The Emergence of Structuralism and Formalism ****************************************************************************************** * International conference ****************************************************************************************** June 24.-26. 2016, Prague Venue Address Catholic Theological Faculty Charles University Thákurova 3 Praha 6 Keynote Speakers: • S. Shapiro • M. Detlefsen • M. Resnik • L. Horsten Friday 24. 6. 9:00 - 12:10 9:10 - 10:10 L. Horsten, Structuralism for Set Theory? [ URL "KTFENG-73-version1-horsten.p 10:10 - 10:40 N. Tennant, Structuralism about Truth Itself [ URL "KTFENG-73-version1-tenna coffee break 10:50 - 11:20 V. Kolman, Intuition and the End of all –isms [ URL "KTFENG-73-version1-kolm 11:20 - 12:10 C. Posy, The Flight from Intuition Revisited [ URL "KTFENG-73-version1-posy2 14:30 - 18:00 14:30 - 15:30 M. Detlefsen, The Elements of Formalism [ URL "KTFENG-73-version1-detlefsen. 15:30 - 16:00 M. Steiner, Wittgenstein against Formalism [ URL "KTFENG-73-version1-steiner coffee break 16:15 - 16:45 M. Gabbay, Formalism and (set theoretic) truth [ URL "KTFENG-73-version1-gab 16:45 - 17:15 D. Svoboda, The Emergence of Formalism and a new Conception of Science [ URL version1-svoboda.pdf"] 17:15 - 17:45 C. M. Wilson, Formalization and Justification [ URL "KTFENG-73-version1-wils Saturday 25.6. 9:00 - 12:00 9:00 - 10:00 O. Linnebo, Structure Abstraction [ URL "KTFENG-73-version1-linnebo.pdf"] 10:00 - 10:30 J. Wigglesworth, Non-eliminative Structuralism, Fregean Abstraction, and Non [ URL "KTFENG-73-version1-wigglesworth.pdf"] coffee break 10:45 - 11:15 L. Kvasz, Structuralism as a Philosophy of Mathematics – What it is about? [ version1-kvasz.pdf"] 11:15 - 11:45 J. Menšík, Mathematical Structuralism: Internal and External [ URL "KTFENG-7 mensik.pdf"] 14:30 - 18:00 14:30 - 15:30 M. Resnik, Non-Ontological Structuralism [ URL "KTFENG-73-version1-resnik.pd 15:30 - 16:00 P. Sousedík, Ante-rem Structuralism and Identity [ URL "KTFENG-73-version1-s coffee break 16:20 - 16:50 J. Seldin, Formalism and Structuralism, a Synthesis the Philosophical Ideas "KTFENG-73-version1-seldin.pdf"] 16:50 - 17:20 G. Schiemer, Klein`s invariant-theoretic Structuralism [ URL "KTFENG-73-vers schiemer.pdf"] 18:00 banquet Sunday 26.6. 9:00 - 12:00 9:00 - 10:00 S. Shapiro, R. Samuels, E. Snyder, Neo-logicism, Structuralism and Frege Appl Constraints [ URL "KTFENG-73-version1-shapirosamuelssnyder.pdf"] 10:00 - 10:30 D, Macbeth, A Non-structuralist Alternative to Formalism [ URL "KTFENG-73-ve macbeth.pdf"] coffee break 10:45 - 11:15 A. Islami, Formalism in the Face of Complex Numbers [ URL "KTFENG-73-version 11:15 - 11:45 F. Doherty, The Structuralist Roots of Formalism: Hilbert`s Early Views [ UR version1-doherty.pdf"] 14:30 - 16:30 14:30 - 15:00 Jan von Plato, Formal Computation as Deduction [ URL "KTFENG-73-version1-pla coffee break 15:15 - 15:45 M. Schirn, On Hilbert’s Formalist Approach before and after Gödel’s Incomple [ URL "KTFENG-73-version1-schirn.pdf"] 15:45 - 16:15 V. Švejdar, Modern Czech Logic: Vopěnka and Hájek, History and Background [ version1-svejdar2.pdf"] 17:00 Prague sightseeing tour Program .pdf [ URL "KTFENG-73-version1-conference_pozvpgm.pdf"] Organizers Catholic Theological Faculty, Charles University Thákurova 3, Praha 6 Czech Republic Institute of Philosophy, Czech Academy of Sciences, v.v.i. Jílská 1, Praha 1 Czech Republic The Emergence of Structuralism and Formalism On the common view, mathematics is a theoretical discipline whose subject matter is quanti traditional conception is defied by the fact that mathematicians hardly speak of the subje enquiry. Their way of speaking is rather of a practical nature: they produce diagrams or c They therefore act not as theorists, who contemplate the subject of their study, but rathe who produce something. Since Plato, philosophers have been disputing what attitude to take in respect of this con Looking over the history of these discussions, two possible solutions can be distinguished of one (e.g. some scholastics) had let themselves be “seduced” by mathematical practice an classified their discipline as a mere art. Representatives of the other (e.g. adherents of emphasised the uniqueness of mathematics and assigned a distinctly theoretical status to i incentives to solving the dilemma can be encountered in the 19th century. At that time mat transformed and is sometimes said to have been founded anew. From our point of view it is significant that these discoveries were reflected by a transformation of mathematical prac was gradually abandoned and was replaced by mere manipulation with symbols, with which it difficult to associate a meaning. This process of “expelling intuition” from mathematics c tendencies, according to which mathematics has no subject matter and is therefore in a cer technique. We believe that discussions on the nature of mathematics in the 19th and 20th century can understood, if we view them from the perspective of the two approaches to its nature descr there again crystalizes a current of views according to which mathematics studies a certai and is therefore a theoretical discipline in the traditional sense of the word, and alongs emphasizing its non-intuitive practice, according to which mathematics is a kind of techni Our conference will focus on how the nature of mathematics is regarded by representatives structuralism. On the one hand, these two currents have much in common (they both agree th is not intuitive). On the other hand, they differ precisely in how they approach the probl mathematics does or does not have subject matter. Formalists reduce mathematics to mere ma signs, thereby giving rise to the appearance that on their view mathematics cannot have an while many structuralists admit objective grounding of mathematics and thereby return to t theoretical conception of science. We divide the problems we wish to address at the conference into historical ones and syste In the first thematic area we will ask what earlier trends formalism and structuralism fol these current were constituted, and how they eventually became respected philosophical pos second area we will welcome reflections addressing the relationship between formalism and (similarities and dissimilarities), and further also solutions to some contemporary proble with these two approaches.