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38198.50967
This paper concerns the question of which collections of general relativistic space-times are deterministic relative to which definitions. We begin by considering a series of three definitions of increasing strength due to Belot (1995). The strongest of these definitions is particularly interesting for spacetime theories because it involves an asymmetry condition called “rigidity” that has been studied previously in a different context (Geroch 1969; Halvorson and Manchak 2022; Dewar 2024). We go on to explore other (stronger) asymmetry conditions that give rise to other (stronger) forms of determinism. We introduce a number of definitions of this type and clarify the relationships between them and the three considered by Belot. We go on to show that there are collections of general relativistic spacetimes that satisfy much stronger forms of determinism than previously known. We also highlight a number of open questions.
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38218.509734
Determinism is the thesis that the past determines the future, but eorts to dene it precisely have exposed deep methodological disagreements. Standard possible-worlds formulations of determinism presuppose an "agreement" relation between worlds, but this relation can be understood in multiple ways none of which is particularly clear. We critically examine the proliferation of denitions of determinism in the recent literature, arguing that these denitions fail to deliver clear verdicts about actual scientic theories. We advocate a return to a formal approach, in the logical tradition of Carnap, that treats determinism as a property of scientic theories, rather than an elusive metaphysical doctrine. We highlight two key distinctions: (1) the dierence between qualitative and "full" determinism, as emphasized in recent discussions of physics and metaphysics, and (2) the distinction between weak and strong formal conditions on the uniqueness of world extensions. We argue that dening determinism in terms of metaphysical notions such as haecceities is unhelpful, whereas rigorous formal criteria such as Belot's D1 and D3 oer a tractable and scientically relevant account. By clarifying what it means for a theory to be deterministic, we set the stage for a fruitful interaction between physics and metaphysics.
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38262.509744
This paper considers the mundane ways in which AI is being incorporated into scientific practice today, and particularly the extent to which AI is used to automate tasks perceived to be boring, “mere routine” and inconvenient to researchers. We label such uses as instances of “Convenience AI” — that is situations where AI is applied with the primary intention to increase speed and minimize human effort. We outline how attributions of convenience to AI applications involve three key characteristics: (i) an emphasis on speed and ease of action, (ii) a comparative element, as well as (iii) a subject-dependent and subjective quality. Using examples from medical science and development economics, we highlight epistemic benefits, complications, and drawbacks of Convenience AI along these three dimensions. While the pursuit of convenience through AI can save precious time and resources as well as give rise to novel forms of inquiry, our analysis underscores how the uncritical adoption of Convenience AI for the sake of shortcutting human labour may also weaken the evidential foundations of science and generate inertia in how research is planned, set-up and conducted, with potentially damaging implications for the knowledge being produced. Critically, we argue that the consistent association of Convenience AI with the goals of productivity, efficiency, and ease, as often promoted also by companies targeting the research market for AI applications, can lower critical scrutiny of research processes and shift focus away from appreciating their broader epistemic and social implications.
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203256.509757
Two problems are investigated. Why is it that in his solutions to logical problems, Boole’s logical/numerical operations can be difficult to pin down, and why did his late manuscript attempt to get rid of division by zero fall short of that goal? It is suggested that the former is due to different readings that he gives to the operations according to the stage of the solution routine, and the latter is due to a strict confinement to equational reasoning.
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203276.509768
Ancient formulations of the distinction between continuous and separative hypotheticals, made by Peripatetics working under Stoic influence, can be vague and confusing. Perhaps the clearest expositor of the matter was Galen. We review his account, provide two formal articulations of it, verify their equivalence, and show that for what we call ‘simple’ hypotheticals, the formal line of demarcation is independent of whether or not modality is taken into account.
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377473.509778
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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377494.509785
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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476217.509793
The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates non-linear utility while preserving essential rationality properties. We establish core axioms for function-coherence and prove a representation theorem that characterizes acceptable gambles through continuous linear functionals. The framework is then applied to analyze various forms of discounting in intertemporal choice, including hyperbolic, quasi-hyperbolic, scale-dependent, and state-dependent discounting. We demonstrate how these alternatives to constant-rate exponential discounting can be integrated within the function-coherent framework. This unified treatment provides theoretical foundations for modeling sophisticated patterns of time preference within the desirability paradigm, bridging a gap between normative theory and observed behavior in intertemporal decision-making under genuine uncertainty.
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557318.509799
Physics not only describes past, present, and future events but also accounts for unrealized possibilities. These possibilities are represented through the solution spaces given by theories. These spaces are typically classified into two categories: kinematical and dynamical. The distinction raises important questions about the nature of physical possibility. How should we interpret the difference between kinematical and dynamical models? Do dynamical solutions represent genuine possibilities in the physical world? Should kinematical possibilities be viewed as mere logical or linguistic constructs, devoid of a deeper connection to the structure of physical reality? This chapter addresses these questions by analyzing some of the most significant theories in physics: classical mechanics, general relativity and quantum mechanics, with a final mention to quantum gravity. We argue that only dynamical models correspond to genuine physical possibilities.
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557360.509808
I argue that John Norton’s notions of empirical, hypothetical, and counterfactual possibility canbe successfully used to analyze counterintuitive examples of physical possibility and align better with modal intuitions of practicing physicists. First, I clarify the relationship between Norton’s possibility notions and the received view of logical and physical possibility. In particular, I argue that Norton’s empirical, hypothetical, and counterfactual possibility cannot coincide with the received view of physical possibility; instead, the received view of physical possibility is a special case of Norton’s logical possibility. I illustrate my claims using examples from Classical Mechanics, General Relativity, and Quantum Mechanics. I then arrive at my conclusions by subsuming Norton’s empirical, hypothetical, and counterfactual possibilities under a single concept of conditional inductive possibility and by Philosophy analyzing the types and degrees of strengths that can be associated with it.
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557380.509816
A critique is given of the attempt by Hettema and Kuipers to formalize the periodic table. In particular I dispute their notions of identifying a naïve periodic table with tables having a constant periodicity of eight elements and their views on the different conceptions of the atom by chemists and physicists. The views of Hettema and Kuipers on the reduction of the periodic system to atomic physics are also considered critically.
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615123.509825
De Haro, S. [2025]: ‘James Read’s Background Independence in Classical and Quantum Gravity’, BJPS Review of Books, 2025, https://doi.org/10.59350/693wk-sqn26 Background-independence has been a much-debated topic in spacetime theories. One of the main lessons of the general theory of relativity is that spacetime is not xed, as in Newton’s theory, but is dynamical. Since the shape of a spacetime depends on its matter content, the relation between geometry and matter is dynamic. Thus there is no privileged spacetime background on which physics is to be done; unlike the cases of Newtonian space and time, and special relativity’s Minkowski spacetime.
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615180.509835
Here are two statements that are both very plausibly true, but which seem to be in serious tension: (1) In 1879 A. A. Michelson measured the speed of light to within 99% accuracy (2) Strictly speaking, there is no speed of light in Special relativity. The purpose of this paper will be to resolve the tension between (1) and (2). The majority of what follows will be devoted to defending the second claim, which is remarkably controversial even among working physicists and philosophers of science. I argue that this controversy is due to a confusion about the role of co-ordinate representations in characterizing different theories of space-time. Once this confusion is resolved, it becomes clear that the claim that light has a speed at all is nothing more than an artifact of our representational scheme, and not an accurate reflection of the space-time structure of relativity. Before going into all that, I will say a few things in favor of (1).
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615200.509843
The growing interest in the concept of probability of self-location of a conscious agent created multiple controversies. Considering David Albert’s setup in which he described his worries about consistency of the concept, I identify the sources of these controversies and argue that defining “self” in an operational way provides a satisfactory meaning for the probability of self-location of an agent in a quantum world. It keeps the nontrivial feature of having subjective ignorance of self-location without ignorance about the state of the universe. It also allows defining the Born rule in the many-worlds interpretation of quantum mechanics and proving it from some natural assumptions.
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900134.50985
Years ago, in ‘Expected Value without Expecting Value’, I noted that “The vast majority of students would prefer to save 1000 lives for sure, than to have a 10% chance of saving a million lives. This, even though the latter choice has 100 times the expected value.”
Joe Carlsmith’s essay on Expected Utility Maximization nicely explains “Why it’s OK to predictably lose” in this sort of situation. …
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944897.509856
In two interdependent dissertations published in 1611 and 1621, the Swedish theologian and bishop Johannes Rudbeckius (1581–1646) takes up the question of whether the world is eternal. He formulates a number of alternative philosophical arguments in order to justify a negative answer. Without noticing this, he employs two mutually independent notions of eternity. I comment on five of Rudbeckius’s arguments from a systematic point of view. The arguments make use of explicit reasoning about infinite cardinalities, including the use of explicit assumptions regarding arithmetic operations applied to infinite quantities. It is observed that each argument has its origin in medieval scholastic philosophy or is adapted from texts written by Roman authors. The affinity of Rudbeckius’s approach to the scholastic tradition gets highlighted: he is convinced that reason and revelation are not mutually exclusive sources of knowledge: certain theologically relevant propositions can even be proven by philosophical arguments.
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1012058.509867
Researchers worried about catastrophic risks from advanced AI have argued that we should expect sufficiently capable AI agents to pursue power over humanity because power is a convergent instrumental goal, something that is useful for a wide range of final goals. Others have recently expressed skepticism of these claims. This paper aims to formalize the concepts of instrumental convergence and power-seeking in an abstract, decision-theoretic framework, and to assess the claim that power is a convergent instrumental goal. I conclude that this claim contains at least an element of truth, but might turn out to have limited predictive utility, since an agent’s options cannot always be ranked in terms of power in the absence of substantive information about the agent’s final goals. However, the fact of instrumental convergence is more predictive for agents who have a good shot at attaining absolute or near-absolute power.
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1076650.509877
Smeenk, C. [2024]: ‘Gordon Belot’s Accelerating Expansion’, BJPS Review of Books, 2024 What would be the consequences of taking de Sitter spacetime as more fundamental to understanding physical geometry than Minkowski spacetime? De Sitter discovered his eponymous spacetime shortly after Einstein formulated general relativity, and it is the simplest—maximally symmetric—solution of the eld equations with a positive cosmological constant (Λ). The standard model of cosmology attributes the majority of energy density in the universe to Λ. A cosmological constant remains (as the name suggests) constant as the universe evolves, and comes to dominate dynamically as other forms of matter and energy dilute with cosmic expansion—driving the large scale structure of spacetime towards de Sitter spacetime in the far future. Adding a non-zero Λ furthermore has a profound impact on the description of other domains, such as gravitational waves and black holes. As is familiar from the study of di erential equations, adding a term to a set of equations, even if it is ‘small’, can radically change the structure of the space of solutions. In this case, the Λ → 0 limit, to recover Minkowski spacetime, is not well behaved, undermining the use of mathematical techniques that exploit its structural features. There is now a substantial research literature devoted to the physics of de Sitter spacetime (and related spacetimes). It is hard to disagree with Belot’s assessment that this is a ‘ eld in which open problems extend as far as the eye can see’ (p. x), and the literature abounds with ideas sure to provoke philosophers. Accelerating Expansion makes a compelling case that philosophers should get to work on these open problems—not only because they concern central questions regarding the applicability of physics and our epistemic situation, but because the provocations often stem from bizarre assumptions—and provides an orientation and training programme for those eager to join the e ort.
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1134459.509885
In Yang-Mills gauge theory on a Euclidean Cauchy surface the group of gauge symmetries carrying direct empirical significance is often believed to be GDES = GI/G , where GI is the group of boundary-preserving gauge symmetries and G is its subgroup of transformations that are generated by the constraints of the theory. These groups are identified respectively as the gauge transformations that become constant asymptotically and those that become the identity asymptotically. In the Abelian case G = U(1) the quotient is then identified as the group of global gauge symmetries, i.e. U( ) itself. However, known derivations of this claim are imprecise, both mathematically and conceptually. We derive the physical gauge group rigorously for both Abelian and non-Abelian gauge theory. Our main new point is that the requirement to restrict to GI does not follow from finiteness of energy only, but from the requirement that the Lagrangian of Yang-Mills theory be defined on a tangent bundle to configuration space. Moreover, we explain why the quotient consists precisely of a copy of the global gauge group for every homotopy class, even if the various gauge transformations apparently have different asymptotic rates of convergence. Lastly, we consider Yang-Mills- Higgs theory in our framework and show that asymptotic boundary conditions differ in the unbroken and broken phases.
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1186146.509893
Critical-Level Utilitarianism entails one of the Repugnant Conclusion and the Sadistic Conclusion (both of which are counter-intuitive), depending on the critical level. Indeterminate Critical-Level Utilitarianism is a version of Critical- Level Utilitarianism where it is indeterminate which well-being level is the critical level. Undistinguished Critical-Range Utilitarianism is variant of Critical-Level Utilitarianism where additions of lives in a range of well-being between the good and the bad lives makes the resulting outcome incomparable to the original outcome. These views both avoid the Repugnant Conclusion and avoid the Sadistic Conclusion. And they agree about all comparisons of outcomes that do not involve indeterminacy or incomparability. So it is unclear whether we have any reason to favour one of these theories over the other. I argue that Indeterminate Critical-Level Utilitarianism still entails the disjunction of the Repugnant Conclusion and the Sadistic Conclusion, which is also repugnant. Whereas, Undistinguished Critical- Range Utilitarianism does not entail this conclusion.
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1349324.5099
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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1349346.509907
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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1356601.509914
Time-travel fiction commonly depicts time travelers who encounter their past selves or, in the grandfather paradox, their ancestors. In traditional fictional representations of time travel, such as in H. G. Wells’s The Time Machine, travelers age in the same time sense as those visited in the past and future. Elsewhere, fantasy fiction supplies another possibility: the wizard Merlyn in T. H. White’s 1938 fantasy novel, The Sword in the Stone, meets a young Arthur. Merlyn ages in the opposite time sense to Arthur. Arthur’s first meeting with Merlyn is Merlyn’s last meeting with Arthur; and Arthur’s last meeting with him is Merlyn’s first. We can imagine time travelers who arrive in the past to meet their former selves, but now age in the opposite time sense. They are still time travelers since they are meeting their past selves. However, we have now added a twist from another part of the fantasy literature.
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1409198.509921
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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1422745.509927
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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1477863.509934
Hume [Hume 1739: bk.I pt.III sec.XI] held, incredibly, that objective chance is a projection of our beliefs. Bruno de Finetti [1970] gave mathematical substance to this idea. Scientific reasoning about chance, he argued, should be understood as arising from symmetries in degrees of belief. De Finetti’s gambit is popular in some quarters of statistics and philosophy – see, for example, [Bernardo and Smith 2009], [Spiegelhalter 2024], [Skyrms 1984: ch.3], [Diaconis and Skyrms 2017: ch.7], [Jeffrey 2004]. It is safe to say, however, that it has not been widely accepted. Science textbooks generally ignore it. So does the excellent Stanford Encyclopedia entry on “Interpretations of Probability” [Hájek 2023].
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1480478.50994
Traditional arguments against or in favor of continuity rely upon the presupposition that scientific theories can serve as markers of descriptive truth. I argue that such a notion of the term is misguided if we are concerned with the question of how our scientific schemes ought to develop . Instead, a reconstruction of the term involves identifying those concepts which guide the development from one successive scheme to the next and labelling those concepts with the status that they are continuous. I explicitly construct an example of this kind of continuity utilizing two formulations of Quantum Field Theory (QFT) and identify what persists from the standard formulation, beginning with an action, to the successive one, making use of spinor helicity variables. Three concepts persist which are responsible for supplying explicit constraints on our expressions which serve to match onto empirical predictions: Lorentz invariance, locality and unitarity. Further extensions of this kind of analysis to models beyond the physical sciences are proposed.
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1480495.509947
The extravagances of quantum mechanics (QM) never fail to enrich daily the debate around natural philosophy. Entanglement, non-locality, collapse, many worlds, many minds, and subjectivism have challenged generations of thinkers. Its approach can perhaps be placed in the stream of quantum logic, in which the “strangeness” of quantum mechanics is “measured” through the violation of Bell’s inequalities and, from there, attempts an interpretative path that preserves realism yet ends up overturning it, restating the fundamental mechanisms of QM as a logical necessity for a strong realism.
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1480512.509953
Quantum mechanics is a theory that is as effective as it is counterintuitive. While quantum practices operate impeccably, they compel us to embrace enigmatic phenomena like the collapse of the state vector and non-locality, thereby pushing us towards untenable ”hypotheses non fingo” stances. However, a century after its inception, we are presented with a promising interpretive key, intimated by Wheeler as early as 1974[ ]. The interpretative paradoxes of this theory might be resolved if we discern the relationship between logical undecidability and quantum undecidability. It will be demonstrated how both are intricately linked to an observer/observed relational issue, and how the idiosyncratic behaviours of quantum physics can be reconciled with the normative, following this path.
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1480556.50996
In epidemiology, an effect of a dichotomous exposure on a dichotomous outcome is a comparison of risks between the exposed and the unexposed. Causally interpreted, this comparison is assumed to equal a comparison in counterfactual risks if, hypothetically, both exposure states were to occur at once for each subject (Hernán and Robins, 2020). These comparisons are summarized by effect measures like risk difference or risk ratio. Risk difference describes the additive influence of an exposure on an outcome, and is often called an absolute effect measure. Trials occasionally report the inverse of a risk difference, which can also be classified as an absolute measure, as inverting it again returns the risk difference. Measures like risk ratio, which describe a multiplier of risk, are called relative, or ratio measures.