Supergroup BLAST!
Shay Logan
- On Tuesday at 10:00 GMT-5, Damian Szmuc will speak in the Seminario de Lógica Iberoamericana on a very apt topic for these times---*Immune* logics!
- On Thursday at 14:00 GMT-5, Brendan Fong will speak in the Lógicos em Quarentena seminar on compositional perspectives on supervised learning.
- Later on Thursday is the first of our official supergroup talks. At 19:00 GMT-5, Graham Priest will speak in the Melbourne Logic Seminar about Impossible Worlds.
- Finally, on Friday at 11:00 GMT-5, Stephen Read will talk to us about Paul of Venice's solutions to logical paradoxes.
Supergroup Talk 1:
Speaker: Graham Priest (CUNY)
Title: Mission Impossible
Time and Date: Thursday August 13th, 19:00 GMT-5
Link: https://unimelb.zoom.us/j/846890369?pwd=TktZYmlIUGlYOU9ZaXFJcCt0TFJFZz09
Abstract: Saul Kripke's work on the semantics of non-normal modal logics introduced the idea of non-normal worlds, worlds where logically impossible things may hold. Such worlds can naturally be thought of as impossible worlds. Since Kripke's invention, the notion of an impossible world has undergone much fruitful development and application. Impossible worlds may be of different kinds—or maybe different degrees of impossibility; and these worlds have found application in many areas where hyperintensionality appears to play a significant role: intentional mental states, counterfactuals, meaning, property theory, to name but a few areas. But what, exactly, is an impossible world? How is it best to characterise the notion? To date, the notion is used more by example than by definition. In this paper I will investigate the question and propose a general characterisation, suitable for all standard purposes and tastes. In particular, it can be deployed whatever one takes the correct logic to be.
Supergroup Talk 2:
Speaker: Stephen Read (St. Andrews)
Title: “Everything true will be false”: Paul of Venice’s two solutions to the logical paradoxes
Time and Date: Friday August 14th, 11:00 GMT-5
Link: https://ksu.zoom.us/j/96831198878?pwd=ZnZTVmhFQjdIYUJJUXlXbkxkaUZodz09
Meeting ID: 968 3119 8878
Passcode: OfVenice
Abstract: In his Quadratura, Paul of Venice (1369-1429) considers a sophism involving time and tense which appears to show that there is a valid inference which is also invalid. His argument runs as follows: consider the inference concerning some proposition A: A will signify only that everything true will be false, so A will be false. Call this inference B. Then B is valid because the opposite of its conclusion is incompatible with its premise. In accordance with the standard medieval doctrine of ampliation, Paul takes A to be equivalent to ‘Everything that is or will be true will be false’. But he proceeds to argue that it is possible that B’s premise (‘A will signify only that everything true will be false’) could be true and its conclusion false, so B is not only valid but also invalid. Thus A is the basis of a logical paradox, aka an insoluble.
In his Logica Parva, a self-confessedly elementary texts aimed at students and not necessarily representing his own view, and in the Quadratura, Paul follows the solution found in the Logica Oxoniensis, which posits an implicit assertion of its own truth in insolubles like B. However, in the treatise on insolubles in his Logica Magna, Paul develops and endorses Roger Swyneshed’s solution, which stood out against this “multiple-meanings” approach in offering a solution that took insolubles at face value, meaning no more than is explicit in what they say. On this account, insolubles imply their own falsity, and that is why, in so falsifying themselves, they are false. We consider how both types of solution apply to B and how they complement each other. On both, B is valid. But on one (following Swyneshed), B has true premises and false conclusion, and contradictories can be false together; on the other (following the Logica Oxoniensis), the counterexample is rejected.
Talks by Member Groups:
Seminario de Lógica Iberoamericana:
Speaker: Damian Szmuc (Buenos Aires)
Title: Immune Logics
Time and Date: Tuesday, August 11 10:00am GMT-5
Link: https://us02web.zoom.us/j/89354138458?pwd=eXRmQmltS0xnTzE4anB5Q0hWTGF2Zz09
Meeting ID: 893 5413 8458
Password: 195576
Abstract: In the past few years, the family of many-valued logics called infectious logics received an increasing amount of attention. These systems count with a truth-value that is assigned to a complex formula whenever it is assigned to some of its components---thus, behaving in an infectious way. Rather informally, we could say that these values behave in a "value-in-value-out" fashion. From a mathematical point of view, infectious values of this sort can be thought of as all-purpose zero elements. The aim of this talk is to discuss a family of many-valued logics that can perhaps be considered as duals to the infectious systems---whence, they will be called immune logics. In this vein, these logics count with a truth-value that is never assigned to a complex formula whenever it is assigned to some of its components, except in certain cases. Once again rather informally, we could say that in some of these cases these values behave in a "value-in-different-value-out" manner. Therefore, immune values of this sort can be thought of as all-purpose identity elements. As regards immune logics, our goal is to describe and analyze various three-valued systems. For this purpose, we explore immune logics where validity is defined by letting the immune value be designated, systems where it is undesignated, and systems where mixed notions of validity are adopted. In doing so, we highlight the links to various logics that have already appeared in the literature and some which were not discussed until now.
Lógicos em Quarentena
Speaker: Brendan Fong (MIT)
Title: Backprop as Functor: A compositional perspective on supervised learning
Time and Date: Thursday, August 6 14:00 GMT-5
Link: https://meet.google.com/qhk-kstn-ahy
Abstract: A supervised learning algorithm searches over a set of functions A→B parametrised by a space P to find the best approximation to some ideal function f:A→B. It does this by taking examples (a,f(a))∈A×B, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent---with respect to a fixed step size and an error function satisfying a certain property---defines a monoidal functor from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.
Other Notes and Announcements:
The supergroup finally has its own official website! Woohoo! Here's a link. Thanks to Damian Szmuc for getting this up and running!
Universität Regensburg is hosting a virtual workshop on August 27 and 28. The workshop is title "If ifs and ands were pots and pans ..." Qualitative and quantitative approaches to reasoning and conditionals. For more information visit this link.
The Logic Supergroup has a YouTube channel! Recordings of almost all talks are available at https://www.youtube.com/channel/UCqOAS8SHP-5nGjYEE2FE6xw
To access the supergroup calendar, please follow this link: https://calendar.google.com/calendar?cid=ZGhoanNoanF1bGhmaG9xam5scDJlc2o0bDhAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ
To access the member groups joint calendar, please follow this link: https://calendar.google.com/calendar?cid=aG8wNWljaGxkNXI2N2oyMnZvY3BzdmRoMWNAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ
If you represent a member group and would like your events to appear on the joint calendar, be sure to add them! Contact any of the organizers if you need permission to do so.
Yay for logic!
Walter Alexandre Carnielli
We have an even bountifuller week ahead! We are forgetting
Alfredo Roque Freire (perhaps I had to fill some Supergroup agenda,
and did not...)
In any case, there's still time to add:
==================================
Dear enthusiastic logicians and partisans of Logic:
As part of the Logic Supergroup
(https://sites.google.com/view/logicsupergroup/the-logic-supergroup),
Colloquium Logicar is happy to announce its next meeting on
Wednesday August 12th 2020 ( 2:00 PM, GMT -3 hours) by Alfredo Roque
Freire, who will be talking about a chapter of his PhD thesis (which
I had the privilege to supervise) related to an important topic of
philosophy mathematics:
Title: Unreducible features of set theories
Alfredo Roque Freire
Unicamp/CLE and USP
Abstract: The universalist position in set theory maintains that there
is only a single, maximal universe of sets and, as a result, all
sentences about these objects are ideally verifiable. Often, those who
subscribe to this view are committed to offering a sensible account to
alternative universes familiar to many mathematicians. In this
article, we will analyze the reduction strategies offered by
universalists. Recently, Enayat in [1] proved that no two models of ZF
are bi-interpretable, while Hamkins and I in [2] proved that no two
well-founded models of
ZF are mutually interpretable. In view of these results, we will argue
that the range of the construction for alternative universes in a
single universe is limited. Thus, the adherents of an alternative
universe have sufficient grounds to reject the alleged copy offered by
the universalist as a faithful copy. Finally, we will argue that the
reasons for adding new elements to the multiverse should be specific
instead of being the result of an emulation in a previously known
universe.
[1] Enayat, A. (2017). Variations on a Visserian theme. arXiv preprint
arXiv:1702.07093.
[2] Freire, A. R., & Hamkins, J. D. (2020). Bi-interpretation in weak
set theories. arXiv preprint arXiv:2001.05262.
To participate. please access.
https://conferenciaweb.rnp.br/spaces/unicamp-cle-colloquium-logicae
**Please enter as “anonymous” unless you have an RNP account
Everyone welcome!
Shay Logan
The supergroup finally has its own official website. Here's a link.
Universität Regensburg is hosting a virtual workshop on August 27 and 28 that might be of interest to many members. For more information visit this link.
The Logic Supergroup has a YouTube channel! Recordings of almost all talks are available at https://www.youtube.com/channel/UCqOAS8SHP-5nGjYEE2FE6xw
Supergroup Talk:
Speaker: Eleonora Cresto
Title: The Logic of Ungrounded Payoffs
Time and Date: Friday August 21, 0900 GMT-5
Link: https://ksu.zoom.us/j/98598883520?pwd=N09pdjdyU2NDK2xISU9kcGRCek9VQT09
Meeting ID: 985 9888 3520
Passcode: Payoffs
Abstract: Higher order likes and desires sometimes lead agents to have ungrounded or paradoxical preferences. This situation is particularly problematic in the context of games. If payoffs are interdependent, the overall assessment of particular courses of action becomes ungrounded; in such cases the matrix of the game is radically under-determined. In this talk I propose a dynamic doxastic and preference logic that can mimic the search for a suitable matrix. Upgrades are triggered by conjectures on other players’ utilities, which can in turn be based on behavioral or verbal cues. We can prove that, under certain conditions, pairs of agents with paradoxical preferences eventually come to believe that they are not able to interact in a game. As a result I hope to provide a better understanding of game-theoretic ungroundedness, and, more generally, of the structure of higher order preferences and desires.
Talks by Member Groups:
Lógicos em Quarentena
Speaker: Jeremy Avigad
Title: Formal Mathematics and the Lean Theorem Prover
Time and Date: Thursday, August 20 14:00 GMT-5
Link: https://meet.google.com/ijx-mwhr-fjg
Abstract: Since the early twentieth century, it has been understood that mathematical statements can be expressed in formal languages, and mathematical proofs can be represented in formal deductive systems with precise rules and semantics, at least in principle. Remarkably, the development of computational proof assistants over the last few decades has made it possible to do this in practice. The technology is firmly based on the methods and concepts of modern logic, and in many ways the practice represents the contemporary embodiment of the foundational tradition.
In this informal talk, I will provide a brief overview of interactive theorem proving and the body of logic that supports it. I will then discuss a particular theorem prover, Lean, its formal library, mathlib, which are attracting a growing community of mathematical users. The Lean community web pages provide a good starting point for more information: https://leanprover-community.github.io/.
Other Notes and Announcements:
Walter Alexandre Carnielli
As part of the Logic Supergroup
(https://sites.google.com/view/logicsupergroup/the-logic-supergroup),
seminar with the OCIE Seminar in the History and Philosophy of
Mathematics and Logic, University of California Irvine as of
Tuesday 8th September, 4pm-6pm hours (GMT -7) by Alfredo Roque
Freire;
=============================================
Title: " Intentional theory dichotomy and twisted models of set theory"
Alfredo Roque Freire
Post-Doc Researcher
Centre for Logic, Epistemology and the History of Science
University of Campinas-Unicamp, Brazil
Two modes of description were familiar to modern mathematicians: (i)
descriptions of mathematical types to be satisfied by various
structures, such as rings, fields, monoids; and (ii) intentional
descriptions, which seek to specify mathematical objects as in
geometry, arithmetic and real analysis. Due to the various limiting
theorems in relation to formal systems (e.g. G\"odel's incompleteness
and Loweinhein-Skolem theorems), it has become common to maintain that
there is no sharp boundary between intentional and non-intentional
theories. Since it is not possible to fix a single model for first
order arithmetic, its axioms work in a similar way to axioms of
general algebraic structures. This conclusion is the result of the
following dichotomy: either there are precise and unambiguous ways to
describe general collections of objects or there is no clear boundary
between intentional theories and non-intentional theories. However,
recent results on interpretability [1,2,3] develop restricted versions
of absoluteness regarding theories historically considered to be
intentional. In fact, models of arithmetic and set theory are unique
with respect to bi-interpretations. We will argue that these results
allow us not only to recover the dichotomy that separates intentional
from non-intentional theories, but still remain compatible with
pluralism regarding theories such as arithmetic and set theory.
Finally, we will show to what extent conditions of absoluteness may be
used as sufficient to incorporate non-classical set theories to the
multiverse. We believe this absoluteness conditions are possibly
obtained for the novel twisted valued models developed by Carnielli
and Coniglio [4]. We will argue that these paraconsistent models have
the virtue of being sufficiently rigid, and thus may be successfully
included in the multiverse.
[1] Friedman, H. M., & Visser, A. (2014). When bi-interpretability
implies synonymy. Logic Group Preprint Series, 320, 1-19.
[2] Enayat, A. (2017). Variations on a Visserian theme. arXiv preprint
arXiv:1702.07093.
[3] Freire, A. R., & Hamkins, J. D. (2020). Bi-interpretation in weak
three-valued paraconsistent set theory.
Logic and Logical Philosophy,, ON LINE FIRST:
https://apcz.umk.pl/czasopisma/index.php/LLP/article/view/LLP.2020.015
=====================
Everyone is invited to join us on Zoom:
Zoom link: https://uci.zoom.us/j/95859575948
===================================================
Walter Carnielli
https://waltercarnielli.com/
Centre for Logic, Epistemology and the History of Science and
Department of Philosophy
University of Campinas –UNICAMP
13083-859 Campinas -SP, Brazil
Walter Alexandre Carnielli
by Alfredo Roque Freire is being organized by the following consortium:
Chapman University, USC San Bernardino, Claremont University, UC
Riverside and Colloquium Logicae of CLE-Unicamp;
=============================================
Title: " Intentional theory dichotomy and twisted models of set theory"
Alfredo Roque Freire
Post-Doc Researcher
Centre for Logic, Epistemology and the History of Science
University of Campinas-Unicamp, Brazil
Everyone is invited to join us on Zoom:
Zoom link: https://uci.zoom.us/j/95859575948
==================================================