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82934.363206
What do large language models actually model? Do they tell us something about human capacities, or are they models of the corpus we’ve trained them on? I give a non-deflationary defence of the latter position. Cognitive science tells us that linguistic capabilities in humans rely supralinear formats for computation. The transformer architecture, by contrast, supports at best a linear formats for processing. This argument will rely primarily on certain invariants of the computational architecture of transformers. I then suggest a positive story about what transformers are doing, focusing on Liu et al. (2022)’s intriguing speculations about shortcut automata. I conclude with why I don’t think this is a terribly deflationary story. Language is not (just) a means for expressing inner state but also a kind of ‘discourse machine’ that lets us make new language given appropriate context. We have learned to use this technology in one way; LLMs have also learned to use it too, but via very different means.
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333614.363253
The early study Tennant [11] sought to show how the role played by formal semantics in furnishing models that would invalidate unprovable first-order arguments from premise-sets to conclusions could be taken over by proofs and disproofs. (A disproof of a set of premises is a proof of ⊥, i.e., absurdity, from it.) For any given invalid first-order argument, these latter would be proofs and disproofs in Peano Arithmetic (PA), employing suitable substitutions of arithmetical predicates for the primitive predicates involved in the argument. PA-proofs would be furnished for the premises of the invalid argument, and a PA-disproof would be furnished for its conclusion. This was an early move towards a general proof-theoretic semantics—the approach to By a theorem of Hilbert and Bernays [4], these arithmetical predicates can be taken to be of arithmetical complexity no greater than Δ .
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443730.363262
Reminder: everyone is welcome here, but paid subscriptions are what enable me to devote the necessary time to researching and writing this newsletter, including pieces like this one on Katie Johnson, the woman who alleged Trump sexually assaulted her at the age of thirteen at a party of Jeffrey Epstein’s. …
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1189901.363268
The family of relevant logics can be faceted by a hierarchy of increasingly fine-grained variable sharing properties—requiring that in valid entailments A → B, some atom must appear in both A and B with some additional condition (e.g., with the same sign or nested within the same number of conditionals). In this paper, we consider an incredibly strong variable sharing property of lericone relevance that takes into account the path of negations and conditionals in which an atom appears in the parse trees of the antecedent and consequent. We show that this property of lericone relevance holds of the relevant logic BM (and that a related property of faithful lericone relevance holds of B) and characterize the largest fragments of classical logic with these properties. Along the way, we consider the consequences for lericone relevance for the theory of subject-matter, for Logan’s notion of hyperformalism, and for the very definition of a relevant logic itself.
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1363225.363274
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external structures, making the meaning of expressions depend solely on their constituent symbols. Terms and formulas are unified into a single notion of expression, with set-builder notation integrated as a primitive construct. Connectives and quantifiers are treated as operators among others rather than as privileged primitives. The deductive framework is minimal and intuitive, with soundness and consistency established and completeness examined. While computability requirements may limit universality, the system offers a unified and potentially more faithful model of human mathematical deduction, providing an alternative foundation for formal reasoning.
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1478698.363279
While causal models are introduced very much like a formal logical system, they have not yet been taken to the level of a proper logic of causal reasoning with structural equations. In this paper, we furnish causal models with a distinct deductive system and a corresponding model-theoretic semantics. Interventionist conditionals will be defined in terms of inferential relations in this logic of causal models.
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1857722.363284
This commentary aims to support Tim Crane’s account of the structure of intentionality by showing how intentional objects are naturalistically respectable, how they pair with concepts, and how they are to be held distinct from the referents of thought. Crane is right to reject the false dichotomy that accounts of intentionality must be either reductive and naturalistic or non-reductive and traffic in mystery. The paper has three main parts. First, I argue that the notion of an intentional object is a phenomenological one, meaning that it must be understood as an object of thought for a subject. Second, I explain how Mark Sainsbury’s Display Theory of Attitude Attribution pairs well with Crane’s notion of an intentional object and allows for precisification in intentional state attributions while both avoiding exotica and capturing the subject’s perspective on the world. Third, I explain the reification fallacy, the fallacy of examining intentional objects as if they exist independently of subjects and their conceptions of them. This work helps to bring out how intentionality can fit in the natural world while at the same time not reducing aboutness to some non-intentional properties of the natural world.
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1872221.363294
— We present a reformulation of the model predictive control problem using a Legendre basis. To do so, we use a Legendre representation both for prediction and optimization. For prediction, we use a neural network to approximate the dynamics by mapping a compressed Legendre representation of the control trajectory and initial conditions to the corresponding compressed state trajectory. We then reformulate the optimization problem in the Legendre domain and demonstrate methods for including optimization constraints. We present simulation results demonstrating that our implementation provides a speedup of 31-40 times for comparable or lower tracking errors with or without constraints on a benchmark task.
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1943235.3633
Commemorative artefacts purportedly speak—they communicate messages to their audience, even if no words are uttered. Sometimes, such artefacts purportedly communicate demeaning or pejorative messages about some members of society. The characteristics of such speech are, however, under-examined. I present an account of the paradigmatic characteristics of the speech of commemorative artefacts (or, “commemorative artefactual speech”), as a distinct form of political speech. According to my account, commemorative artefactual speech paradigmatically involves the use of an artefact by an authorised member of a group to declare the importance of remembering a subject, in virtue of some feature of the subject. Then, I outline a variety of ways that commemorative artefactual speech can go awry. Such speech can be unauthorised, involve unfair exclusion or incorrect identification, be aesthetically inadequate, invoke clandestine explanations, and be directed at inappropriate subjects. I conclude with a discussion of the implications of my account for resisting problematic commemorative artefactual speech.
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2091935.363305
We introduce a challenge designed to evaluate the capability of Large Language Models (LLMs) in performing mathematical induction proofs, with a particular focus on nested induction. Our task requires models to construct direct induction proofs in both formal and informal settings, without relying on any preexisting lemmas. Experimental results indicate that current models struggle with generating direct induction proofs, suggesting that there remains significant room for improvement.
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2100090.36331
On its surface, a sentence like If Laura becomes a zombie, she wants you to shoot her looks like a plain conditional with the attitude want in its consequent. However, the most salient reading of this sentence is not about the desires of a hypothetical zombie- Laura. Rather, it asserts that the actual, non-zombie Laura has a certain restricted attitude: her present desires, when considering only possible states of affairs in which she becomes a zombie, are such that you shoot her. This can be contrasted with the shifted reading about zombie-desires that arises with conditional morphosyntax, e.g., If Laura became a zombie, she would want you to shoot her. Furthermore, as Blumberg and Holguín (J Semant 36(3):377–406, 2019) note, restricted attitude readings can also arise in disjunctive environments, as in Either a lot of people are on the deck outside, or I regret that I didn’t bring more friends. We provide a novel analysis of restricted and shifted readings in conditional and disjunctive environments, with a few crucial features. First, both restricted and shifted attitude conditionals are in fact “regular” conditionals with attitudes in their consequents, which accords with their surface-level appearance and contrasts with Pasternak’s (The mereology of attitudes, Ph.D. thesis, Stony Brook University, Stony Brook, NY, 2018) Kratzerian approach, in which the if -clause restricts the attitude directly. Second, whether the attitude is or is not shifted—i.e., zombie versus actual desires—is dependent on the presence or absence of conditional morphosyntax. And third, the restriction of the attitude is effected by means of aboutness, a concept for which we provide two potential Kai von Fintel and Robert Pasternak are listed alphabetically and share joint lead authorship of this work.
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2515858.363316
philosophical logic may also interest themselves with the logical appendices, one of which presents modal logic as a subsystem of the logic of counterfactuals. Last but not least, the work also includes an afterword that is both a severe reprimand to the analytic community for a certain sloppiness and an exhortation to all colleagues to apply more rigor and patience in addressing metaphysical issues. People familiar with Williamson’s work will not be surprised by the careful and detailed (sometimes a bit technical) argumentation, which demands careful attention from the reader. As expected, this is a most relevant contribution to an increasingly popular topic by one of today’s leading analytic philosophers.
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2629157.363321
PEA Soup is pleased to introduce the July Ethics article discussion on “Gender, Gender Expression, and the Dilemma of the Body” by Katie Zhou (MIT). The précis is from Cressida Heyes (University of Alberta). …
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2688479.363328
The paper proposes and studies new classical, type-free theories of truth and determinateness with unprecedented features. The theories are fully compositional, strongly classical (namely, their internal and external logics are both classical), and feature a defined determinateness predicate satisfying desirable and widely agreed principles. The theories capture a conception of truth and determinateness according to which the generalizing power associated with the classicality and full compositionality of truth is combined with the identification of a natural class of sentences – the determinate ones – for which clear-cut semantic rules are available. Our theories can also be seen as the classical closures of Kripke-Feferman truth: their ω-models, which we precisely pinned down, result from including in the extension of the truth predicate the sentences that are satisfied by a Kripkean closed-off fixed point model. The theories compare to recent theories proposed by Fujimoto and Halbach, featuring a primitive determinateness predicate. In the paper we show that our theories entail all principles of Fujimoto and Halbach’s theories, and are proof-theoretically equivalent to Fujimoto and Halbach’s CD . We also show establish some negative results on Fujimoto and Halbach’s theories: such results show that, unlike what happens in our theories, the primitive determinateness predicate prevents one from establishing clear and unrestricted semantic rules for the language with type-free truth.
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2724335.363334
The concept of preference spans numerous research fields, resulting in
diverse perspectives on the topic. Preference logic specifically
focuses on reasoning about preferences when comparing objects,
situations, actions, and more, by examining their formal properties. This entry surveys major developments in preference logic to date. Section 2
provides a historical overview, beginning with foundational work by
Halldén and von Wright, who emphasized the syntactic aspects of
preference. In
Section 3,
early semantic contributions by Rescher and Van Dalen are introduced. The consideration of preference relations over possible worlds
naturally gives rise to modal preference logic where preference
lifting enables comparisons across sets of possible worlds.
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3200144.363339
When thinking about online speech, it’s tempting to start with questions like: What’s new here? Do online speech environments enable new types of speech acts, new semantic phenomena, new expressive effects? In other words, how has the shift to online speech fundamentally changed how we use language to communicate, coordinate, obfuscate, rouse, empower, disempower, insult, etc.? What hidden truths might online speech reveal about the nature of meaning and communication more broadly?
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3314825.363347
We present a logic which deals with connexive exclusion. Exclusion (also called “co-implication”) is considered to be a propositional connective dual to the connective of implication. Similarly to implication, exclusion turns out to be non-connexive in both classical and intuitionistic logics, in the sense that it does not satisfy certain principles that express such connexivity. We formulate these principles for connexive exclusion, which are in some sense dual to the well-known Aristotle’s and Boethius’ theses for connexive implication. A logical system in a language containing exclusion and negation can be called a logic of connexive exclusion if and only if it obeys these principles, and, in addition, the connective of exclusion in it is asymmetric, thus being different from a simple mutual incompatibility of propositions. We will develop a certain approach to such a logic of connexive exclusion based on a semantic justification of the connective in question. Our paradigm logic of connexive implication will be the connexive logic C, and exactly like this logic the logic of connexive exclusion turns out to be contradictory though not trivial.
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3631097.363353
Robert H. Jackson was an Associate Justice on the U.S. Supreme Court by day, and one of the most eloquent men alive. In 1945-46 he led the American prosecution at the Nuremberg Trials, “perhaps the greatest opportunity ever presented to an American lawyer.” His powerful opening statement testifies to the power of words, used well, to shape the meaning of events:
That four great nations, flushed with victory and stung with injury stay the hand of vengeance and voluntarily submit their captive enemies to the judgment of the law is one of the most significant tributes that Power ever has paid to Reason. …
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4760703.363359
Apparently, Italy requires residents to secure a medical certificate before joining a gym, sports club, or other source of regular physical exercise. This is (very loosely) estimated to prevent a few deaths per year from sudden cardiac events but at a net cost of thousands of QALYs lost due to exercise deterrence. …
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4922135.363364
There is a longstanding puzzle about empty names. On the one hand, the principles of classical logic seem quite plausible. On the other hand, there would seem to be truths involving empty names that require rejecting certain classically valid principles.
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4922185.363372
Consider the property of being something that is identical to Hesperus. For short, call this the property of being Hesperus. What is the nature of this property? How does it relate to the property of being Phosphorus? And how do these properties relate to the purely haecceitistic property of being v—the unique thing that has the property of being Hesperus and the property of being Phosphorus?
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5000426.36338
Casajus (J Econ Theory 178, 2018, 105–123) provides a characterization of the class of positively weighted Shapley value for …nite games from an in…nite universe of players via three properties: e¢ ciency, the null player out property, and superweak differential marginality. The latter requires two players’payoffs to change in the same direction whenever only their joint productivity changes, that is, their individual productivities stay the same. Strengthening this property into (weak) differential marginality yields a characterization of the Shapley value. We suggest a relaxation of superweak differential marginality into two subproperties: (i) hyperweak differential marginality and (ii) superweak differential marginality for in…nite subdomains. The former (i) only rules out changes in the opposite direction. The latter (ii) requires changes in the same direction for players within certain in…nite subuniverses. Together with e¢ ciency and the null player out property, these properties characterize the class of weighted Shapley values.
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5020465.363385
In this paper, I distinguish and compare three kinds of logical expressivism. The first, reminiscent of attitude expressivism in meta-ethics, holds that logic is expressive in that logical vocabulary serves to express attitudes. For instance, traditional attitude expressivism about negation, going back to the work of Frank Plumpton Ramsey, Huw Price and others, holds that not expresses disbelief. The second kind of logical expressivism, reminiscent of deflationism about truth and championed by Robert Brandom, holds that logic is expressive in that logical vocabulary serves to make explicit—typically, by expressing them as contents of assertions—the commitments that are implicit in our discursive practices. For instance, content expressivism about the conditional holds that if expresses as content commitment to the goodness of certain inferential moves. The third kind of logical expressivism, and the one I will be arguing for, holds that, in a sense, logic is expressive in both ways: logical vocabulary serves to make explicit commitments to expressions of attitudes.
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5021938.363394
In a system with identity, quotation, and an axiom predicate, a classical extension of the system yields a falsity. The result illustrates a novel form of instability in classical logic. Notably, the phenomenon arises without vocabulary such as ’true’ or ’provable’. Conservative extensions are safe expansions: They add expressive resources while proving the same theorems (or at most, terminological variants thereof). Conservative extensions are foundational for major developments, including the Lowenheim-Skolem theorems, precise comparisons of proof-theoretic strength (Simpson 2009), and the understanding of reflection principles in arithmetic and set theory (Feferman 1962). The purpose here is not to question these developments, but rather to advise caution for the future. Some extensions that appear quite conservative end up not being so. In a system with identity, quotation, and a metalinguistic singular term, a purely syntactic predicate for axioms can create instability under an innocent-looking extension.
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5021960.363404
It is known that some diagonal arguments, when formalized, do not demonstrate the impossibility of the diagonal object, but instead reveal a breakdown in definability or encoding. For example, in a formal setting, Richard’s paradox does not yield a contradiction; it instead reflects that one of the relevant sets is ill-defined. (For elaboration and other examples, see Simmons 1993, Chapter 2.) This invites the possibility that other diagonal arguments may reflect similar anomalies. The diagonal argument against a universal p.r. function is considered in this light. The impetus is an algorithm which appears to satisfy all standard criteria for being p.r. while simulating the computation of fi(i, n) for any index i of a binary p.r. function. The paper does not attempt to explain why this construction apparently survives the usual diagonal objection, but presents it in a form precise enough to support that analysis.
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5084901.363409
In logic and philosophy of logic, “formalization” covers a broad range of interrelated issues: some philosophers hold that logical systems are means to formalize theories and reasoning (Dutilh Novaes 2012), others seek to formalize semantical by syntactical systems (Carnap 1942/43), ask whether logical languages are formalizations of natural languages (Stokhof 2018), teach undergraduates to formalize arguments using elementary logic, debate how to formalize notions such as moral obligation (Hansson 2018), or develop formalizations of belief change processes (Rott 2001). This variety goes hand in hand with an equally broad range of general views about what logic and its role in philosophy is or should be – whether, for example, logic is first of all a tool for reasoning (Dutilh Novaes 2012), a mathematical theory of certain formal structures which can be used to model philosophically interesting phenomena (Hansson 2018; Sagi 2020a; Stokhof 2018), or a theory that studies inferential relations in natural language and enables us to show that certain ordinary-language arguments are valid (Peregrin/Svoboda 2017), to name just a few. More or less implicitly, these approaches contain views on what the target phenomena of formalizing are (languages, arguments, …), what kind of relation formalizations have to it (model, tool, …) and whether formalizing is an integral part of logic or an application of it.
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5195558.363415
It was a particularly cruel heckling. Ketel Marte, a star baseball player for the Arizona Diamondbacks, was brought to tears by a heckler who shouted derogatory comments about Marte’s late mother, Elpidia Valdez, who died in a car crash in 2017. …
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5542492.36342
In recent years, there has been heightened interest in (at least) two threads regarding geometrical aspects of spacetime theories. On the one hand, physicists have explored a richer space of relativistic spacetime structures than that of general relativity, in which the conditions both of torsion-freeness and of metric compatibility are relaxed—this has led to the study of so-called ‘metricaffine theories’ of gravitation, on which see e.g. Hehl et al. (1995) for a masterly review. On the other hand, physicists have been increasingly interested in securing a rigorous and fully general understanding of the non-relativistic limit of general relativity—this has to novel version of Newtonian physics, potentially with spacetime torsion (‘Type II’ Newton–Cartan theory—see Hansen et al. (2022) for a systematic overview).
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5729754.363426
When we count, we often count fractions, too. We contend that fractional counting involves partial entities, which are merely possible parts of entities of the counted kind. The size of these possible parts is measured with respect to the size of a possible member of that kind. Therefore, partialhood is mereomodal, and the logical form of fractional counting claims includes mereological predicates, modal operators, and a measurement functor. Different varieties of modality and forms of measurement are involved, depending on the kinds of entities to be counted and the context. The mereomodal account validates the idea that fractional counting is a way of counting by identity, in continuity with logic-based accounts of non-fractional counting, albeit more complex than them. Such an account also explains why some kinds of entities are not involved in partialhood and cannot be fractionally counted, while others only have marginal involvement in these phenomena. In the last part, we discuss some difficult cases and show that an integrity condition for partial entities is required in the logical form of some fractional counting claims.
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5825119.363431
The present review discusses the literature on how and when social category information and individuating information influence people’s implicit judgments of other individuals who belong to existing (i.e., known) social groups. After providing some foundational information, we discuss several key principles that emerge from this literature: (a) individuating information moderates stereotype-based biases in implicit (i.e., indirectly measured) person perception, (b) individuating information usually exerts small to no effects on attitude-based biases in implicit person perception, (c) individuating information influences explicit (i.e., directly measured) person perception more than implicit person perception, (d) social category information affects implicit person perception more than it affects explicit person perception, and (e) the ability of other variables to moderate the effects of individuating information on stereotype- and attitude-based biases in implicit person perception varies. Within the discussion of each of these key points, relevant research questions that remain unaddressed in the literature are presented. Finally, we discuss both theoretical and practical implications of the principles discussed in this review.