Edizioni FrancoAngeli - Last issue of PARADIGMI (3/2011)

Presentazione

Fri, 15 Dec 2011 8:00:00 GMT

Carlo Cellucci

Philosophy of Mathematics and Philosophy of History

Fri, 15 Dec 2011 8:00:00 GMT

Emily R. Grosholz
If we suppose that the central activity of mathematicians is analysis, the search for the conditions of solvability of a problem (and more generally, a search for the conditions of intelligibility of the things that mathematics problems concern), then mathematical reasoning must concern narrative as well as argument. It follows as well that philosophers of mathematics must use historical method as well as logic and the deductive methods of natural science. I illustrate these claims by Andrew Wiles’ proof of Fermat’s Last Theorem, and criticize Philip Kitcher’s ahistorical account of mathematical knowledge.

Meno-like Discoveries in Mathematics and Science

Fri, 15 Dec 2011 8:00:00 GMT

Donald Gillies
This paper begins by analysing Plato’s treatment of the problem of discovery in the Meno. The discussion is then related to some 20th century discoveries in science and mathematics. This leads to characterising a particular type of discovery as a Meno-like discovery. However it is argued that Pasteur’s principle that «fortune favours the prepared mind» gives a better explanation of such discoveries than Plato’s original theory.

Intuition and Logic

Fri, 15 Dec 2011 8:00:00 GMT

Gabriele Lolli
The early twentieth century discussions on the principle of choice and related arguments, especially those around Zermelo’s 1904 proof of the well-ordering theorem, make an interesting example of the relationship of intuition and logic in the growth of mathematics. There are two opposed views confronting themselves: mathematics as a human construction, where constraints are determined by the supposed limitations of the effective capabilities, even if idealized, of the subjects; and mathematics as an objective reality. But in the case of the infinite process of choices, there is a paradox: those insisting on the human construction conception are wary of intuition, in so far as it tends to push the process beyond effective feasibility, while Zermelo with his logical formulation of the principle is the one willing to recognize the soundness of the original pre-mathematical intuition.

Mathematics and Rhetoric

Fri, 15 Dec 2011 8:00:00 GMT

Cesare Cozzo
The traditional opposition between mathematical proof and rhetorical argument is based on a non-contextual picture of mathematical proof, against which historical and theoretical objections have been raised. The author advocates a different opposition, between epistemic rhetoric and instrumental rhetoric. Instrumental rhetoric aims at persuasion without caring for truth. Epistemic rhetoric is a practice aimed at both persuasion and truth. Aiming at truth is a way of acting, which can be characterized in terms of epistemically virtuous behavioural traits. In this sense epistemic rhetoric aims at truth, even though it is contextual and addressed to a particular audience. Real life mathematical proofs are instances of epistemic rhetoric and contextual rigour. But it is right to contrast proofs with the arguments of instrumental rhetoric.

Effectivity and Efficiency

Fri, 15 Dec 2011 8:00:00 GMT

Paolo Zellini
The aim of this paper is to identify a concept of "computational efficiency", to be added as a requirement to the "effectiveness" of an algorithmic process. An algorithm must be computationally efficient mainly in the sense that it must satisfy certain computational complexity bounds, as well as certain error bounds concerning the approximation of exact operations by machine operations. The paper analyzes the meaning of efficiency in relation to some of the main trends in last century mathematics and computer science, such as the arithmetization of analysis, the science of algorithms developed after the design of the first digital computers, and the development of applied mathematics in the last decades.

Sets and Infinite Sets. Suggestions from Cognitive Sciences

Fri, 15 Dec 2011 8:00:00 GMT

Tatiana Arrigoni
In the history of Western thought it has been denied both that an infinite manifold of individuals could be conceived and described as a totality (i.e., as an infinite set), and that a finite manifold of individuals could be conceived and described as a unity (i.e., as a set), except in mathematics. On the contrary, in mathematical contexts, the notion of finite set is often characterized as being general, and that of infinite set as being inevitable. In this paper the author discusses this question, arguing for the generality and the inevitability of the notions at issue by using results from contemporary cognitive science.

Top-down and bottom-up Philosophy of Mathematics

Fri, 15 Dec 2011 8:00:00 GMT

Carlo Cellucci
The philosophy of mathematics of the last few decades is commonly distinguished into mainstream and maverick. In this paper the limitations of both such philosophies of mathematics are analysed, proposing as an alternative a bottom-up approach, according to which there is continuity between the problem solving procedures that evolution has embodied in organisms and the procedures by means of which mathematical problems are solved in mathematics as a discipline. It is argued that traditional questions of the philosophy of mathematics, such as the nature of mathematical objects, can be dealt with in terms of such procedures.

The Continuing Relevance of Bühler

Fri, 15 Dec 2011 8:00:00 GMT

Federico Albano Leoni
The paper offers a brief review of Bühler’s Sprachtheorie and other writings from a linguistic point of view. Attention focuses on the continued, and not yet fully exploited, topicality of certain issues in the context of the present theoretical debate regarding the science of language. In particular, the paper explores: a) the notion of ‘field’; b) the theory of two fields and the interaction of the symbolic and the deictic fields with a consideration of ellipsis; c) Bühler’s axiomatics, focussing on his model of ‘sign’ and system of symbol/field; d) the gestaltic perspective in the representation of the sound of language.

Subjectivistic Relativism and Epistemic Pragmatism

Fri, 15 Dec 2011 8:00:00 GMT

Nicla Vassallo
After clarifying some tenets of relativism, also in comparison to contextualism, I will concentrate on the conception of truth that springs from subjective relativism. My aim is to understand what kind of epistemic values and knowledge it can support. In order to strengthen such relativism, I will employ some arguments of a recent account of epistemic pragmatism. Unfortunately, those arguments will turn out to be not only inconsistent, but also well intertwined with relativistic arguments. Against this alliance of relativism and pragmatism, I will favour a conception according to which the world imposes itself on us, thereby guaranteeing to us beliefs that can become knowledge, if we are confident in the conception of objective truth.

Experiments in Philosophy

Fri, 15 Dec 2011 8:00:00 GMT

Massimo Marraffa
"Experimental Philosophy" is the use of the methods of cognitive sciences to answer empirical questions that are relevant to philosophical debates. In this article some important work in experimental philosophy is reviewed and two different interpretations of its metaphilosophical implications are discussed. The "reformists" see the findings of experimental philosophy as an essential completion of the method that consists in using intuitions about possible cases (thought experiments) as evidence in the evaluation of philosophical claims. In contrast, the "eliminativists" view the data from experimental philosophy as a death knell for the practice of the appeal to intuitions in philosophy. In both cases, it is argued, experimental philosophy is to be praised for making a further step in the establishment of the sort of naturalistic, scientifically engaged approach to philosophy that Quine promoted.

Anti-Foundationalism and the Myth of Jones. Brandom and McDowell interpreting Sellars

Fri, 15 Dec 2011 8:00:00 GMT

Paolo Tripodi
In Sellar’s Empiricism and the Philosophy of Mind. The argument against the Myth of the Given depends his account of observational experience. On the one hand, as McDowell points out (contra Brandom), such an account depends on the Myth of Jones. On the other hand, as Brandom claims (contra McDowell), the "dénouement" of the Myth of Jones must be interpreted in terms of the so-called "two-ply account" of observational reports. Since such an account fails, the Myth of Jones, considered as an argument in narrative form, is a bad argument. Thus Sellars’s argument against the Myth of the Given is invalid.

The "Bergmann-Renaissance"

Fri, 15 Dec 2011 8:00:00 GMT

Nevia Dolcini
Gustav Bergmann (1906-1987) is currently regarded as one of the most significant ontologists of the 20th century. Nevertheless, for many decades his works and ideas have been widely neglected, and he himself was more or less explicitely marginalized from the philosophical mainstream of his own time. Yet, a recent revival of interest for Bergmann has changed the situation. This paper presents the main phases, actors and events of a movement which may be styled as a Bergmann-Renaissance.

Abstracts

Fri, 15 Dec 2011 8:00:00 GMT

Inidice dell'annata 2011

Fri, 15 Dec 2011 8:00:00 GMT