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21441.480809
In contemporary philosophy of physics, there has recently been a renewed interest in the theory of geometric objects—a programme developed originally by geometers such as Schouten, Veblen, and others in the 1920s and 30s. However, as yet, there has been little-to-no systematic investigation into the history of the geometric object concept. I discuss the early development of the geometric object concept, and show that geometers working on the programme in the 1920s and early 1930s had a more expansive conception of geometric objects than that which is found in later presentations— which, unlike the modern conception of geometric objects, included embedded submanifolds such as points, curves, and hypersurfaces. I reconstruct and critically evaluate their arguments for this more expansive geometric object concept, and also locate and assess the transition to the more restrictive modern geometric object concept.
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21596.480965
“AI4Science” refers to the use of Artificial Intelligence (AI) in scientific research. As AI systems become more widely used in science, we need guidelines for when such uses are acceptable and when they are unacceptable. To that end, I propose that the distinction between the context of discovery and the context of justification, which comes from philosophy of science, may provide a preliminary but still useful guideline for acceptable uses of AI in science. Given that AI systems used in scientific research are black boxes, for the most part, we should use such systems in the context of discovery but not in the context of justification. The former refers to processes of idea generation, which may be unproblematically opaque whether they occur in human brains or artificial neural networks, whereas the latter refers to scientific methods by which scientific ideas are tested, confirmed, verified, and justified, which should be transparent.
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34958.480978
It is uncontroversial that definite plurals in natural language stand for pluralities and permit predicates that are inherently distributive as in (1a) as well as predicates that can apply both collectively or distributively, as in (1b): (1) a. The stones are grey. b. The stones are heavy.
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79253.480988
This paper presents a novel approach: using a digital calculation method for propositional logical reasoning. The paper demonstrates how to discover the primitive numbers and the digital calculation formulas by analyzing the truth tables. Then it illustrates how to calculate and compare the truth values of various expressions by using the digital calculation method. As an enhanced alternative to existing approaches, the proposed method transforms the statement-based or table-based reasoning into number-based reasoning. Thereby, it eliminates the need for using truth tables, and obviates the need for applying theorems, rewriting statements, and changing symbols. It provides a more streamlined solution for a single reasoning, while demonstrating more efficiency for multiple reasonings in long-term use. It is suitable for manual calculation, large-scale computation, AI and automated reasoning.
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122991.480997
How the semantic significance of numerical discourse gets determined is a metasemantic issue par excellence. At the sub-sentential level, the issue is riddled with difficulties due to the contested metaphysical status of the subject matter of numerical discourse, i.e. numbers and numerical properties and relations. I propose to set those difficulties aside and focus instead on the sentential level, specifically, on obvious affinities between whole numerical and non-numerical sentences and how their significance is determined. From such a perspective, Frege’s 1884 construction of number, while famously mathematically untenable, fares better than other approaches in the philosophy of mathematics. Despite the work’s foundational untenability, it is metasemantically superior to extant alternatives.
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194516.481005
Recently, several philosophers and physicists have increasingly noticed the hegemony of unitarity in the black hole information loss discourse and are challenging its legitimacy in the face of the measurement problem. They proclaim that embracing non-unitarity solves two paradoxes for the price of one. Though I share their distaste over the philosophical bias, I disagree with their strategy of still privileging certain interpretations of quantum theory. I argue that information-restoring solutions can be interpretation-neutral because the manifestation of non-unitarity in Hawking’s original derivation is unrelated to what’s found in collapse theories or generalized stochastic approaches, thereby decoupling the two puzzles.
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194533.481013
Theorists of probabilistic causality viewed causation as probability raising relative to particular contexts. In contrast, more recent graphical theories do not specify whether a cause raises or lowers the probability of its effect as part of the causal representation, but enable one to infer such quantitative facts from the joint probability distribution and additional causal assumptions. This difference between the accounts may seem minor, but here I argue that the emphasis among probabilistic theorists on probability raising reflected their not having an adequate theory of confounding and thus of the relationship between causal and probabilistic claims. The graphical account of confounding clarifies why causal relationships need not be identified with particular probabilistic relationships in particular populations, and thus why many of the earlier debates about probability raising in retrospect no longer appear to reflect substantive philosophical differences.
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194611.48102
The so-called Geometric Trinity of Gravity includes General Relativity (GR), based on spacetime curvature; the Teleparallel Equivalent of GR (TEGR), which relies on spacetime torsion; and the Symmetric Teleparallel Equivalent of GR (STEGR), grounded in nonmetricity. Recent studies demonstrate that GR, TEGR, and STEGR are dynamically equivalent, raising questions about the fundamental structure of spacetime, the under-determination of these theories, and whether empirical distinctions among them are possible. The aim of this work is to show that they are equivalent in many features but not exactly in everything. In particular, their relationship with the Equivalence Principle (EP) is different.
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309975.481029
Relational quantum mechanics (RQM) explains the world in terms of an ontology of systems and events, where an event consists of a variable of a system taking a value relative to another system. Two strands of RQM may be distinguished depending on whether events are taken to be absolute or relative. The arguments in this paper apply to both. I argue that, in order to solve the problem of measurement, RQM needs to offer a specification of the circumstances in which events occur. Current formulations of RQM claim that events occur whenever interactions occur, without further defining what is meant by ‘interaction’. I develop the most plausible ways of understanding the notion of interaction, but I show that they fail to provide a satisfactory specification for the occurrence of events. In light of these failed constructive efforts, I conclude that the prospects for formulating a version of RQM which both satisfies its aims and solves the problem of measurement are dim. Key words: Relational Quantum Mechanics, Quantum Mechanics, Measurement Problem.
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309998.481039
Discussions of theoretical equivalence typically only concern a theory’s dynamically possible models. Recently, however, March (2024) has shown that a theory’s kinematically possible models are also relevant to questions of theoretical equivalence. We apply March’s notion of kinematic equivalence to the difference between reduced and sophisticated theories introduced by Dewar (2019). Although Dewar claims that these are equivalent, Jacobs (2024) has argued that only sophisticated theories can explain what are otherwise ‘cosmic conspiracies’. We show that this is a consequence of reduced and sophisticated theories’ kinematical inequivalence. Furthermore, we use Caulton’s (2024) ‘downwards Hume’s dictum’ to show that kinematically inequivalent are also ontologically inequivalent.
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367733.481047
Two views on the direction of time can be distinguished—primitivism and nonprimitivism. According to the former, time’s direction is an in-built, fundamental property of the physical world. According to the latter, time’s direction is a derivative property of a fundamentally directionless reality. In the literature, non-primitivism has been widely supported since most (if not all) our fundamental dynamical laws are time-reversal invariant. In this paper, I offer a way out to the primitivist. I argue that we do have good grounds to support a primitive direction of time in the quantum realm. The rationale depends on exploiting the metaphysical and dynamical underdetermination of quantum theories to make a case in favor of primitivism. In particular, primitivism can be grounded in spontaneous collapse theories (e.g., GRW and CSL). The specific sense in which these theories capture a primitive direction of time is that, when the ontology of the theory is seriously taken into account, it does not remain invariant under time reversal. In taking GRW with a matter-density field (GRWm), I will argue that primitivism about the direction of time can be defended in the quantum case.
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367766.481054
It has been argued that measurement-induced collapses in Orthodox Quantum Mechanics generates an intrinsic (or built-in) quantum arrow of time. In this paper, I critically assess this proposal. I begin by distinguishing between an intrinsic and non-intrinsic arrow of time. After presenting the proposal of a collapse-based arrow of time in some detail, I argue, first, that any quantum arrow of time in Orthodox Quantum Mechanics is non-intrinsic since it depends on external information about the measurement context, and second, that it cannot be global, but just local. I complement these arguments by assessing some criticisms and considerations about the implementation of time reversal in contexts wherein measurement-induced collapses work. I conclude that the quantum arrow of time delivered by Orthodox Quantum Mechanics is much weaker than usually thought.
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483097.481061
Recently Chiao and his collaborators proposed a new version of the electric Aharonov-Bohm effect [Phys. Rev. A 107, 042209 (2023)]. They argued that a quantum system confined in a Faraday cage with a time varying but spatially uniform electric scalar potential can pick up the Aharonov-Bohm phase, and the observable consequence is the energy level shift of the quantum system. In this paper, I argue that Chiao et al’s analysis is problematic, and a time varying, spatially uniform electric scalar potential cannot result in observable energy level shift of quantum systems. A possible explanation of this seemingly puzzling result is also given based on the one true gauge principle.
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483154.481068
Symmetry fundamentalism claims that symmetries should be taken metaphysically seriously as part of the fundamental ontology. The main aim of this paper is to bring some novel objections against this view. I make two points. The first places symmetry fundamentalism within a broader network of philosophical commitments. I claim that symmetry fundamentalism entails idealization realism which, in turn, entails the reification of further theoretical structures. This might lead to an overloaded ontology as well as open the way to criticisms from metaphysical frameworks that reject such reifications. The second point contrasts symmetry fundamentalism with the now common view that regards symmetries as stipulations guiding empirical research and theory construction. I claim that both views clash each other and cannot be held together. I finish the paper with a more positive prospect that will be developed in future work—symmetry deflationism.
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483197.481075
Symmetry-based inferences have permeated many discussions in philosophy of physics and metaphysics of science. It is claimed that symmetries in our physical theories would allow us to draw metaphysical conclusions about the world, a view that I call ‘symmetry inferentialism’. This paper is critical to this view. I claim that (a) it assumes a philosophically questionable characterization of the relevant validity domain of physical symmetries, and (b) it overlooks a distinction between two opposing ways through which relevant physical symmetries become established. My conclusion is that symmetry inferentialism loses persuasive force when these two points are taken into consideration.
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615668.481082
It is increasingly easy to acquire a large amount of data about a problem before formulating a hypothesis. The idea of exploratory data analysis (EDA) predates this situation, but many researchers find themselves appealing to EDA as an explanation of what they are doing with these new resources. Yet there has been relatively little explicit work on what EDA is or why it might be important. I canvass several positions in the literature, find them wanting, and suggest an alternative: exploratory data analysis, when done well, shows the expected value of experimentation for a particular hypothesis.
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656121.481106
Traditional attempts to understanding inductive reasoning in science have typically involved analyzing language, focusing on statements or propositions. However, recent arguments suggest that this approach misconceives induction, prompting the need for a new perspective. This study offers a fresh view on induction by integrating William Whewell's theory of induction, which distinguishes two forms of reasoning: interpretation and representation. This perspective suggests that induction can be seen as a reasoning process based on semantic and pragmatic models rather than statements or propositions.
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814207.481119
The past is settled and the assertion in the past is either true or false. The future (even if deterministic) is cannot be known and what we say about the future is perceived as a prediction that can turn out to be true or false. Will is not a tense but a modal.
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829075.481131
The question of the reduction of chemistry to quantum mechanics has been inextricably linked with the development of the philosophy of chemistry since the field began to develop in the early 1990s. In the present chapter I would like to describe how my own views on the subject have developed over a period of roughly 30 years. A good place to begin might be the frequently cited reductionist dictum that was penned in 1929 by Paul Dirac, one of the founders of quantum mechanics.
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829121.481143
The article begins with a response to a recent contribution by Jensen, in which he has criticized several aspects of the use of triads of elements, including Döbereiner’s original introduction of the concept and the modern use of atomic number triads by some authors including myself. Such triads are groups of three elements, one of which has approximately the average atomic weight of the other two elements, as well as having intermediate chemical reactivity. I also examine Jensen’s attempted reconstruction Mendeleev’s use of triads in predicting the atomic weights of three hitherto unknown elements, that were subsequently named gallium, germanium and scandium. The present article then considers the use of atomic number triads, in conjunction with the phenomenon of first member anomaly, in order to offer support for Janet’s left-step periodic table, in which helium is relocated into group 2 of the table. Such a table features triads in which the 2nd and third elements of each group, without fail, fall into periods of equal length, a feature that is absent in the conventional 18-column or the conventional 32-column table. The dual sense of the term element, which is the source of much discussion in the philosophy of chemistry, is alluded to in further support of such a relocation of helium that may at first appear to contradict chemical intuition.
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886855.481163
Jack Spencer and Ian Wells have recently argued that Causal Decision Theory faces special difficulty in cases of decision-instability where a play-it-safe option is present. They argue that CDT recommends taking a risky option, while the rational thing to do is to play it safe. In this paper I will show that CDT only recommends the risky option if we assume risk neutrality—a risk-averse CDT can play it safe. This opens two lines of response to Causalists: They can embrace a risk-averse CDT. Or they can reject the intuition to play it safe on the general grounds that risk-aversion is irrational. I will also generalise this argument to several other examples involve decision-instability. Of course, risk-aversion cannot explain all CDT’s problems and I will bolster the case for risk-aversion playing a special role in these cases by showing it cannot help in all such cases.
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927006.481179
We consider a model of case-based planning, where a position is a vector of numbers, and a case is an edge in the directed graph of positions. The planner generates new plans by using cases that are similar to those she has observed in the past. In the benchmark model presented here, similarity is de…ned by equality of differences (between the target and the source position). We prove a complexity result that shows why planning requires imagination and is not easily done algorithmically. We put this result in the context of learning and expertise in case-based models, distinguishing among information, insight, and imagination.
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956037.481191
God must create the best. But there is no best. Therefore, there is no God. Various philosophers—among them Stephen Grover and William Rowe—have endorsed more elaborate versions of this argument. Dean Zimmerman (in “Resisting Rowe’s No-Best-World Argument for Atheism”) has subjected their defenses of the argument to careful scrutiny—scrutiny that was in fact so careful that there remains very little to say about the argument. This essay contains my attempt to supply that very little.
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1016477.481202
Remember that old Woody Allen movie, “Midnight in Paris,” where the main character (I forget who plays it, I saw it on a plane), a writer finishing a novel, steps into a cab that mysteriously picks him up at midnight and transports him back in time where he gets to run his work by such famous authors as Hemingway and Virginia Wolf? …
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1029820.481241
I recently wrote about how the Parker Solar Probe crossed the Sun’s ‘Alfvén surface’: the surface outside which the outflowing solar wind becomes supersonic. This is already pretty cool—but even better, the ‘sound’ here is not ordinary sound: it consists of vibrations in both the hot electrically conductive plasma of the Sun’s atmosphere and its magnetic field! …
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1059823.481252
Hempel publicly abandoned the Received View on scientific theories in the 1960s in favor of a new view. However, Hempel misrepresents his own works within the Received View in a number of his criticisms, and his new view turns out to be identical to the Received View on correspondence rules, observational terms, theoretical terms, and the demarcation between basic principles of a theory and correspondence rules. Hempel’s criticism of the assumption of axiomatization has counterexamples in his own previous work within the Received View, and his criticism of the meaning of theoretical terms in the Received View ignores developments he witnessed and discussed.
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1059865.481265
The Received View on scientific theories is a framework for formalizing and analyzing theories mainly developed by Rudolf Carnap and Carl Gustav Hempel within logical empiricism. Its central assumptions are that theories and observations can be formalized in predicate logic, that the language of formalization has a context-dependent observational sub-language or separate observation language, and that the interpretation of the language is restricted only by theories and the interpretation of the observational language. For the observational language as a sub-language, non-observational terms were initially assumed to be explicitly definable in observational terms, and later assumed to have necessary or sufficient conditions in observational terms. In the final version of the Received View, no specific relations between observational terms and theoretical terms were assumed. The Received View also provided the framework for conceptualizations of explanation, confirmation, reduction, criteria of cognitive significance, the analytic-synthetic distinction, and concept formation. Many criticisms of the Received View in the philosophy of science rely on misrepresentations.
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1113385.481273
I took a side trip to David Cox’s famous “weighing machine” example” a month ago, an example thought to have caused “a subtle earthquake” in foundations of statistics, because knew we’d be coming back to it at the end of December when we revisit the (strong) Likelihood Principle [SLP]. …
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1232912.481283
Using the fiber bundle framework, this work investigates the conceptual and mathematical foundations of reference frames in General Relativity by contrasting two paradigms. The View from Nowhere interprets frame representations as perspectives on an invariant equivalence class, while the View from Everywhere posits each frame representation as constituting reality itself. This conception of reality is termed ”Relality.” The paper critically examines the philosophical and practical implications of these views, with a focus on reconciling theory with experimental practice. Central to the discussion is the challenge of providing a perspicuous characterisation of ontology. The View from Nowhere aligns with the so-called ‘sophisticated approach on symmetries’ and it complicates the empirical grounding of theoretical constructs. In contrast, the View from Everywhere offers a relational ontology that avoids the abstraction of equivalence classes.
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1704952.48129
We present a new uniform method for studying modal companions of superintuitionistic rule systems and related notions, based on the machinery of stable canonical rules. Using this method, we obtain alternative proofs of the Blok-Esakia theorem and of the Dummett-Lemmon conjecture for rule systems. Since stable canonical rules may be developed for any rule system admitting filtration, our method generalizes smoothly to richer signatures. Using essentially the same argument, we obtain a proof of an analogue of the Blok-Esakia theorem for bi-superintuitionistic and tense rule systems, and of the Kuznetsov-Muravitsky isomorphism between rule systems extending the modal intuitionistic logic KM and modal rule systems extending the provability logic GL. In addition, our proof of the Dummett-Lemmon conjecture also generalizes to the bi-superintuitionistic and tense cases.