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31504.193604
We furnish a core-logical development of the Gödel numbering framework that allows metamathematicians to attain limitative results about arithmetical truth without incorporating a genuine truth predicate into the language in a way that would lead to semantic closure. We show how Tarski’s celebrated theorem on the arithmetical undefinability of arithmetical truth can be established using only core logic in both the object language and the metalanguage. We do so at a high level of abstraction, by augmenting the usual first-order language of arithmetic with a primitive predicate Tr and then showing how it cannot be a truth predicate for the augmented language. McGee established an important result about consistent theories that are in the language of arithmetic augmented by such a “truth predicate” Tr and that use Gödel numbering to refer to expressions of the augmented language. Given the nature of his sought result, he was forced to use classical reasoning at the meta level. He did so, however, on the additional and tacit presupposition that the arithmetical theories in question (in the object language) would be closed under classical logic. That left open the dialectical possibility that a constructivist (or intuitionist) could claim not to be discomfited by the results, even if they were to “give a pass” on the unavoidably classical reasoning at the meta level. In this study we “constructivize” McGee’s result, by presuming only core logic for the object language. This shows that the perplexity induced by McGee’s result will confront the constructivist (or intuitionist) as well.
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31525.193671
Berry’s Paradox, like Russell’s Paradox, is a ‘paradox’ in name only. It differs from genuine logico-semantic paradoxes such as the Liar Paradox, Grelling’s Paradox, the Postcard Paradox, Yablo’s Paradox, the Knower Paradox, Prior’s Intensional Paradoxes, and their ilk. These latter arise from semantic closure. Their genuine paradoxicality manifests itself as the non-normalizability of the formal proofs or disproofs associated with them. The Russell, the Berry, and the Burali-Forti ‘paradoxes’, by contrast, simply reveal the straightforward inconsistency of their respective existential claims—that the Russell set exists; that the Berry number exists; and that the ordinal of the well-ordering of all ordinals exists. The disproofs of these existential claims are in free logic and are in normal form. They show that certain complex singular terms do not—indeed, cannot—denote. All this counsels reconsideration of Ramsey’s famous division of paradoxes and contradictions into his Group A and Group B. The proof-theoretic criterion of genuine paradoxicality formally explicates an informal and occasionally confused notion. The criterion should be allowed to reform our intuitions about what makes for genuine paradoxicality, as opposed to straightforward (albeit surprising) inconsistency.
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430954.193686
Philosophers of language have tended to treat names merely as tools for talking about individuals, either directly or as part of a denoting phrase. We argue that names are every bit as much tools for tracking, maintaining, and performatively updating our positions in social space, as well as projecting a linguistic persona. This pushes us towards a revised picture of the meanings of names, one which incorporates what we shall call a ‘social sense’.
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1003355.193705
In this short note, which is the final chapter of the volume 60 Years of Connexive Logic, we list ten open problems. Some of these problems are technical and precisely stated, while others are less technical and even speculative. We hope that the list inspires some readers to contribute to the field by tackling one or many of the problems.
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1003377.193716
The present article aims at generalizing the approach to connexive logic that was initiated in [27], by following the work by Paul Egré and Guy Politzer. To this end, a variant of the connexive modal logic CK is introduced and some basic results including soundness and completeness results are established. A tableau calculus is also presented in an appendix.
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1018735.193726
In Family Values, Harry Brighouse and Adam Smith ask whether children need parents. That inquiry seems a wild project, but then philosophers are supposed to question everything and follow the argument where it leads. …
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1063229.193735
This paper investigates two forms of the Routley star operation, one in Routley & Routley 1972 and the other in Leitgeb 2019. We use object theory (OT) to define both forms and show that in OT’s hyperintensional logic, (a) the two forms aren’t equivalent, but (b) become equivalent under certain conditions. We verify our definitions by showing that the principles governing both forms become derivable and need not be stipulated. Since no mathematics is assumed in OT, the existence of the Routley star image s of a situation s is therefore guaranteed not by set theory but by a theory of abstract objects. The work in the paper integrates Routley star into a more general theory of (partial) situations that has previously been used to develop the theory of possible worlds and impossible worlds.
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1076776.193744
In this paper, we provide an axiom system for the relevant logic of equivalence relation frames and prove completeness for it. This provides a partial answer to the longstanding open problem of axiomatizing frames for relevant modal logics where the modal accessibility relation is symmetric. Following this, we show that the logic enjoys Hallden completeness and that a related logic enjoys the disjunction property.
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1112201.193754
Through a series of empirical studies involving native speakers of English, German, and Chinese, this paper reveals that the predicate “true” is inherently ambiguous in the empirical domain. Truth statements such as “It is true that Tom is at the party” seem to be ambivalent between two readings. On the first reading, the statement means “Reality is such that Tom is at the party.” On the second reading, the statement means “According to what X believes, Tom is at the party.” While there appear to exist some cross-cultural differences in the interpretation of the statements, the overall findings robustly indicate that “true” has multiple meanings in the realm of empirical matters.
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1112221.193763
Semantic features are components of concepts. In philosophy, there is a predominant focus on those features that are necessary (and jointly sufficient) for the application of a concept. Consequently, the method of cases has been the paradigm tool among philosophers, including experimental philosophers. However, whether a feature is salient is often far more important for cognitive processes like memory, categorization, recognition and even decision-making than whether it is necessary. The primary objective of this paper is to emphasize the significance of researching salient features of concepts. I thereby advocate the use of semantic feature production tasks, which not only enable researchers to determine whether a feature is salient, but also provide a complementary method for studying ordinary language use. I will discuss empirical data on three concepts, conspiracy theory, female/male professor, and life, to illustrate that semantic feature production tasks can help philosophers (a) identify those salient features that play a central role in our reasoning about and with concepts, (b) examine socially relevant stereotypes, and (c) investigate the structure of concepts.
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1235943.193773
Jeremy Kuhn, Carlo Geraci, Philippe Schlenker, Brent Strickland. Boundaries in space and time: Iconic biases across modalities. Cognition, 2021, 210, pp.104596. �10.1016/j.cognition.2021.104596�.
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1480625.193782
The nature of branching in the many-worlds interpretation (MWI) of quantum mechanics remains an open question, particularly regarding its locality and compatibility with special relativity. This paper challenges the conventional view that branching is either global or local, demonstrating instead that it is nonlocal for entangled systems. Through a new analysis of the EPR-Bohm experiment, I argue that global branching has several potential issues and can hardly be justified. At the same time, I argue that branching cannot be entirely local, as entangled particles exhibit simultaneous, spacelike-separated branching, manifesting an apparent action at a distance within individual worlds. However, while nonlocal branching suggests the emergence of a preferred Lorentz frame within each world, the multiverse as a whole retains full Lorentz invariance, ensuring no superluminal signaling. By refining the ontology of branching and resolving tensions between MWI and relativistic constraints, this analysis may help advance our understanding of quantum nonlocality and also strengthen MWI’s standing as a viable interpretation of quantum mechanics.
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1809984.193791
The inference pattern known as disjunctive syllogism (DS) appears as a derived rule in Gentzen’s natural deduction calculi NI and NK. This is a paradoxical feature of Gentzen’s calculi in so far as DS is sometimes thought of as appearing intuitively more elementary than the rules ∨E, ¬E, and EFQ that figure in its derivation. For this reason, many contemporary presentations of natural deduction depart from Gentzen and include DS as a primitive rule. However, such departures violate the spirit of natural deduction, according to which primitive rules are meant to relationally define logical connectives via universal properties (§2). This situation raises the question: Can disjunction be relationally defined with DS instead of with Gentzen’s ∨I and ∨E rules? We answer this question in the affirmative and explore the duality between Gentzen’s definition and our own (§3). We argue further that the two universal characterizations, rather than provide competing relational definitions of a single disjunction operator, disambiguate natural language’s “or” (§4). Finally, this disambiguation is shown to correspond exactly with the additive and multiplicative disjunctions of linear logic (§5). The hope is that this analysis sheds new light on the latter connective, so often deemed mysterious in writing about linear logic.
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1937861.193801
This paper argues for a unified account of semantic and pragmatic infelicity. It is argued that an utterance is infelicitous when it communicates an inconsistent set of propositions, given the context. In cases of semantic infelicity the relevant utterance expresses a set of inconsistent propositions, whereas pragmatic infelicity is a matter of the utterance conflicting with contextual expectations or assumptions. We spell out this view within the standard framework according to which a central aim of communication is to update a body of information shared among the participants. We show that this account explains different kinds of infelicity for both declarative and non-declarative utterances. Further, the account is seen to make correct predictions for a range of cases involving irony, joking, and related non-assertoric utterances.
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2048013.19381
Until the ‘70s, the received view in the theory of reference was that the referent of a term was identified by certain descriptions that competent speakers associated with the term; for example, the referent of the proper name ‘Aristotle’ was determined by its association with a description like ‘the pupil of Plato and teacher of Alexander the Great’; the reference of the natural kind term ‘tiger’, by a description like ‘large feline with yellow and black stripes and a white belly’. But then came the revolution in the theory of reference, stemming particularly from the works of Kripke (1980) and Putnam (1975). It was argued that this “Description Theory” was fundamentally wrong for many terms, including ‘Aristotle’ and ‘tiger’. “Ignorance and error” arguments were particularly influential. People are often too ignorant to supply descriptions that would uniquely identify the referents of their terms. Most of us refer successfully with ‘elm’, but could not come close to describing those trees well enough to distinguish them from other trees like beeches. Speakers can also associate erroneous descriptions with a term; some who use ‘Einstein’ to refer successfully to the famous physicist wrongly think he invented the atomic bomb.
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2048028.193823
In our paper, “The reference of proper names” (2018), we raised and rebutted the “New-Meaning” objection to our methodology. Our rebuttal rested on theoretical considerations and experimental results. In “Do the Gödel vignettes involve a new descriptivist meaning?”, Nicolò D’Agruma provides an interesting argument against our theoretical considerations (but does not address the experimental evidence). Our present paper argues against D’Agruma. So, our original rebuttal of the objection still stands. We offer further evidence against the objection.
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2048044.193836
Una Stojnic´ urges the radical view that the meaning of context-sensitive language is not “partially determined by non-linguistic features of utterance situation”, as traditionally thought, but rather “is determined entirely by grammar—by rules of language that have largely been missed”. The missed rules are ones of discourse coherence. The paper argues against this radical view as it applies to demonstrations, demonstratives, and the indexical ‘I’. Stojnic´’s theories of demonstrations and demonstratives are found to be seriously incomplete, failing to meet the demands on any theory of reference. Furthermore, the paper argues that, so far as Stojnic´’s theories of these terms go, they are false. This argument appeals to perception-based theories of demonstratives, a part of the tradition that Stojnic´ strangely overlooks. The paper ends by arguing briefly that though coherence has a place in a theory of understanding, it has no place in a theory of meaning.
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2048116.193848
Stojnić holds the radical view that coherence relations determine the reference of context-sensitive language. I argue against this from the theoretical perspective presented in Overlooking Conventions (2021). Theoretical interest in language comes from an interest in thoughts and their communication. A language is a system of symbols, constituted by a set of governing rules, used (inter alia) to communicate the meanings (contents) of thoughts. Thought meanings, hence speaker meanings, are explanatorily prior to semantic meanings. So, we start our consideration of the theoretical place of coherence by considering the bearing of coherence on thought meanings. The paper argues that a person can have any thought at all, however incoherent. So, a thought’s meaning is independent of its coherence. Any thought can be expressed in an utterance. The semantic meaning of any utterance governed by the linguistic rules will be the meaning of the thought it expresses. So, the utterance’s meaning is independent of its coherence. The paper concludes that coherence has no place in the theory of meaning or reference. Nonetheless, it has a place in the theory of communication. I suspect that the error exemplifi es the widespread confusion of the metaphysics of meaning with the epistemology of interpretation.
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2262345.19386
This paper gives a semantic analysis of ‘completion-related verbs of absence’ such as 'lack' and 'be missing' in English. The analysis is based on the notion of a conceptual (integrated or ideal) whole, the notion of a variable object and its variable parts, and an ontology of 'lacks' as entities whose satisfaction involves parts. The semantics will be embedded into that of object-based truthmaker semantics of modals.
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2693579.193873
Discussions on the compositionality of inferential roles concentrate on extralogical vocabulary. However, there are nontrivial problems concerning the compositionality of sentences formed by the standard constants of propositional logic. For example, is the inferential role of AB uniquely determined by those of A and B? And how is it determined? This paper investigates such questions. We also show that these issues raise matters of more significance than may prima facie appear.
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3131203.193883
This paper is a contribution to a symposium on Herman Cappelen’s 2023 book The Concept of Democracy: An Essay on Conceptual Amelioration and Abandonment. In that book, Cappelen develops a theory of abandonment—a theory of why and how to completely stop using particular linguistic expressions—and then uses that theory to argue for the general abandonment of the words “democracy” and “democratic”. In this paper, I critically discuss Cappelen’s arguments for the abandonment of “democracy” and “democratic” in political theory specifically.
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3149158.193892
Incurvati and Schlöder (Journal of Philosophical Logic, 51(6), 1549–1582, 2022) have recently proposed to define supervaluationist logic in a multilateral framework, and claimed that this defuses well-known objections concerning supervaluationism’s apparent departures from classical logic. However, we note that the unconventional multilateral syntax prevents a straightforward comparison of inference rules of different levels, across multi- and unilateral languages. This leaves it unclear how the supervaluationist multilateral logics actually relate to classical logic, and raises questions about Incurvati and Schlöder’s response to the objections. We overcome the obstacle, by developing a general method for comparisons of strength between multi-and unilateral logics. We apply it to establish precisely on which inferential levels the supervaluationist multilateral logics defined by Incurvati and Schlöder are classical. Furthermore, we prove general limits on how classical a multilateral logic can be while remaining supervaluationistically acceptable. Multilateral supervaluationism leads to sentential logic being classical on the levels of theorems and regular inferences, but necessarily strictly weaker on meta- and higher-levels, while in a first-order language with identity, even some classical theorems and inferences must be forfeited. Moreover, the results allow us to fill in the gaps of Incurvati and Schlöder’s strategy for defusing the relevant objections.
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3204560.193902
In this paper, I contrast two broad decompositional approaches to verb semantics. One, especially associated with David Dowty, involves translating verbs using a set of precisely interpreted primitive predicates such as cause and become, in order to facilitate semantic generalizations such as patterns of entailment between sentences. Another, with multiple origins in both temporal semantics and theories of the syntax/semantics interface (including, notably, work by Pustejovsky and Piñón), involves developing a theory of the internal part structure of the eventualities that verbs and other expressions describe; I refer to this approach, following Pianesi and Varzi, as mereotopological. These two approaches to decomposition are not, strictly speaking, incompatible, and they have sometimes been combined; however, perhaps surprisingly, comparison of them has been unsystematic. I address this gap by describing more systematically how the approaches differ from each other, illustrating with differences in the insights they offer into specific aspects of the semantics of simple change of state verbs and unselected object resultatives. I especially aim to promote interest in the development of more sophisticated, cross-linguistically applicable theories of so-called event structure through appeal to a wider range of notions from mereotopology.
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3211287.193911
I would like to begin this review by stating that this is an absolutely wonderful book that is full of gems about the elements and the periodic table. In my own 2007 book on the periodic table I concluded that we should perhaps think of the variety of tables that have appeared as spanning a spectrum running from the most abstract and ‘perfect’ tables such as Janet’s left-step table representation, to the unruly tables that emphasize the uniqueness of elements. To illustrate the latter category, I featured an image of Rayner-Canham’s table that is also the table shown on the front cover of his new book now under review. Rayner Canham’s book is all about the individuality of elements and how so many of the commonly held trends in the periodic table are far more complicated than we normally acknowledge.
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3211307.193921
In this paper, we introduce a concept of non-dependence of variables in formulas. A formula in first-order logic is non-dependent of a variable if the truth value of this formula does not depend on the value of that variable. This variable non-dependence can be subject to constraints on the value of some variables which appear in the formula, these constraints are expressed by another first-order formula. After investigating its basic properties, we apply this concept to simplify convoluted formulas by bringing out and discarding redundant nested quantifiers. Such convoluted formulas typically appear when one uses a translation function interpreting a theory into another.
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3442063.193931
This paper introduces a digital method for analyzing propositional logical equivalences. It transforms the theorem-proof method from the complex statement-derivation method to a simple number-comparison method. By applying the digital calculation method and the expression-number lookup table, we can quickly and directly discover and prove logical equivalences based on the identical numbers, no additional operations are needed. This approach demonstrates significant advantages over the conventional methods in terms of simplicity and efficiency.
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3444284.193941
Flannery O’Connor’s stories are, by her own account, “preoccupied with the grotesque.” The reason, some argue, is that the grotesque is fascinating to the southern imagination. And indeed her grotesques have many southern precedents, most notably those of William Faulkner, whose novel The Sound and the Fury is famously narrated in part by an idiot. …
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3546446.19395
For Austin, Grice, and many others, undertaking a speech act like asserting or promising requires uttering something with a particular sense and reference in mind. We argue that the phenomenon of open-ended promises reveals this ‘Locutionary Thesis’ to be mistaken.
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4018733.193964
Since the early debates on teleosemantics, there have been people objecting that teleosemantics cannot account for evolutionarily novel contents such as “democracy” (e.g., Peacocke 1992). Most recently, this objection was brought up by Garson (2019) and in a more moderate form by Garson & Papineau (2019). The underlying criticism is that the traditional selected effects theory of functions on which teleosemantics is built is unable to ascribe new functions to the products of ontogenetic processes and thus unable to ascribe functions to new traits that appear during the lifetime of an individual organism. I will argue that this underlying thought rests on rather common misunderstandings of Millikan’s theory of proper functions, especially her notions of relational, adapted, and derived proper functions (Millikan 1984: Ch. 2). The notions of relational, adapted, and derived proper functions not only help us solve the problem of novel contents and can ascribe functions to the products of ontogenetic selection mechanisms but are indispensable parts of every selected effects theory.
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4176491.193976
Stanisław Ja´skowski is known to be one of the modern founders of paraconsistent logic, together with Newton C. A. da Costa. The most important contribution of Ja´skowski is that he clearly distinguished two notions for a theory, namely a theory being contradictory (or inconsistent in [18]) and a theory being trivial (or overfilled in [18]). In addition to this distinction, he also presented a system of paraconsistent logic known as D2 which is often referred to as discursive logic or discussive logic (cf. [18, 19]). In this article, the disjunction-free fragment of Ja´skowski’s discussive logic is shown to be complete with respect to three- and four-valued semantics. Note here that D2 is known to be not complete with respect to any finitely many-valued semantics, which is proved by Jerzy Kotas in [20]. As a byproduct of the main result, a simple axiomatization of the disjunction-free fragment of Ja´skowski’s discussive logic in the language of classical logic is obtained. For the problem of axiomatization of D2, see [24].