(apologies for cross-posting)
Conference Announcement & Call for Papers
*Updated: List of invited speakers and scientific committee*
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
Hourya Benis Sinaceur (IHPST, Paris)
Patricia Blanchette (Notre Dame)
Paola Cantù (CEPERC, Université de Provence)
Paolo Mancosu (Berkeley)
Paul Rusnock (Ottawa)
Lisa Shabel (Ohio State)
Stewart Shapiro (Ohio State/St. Andrews)
Eric Schliesser (Ghent)
Organising committee: Arianna Betti (chair), Hein van den Berg,
Lieven Decock, Wim de Jong, Iris Loeb & Stefan Roski, VU Amsterdam
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
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
(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
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 Aristotle’s
"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
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 (München),
Béatrice Longuenesse (New York), Christoph Lüthy (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
- Russell’s 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
- 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,
*Please notice that we are currently trying to arrange conference child care
for speakers. More information on this facility will follow.*
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, Schröder, 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 Cantù, 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
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