The Logic and Metaphysics Workshop will meet on November 15th from 4:15-6:15 (NY time) via Zoom for a talk by Sara Uckelman (Durham).

Title: John Eliot’s Logick Primer: A bilingual English-Algonquian logic textbook

Abstract: In 1672 John Eliot, English Puritan educator and missionary, published The Logick Primer: Some Logical Notions to initiate the INDIANS in the knowledge of the Rule of Reason; and to know how to make use thereof [1]. This roughly 80 page pamphlet focuses on introducing basic syllogistic vocabulary and reasoning so that syllogisms can be created from texts in the Psalms, the gospels, and other New Testament books. The use of logic for proselytizing purposes is not distinctive: What is distinctive about Eliot’s book is that it is bilingual, written in both English and Massachusett, an Algonquian language spoken in eastern coastal and southeastern Massachusetts. It is one of the earliest bilingual logic textbooks, it is the only textbook that I know of in an indigenous American language, and it is one of the earliest printed attestations of the Massachusett language. In this talk, I will: (1) Introduce John Eliot and the linguistic context he was working in; (2) Introduce the contents of the Logick Primer—vocabulary, inference patterns, and applications; (3) Discuss notions of “Puritan” logic that inform this primer; (4) Talk about the importance of his work in documenting and expanding the Massachusett language and the problems that accompany his colonial approach to this work.

[1] J.[ohn] E.[liot]. The Logick Primer: Some Logical Notions to initiate the INDIANS in the knowledge of the Rule of Reason; and to know how to make use thereof. Printed by M. J., 1672.

The Logic and Metaphysics Workshop will meet on October 18th from 4:15-6:15 (NY time) via Zoom for a talk by Rohit Parikh (CUNY GC).

Title: States of Knowledge

Abstract: We know from long ago that among a group of people and given a true proposition P, various states of knowledge of P are possible. The lowest is when no one knows P and the highest is when P is common knowledge. The notion of common knowledge is usually attributed to David Lewis, but it was independently discovered by Schiffer. There are indications of it also in the doctoral dissertation of Robert Nozick. Aumann in his celebrated Agreeing to Disagree paper is generally thought to be the person to introduce it into game theory. But what are the intermediate states? It was shown by Pawel Krasucki and myself that there are only countably many and they correspond to what S. C. Kleene called regular sets. But different states of knowledge can cause different group actions. If you prefer restaurant A to B and so do I, and it is common knowledge, and we want to eat together, then we are likely to both go to A. But without that knowledge we might end up in B, or one in A and one in B. This was discussed by Thomas Schelling who also popularized the notion of focal points. Do different states of knowledge always lead to different group actions? Or can there be distinct states which cannot be distinguished through action? The question seems open. It obviously arises when we try to infer the states of knowledge of animals by witnessing their actions. We will discuss the old developments as well as some more recent ideas.

The Logic and Metaphysics Workshop will meet on November 8th from 4:15-6:15 (NY time) via Zoom for a talk by Roman Kossak (CUNY GC).

Title: How undefinable is truth?

Abstract: Almost any set of natural numbers you can think of is first-order definable in the standard model of arithmetic. A notable exception is the set Tr of Gödel numbers of true first-order sentences about addition and multiplication. On the one hand—by Tarski’s undefinability of truth theorem—Tr has no first order definition in the standard model; on the other, it has a straightforward definition in the form of an infinite disjunction of first order formulas. It is definable in a very mild extension of first-order logic. In 1963, Abraham Robinson initiated the study of possible truth assignments for sentences in languages represented in nonstandard models of arithmetic. Such assignments exist, but only in very special models; moreover they are highly non-unique, and—unlike Tr—they are not definable any  reasonable formal system. In the talk, I will explain some model theory behind all that and I will talk about  some recent results in the study of axiomatic theories of truth.

The Logic and Metaphysics Workshop will meet on October 4th from 4:15-6:15 (NY time) via Zoom for a talk by Yale Weiss (CUNY GC).

Title: Bisemilattice Semantics for Intuitionistic and Relevant Modal Logics

Abstract: In this talk, I consider modal logics extending J (intuitionistic logic) and RMO (sometimes called ‘constructive mingle’). Adapting previous work of Humberstone, all of these systems are given a purely operational bisemilattice semantics and soundness and completeness results are proved. I consider a way of exactly translating each intuitionistic modal system into a relevant modal companion and discuss what, if any, light this sheds on the interpretation of the relevant companions. Various applications are examined (e.g., to developing constructive theories of entailment) and results germane to those applications are proved. I also discuss connections between the present semantic framework and related frameworks, including Fine’s hybrid operational-partial order semantics, inquisitive semantics, and Urquhart’s semilattice semantics.

The Logic and Metaphysics Workshop will meet on September 27th from 4:15-6:15 (NY time) via Zoom for a talk by Rashed Ahmad (University of Connecticut).

Title: A Recipe for Paradox (A Better Schema than the Inclosure Schema)

Abstract: In this talk, we provide a recipe that not only captures the common structure between semantic paradoxes but it also captures our intuitions regarding the relations between these paradoxes. Before we unveil our recipe, we first talk about a popular schema introduced by Graham Priest, namely, the inclosure schema. Without rehashing previous arguments against the inclosure schema, we contribute different arguments for the same concern that the inclosure schema bundles the wrong paradoxes together. That is, we will provide alternative arguments on why the inclosure schema is both too broad for including the Sorites paradox, and too narrow for excluding Curry’s paradox. We then spell out our recipe. Our recipe consists of three ingredients: (1) a predicate that has two specific rules, (2) a simple method to find a partial negative modality, and (3) a diagonal lemma that would allow us to let sentences be their partial negative modalities. The recipe shows that all of the following paradoxes share the same structure: The liar, Curry’s paradox, Validity Curry, Provability Liar, a paradox leading to Löb’s theorem, Knower’s paradox, Knower’s Curry, Grelling-Nelson’s paradox, Russell’s paradox in terms of extensions, alternative liar and alternative Curry, and other unexplored paradoxes. We conclude the talk by stating the lessons that we can learn from the recipe, and what kind of solutions does the recipe suggest if we want to adhere to the Principle of Uniform Solution.

The Logic and Metaphysics Workshop will meet on September 20th from 4:15-6:15 (NY time) via Zoom for a talk by Teresa Kouri Kissel (Old Dominion University).

Title: Carnap is not a Pluralist

Abstract: Rudolf Carnap is often thought to be a prototype of a logical pluralist. That is, Carnap is thought to hold that more than one logic is correct. I will show in this paper that he cannot be a logical pluralist. I will also show that he cannot be a logical monist or nihilist. In effect, depending on how and where we ask “is logical pluralism true?”, or “how many logics are correct?”, we will find that the answer differs. Thus, he cannot be said to hold that only one of those theories is correct.

The Logic and Metaphysics Workshop will meet on September 13th from 4:15-6:15 (NY time) via Zoom for a talk by Ricki Bliss (Lehigh University).

Title: Metaphysical Overdetermination

Abstract: It is widely recognized by proponents of the notion that grounding can be, indeed is, overdetermined.  Further to this, it seems safe to suppose that something of a consensus has emerged: grounding is overdetermined and there is nothing about it, either conceptually or metaphysically, that we ought to find concerning.  But from a small sampling of alleged cases no such conclusions can responsibly be drawn.  This paper aims to demonstrate that there is nothing obvious or straightforward about grounding overdetermination and that the topic is deserving of much more serious philosophical attention.

The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 (NY time) entirely online, unless otherwise noted. The provisional schedule is as follows:

Sep 13. Ricki Bliss (Lehigh University)

Sep 20. Teresa Kouri Kissel (Old Dominion University)

Sep 27. Rashed Ahmad (University of Connecticut)

Oct 4. Yale Weiss (CUNY GC)

Oct 11. NO MEETING

Oct 18. Rohit Parikh (CUNY GC)

Oct 25. Noah Friedman-Biglin (San José State University)

Nov 1. Thomas Macaulay Ferguson (University of Amsterdam)

Nov 8. Roman Kossak (CUNY GC)

Nov 15. Sara Uckelman (Durham University)

Nov 22. Konstantinos Georgatos (John Jay)

Nov 29. Martin Pleitz (Münster)

Dec 6. Dirk Batens (University of Ghent)

Dec 13. Dolf Rami (Ruhr-Universität Bochum)