Dear Cheerful Logicians and Friends of Logic, Before getting to the week's events, two notes. First, The Canadian Society for Epistemology is hosting their annual conference this week. The topic of the conference is "the nature and role of deductive reasoning," which was chosen in light of the forthcoming book by Catarina Dutilh Novaes. More detail about the conference can be found at their website: http://sce-cse.recherche.usherbrooke.ca/cse-2020/ or on the supergroup member groups calendar.
Second, if you are a member group and would like to host your videos on the supergroup's youtube channel, get in touch, and I am happy to work with you to help make this possible. Now to the week's events: in addition to the CSE conference just mentioned, there are five other events listed on the calendar at this time; one on Monday, two on Thursday, and two on Friday. Details follow. Supergroup Talk Number 1 Speaker: Yao Tang (La Trobe) Title: Recursive relations on the set of words with 2 letters Time and Date: Thursday, October 15 19:00 GMT-5 *Link: * https://unimelb.zoom.us/j/846890369?pwd=TktZYmlIUGlYOU9ZaXFJcCt0TFJFZz09 *Abstract: *Recursive functions on the natural numbers can be characterized as the class of functions generated from a specified list of initial functions and inductive conditions. In “Undecidability without Arithmetization”, Andrzej Grzegorczyk constructed a class GD of relations on theset of words with 2 letters, which is characterized in a similar way (as the class of relations generated from a specified list of initial relations and inductive conditions). We want to show that GD is precisely the class of relations on the set of words with 2 letters that are also recursive sets. Supergroup Talk Number 2 Speaker: Edson Bezerra (UNICAMP) Title: Squeezing arguments and the plurality of informal notions Time and Date: Friday, October 16 9:00 GMT-5 *Link: * https://ksu.zoom.us/j/94976439500?pwd=VmV4N01FK3pkUjE1RSthaS83a1JWZz09 *Meeting ID:* 949 7643 9500 *Passcode:* informal *Abstract: *Kreisel's squeezing argument (1967) shows that there is an informal notion of validity which is irreducible to both model-theoretic and proof-theoretic validity of First-Order Logic (FOL), but coextensive with both formal notions. His definition of informal validity as truth in all structures received some criticisms in the literature for being heavily model-theoretical (Smith (2011) and Halbach (2020)). However, because of its simple and schematic form, variants squeezing argument has been presented for capturing other intuitive notions of validity closer to our pre-theoretical notion of validity (Shapiro, 2005). Therefore, the different squeezing arguments we find in the literature show that there are other informal notions of logical validity, which are coextensive with their corresponding formal definition of logical validity. In this talk, we argue for an even form of pluralism, showing that squeezing arguments cannot squeeze in the uniqueness of the corresponding informal notion. Indeed, we maintain that a complete logical system can be compatible with different notions of informal validity. Talks by Other Groups: *Logic and Metaphysics Workshop* (CUNY) *Speaker: *Brian Cross Porter (CUNY) *Title: *A Metainferential Hierarchy of Validity Curry Paradoxes *Time and Date: *Monday, October 12, 15:15 GMT-5 *Link: * https://gc-cuny.zoom.us/j/93339421821?pwd=WUlGdG4xUGdob05pbEk3T29pckdjUT09 *Meeting ID: *933 3942 1821 *Passcode: *292620 *Abstract: *The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of meta-n-inferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox. *Lógicos em Quarentena* Speaker: Hugo Luiz Mariano Time and Date: Thursday, October 15, 14:00 GMT-5 *Title: *An algebraic framework to a theory of sets based on the surreal numbers *Link: *https://meet.google.com/sqh-iepr-ges *Abstract: *The surreal numbers constitute a linearly ordered (proper) class $No$ containing the class of all ordinal numbers ($On$), that satisfies many interesting properties. In an attempt to codify the universe of sets directly within the surreal number class, we have founded some clues that suggest that this class is not suitable for this purpose. Carefully formalizing the definition of the class of pre-(surreal) numbers (and some variants), which is an intermediate stage in the construction of the Conway surreal numbers, we obtain structures which have copies of $No$ as well the class the universe of all sets ($V$).as well as copies of the class of surreal numbers. Thus, in particular, we gave first steps toward a certain kind of "relative set theory", in this new setting. The main aim of this work is to isolate and explore properties of these new constructions and present the notion of (partial) SUR algebra, an attempt to obtain an "algebraic theory for surreal numbers" along the lines of the Algebraic Set Theory of Joyal and Moerdijk: to establish (abstract and general) links between the class of all surreal numbers and a universe of "surreal sets" similar to the relations between the classes $On$ and $V$, of all ordinals and the class of all sets, that respects and expands the links between the linearly ordered class $On$ and $No$ of all ordinals and of all surreal numbers. *OCIE seminar in HPML* *Speaker: *Ekaterina Babintseva *Time and Date: *Friday, October 16, 11:00 GMT-5 *Title: *Of Minds and Computers: Harnessing Mathematical Creativity *Link: * https://pitzer.zoom.us/j/96937631191?pwd=RkZZKzQyT2Z3Y3B2OHk0Y0I3SzZMdz09 *Abstract: *In the mid-20th century, “creative thinking” became a prominent category in American psychology and pedagogy. Advanced by cognitive psychologists as both a descriptive and a normative characteristic of the human self, the notion of creative thinking soon came to shape many mid-century debates in mathematics pedagogy. This paper traces the work of the educational psychologists and mathematicians at the University of Illinois who attempted to create special computer software that would teach creative thinking in mathematics. Developed for the University of Illinois’ PLATO (Programmed Logic for Automated Teaching Operations) teaching computer, this software sought to introduce students to the intuitive aspect of mathematical thinking. Following this research through the 1960s-1970s, this paper discusses how scientists used PLATO as a laboratory for testing mid-century theories of learning and approaches to math education. Other Notes and Announcements: - *The Logic Supergroup has a YouTube channel!* Recordings of almost all talks are available at https://www.youtube.com/channel/UCqOAS8SHP-5nGjYEE2FE6xw Yay for logic! -- Você está recebendo esta mensagem porque se inscreveu no grupo "LOGICA-L" dos Grupos do Google. Para cancelar inscrição nesse grupo e parar de receber e-mails dele, envie um e-mail para [email protected]. Para ver esta discussão na web, acesse https://groups.google.com/a/dimap.ufrn.br/d/msgid/logica-l/CAMTR990UmJGM-1rkNuWuYbBOZSuytyM9uwwj-uDM7AS3qVdvgQ%40mail.gmail.com.
