Ph.D. Seminar in Philosophy of Science

Wednesday 26 — Thursday 27 September 2001

PROGRAM

WEDNESDAY 26

10:00 Viola Schiaffonati (Philosophy of Artificial Intelligence)

*Agencies and scientifical discovery*

11:00 Massimiliano Badino (History and Philosophy of Phisics)

The foundational value of ergothic theory

12:00 Alessandro Dell’Anna (Epistemology)

*Semantics and direct perception*

13:00 Lunch Break

15:00 Arianna Betti (History and Philosophy of Logic and Semantics)

*Sachertorte and Sachverhalt, or Wie die Sacher sich zueinander verhalten. On the History *

and Philosophy of an Austrian Delikatesse.

16:30 Tatiana Arrigoni (Philosophy of Mathematics)

*Two versions of mathematical realism*

THURSDAY 27

10:00 Paola Cantú (History and philosophy of mathematics)

*Mathematics as Theory of Forms: Hermann and Robert Grassmann
*

11:30 Roberto Arpaia (Logic)

*On the concept of algebraization of a logic*

ABSTRACTS AND CURRICULA VITAE

**ARPAIA, Roberto **(robertoarpaia@tiscalinet.it)

Roberto Arpaia, born in 1975, is since 1999 a Ph.D. student in philosophy of science at the University of Genova (tutor: prof. Dario Palladino). He got his M.A. in philosophy at the University of Firenze in 1998, with a thesis titled *Contributions to the history of the axiom of foundation*,* * under the direction of prof. Ettore Casari and Dr. Pierluigi Minari. His current researches includes history of logic (especially set theory) and algebraic logic, the latter in collaboration with prof. Annalisa Marcja (University of Florence) and with prof. Ventura Verdù and prof. Ramon Jansana (University of Barcelona).

*Argument of the lecture*: **On the concept of algebraization of a logic.**

In 1935 appeared Tarski’s fundamental paper *Foundations of the calculus of system*, where for the first time the idea of the *Lindembaum algebra of formulas* is explained, and a proof is sketched of how to obtain a Boolean algebra from the classical (propositional) logic. Since 1935 an intensive program of research has been carried on by many scholars all over the world, investigating the different kinds of algebraical varieties (and quasivarieties) that arise from *non classical* logics.

In the talk the concept of algebraization of a logic, as defined in the book *Algebraizable logics* by Block and Pigozzi (Memoirs of the AMS, 1989), will be quickly illustrate, examples of algebraizable, protoalgebaical and non algebraizable logics taken from contemporary literature will be shown, as well as the difference, from an algebraical point of view, beetween a *closure operator*, an *Hilbert-style* or a *Gentzen-style* formulation of a logic.

**ARRIGONI, Tatiana **(arrigonitatiana@hotmail.com)

*Argument of the lecture*:** Two versions of mathematical realism.**

In my talk I'll briefly sketch how mathematical realism is formulated in K. Gödel works, from the strong platonism of Gödel (1944) to the epistemologically realism of Gödel (1964). The analysis of this question will take particularly into account Gödel's turn to phenomenology, which he started studying in 1959, examining how Husserl's analysis of intuition could help to make sense of Godel's views about mathematical intuition and the objective existence of mathematical objects.

**BADINO, Massimiliano **(__badino@libero.it__)

*Argument of the lecture* : **The foundational value of ergothic theory**.

A general historical and theoretical survey of the ergodic theory from the Birkhoff's theorem to the Khinchin's programme is presented. Furthermore, some thesis about its foundational role are discussed.

**BETTI, Arianna **(http://www.fmag.unict.it/PolPhil/Betti.html , __a.betti@aws.fmag.unict.it__)

Arianna Betti is a postdoc researcher at the Faculty of Philosophy of Leyden University in the Netherlands. Now working with G. Sundholm, she got her MA at Florence with E. Casari and her PhD in Genova with M. Marsonet. Her specialties and interests are mainly logic and philosophy in Central Europe (with a *Schwerpunkt* on the development of Polish logic) and analytic metaphysics. Her PhD thesis was on logic, truth and time in Austro-Polish philosophy (which should soon become her first book). She is currently working on the conceptual relationship between Lesniewski's and Tarski's thought, on Lukasiewicz's early writings, on Sachverhalt ontologies in Austrian philosophy, and editing manuscripts by Twardowski in Polish and German. Papers by her appeared in collections published by Kluwer, in the Polish *Filozofia Nauki *and in *Rivista di Filosofia*. She was invited to give a talk at the Tarski Centenary Conference in Warsaw last May.

*Argument of the lecture* : **Sachertorte and Sachverhalt, or Wie die Sacher sich zueinander verhalten. On the History and Philosophy of an Austrian Delikatesse.**

You may ask what Sachertorte and Sachverhalt have in common. At least two connected things: they are exquisitely Austrian and there is no nice English name to name them (plural denotation of names is something you have to buy in the package, as Austrians did not, in general, share the prejudice of having only *singular *names). My talk will discuss the historical hypothesis that Twardowski had Sachverhalte in his ontology and that he introduced them in Vienna in 1894. Yet to discuss such an issue we must first know what is a Sachverhalt. And here we have all the differences with a Sachertorte we wish. The ingredients of a complex object like a Sachertorte you can easily find, whereas this is not the case with a Sachverhalt: and does a Sachverhalt have ingredients after all? or maybe parts? or constituents? What is it then? Whatever a Sachverhalt is, is definitely not a piece of cake.

**CANTÙ, Paola **(paola.cantu@unimi.it)

Paola Cantù is PhD Student in Philosophy of Science at the University of Genua (Tutor: Dario Palladino). In 1998 she got a MA at the University of Milan with S. Bozzi e C. Mangione (her MA thesis Giuseppe Veronese and the Foundations of Geometry has been published in 1999 by Unicopli, Milan). She has followed courses by Jonathan Barnes and Kevin Mulligan on Frege and Bolzano at the University of Geneva and has studied the works of Hermann and Robert Graßmann at the Friedrich-Alexander-Universität Erlangen (Prof. Ch. Thiel e V. Peckhaus). Current research concerns Theory of Forms in 19tth Century Mathematics. Special attention is paid to the philosophical notion of form in Naturphilosophie, to geometrical enquiries, to the origin of algebraic and logical calculus, to the definition of mathematics as Formenlehre, to the development of the concept of structure.

*Argument of the lecture*: **Mathematics as Theory of Forms.** **Hermann and Robert Grassmann.**

An enquiry into the first definitions of mathematics as Theory of Forms implies an analysis of some related terms, such as quantity, operation, calculus and structure.

The works of Hermann and Robert Grassmann constitute a rich source of information on this subject: Ausdehnungslehre and Formenlehre contribute to the understanding of the algebraic calculus and to the origins of the concept of structure and in addition reveal connections between

the mathematical and the philosophical concept of form.

**DELL’ANNA, Alessandro **(__a_dellanna@hotmail.com__)

*Argument of the lecture*: **Semantics and Direct Perception **

If I say "I see a grass esplanade stretching until the orizon", I could be amended in different way. For example, a friend who studies computer-vision science could object that my assertion is not a pure observation, but an inference of some elaboration processof my vision module, that reach this conclusion only after many *representative sketches* (Marr).

But a gibsonian won’t be happy at all, and would protest that I see what I’m saying to see because of the *texture gradient law*. The problem seems that we can have different context of description (Austin), and the perceptual one is recognized even by the ordinary language semantics. Is the world taken into account by it completly undetermined, as Quine’s theory of ontological relativity suggests? By mean of some empirical discovery in the field of visual perception we’ll try to refuse this theory (rehabilitating obstensive definitions), shawing that a more intensive relationship is required between semantics and direct approches to the study of perception.

**SCHIAFFONATI, Viola **(schiaffo@fusberta.elet.polimi.it)

*Argument of the lecture *: **Agencies and scientific discovery.**

Scientific agencies are multiagent systems of distributed artificial intelligence that promote a new approach to scientific discovery. I willintroduce the idea of scientific agency and its double role as a concrete device for assisting scientists in their activity and as a conceptual tool for representing the products of their research.