Dear Cheerful Logicians and Friends of Logic, Before getting to the week's events, a note: throughout the day on Friday, there is a workshop being hosted jointly by CUNY's Logic and Metaphysics Group and the Saul Kripke Center. The topics are substructural Logics, hierarchies thereof, and solutions to the Liar. You can find a schedule of talks together with abstracts here <https://logic.commons.gc.cuny.edu/wp-content/blogs.dir/3617/files/2020/10/October-30-Workshop-Abstracts.pdf>. For more information and to register for the meeting, please email Graham Priest ([email protected]).
There are a whopping eight events to announce this week: one each on Monday, three on Wednesday, one on Thursday and another three on Friday. Details below. Supergroup Talk 1 *Speaker: *Koji Tanaka (ANU) *Title: *Empirical and Normative Arguments for Paraconsistency *Time and Date: *Thursday, October 29th 19:00 GMT-5 *Link: * https://unimelb.zoom.us/j/846890369?pwd=TktZYmlIUGlYOU9ZaXFJcCt0TFJFZz09 *Abstract: * How can we know which inferences are valid and which ones are not? In particular, how can we know that ex contradictione quodlibet (ECQ) (A, ¬A ⊨ B for every A and B) is invalid as paraconsistent logicians claim? A popular view to answer these questions in recent years is abductivism. According to this view, we should accept a logical theory which best explains the relevant data. One central tenet of abductivism as it is used by paraconsistent logicians is a broadly empirical methodology. Paraconsistent logicians consider empirically observable data and use this to argue that ECQ is invalid. In this paper, I will defend this empirical methodology. First, I will show that some paraconsistent logicians employ an empirical methodology in arguing for the paraconsistent nature of logic. Second, I will present a view of normativity that is compatible with an empirical methodology. Third, I will develop an anti-exceptionalist view that takes logic to be normative, yet continuous with empirical sciences. Fourth, I will argue against the a priori conception of logic. My conclusion will be that the empirical methodology employed by some paraconsistent logicians is defensible. Supergroup Talk 2 *Speaker: *Gisele Secco (UFSM) *Title: *How are they the same? Notes on the identity of the proofs of the Four-Colour Theorem *Time and Date: *Friday, October 30th 9:00 GMT-5 *Link: * https://ksu.zoom.us/j/96049039729?pwd=REVWcDFrU1ZPbEhyazRPT3NkYjQxUT09 *Meeting ID:* 960 4903 9729 *Passcode:* proofs *Abstract: * The Four-Color Theorem (4CT, delivered in [1] and [2]) is the first case of an original mathematical result obtained through the massive use of computing devices. Despite having been the subject of exceptional amounts of advertising and philosophical commentary, this notorious mathematical result is still relevant as a case study in the philosophy of mathematical practice and, more broadly, in the history of mathematics, for two reasons. In the one hand, given the existence of (at least) two other versions of the proof ([3] and [4]) the case suggests a discussion about the criteria for establishing the identity of computer-assisted proofs (with a corollary question about the identity of computer programs, proof assistants etc..). On the other hand, a vital dimension of the proof has not yet been analysed: the interplay between its computational and the diagrammatical elements. Building on the methodological guidelines suggested in [5], I offer a partial description of [1] and [2], showing how computing devices interact with diagrams in these texts. With such a description, I offer a new way of tackling the question about the identity of proofs, articulating both reasons for defending the relevance of the 4CT for the history and the philosophy of mathematical practice. Talks by Other Groups: *Logic and Metaphysics Workshop* (CUNY) *Speaker: *Lisa Warenski (CUNY) *Title: *The Metaphysics of Epistemic Norms *Time and Date: *Monday, October 26th 15:15 GMT-5 *Link:* https://gc-cuny.zoom.us/j/96888694042?pwd=cERxN3hhT3k2TmZvdlQzL3dPdzhyZz09 *Meeting ID:* 968 8869 4042 *Passcode:* 847819 *Abstract: *A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain. A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory. Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms. But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment? In this paper, I take up these questions for epistemic norms. Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values. Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth. *Helsinki Logic Seminar* *Speaker: *Yurii Khomskii (Amsterdam University College and Universität Hamburg) *Title: *Bounded Symbiosis and Upwards Reflection *Time and Date: *Wednesday, October 28th 05:00 GMT-5 *Link: * https://us02web.zoom.us/j/4762106037?pwd=ckc1UzhDSHJmQ3I2bEpmNjNWcDNsZz09 *Abstract: *In [1], Bagaria and Väänänen developed a framework for studying the large cardinal strength of Löwenheim-Skolem theorems of strong logics using the notion of Symbiosis (originally introduced by Väänänen in [2]). Symbiosis provides a way of relating model theoretic properties of strong logics to definability in set theory. We continue the systematic investigation of Symbiosis and apply it to upwards Löwenheim-Skolem theorems and upwards reflection principles. To achieve this, the notion of Symbiosis is adapted to what we call "Bounded Symbiosis". As an application, we provide some upper and lower bounds for the large cardinal strength of upwards Löwenheim-Skolem principles of second order logic. This is joint work with Lorenzo Galeotti and Jouko Väänänen. [1] Joan Bagaria and Jouko Väänänen, “On the Symbiosis Between Model-Theoretic and Set-Theoretic Properties of Large Cardinals”, Journal of Symbolic Logic 81 (2) P. 584-604 [2] Jouko Väänänen, "Abstract logic and set theory. I. Definability.” In Logic Colloquium ’78 (Mons, 1978), volume 97 of Stud. Logic Foundations Math., pages 391–421. North-Holland, Amsterdam-New York, 1979. *Lógicos em Quarentena* *Speaker: *Daniele Nantes *Title: *Nominal Equational Problems *Time and Date: *Wednesday, October 28th 14:00 GMT-5 *Link: *https://meet.google.com/row-kniu-dgm *Abstract: *We consider nominal equational problems of the form \exists \vec{W} \forall \vec{Y} :P, where P consists of conjunctions and disjunctions of equations s\approx_\alpha t (read: ``s is \alpha-equivalent to t''), freshness constraints a# t (read: ``a is fresh for t'') and their negations s \not \approx_\alpha t and \neg(a# t), where a is an atom and s, t are nominal terms. In addition to existential and universally quantified variables, problems can also have free variables. We give a general definition of solution parametric on the algebra used to provide semantics to the problem, and a set of simplification rules that can be used to compute solutions in the nominal term algebra. For the latter, we define notions of solved form from which solutions can be easily extracted, and show that the simplification rules are sound, preserving and complete. With a particular strategy of application for the rules, the simplification process terminates, specifying an algorithm to solve nominal equational problems. In particular, the algorithm can be used to decide the validity of a first-order equational formula in the nominal term algebra. *IU Logic Seminar* *Speaker: *Marko Malink (NYU) and Anubav Vasudevan (University of Chicago) *Title: *Peripatetic Connexive Logic *Time and Date: *Wednesday, October 28th 15:00 GMT-5 *Link: * https://iu.zoom.us/j/95326399432?pwd=VmVUWGxHeG5KQjEzQVozb3pCRHJVZz09 *Meeting ID:* 953 2639 9432 *Password:* Smullyan *Abstract: *Ancient Peripatetic logicians sought to establish the priority of categorical over propositional logic by reducing various modes of propositional reasoning to categorical form. In the context of such a reduction, the conditional φ-->ψ is interpreted as a categorical proposition A holds of all B, in which B corresponds to the antecedent φ and A to the consequent ψ. Under this interpretation, Aristotle’s law of subalternation (A holds of all B, therefore A holds of some B) corresponds to a version of Boethius' Thesis (φ-->ψ, therefore not-(φ-->not-ψ)). Jonathan Barnes has argued that this consequence renders the Peripatetic program of reducing propositional to categorical logic inconsistent. In this paper, we will challenge Barnes's verdict. We will argue that the system of connexive logic that most closely aligns with the reduction of propositional to categorical logic envisioned by the ancient Peripatetics is both non-trivial and consistent. Such consistency is achieved by limiting the system to first-order conditionals, in which both the antecedent and the consequent are simple categorical propositions. *UConn Logic Group* *Speaker: *Ethan Brauer, Øystein Linnebo, and Stewart Shapiro *Title: *Divergent potentialism: A modal analysis with an application to choice sequences *Time and Date: *Friday, October 30 10:00 GMT-5 *Link: * https://us02web.zoom.us/j/85801711433?pwd=QVBTYW1UaUJsMytJV1ZnaUEweDJUQT09 *Meeting ID:* 858 0171 1433 *Passcode:* choice *Abstract: *Modal logic has recently been used to analyze potential infinity and potentialism more generally. However, this analysis breaks down in cases of divergent possibilities, where the modal logic is weaker than S4.2. This talk has three aims. First, we use the intuitionistic theory of free choice sequences to motivate the need for a modal analysis of divergent potentialism and explain the challenge of connecting the ordinary theory of choice sequences with our modal explication. Then, we use the so-called Beth-Kripke semantics for intuitionistic logic to overcome those challenges. Finally, we apply the resulting modal analysis of divergent potentialism to make choice sequences comprehensible in classical terms. *Berkeley Logic Colloquium* *Speaker: *Anush Tserunyan *Title: *A backward ergodic theorem and its forward implications *Time and Date: *Friday, October 30 18:10 GMT-5 *Link: *http://logic.berkeley.edu/events.html *Abstract: *In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation T, one takes averages of a given integrable function over the intervals {x, T(x), T2(x), …, Tn(x)} in front of the point x. We prove a “backward” ergodic theorem for a countable-to-one pmp T, where the averages are taken over subtrees of the graph of T that are rooted at x and lie behind x (in the direction of T − 1). Surprisingly, this theorem yields forward ergodic theorems for countable groups, in particular, one for pmp actions of finitely generated groups, where the averages are taken along set-theoretic (but right-rooted) trees on the generating set. This strengthens Bufetov’s theorem from 2000, which was the most general result in this vein. This is joint work with Jenna Zomback. 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 If you are part of a member group, are recording talks, and would like the supergroup to host them, then let us know! We'd be happy to help. 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