The Classical Model of Science II

The Axiomatic Method, the Order of Concepts and the Hierarchy of Sciences from Leibniz to Tarski

August 2-5, 2011 Vrije Universiteit Amsterdam, The Netherlands.

Introduction

This conference is devoted to the development of the axiomatic method, with

particular attention for the period from Leibniz to Tarski. In particular,

we aim to achieve a better historical and philosophical understanding of the

way the axiomatic method in the sense of an ideal of scientific knowledge as

"cognitio ex principiis" has influenced the development of modern science.

The overarching framework for this will be the so-called "Classical Model of

Science".

The Classical Model (or Ideal) of Science consists of the

following conditions for counting a system S as properly scientific (de Jong

& Betti 2010: http://bit.ly/f7QKXW):

(1) All propositions and all concepts (or terms) of S concern a specific set

of objects or are about a certain domain of being(s).

(2a) There are in S a number of so-called fundamental concepts (or terms).

(2b) All other concepts (or terms) occurring in S are composed of (or are

definable from) these fundamental concepts (or terms).

(3a) There are in S a number of so-called fundamental propositions.

(3b) All other propositions of S follow from or are grounded in (or are

provable or demonstrable from) these fundamental propositions.

(4) All propositions of S are true.

(5) All propositions of S are universal and necessary in some sense or

another.

(6) All propositions of S are known to be true. A non-fundamental

proposition is known to be true through its proof in S.

(7) All concepts or terms of S are adequately known. A

non-fundamental concept is adequately known through its composition (or

definition).

This systematization represents a general historical hypothesis insofar as

it aims at capturing an ideal that many philosophers and scientists adhered

to for more than two millennia, going back ultimately to Aristotleï¿½s

"Analytica Posteriora". This cluster of conditions has been set up as a

rational reconstruction of particular philosophical systems, which is also

meant to serve as a fruitful interpretative framework for a comparative

evaluation of the way certain concepts/ideas evolved in the history of

philosophy.

Scientific Committee (confirmed members): Mark van Atten (Paris IHPST),

Jonathan Barnes (Paris IV), Michael Beaney (York), Gabriella Crocco (CEPERC

UMR-CNRS 6059, Provence), Mary Domski (New Mexico), Catarina Dutilh Novaes

(Amsterdam UvA), Juliet Floyd (Boston), Leila Haaparanta (Tampere), Mirja

Hartimo (Helsinki), Anita Konzelmann-Ziv (Geneva), Hannes Leitgeb (Mï¿½nchen),

Bï¿½atrice Longuenesse (New York), Christoph Lï¿½thy (Nijmegen), Danielle

Macbeth (Haverford), Elena Anne Marchisotto (California State), Marije

Martijn (VU Amsterdam), Massimo Mugnai (Pisa), Roman Murawski (Poznan),

Venanzio Raspa (Urbino), Philippe de Rouilhan (Paris IHPST), John Symons (El

Paso), Joan Weiner (Indiana).

Call for papers

The focus of this conference will be the rise of the (formal) axiomatic

method in the deductive sciences from Leibniz to Tarski on the basis of the

so-called Classical Model (or Ideal) of Science. Although preference will be

given to contributions matching this focus, *we welcome and strongly

encourage submissions* discussing historical developments of the ideal of

scientific knowledge as "cognitio ex principiis" as sketched above

*concerning any epoch or longer period*. The historical studies should aim

at a philosophical understanding of the role and development of the seven

conditions listed above in the rise of modern science. Contributed papers

will be programmed in parallel sessions (30-40 minute presentations, of

which about half for discussion).

Topics of interest include, but are not limited to:

- Leibniz's Characteristica universalis, and the ideals of

"lingua characteristica" and "calculus ratiocinator"

- Analysis and proper scientific explanation in Wolff and Kant

- Grounding and Logical Consequence from Bolzano to Tarski

- Explanation in mathematics from Leibniz to Tarski

- Epistemology and metatheory in Frege

- The relation between descriptive psychology, ontology, logic and axiomatic

method in Meinong

- Knowing the principles and self-evidence in Husserl's conception of logic

- Mereology and axiomatics in 19th century mathematics

- The role of mereology as formal ontology in the system of sciences

- The notion of form in 19th and 20th century logic and mathematics

- Russellï¿½s conception of axiomatics

- The disappearance of epistemology from 19th and 20th century geometry

- Axiomatics, truth and consequence in the Lvov-Warsaw School

- Logic as calculus, logic as language

- Type theory, range of quantifiers and domain of discourse in the early

20th century

- Interpretation, satisfaction and the history of model theory

- The axiomatisation of particular disciplines such as logic, mereology, set

theory, geometry and physics but also biology, chemistry and linguistics

- Constitution systems

- The analytic-synthetic distinction

- The unity of science

- Axiomatics and model theory

- Axiomatics and extensionality constraints

Abstracts (maximum 500 words) must be sent in electronic form to

axiom....@gmail.com. They must contain the author's name,

address, institutional affiliation and e-mail address.

Deadline for submission: April 15th, 2011

Authors will be notified of the acceptance of their submission by May 1st,

2011.

*Please notice that we are currently trying to arrange conference child care

for speakers. More information on this facility will follow.*

Additional information

The history of the methodology systematised in the model as presented above

knows three milestones: Aristotle's "Analytica Posteriora", the "Logic of

Port-Royal" (1662) and Bernard Bolzano's "Wissenschaftslehre" (1837). In all

generality the historical influence of this model has been enormous. In

particular, it dominated the philosophy of science of the Seventeenth, and

Eighteenth Century (Newton, Spinoza, Descartes, Leibniz, Wolff, Kant) but

its influence is still clear in Husserl, Frege and Lesniewski.

The axiomatisation of various scientific disciplines involved a

strict characterisation of the 'domain' of objects and the list of

primitive predicates, strict rules of composition of well-formed formulas,

the determination of fundamental axioms (or axiom schemas), formal inference

rules, a formalisation of the truth-concept, and a formalisation of

modality. The success of the model can be seen in the formalisation of logic

(Boole, Schrï¿½der, Peirce, Frege, Whitehead & Russell, Lesniewski), the

axiomatisation of geometry (Hilbert, Veblen, Whitehead), the axiomatisation

of set theory (Zermelo, Fraenkel, Bernays, von Neumann), the axiomatisation

of physics (Vienna Circle), or in the construction of constitution systems

(Carnap, Goodman). However, full and rigorous formalisation also made

visible some of the intrinsic limitations of classical axiomatic

methodology: problems with the determination of ontological domains (e.g.

pure set theory instead of physical Ur-elements, de-interpretation and the

rise of model theory), problems with the characterisation of

fundamental concepts (e. g. the debate on the analytic-synthetic

distinction), the separation between truth and proof, the demise of the

ideal of the unity of science, etc.

The first Classical Model of Science conference took place in January 2007.

For more information on the Classical Model of Science, its formulation and

its application as an interpretive tool from Proclus to Lesniewski and until

today, see the papers in Betti & de Jong 2010 (http://bit.ly/hlB5yb by

Arianna Betti, Paola Cantï¿½, Wim de Jong, Tapio Korte, Sandra Lapointe and

Marije Martijn) and in Betti, de Jong and Martijn forthcoming (

http://bit.ly/hERked, by Hein van den Berg, Jaakko Hintikka, Anita

Konzelmann-Ziv, F. A. Muller, Dirk Schlimm and Patrick Suppes).

--

Vrije Universiteit Amsterdam, http://axiom.vu.nl/~arianna/

ERC Starting Grantee, Member of De Jonge Akademie of the Royal Academy

of Arts and Sciences of the Netherlands (KNAW) & of the Global Young

Academy

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