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3613.98047
In the topic-sensitive theory of the logic of imagination due to Berto [3], the topic of the imaginative output must be contained within the imaginative input. That is, imaginative episodes can never expand what they are about. We argue, with Badura [2], that this constraint is implausible from a psychological point of view, and it wrongly predicts the falsehood of true reports of imagination. Thus the constraint should be relaxed; but how? A number of direct approaches to relaxing the controversial content-inclusion constraint are explored in this paper. The core idea is to consider adding an expansion operator to the mereology of topics. The logic that results depends on the formal constraints placed on topic expansion, the choice of which are subject to philosophical dispute. The first semantics we explore is a topological approach using a closure operator, and we show that the resulting logic is the same as Berto’s own system. The second approach uses an inclusive and monotone increasing operator, and we give a sound and complete axiomatiation for its logic. The third approach uses an inclusive and additive operator, and we show that the associated logic is strictly weaker than the previous two systems, and additivity is not definable in the language. The latter result suggests that involved techniques or a more expressive language is required for a complete axiomatization of the system, which is left as an open question. All three systems are simple tweaks on Berto’s system in that the language remains propositional, and the underlying theory of topics is unchanged.
-
76888.980609
A seminal controversy in statistical inference is whether error probabilities associated with an inference method are evidentially relevant once the data are in hand. Frequentist error statisticians say yes; Bayesians say no. …
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262071.980636
The interpretation of quantum measurements presents a fundamental challenge in quantum mechanics, with concepts such as the Copenhagen Interpretation (CI), Many-Worlds Interpretation (MWI), and Bohmian Mechanics (BM) offering distinct perspectives. We propose the Branched Hilbert Subspace Interpretation (BHSI), which describes measurement as branching the local Hilbert space of a system into parallel subspaces. We formalize the mathematical framework of BHSI using branching and the engaging and disengaging unitary operators to relationally and causally update the states of observers. Unlike the MWI, BHSI avoids the ontological proliferation of worlds and copies of observers, realizing the Born rule based on branch weights. Unlike the CI, BHSI retains the essential features of the MWI: unitary evolution and no wavefunction collapse. Unlike the BM, BHSI does not depend on a nonlocal structure, which may conflict with relativity. We apply BHSI to examples such as the double-slit experiment, the Bell test, Wigner and his friend, and the black hole information paradox. In addition, we explore whether recohering branches can be achieved in BHSI. Compared to the CI and MWI, BHSI provides a minimalist, unitarity-preserving, collapse-free, and probabilistically inherent alternative interpretation of quantum measurements.
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262092.980653
Recent results have shown that singularities can be avoided from the general relativistic standpoint in Lorentzian-Euclidean black holes by means of the transition from a Lorentzian to an Euclidean region where time loses its physical meaning and becomes imaginary. This dynamical mechanism, dubbed “atemporality”, prevents the emergence of black hole singularities and the violation of conservation laws. In this paper, the notion of atemporality together with a detailed discussion of its implications is presented from a philosophical perspective. The main result consists in showing that atemporality is naturally related to conservation laws.
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319855.98067
Marletto and Vedral [Phys. Rev. Lett. 125, 040401 (2020)] propose that the Aharonov-Bohm (AB) phase is locally mediated by entanglement between a charged particle and the quantized electromagnetic field, asserting gauge independence for non-closed paths. Using quantum electrodynamics (QED), we critically analyze their model and demonstrate that the AB phase arises from the interaction with the vector potential A, not from entanglement, which is merely a byproduct of the QED framework. We show that their field-based energy formulation, intended to reflect local electromagnetic interactions, is mathematically flawed due to an incorrect prefactor and involves fields inside the solenoid, failing to support local mediation of the phase. Its equivalence to qv · A holds only in the Coulomb gauge, undermining their claim of a gauge-independent local mechanism. Furthermore, we confirm that the AB phase is gauge-dependent for non-closed paths, contradicting their assertion. Our analysis reaffirms the semi-classical interpretation, where the AB phase is driven by the vector potential A, with entanglement playing no causal role in its generation.
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319884.980684
This paper reconsiders the metaphysical implication of Einstein algebras, prompted by the recent objections of Chen (2024) on Rosenstock et al. (2015)’s conclusion. Rosenstock et al.’s duality theorem of smooth manifolds and smooth algebras supports a conventional wisdom which states that the Einstein algebra formalism is not more “relationalist” than the standard manifold formalism. Nevertheless, as Chen points out, smooth algebras are different from the relevant algebraic structure of an Einstein algebra. It is therefore questionable if Rosenstock et al.’s duality theorem can support the conventional wisdom. After a re-visit of John Earman’s classic works on the program of Leibniz algebras, I formalize the program in category theory and propose a new formal criterion to determine whether an algebraic formalism is more “relationalist” than the standard manifold formalism or not. Based on the new formal criterion, I show that the conventional wisdom is still true, though supported by a new technical result. I also show that Rosenstock et al. (2015)’s insight can be re-casted as a corollary of the new result. Finally, I provide a justification of the new formal criterion with a discussion of Sikorski algebras and differential spaces. The paper therefore provides a new perspective for formally investigating the metaphysical implication of an algebraic formalism for the theory of space and time.
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319901.980699
This dissertation defends Causal Decision Theory(CDT) against a recent (alleged) counterexample. In Dicing with Death (2014), Arif Ahmed devises a decision scenario where the recommendation given by CDT apparently contradicts our intuitive course of action. Similar to many other alleged counterexamples to CDT, Ahmed’s story features an adversary with fantastic predictive power—Death himself, in this story. Unlike many other alleged counterexamples, however, Ahmed explicitly includes the use of a costly randomization device as a possible action for the agent. I critically assess these two features of Ahmed’s story. I argue that Death’s fantastic predictive power cannot be readily reconciled with the use of randomization device. In order to sustain Dicing with Death as a coherent decision scenario, background explanations must be given about the nature of Death’s fantastic predictive power. After considering a few such explanations, however, it becomes unclear if the initial intuition which CDT apparently contradicts still holds up. Finally, I consider two contrasting decision scenarios to illustrate why Ahmed’s intuition in this case is ultimately false. I conclude that biting the bullet can perhaps be a legitimate response from CDT to many similar cases where evidentially correlated but causally isolated acts seem to force CDT to give counterintuitive recommendations.
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319941.980712
This paper aims to resolve the incompatibility between two extant gauge-invariant accounts of the Abelian Higgs mechanism: the first account uses global gauge symmetry breaking, and the second eliminates spontaneous symmetry breaking entirely. We resolve this incompatibility by using the constrained Hamiltonian formalism in symplectic geometry. First we argue that, unlike their local counterparts, global gauge symmetries are physical. The symmetries that are spontaneously broken by the Higgs mechanism are then the global ones. Second, we explain how the dressing field method singles out the Coulomb gauge as a preferred gauge for a gauge-invariant account of the Abelian Higgs mechanism. Based on the existence of this group of global gauge symmetries that are physical, we resolve the incompatibility between the two accounts by arguing that the correct way to carry out the second method is to eliminate only the redundant gauge symmetries, i.e. those local gauge symmetries which are not global. We extend our analysis to quantum field theory, where we show that the Abelian Higgs mechanism can be understood as spontaneous global U(1) symmetry breaking in the C -algebraic sense.
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372119.980729
Some authors maintain that we can use causal Bayes nets to infer whether X → Y or X ← Y by consulting a probability distribution defined over some exogenous source of variation for X or Y . We raise a problem for this approach. Specifically, we point out that there are cases where an exogenous cause of X (Ex) has no probabilistic influence on Y no matter the direction of causation — namely, cases where Ex → X → Y and Ex → X ← Y are probabilistically indistinguishable. We then assess the philosophical significance of this problem and discuss some potential solutions.
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405713.980751
[Editor’s Note: The following new entry by Klaas Kraay replaces the
former entry on this topic by the previous author.]
The topic of divine freedom concerns the extent to which a divine
being — in particular, the supreme divine being, God — can
be free. There are, of course, many different conceptions of who or
what God is. This entry will focus on one enormously important and
influential model, according to which God is a personal being who
exists necessarily, who is essentially omnipotent, omniscient,
perfectly good, and perfectly rational, and who is the creator and
sustainer of all that contingently
exists.[ 1 ]
(For more discussion of these attributes, see the entries on
omnipotence,
omniscience,
perfect goodness,
and
creation and conservation.)
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429673.980765
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic supports higher-order and dependently-typed goals, structural recursion over indexed inductive types, and definitional equality. Canonical finds proofs for 84% of Natural Number Game problems in 51 seconds total.
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483888.980779
Visual illusions provide a means of investigating the rules and principles through which approximate number representations are formed. Here, we investigated the developmental trajectory of an important numerical illusion – the connectedness illusion, wherein connecting pairs of items with thin lines reduces perceived number without altering continuous attributes of the collections. We found that children as young as 5 years of age showed susceptibility to the illusion and that the magnitude of the effect increased into adulthood. Moreover, individuals with greater numerical acuity exhibited stronger connectedness illusions after controlling for age. Overall, these results suggest the approximate number system expects to enumerate over bounded wholes and doing so is a signature of its optimal functioning.
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582701.980795
The desirable gambles framework provides a rigorous foundation for imprecise probability theory but relies heavily on linear utility via its coherence axioms. In our related work, we introduced function-coherent gambles to accommodate nonlinear utility. However, when repeated gambles are played over time—especially in intertemporal choice where rewards compound multiplicatively— the standard additive combination axiom fails to capture the appropriate long-run evaluation. In this paper we extend the framework by relaxing the additive combination axiom and introducing a nonlinear combination operator that effectively aggregates repeated gambles in the log-domain. This operator preserves the time-average (geometric) growth rate and addresses the ergodicity problem. We prove the key algebraic properties of the operator, discuss its impact on coherence, risk assessment, and representation, and provide a series of illustrative examples. Our approach bridges the gap between expectation values and time averages and unifies normative theory with empirically observed non-stationary reward dynamics. Keywords. Desirability, non-linear utility, ergodicity, intertemporal choice, non-additive dynamics, function-coherent gambles, risk measures.
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639141.980808
A firm wishes to persuade a patient to take a drug by making either positive statements like “if you take our drug, you will be cured”, or negative statements like “anyone who was not cured did not take our drug”. Patients are neither Bayesian nor strategic: They use a decision procedure based on sampling past cases. We characterize the firm’s optimal statement, and analyze competition between firms making either positive statements about themselves or negative statements about their rivals. The model highlights that logically equivalent statements can differ in effectiveness and identifies circumstances favoring negative ads over positive ones.
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781216.980822
In this paper, we investigate the treatment of the direction of time in Bohmian mechanics. We show how Bohmian mechanics can account for the direction of time in different ways. In particular, we argue that Bohmian mechanics can be employed to accommodate reductionism, because there always is an asymmetry in the initial conditions when forward and backward evolutions of the configuration of matter are compared. It can also be employed to accommodate primitivism and relationalism due to the fact that Bohmian mechanics is a first order theory that recognizes only position as a primitive physical magnitude. We show how this fact can be employed to support a primitive direction of time by assuming Leibnizian relationalism, which reduces the direction of time to change in the configuration of matter with that change being directed as a primitive matter of fact.
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785428.980836
Causal Finitism—the thesis that nothing can have an infinite causal history—implies that there is a first cause, and our best hypothesis for what a first cause would be is God. Thus:
- If Causal Finitism is true, God exists. …
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1003131.980851
Maribel Barroso suggests exploration of an interesting avenue for inductive inference. The material theory, as I have formulated it, takes as its elements propositions that assert scientific facts. Relations of inductive support among them assess their truth or falsity. She proposes that we should take models as the elements instead of proposition. In favor of this proposal is that models have a pervasive presence in science. We should be able to confront them with evidence in a systematic way. Reconfiguring inductive inference as relations over models faces some interesting questions. Just what is it for models to be supported inductively? Can the material theory be adapted to this new case? In works cited in her review, Barroso has already begun the study of inductive relations among models in science, using insights from Whewell’s work. She is, it seems to me, well placed to seek answers to these questions. I wish her well in her continuing efforts.
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1011940.980865
The nodes of the ‘geometric trinity’ are: (i) general relativity (in which gravitational effects are a manifestation of spacetime curvature), (ii) the ‘teleparallel equivalent’ of general relativity (which trades spacetime curvature for torsion), and (iii) the ‘symmetric teleparallel equivalent’ of general relativity (which trades spacetime curvature for non-metricity). One popular reformulation of (iii) is ‘coincident general relativity’, but this theory has yet to receive any philosophical attention. This article aims both to introduce philosophers to coincident general relativity, and to undertake a detailed assessment of its features.
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1011958.980879
How to articulate the common ontological commitments of symmetry-related models of physical theories? This is a central (perhaps the central) question in the philosophical literature on symmetry transformations in physics; recently, Dewar (2019) has proposed a strategy for answering this question which goes by the name of ‘external sophistication’. And yet: this strategy has been accused of being hopelessly obscure by, among others, Martens and Read (2020). In this article, I demonstrate that not all cases of external sophistication are subject to this charge—for reasons which will become clear, the cases for which this is not so give us what I’ll call ‘good VIBES’. Having established this, I then go on to consider good VIBES in the context of the analysis of hidden symmetries, in dialogue with recent work on that topic by Bieli nska and Jacobs (2024).
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1063678.980893
Indicative conditional antecedents appear to be remarkably scopeless: they are scopeless with respect to the truth-functional connectives, scopeless with respect to epistemic modals, and scopeless with respect to each other (i.e., commutative). This pervasive scopelessness is a basic explanandum for any theory of indicatives, and the subject of much recent work. In this paper I revisit the theory of McGee [1989], which already comes surprisingly close to delivering a simple and powerful account of all of this scopelessness. I reformulate the theory as information-sensitive in the contemporary sense, and extend it with epistemic modals. On the resulting theory, epistemic modals become in e!ect quantifiers over choice functions, and their scopeless interaction with indicative antecedents drops out naturally. I give McGee’s logic a new axiomatization, and show that if his Import-Export axiom is replaced with a weaker Commutativity axiom stating that indicative antecedents commute, then Import-Export can be derived. I explain how the issue of commutativity interacts with the question how to extend information-sensitive theories of the indicative to modal antecedents. Along the way I add to the collapse results of both McGee [1985] and Mandelkern [2021], showing that under weak assumptions, Commutativity is in tension with Modus Ponens and (more generally) with the principle Mandelkern calls Ad Falsum. I convict Ad Falsum, and refine the case against Modus Ponens.
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1127303.98091
I argue that different ways that branching fits within Minkowski spacetime are merely different descriptions of an invariant notion of branching and are due to the relativity of simultaneity. The argument fits in the wider framework of Everett branches as real patterns, and is both developed in the abstract setting of the (generalised) histories formalism, and discussed comparing the concrete examples of hypersurface-dependent branching and of branching along the forward lightcone. I formulate the latter in terms of branching spacetime, suggesting this is a way in which spacetime can emerge from the universal wavefunction, and I make tentative connections with causal set theory. The proposed view is compatible with both the Schrodinger and Heisenberg picture.
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1131302.980925
Standardized testing is glorious, but many standardized tests royally suck. The worst prominent test is almost surely the Graduate Record Exam (GRE). About 9% of test-takers get a perfect score of 170 on the Quantitative part of the exam. …
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1185137.980938
While the problem of the philosophical significance of Riemann's theorem on conditionally convergent series has been discussed in detail for some time, specific versions of it have appeared in the literature very recently, over which there have been widespread disagreements. I argue that such discrepancies can be clarified by introducing a rather conventional type of composition rule for the treatment of some infinite systems (as well as supertasks) while analysing and clarifying the role of the concept of continuity by stripping it of the excesses that its application by the Leibnizian tradition has led to. The conclusion reached is that the indeterminacy associated with conditional convergence has a clear philosophical significance, but no fundamental ontological significance. Keywords: Conditional Convergence; Continuity; Expansionist Analysis; Balance Principle; Ross Paradox.
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1185161.980952
Bell’s theorem states that no model that respects Local Causality and Statistical Independence can account for the correlations predicted by quantum mechanics via entangled states. This paper proposes a new approach, using backward-in-time conditional probabilities, which relaxes conventional assumptions of temporal ordering while preserving Statistical Independence as a “fine-tuning” condition. It is shown how such models can account for EPR/Bell correlations and, analogously, the GHZ predictions while nevertheless forbidding superluminal signalling.
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1291499.980968
My earlier volume, The Material Theory of Induction, asserts that inductive inferences are warranted materially by facts and not by conformity with universally applicable schemas. A few examples illustrate the assertion. Marie Curie inferred that all samples of radium chloride will be crystallographically like the one sample she had prepared. The inference was warranted, not by the rule of enumerative induction, but by factual discoveries in the 19th century on the properties of crystalline substances. Galileo inferred to the heights of mountains on the moon through an analogy with mountain shadows formed on the earth. The inference was not warranted by a similarity in the reasoning in the two cases conforming with some general rule, but by the warranting fact that the same processes of linear light propagation formed the patterns of light and dark in both cases. Probabilistic inductive inferences are not warranted by the tendentious supposition that all uncertainties can be represented probabilistically. They are warranted on a case-by-case basis by facts specific to the case at hand. That we can infer probabilistically from samples to the population as a whole depends on the fact that the samples were taken randomly, that is, with each individual having an equal probability of selection. If no such warranting facts prevail, we are at serious risk of spurious inferences whose results are an artifact of misapplied logic.
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1333838.980982
An adequate theory of representation should distinguish between the structure of a representation and the structure of what it represents. I argue that the simplest sorts of transformers (the architecture that underlies most familiar Large Language Models) have only a very lightweight structure for their representations: insofar as they work with the structure of language, they represent it but do not use it. In addition to being interesting in its own right, this also shows how we may use high-level invariants at the computational level to place constraints on representational formats at the algorithmic level.
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1704082.980996
Quantum mechanics and general relativity require unied theoretical treatment, particularly regarding the cosmological constant's observed value (≈ 10−123 in Planck units). This paper presents the Minimal Causal-Informational Model of Emergent Space-Time (MCIMES), which establishes quantum information as the fundamental entity underlying emergent space-time geometry. The model adopts quantum structural realism as its interpretive framework, implemented through rigorous category theory formalism. MCIMES is mathematically constructed on an abstract interaction graph, represented as a monoidal category CA with functorial mappings to physical observables. The system's dynamics are governed by a variational principle of minimal information loss, expressible through natural transformations between functors. The framework demonstrates how metric properties, Lorentzian signature, and causal structure emerge from quantum correlations without presupposing space-time. Topological invariants, particularly Betti numbers bp of the interaction graph, play a crucial role in quantifying universal properties of space-time uctuations and thermodynamic behavior. From this background-independent formulation, Einstein's equations emerge in the continuum limit as the optimal conguration that minimizes information loss.
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1704099.98101
Deng, Hani, and Ma [arXiv:2503.01800] claim to resolve Hilbert’s Sixth Problem by deriving the Navier-Stokes-Fourier equations from Newtonian mechanics via an iterated limit: a Boltzmann-Grad limit (ε → 0, N εd−1 = α fixed) yielding the Boltzmann equation, followed by a hydrodynamic limit (α → ∞) to obtain fluid dynamics. Though mathematically rigorous, their approach harbors two critical physical flaws. First, the vanishing volume fraction (N ε → 0) confines the system to a dilute gas, incapable of embodying dense fluid properties even as α scales, rendering the resulting equations a rescaled gas model rather than a true continuum. Second, the Boltzmann equation’s reliance on molecular chaos collapses in fluid-like regimes, where recollisions and correlations invalidate its derivation from Newtonian dynamics. These inconsistencies expose a disconnect between the formalism and the physical essence of fluids, failing to capture emergent, density-driven phenomena central to Hilbert’s vision. We contend that the Sixth Problem remains open, urging a rethink of classical kinetic theory’s limits and the exploration of alternative frameworks to unify microscale mechanics with macroscale fluid behavior.
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1704120.981023
Summary. In the first part of this contribution I will present aspects and attitudes towards ’axiomatic thinking’ in various branches of theoretical physics. In the second and more technical part, which is approximately of the same size, I will focus on mathematical results that are relevant for axiomatic schemes of space-time in connection with attempts to axiomatise Special and General Relativity.
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1737492.981038
I consider the sense in which teleparallel gravity and symmetric teleparallel gravity may be understood as gauge theories of gravity. I first argue that both theories have surplus structure. I then consider the relationship between Yang-Mills theory and Poincare Gauge Theory and argue that though these use similar formalisms, there are subtle disanalogies in their interpretation.