June 24.-26. 2016, Prague
Catholic Theological Faculty
Friday 24. 6.
9:00 - 12:10
9:10 - 10:10 L. Horsten, Structuralism for Set Theory?
10:10 - 10:40 N. Tennant, Structuralism about Truth Itself
10:50 - 11:20 V. Kolman, Intuition and the End of all –isms
11:20 - 12:10 C. Posy, The Flight from Intuition Revisited
14:30 - 18:00
14:30 - 15:30 M. Detlefsen, The Elements of Formalism
15:30 - 16:00 M. Steiner, Wittgenstein against Formalism
16:15 - 16:45 M. Gabbay, Formalism and (set theoretic) truth
16:45 - 17:15 D. Svoboda, The Emergence of Formalism and a new Conception of Science
17:15 - 17:45 C. M. Wilson, Formalization and Justification
9:00 - 12:00
9:00 - 10:00 O. Linnebo, Structure Abstraction
10:00 - 10:30 J. Wigglesworth, Non-eliminative Structuralism, Fregean Abstraction, and Non-Rigid Structures
10:45 - 11:15 L. Kvasz, Structuralism as a Philosophy of Mathematics – What it is about?
11:15 - 11:45 J. Menšík, Mathematical Structuralism: Internal and External
14:30 - 18:00
14:30 - 15:30 M. Resnik, Non-Ontological Structuralism
15:30 - 16:00 P. Sousedík, Ante-rem Structuralism and Identity
16:20 - 16:50 J. Seldin, Formalism and Structuralism, a Synthesis the Philosophical Ideas H.B. Curry
16:50 - 17:20 G. Schiemer, Klein`s invariant-theoretic Structuralism
9:00 - 12:00
9:00 - 10:00 S. Shapiro, R. Samuels, E. Snyder, Neo-logicism, Structuralism and Frege Application Constraints
10:00 - 10:30 D, Macbeth, A Non-structuralist Alternative to Formalism
10:45 - 11:15 A. Islami, Formalism in the Face of Complex Numbers
11:15 - 11:45 F. Doherty, The Structuralist Roots of Formalism: Hilbert`s Early Views
14:30 - 16:30
14:30 - 15:00 Jan von Plato, Formal Computation as Deduction
15:15 - 15:45 M. Schirn, On Hilbert’s Formalist Approach before and after Gödel’s Incompleteness Theorems
15:45 - 16:15 V. Švejdar, Modern Czech Logic: Vopěnka and Hájek, History and Background
Prague sightseeing tour
June 24.- 26. 2016
Prague, Czech Republic
Catholic Theological Faculty, Charles University
Thákurova 3, Praha 6
Institute of Philosophy, Czech Academy of Sciences, v.v.i.
Jílská 1, Praha 1
The Emergence of Structuralism and Formalism
On the common view, mathematics is a theoretical discipline whose subject matter is quantity. But this traditional conception is defied by the fact that mathematicians hardly speak of the subject of their enquiry. Their way of speaking is rather of a practical nature: they produce diagrams or chains of symbols. They therefore act not as theorists, who contemplate the subject of their study, but rather as technicians, who produce something.
Since Plato, philosophers have been disputing what attitude to take in respect of this contradiction. Looking over the history of these discussions, two possible solutions can be distinguished. Representatives of one (e.g. some scholastics) had let themselves be “seduced” by mathematical practice and therefore classified their discipline as a mere art. Representatives of the other (e.g. adherents of modern science) emphasised the uniqueness of mathematics and assigned a distinctly theoretical status to it. Important incentives to solving the dilemma can be encountered in the 19th century. At that time mathematics was transformed and is sometimes said to have been founded anew. From our point of view it is especially significant that these discoveries were reflected by a transformation of mathematical practice. Intuition was gradually abandoned and was replaced by mere manipulation with symbols, with which it was very difficult to associate a meaning. This process of “expelling intuition” from mathematics confirmed earlier tendencies, according to which mathematics has no subject matter and is therefore in a certain sense a technique.
We believe that discussions on the nature of mathematics in the 19th and 20th century can be fruitfully understood, if we view them from the perspective of the two approaches to its nature described above. For there again crystalizes a current of views according to which mathematics studies a certain subject matter, and is therefore a theoretical discipline in the traditional sense of the word, and alongside it a current emphasizing its non-intuitive practice, according to which mathematics is a kind of technique.
Our conference will focus on how the nature of mathematics is regarded by representatives of formalism and structuralism. On the one hand, these two currents have much in common (they both agree that mathematics is not intuitive). On the other hand, they differ precisely in how they approach the problem whether mathematics does or does not have subject matter. Formalists reduce mathematics to mere manipulation with signs, thereby giving rise to the appearance that on their view mathematics cannot have any subject matter, while many structuralists admit objective grounding of mathematics and thereby return to the traditional theoretical conception of science.
We divide the problems we wish to address at the conference into historical ones and systematic ones. In the first thematic area we will ask what earlier trends formalism and structuralism follow up on, how these current were constituted, and how they eventually became respected philosophical positions. In the second area we will welcome reflections addressing the relationship between formalism and structuralism (similarities and dissimilarities), and further also solutions to some contemporary problems associated with these two approaches.
The conference language is English.
To submit a proposal, please send a proposal of your paper to the following email
Proposals for papers should be prepared for anonymous review. Proposals should include:
Title and abstract of the paper (maximum 500 words).
If you have inquiries about the conference or about the submission process, please write to
SUBMISSION DEADLINE: April 30. 2016
Notification of acceptance on May 10. 2016.
The scheduled length of lectures is 30 minutes including approx. 10 minutes for discussion. Selected contributions will be published.
We would like to draw your attention to the Logica conference which takes place just a few days before our conference. Here is the webpage: http://logika.flu.cas.cz/en/logica