The Logic and Metaphysics Workshop will meet on December 13th from 4:15-6:15 (NY time) via Zoom for a talk by Dolf Rami (Bochum).

Title: Singular existentials and three different kinds of negation

Abstract: In this paper, I will argue for a new semantic analysis of (i) singular existential and (ii) atomic sentences to be able to cover three possible types of negation of them. Firstly, I will show that all three negations of sentences of kind (i) are equivalent if we make use of referring or non-referring names, while on the other hand the three negations of sentences of kind (ii) have several non-equivalent readings if non- referring names are used. Secondly, I will review the partial solutions to our problem given by Russell, Quine and Sainsbury and show in how far they fail. Thirdly, I will propose an alternative solution based on a semantics outlined in Rami (2020). Finally, I will show that we must distinguish two types of negation and that a unification in both directions fails.

The Logic and Metaphysics Workshop will meet on December 6th from 4:15-6:15 (NY time) via Zoom for a talk by Diderik Batens (Ghent).

Title: Every Logic has its Proper Semantics

Abstract: Many logics are sound and complete with respect to a multiplicity of semantic systems. These assign different sets of models to the logic. It will be shown that a series of problems result if all these semantic systems are on a par. I shall present a method to define a unique ‘proper’ semantics for the members of a huge class of logics, containing all usual deductive logics, and argue (i) that the proper semantics is defined in terms of syntactic criteria and so depends fully on the logic, (ii) that there are philosophical arguments to consider a logic’s proper semantics as natural, for example it correctly describes the ‘situations’ that are possible according to the logic. This solves the problems mentioned previously. Implications for the discussion on inferentialism are obvious. For some logics, the proper semantics coincides with the Henkin semantics. For other logics L, the proper semantics counts more models than the Henkin semantics: moreover, not all Henkin models are maximally L-non-trivial. A small change to the Henkin method has the effect that, for every logic L, the Henkin semantics coincides with the proper semantics.

The Logic and Metaphysics Workshop will meet on November 29th from 4:15-6:15 (NY time) via Zoom for a talk by Martin Pleitz (Münster).

Title: Dualism about Generality

Abstract: In my talk I will motivate, outline, and apply a variant of first order predicate logic that can distinguish between two kinds of generality, which I call objectual generality and conceptual generality. To see the difference, compare the two general statements ‘Every human is a featherless biped’ and ‘Every human is a rational animal’. On a charitable understanding, the first sentence is about all humans past and present, as a subcollection of all particular objects currently accessible to us, while the second sentence is not about any particular object at all, but about the interaction of the concepts of being human and being a rational animal. Historically, the quantified sentences of predicate logic have been understood in either of the two ways. Frege understood them as expressing conceptual generalities; hence it was natural for him to call his predicate logic a “Concept Script”. Today, they are usually understood as objectual generalities, manifest both in the idea that a quantified sentence is like a conjunction (or disjunction) of its instances and in the current model theoretic orientation in semantics. But as we can find ourselves in a situation where we want to talk about both kinds of generality (and their interaction), it is worthwhile to develop the resources to express them within a single system. I will outline such a system that results from adding a second pair of quantifiers to regular first order predicate logic, and sketch applications to the notion of analyticity, natural kind predicates, and the ontological argument.

The Logic and Metaphysics Workshop will meet on November 22nd from 4:15-6:15 (NY time) via Zoom for a talk by Konstantinos Georgatos (John Jay).

Title: Similarity through indistinguishability: the geodesic reasoning on Kripke models

Abstract: Several logical operators, such as conditionals, revision, and merge, are often understood through the selection of most similar worlds. In applications, similarity is expressed with distance and “most similar” translates to “closest” using a distance metric. We shall argue that similarity may arise through an indistinguishability relation between possible worlds and employ the geodesic distance of such a model to measure closeness. This understanding allows us to define a variety of operators that correspond to merging and revising. I will present a few systems and representation results and will show that revision, merging, and conditioning are interdefinable thus, in effect, satisfying the Ramsey test.

The Logic and Metaphysics Workshop will meet on November 1st from 4:15-6:15 (NY time) via Zoom for a talk by Thomas Macaulay Ferguson (University of Amsterdam).

Title: The Subject-Matter of Modal Sentences

Abstract: The framework of topic-sensitive intentional modal operators (TSIMs) described by Berto provides a general platform for representing agents’ intentional states of various kinds. For example, a TSIM can model doxastic states, capturing a notion that given the acceptance of antecedent information P, an agent will have a consequent belief Q. Notably, the truth conditions for TSIMs include a subject-matter filter so that the topic of the consequent Q must be “included” within that of the antecedent. To extend the account to languages with richer expressivity thus requires an expanded account of subject-matter. In this talk, I will discuss extending earlier work on the subject-matter of intensional conditionals to the special case of modal sentences whose primary operators are interpreted by possible worlds semantics.

The Logic and Metaphysics Workshop will meet on October 25th from 4:15-6:15 (NY time) via Zoom for a talk by Noah Friedman-Biglin (San José State University).

Title: Regrounding the Unworldly: Pluralism and Politics in Carnap’s Philosophy of Logic

Abstract: The locus classicus of logical pluralism – that is, the view that there is more than on logic, properly so called – since the earliest days of analytic philosophy, can be found in Rudolf Carnap’s ‘principle of tolerance’. Clarifying the principle of tolerance is the focus of this first section of this paper. I will argue that the principle should be understood as widely as possible, and thus we will see that Carnap’s tolerance is a very radical view. In section two, I discuss the motivations Carnap had for his pluralism, and argue that they are based in the Vienna Circle’s “Scientific World-Conception” — a platform of philosophical commitments which set the direction for the Circle’s philosophical investigations as well as a program of social change. What emerges from this discussion is the often-ignored relationship between his logical pluralism and his political views. In short, I will argue that the radical quality of his tolerance is due to these political commitments. In section three, I examine the reasons why this connection is not very well-known. I will argue that the political situation in the United States in the aftermath of World War 2 created conditions where it was dangerous to explicitly link scholarly work and politics, and discuss the reasons that Carnap might have had for distancing himself from – or at least de-emphasizing – the political foundations of his views.

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.