for a theory of meaning. Dummett claims, against Quine, the legitimacy and necessity of the talk of sense: sense is in fact, according to his model, the object of one part of a theory of meaning (theory of sense and theory of reference form its first part, the second part being the theory of force), for no description of how language works can do without an account of what a speaker knows when he speaks competently. Now Dummett's defence of the notion of sense can be understood as a defence, at the same time, of the notion of analyticity: the traditional connection between sense and analyticity is so kept, just like Quine did, the other way round, in criticizing those notions. The traditional definition of analytic sentences as the ones which are true in virtue of their sense turns out nevertheless to be misleading, first of all because Quine's criticism does score a point: some analytic sentences are susceptible to turn out not to be true, if nor to be actually false. Their truth is contingent, for they presuppose other sentences that can possibly be false; now, presupposition being not identical to implication, analyticity does warrant against falsehood, but it does not guarantee truth. Moreover, the link between analyticity and sense fits only one class of intuitively analytic sentences; now, while letting programmatically aside the 'extensionally' analytic sentences (namely those whose truth does not follow from the mere sense of their components, demanding instead logical and/or mathematical axioms having substantial implications), this paper proposes, within a Dumettian framework, a theory of analyticity for the sentences which are true in virtue of their sense and for the sentences of the theory of sense themselves, where the analyticity of the former is strictly tied to that of the latter. A sentence describing the use of an expression is analytic because it makes it explicit how such an expression is used, while some sentences (viz. 'no bachelor is married') are analytic just because of this use, although they do not themselves describe it. Since descriptions are in general informative, for each trivial analytic sentence one can find a nontrivial one describing the use of one expression occurring in it ('bachelor'); and therefore the use of at least one nontrivial and nonanalytic sentence ('x is bachelor'), i.e. the canonical procedure for establishing it (by verification or by resistance to falsification). Now, in describing the use of other sentences, the sentences of a theory of sense do quite a peculiar metalinguistic performance: they strive to say what the latter simply show, although without mentioning, even less reifying, their sense. [ABSTRACT FROM AUTHOR]

This essay seeks to identify the main aspects of the cultural identity of Malta as a microscopic manifestation of the various traits which may build up the Mediterranean culture. It outlines the historical development of the ancient language spoken by the Maltese and explains how Maltese literature eventually became a document of the historical and cultural identity of the whole population. Malta is an island, and this fact determines diverse components of Maltese identity. The concept of an islander is thus interpreted as one of the main sources from which the Maltese view of life derives. [ABSTRACT FROM AUTHOR]

This is the first of a couple of papers in which the problematic relation between quantum ontology and spatio-temporal representation and experience is analyzed. The first paper deals with the deep implications that the discovery of the quantum of action (Planck 1900) and the consequent formulation of quantum theory had on the notion of physical process and the relation part-whole. These implications amount to an ontological degradation of the concept of physical object when processes involving few quanta of action are taken into account. The ontological degradation of the object follows directly from the atomization of processes and entails a dramatic empirical falsification of the worldview of historical atomism (which I call in this paper the spatio-temporal atomism of things). On the other hand, historically, an ontological correlation between the notions of object and process, on the one hand, and those of space and time, on the other, has always been present. Every time there has been a change in the conception of "thing", it has been accompanied, sooner or later, by a corresponding change in the conception of space and time, or vice versa. However, after more than a century since the discovery of process atomization, the ontological degradation of the concept of micro-object does not appear to have affected explicitly the conceptions of space and time. The thesis of the necessity of a deep restructuring of these notions for the solution of the open problems of quantum theory as well as for the synthesis of this theory with general relativity will be defended in the second paper. [ABSTRACT FROM AUTHOR]

The starting point of this paper is an apparent contradiction, often pointed out by commentators of the Poetics: in his treatise on poetry, whose object is human action, why does Aristotle assign a major role to necessity, while in the Rhetoric and the Nicomachean Ethics he clearly states that in the field of human action there is no place for necessity but only for probability? One answer has been, that in the Poetics Aristotle refers to a weaker type of necessity, which in the end is more or less the same as probability. The fact that Aristotle (the argument continues) speaks almost always not only of necessity but also of probability, is proof of this weakening of necessity. I argue, on the contrary, that in the Poetics necessity and probability are two distinct principles, which concern different aspects of tragedy (i.e. the most accomplished poetical work according to Aristotle), and which therefore should not be blurred. The first step is to make clear that the alleged contradiction is only apparent. It is in fact true that in the world of action, according to Aristotle, there can be no necessity, but action is only the object of poetry and not poetry itself. Poetry as such is a technique, which differs from other techniques (like medicine) on account of its ends, and, consequently, also on account of its object. In the world of technique, as is clearly stated both in the Metaphysics and in the Posterior Analytics, there is necessity, in the sense that to reach this or that end you have -- necessarily -- to do this or that. But then -- this is the second step -- what is the relation between technical necessity and the principle of probability? Evidently probability concerns the world of action, the object of poetry. This brings me to the following conclusion: When Aristotle tells us that the aim of the poet is to say what is possible according to probability and necessity, he means that the poet should take probable actions as objects and use them as necessary means to reach a particular end. This end, in the case of tragedy, is the tragic plot. The two principles are then strictly connected (every moment of a tragedy has to be considered from both points of view), but nonetheless distinct. [ABSTRACT FROM AUTHOR]

Second order logic has been always considered by modern logicians quite problematic: so problematic that some of them don't even want to call it logic at all. The main features of second order logic is its high expressive power but, on the other hand, second order logic lacks of completeness, and this seems to be a 'shame' for a formal language who wants to be labelled as logic. Therefore the mainstream, following the idea of Quine, in the logical community has been that when we do second order logic we actually cross the border between logic and mathematics. However, is this line so sharp?, and are we sure that second order logic doesn't deserve a better place in logic? After all, although it is not complete, it can provide cathegorical characterizations for infinite structures, and this is not a bad point. In this paper I show some of the main attempts to "rescue" second order logic: the main points I deal with are both technical and more philosophical. On the one hand a big question is about the semantics: what is the right semantic for second order logic? On the other hand it arises the problem of the ontology: is it possible to accept at least a bit of the ontological entailments coming from second order logic, implications that look so similar to that ones coming from mathematics itself? [ABSTRACT FROM AUTHOR]

As a philosopher and as an experimental scientist, analysing knowledge and its transmission "from within" and with reference to specific contexts, Patrick Suppes evaluated very early the great potential of computer technology in the field of education and gave innovative contributions. The instructional uses of computers at Stanford University, promoted and developed by him and his team, around forty years ago, belong to the history of e-learning, having influenced the practice and the theory of education. During my stay from 1979 at the Institute for Mathematical Studies in the Social Sciences (IMSSS), an outstanding intellectual environment, created and directed by Suppes, I had access to computer facilities exceptional for the time and could take the course on Axiomatic Set Theory, one of the two computerassisted courses (the other one was Introduction to Logic) offered by Suppes since 1974 (and 1972). Constructing proofs of given theorems at one's own pace, through an intense interaction with the computer (selecting axioms, inferential rules, prior relevant definitions and theorems) is a very valuable experience: its outcome is not only learning specific contents, but also understanding at a deeper level the use of a formal language, the structure of an axiomatic system and the very notion of "proof". Computer-assisted instruction (CAI) is not a question of pure technology, but it requires -- in order to be suitably developed -- an inquiry on the psychological and empirical aspects of learning, its difficulties and goals, supported by the capability of abandoning rigid schemata and of foreseeing future possibilities. Suppes was very soon aware that the large quantity of information made accessible at high speed by computers could be structured and directed toward educational uses, characterized by individualization of curricula and high quality learning. Nevertheless, the development of programs adapting to the individual student, i.e. taking into account initial competence and ability, and selecting each learning level on the basis of the evaluation of previous successes and failures, has been more difficult than expected. Many complex problems relevant for the integration of education and technology are still open. In order to situate Suppes' contributions in a more adequate perspective, the paper briefly recalls the evolution of modern technologies applied to educative systems. In the 60's, when the first powerful computers, the so called "mainframes", became available to advanced academic institutions, Suppes started his research on computer-aided teaching and learning, on the basis of a scientific analysis of various aspects and problems of education. He then developed CAI programs better equipped to offer a more "natural" and "intelligent" interaction with the students, evaluating their individual progresses and selecting the difficulty of the subsequent problems on the basis of statistical data about previous answers. The transition from mainframes to personal computer and the diffusion of Internet have deeply changed the scenario: not only knowledge contents, in an enormous amount, are easily reached and updated, but the communication among learners is favoured. The present and close future of e-learning is characterized by tools allowing the cooperative construction of knowledge objects, of which Wikipedia, the on line encyclopaedia, is an example. Computer aided instruction, in its various forms, can consequently be recognized, following Suppes' historical perspective, as one of the great educational innovations, after the introduction of written records and the founding of libraries in ancient times, the development of printing, the (still in progress) diffusion of mass schooling and the contemporary scientific study of testing. [ABSTRACT FROM AUTHOR]

Patrick Suppes' views on probability are discussed focusing particularly on the issues of invariance and pluralism. The claim argued in this paper is twofold: (1) this dualism allows us to understand Suppes' theory of probability and (2) Suppes' strategy intended to solve this dualism contains the key to shed light upon other parts of his thought. In the first section the dualism is discussed. The second, third and fourth sections deal with the formal theory of probability and with Suppes' analysis of the classic philosophical views on probability. In the fifth section I present the probabilistic empiricism as Suppes' peculiar philosophical position on indeterminacy and randomness. [ABSTRACT FROM AUTHOR]

In this paper I present a puzzle about Moore's Proof: how can the current resurgence of interest in the Proof co-exist with the obvious reaction of irritation and dismay readers are bound to have at first encounter with it? Wouldn't it be wiser simply to discard that reaction, or else to stop worrying about the Proof? After defending the puzzle from two opposite ways of deflating it, I turn to presenting and assessing two influential interpretations of the Proof-that is, Wright's and Pryor's. I claim that in the dispute, Pryor's party is certainly wrong, but, in my view, this doesn't show that Wright's is right yet. For there is room for a third -- intermediate -- position, of Wittgensteinian descent, which I present and discuss in some detail. Turning to the original puzzle, I then provide a simple explanation of the Proof's failure which easily explains our reaction in first hearing it. Moreover, such an explanation has another pay-off. Namely, it allows bringing into focus two kinds of sceptical challenge. With such a result in hand, I then provide a solution to our initial puzzle. The solution consists in claiming that our reaction to the Proof and the resurgence of interest in it can peacefully co-exist once it is acknowledged that they are perfectly appropriate responses to these two different kinds of sceptical concern. [ABSTRACT FROM AUTHOR]

An automorphism ϕ of a group G is said to be uniform il for every g ∈ G there exists an h ∈ G such that G= h −1 h ρ . It is a well-known fact that if G is finite, an automorphism of G is uniform if and only if it is fixed-point-free. In [7] Zappa proved that if a polycyclic group G admits an uniform automorphism of prime order p then G is a finite (nilpotent) p′-group. In this paper we continue Zappa’s work considering uniform automorphism of order pg ( p and q distinct prime numbers). In particular we prove that there exists a constant μ (depending only on p and q) such that every torsion-free polycyclic group G admitting an uniform automorphism of order pq is nilpotent of class at most μ. As a consequence we prove that if a polycyclic group G admits an uniform automorphism of order pq then Z μ ( G) has finite index in G. [ABSTRACT FROM AUTHOR]