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25592.491617
Ever since Carlo Rovelli introduced Relational Quantum Mechanics (RQM) to the public [1], it has attracted the interest and stimulated the imagination not only of physicists, but also, and in particular, of philosophers. There are several reasons why that is so. One of them is, quite simply, that a renowned and highly esteemed researcher had offered a new programmatic attempt to make sense of the longstanding puzzles at the foundations of quantum theory, which only happens every so often. What is more, the key to these puzzles was supposed to lie in an essentially conceptual move, in the exposure of an “incorrect notion” [1, p. 1637]. But the modern-day philosopher regards concepts as something like their natural hunting ground. If mention is made of the word, it makes them sit up as if somebody had yelled their name.
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25624.491712
The idea that qualities can be had partly or to an intermediate degree is controversial among contemporary metaphysicians, but also has a considerable pedigree among philosophers and scientists. In this paper, we first aim to show that metaphysical sense can be made of this idea by proposing a partial taxonomy of metaphysical accounts of graded qualities, focusing on three particular approaches: one which explicates having a quality to a degree in terms of having a property with an in-built degree, another based on the idea that instantiation admits of degrees, and a third which derives the degree to which a quality is had from the aspects of multidimensional properties. Our second aim is to demonstrate that the choice between these account can make a substantial metaphysical difference. To make this point, we rely on two case studies (involving quantum observables and values) in which we apply the accounts in order to model apparent cases of metaphysical gradedness.
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35346.491726
A recent result from theoretical computer science provides for the verification of answers to the Halting Problem, even when there is no plausible means by which to derive those answers using a bottom-up approach. We argue that this result has profound implications for the existence of strongly emergent phenomena. In this work we develop a computer science-based framework for thinking about strong emergence and in doing so demonstrate the plausibility of strongly emergent phenomena existing in our universe. We identify six sufficient criteria for strong emergence and detail the actuality of five of the six criteria. Finally, we argue for the plausibility of the sixth criterion by analogy and a case study of Boltzmann brains (with additional case studies provided in the appendices.)
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35370.491745
I will look at Bohr’s contentious doctrine of classical concepts - the claim that measurement requires classical concepts to be understood - and argue that measurement theory supports a similar conclusion. I will argue that representing a property in terms of a metric scale, which marks a shift from the empirical process of measurement to the informational output, introduces the inherently classical assumption of definite states and precise values, thus fulfilling Bohr’s doctrine. I examine how realism about metric scales implies that Bohr’s doctrine is ontological, while more moderate coherentist or model-based approaches to realism render it epistemological. Regardless of one’s stance towards measurement realism, however, measurement cannot be entirely quantum and quantum mechanics can model only the empirical side of measurement, not its informational output. Finally, I discuss how this might influence our understanding of the measurement problem.
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121769.491757
This paper proposes a dynamic temporal logic that is appropriate for modeling the dynamics of scientific knowledge (especially in historical sciences, such as Archaeology, Paleontology and Geology). For this formalization of historical knowledge, the work is divided into two topics: firstly, we define a temporal branching structure and define the terms for application in Philosophy of Science; Finally, we define a logical system that consists of a variation of Public Announcement Logic in terms of temporal logic, with appropriate rules in a tableaux method.
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181077.491768
This is Part II of my commentary on Stephen Senn’s guest post, Be Careful What You Wish For. In this follow-up, I take up two topics:
(1) A terminological point raised in the comments to Part I, and
(2) A broader concern about how a popular reform movement reinforces precisely the mistaken construal Senn warns against. …
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186535.491782
| The boundary problem in normative democratic theory is the problem of who should be entitled to participate in which democratic decision-making. The boundary problem is at the heart of many pressing political issues, including voting rights of resident aliens in their host countries and of expats in their home countries, the legitimacy of border regimes, the justi!ability of global democracy, and the democratic representation of future generations. The two most popular answers to the boundary problem are the
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206603.491797
Very short summary: In this essay, I discuss Gerald Gaus’s argument about the possibility of moral reconciliation in diverse societies. Like Gaus, I use an agent-based model to explore the conditions under which convergence toward a single social rule happens. …
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208052.491819
Advocates of the explanatory indispensability argument for platonism say two things. First, we should believe in the parts of our best scientific theories that are explanatory. Second, mathematical objects play an explanatory role within those theories. I give a two-part response. I start by using a Bayesian framework to argue that the standards many have proposed must be met to show that mathematical objects are dispensable are too demanding. In particular, nominalistic theories may be more probable than platonistic ones even if they are extremely complicated by comparison. This is true even if there are genuine cases of mathematical explanation in science. The point made here is a matter of principle, holding regardless of how one assesses nominalistic theories already on offer. I then examine my recent nominalization of second-order impure set theory in light of the correct, laxer standards. I make a tentative case that my nominalistic theory meets those standards, which would undermine the explanatory indispensability argument. While this case is provisional, I aim to bring attention to my nominalization and others in light of the revised standards for demonstrating dispensability.
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208074.491832
In this paper, I develop a “safety result” for applied mathematics. I show that whenever a theory in natural science entails some non-mathematical conclusion via an application of mathematics, there is a counterpart theory that carries no commitment to mathematical objects, entails the same conclusion, and the claims of which are true if the claims of the original theory are “correct”: roughly, true given the assumption that mathematical objects exist. The framework used for proving the safety result has some advantages over existing nominalistic accounts of applied mathematics. It also provides a nominalistic account of pure mathematics.
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208133.491845
Recent philosophical literature on the epistemology of measurement has relegated measurement uncertainty to a secondary issue, concerned with characterizing the quality of a measurement process or its product. To reveal the deeper epistemological significance of uncertainty, we articulate the problem of usefulness, which is concerned with the tension between the specificity of the conditions under which particular measurements are performed and the broader range of conditions in which measurement results are intended to be – and are – used. This is simultaneously an epistemological and a practical problem.
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208190.491856
The theory of quasi-truth was developed by Newton da Costa and collaborators as a more realistic account of truth, encompassing the incompleteness and inconsistency of scientific knowledge. Intuitively, the idea is that truth is reached when consensus is established at the end of inquiry; until that is reached, we have something less than the whole truth, we have partial or quasi-truth. Formally, the view faces some challenges that have been recently addressed in the literature; they concern a mismatch between the offered formalism and the expected claims to be formalized. In this paper we use inspiration from quasi-truth theory to develop an account of consensus in science encompassing the notion of quasi-truth. We not only present the formal system capturing the idea of a scientific consensus, but also show how quasi-truth may be represented within it too. We compare the original quasi-truth approach to ours, and argue that the latter is able to face some of the difficulties that plagued the former.
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294563.491869
We argue that semiclassical gravity can be rendered consistent by assuming that quantum systems only emit a gravitational field when they interact with stable determination chains (SDCs), which are specific chains of interactions modeled via decoherence and test functions obeying a set of conditions. When systems are disconnected from SDCs, they do not emit a gravitational field. This denies the universality of gravity, while upholding a version of the equivalence principle. We argue that this theory can be tested by experiments that investigate the gravitational field emitted by isolated systems like in gravcats experiments or by investigating the gravitational interactions between entangled systems like in the (Bose- Marletto-Vedral) BMV experiment. Our theory fits into a new framework which holds that in the absence of certain conditions, quantum systems cannot emit a gravitational field. There are many possible conditions for systems to emit a gravitational field, and we will adopt a subset of them. We will show how this subset of conditions provides multiple benefits beyond rendering semiclassical gravity consistent, which includes deriving the value of the cosmological constant from first principles and providing an explanation for why the vacuum does not gravitate.
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640109.491881
Robustness of AI alignment is one of the safety issues of large language models. Can we predict how many mistakes will a model make when responding to a restricted request? We show that when access to the model is limited to in-context learning, the number of mistakes can be proved inapproximable, which can lead to unpredictability of alignment of the model. Against intuition, this is not entirely bad news for AI safety. Attackers might not be able to easily misuse in-context learning to break alignment of the model in a predictable manner because the mistake bounds of safe responses, which were used for alignment, can be proved inapproximable. This inapproximability can hide the safe responses from attackers and make alignment of the model unpredictable. If it were possible to keep the safe responses from attackers, responsible users would benefit from testing and repairing of the model’s alignment despite its possible unpredictability. We also discuss challenges involved in ensuring democratic AI alignment with limited access to safe responses, which helps us to make alignment of the model unpredictable for attackers.
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710818.491893
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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710868.49191
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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789109.491926
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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810621.491937
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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810643.491946
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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812855.491955
A common criticism of medicine is that there is too much focus on treating symptoms instead of patients. This criticism and its sentiment – among other factors – have motivated many ‘humanistic,’ ‘holistic,’ and ‘non-reductionist’ approaches to medicine including the biopsychosocial model, patient-centered medicine, ‘gentle’ medicine, and others. Much has been said detailing and defending these approaches. My aim here is not to further defend one or any of these. Rather, my aim is to better understand what is at the heart of the ‘common criticism,’ i.e., that treating symptoms – not patients – is bad. What does this mean? Are symptoms not something patients have? By treating symptoms, do clinicians not necessarily treat the patients that have them?
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873584.491967
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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985498.491977
In this paper we will try to provide a solid form of intrinsic set theoretical optimism. In other words, we will try to vindicate Gödel’s views on phenomenology as a method for arriving at new axioms of ZFC in order to decide independent statements such as CH. Since we have previously written on this very same subject [41, 43, 44], it is necessary to provide a justification for addressing it once again.
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985549.49199
I discuss the distinction between extrinsic and intrinsic approaches to reformulating a theory with symmetries, and offer an account of the special value of intrinsic formalisms, drawing on a distinction between which mathematical expressions are meaningful within an extrinsic formalism and which are not.
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985594.492
This work explores the connection between logical independence and the algebraic structure of quantum mechanics. Building on results by Brukner et al., it introduces the notion of onto-epistemic ignorance : situations in which the truth of a proposition is not deducible due to an objective breakdown in the phenomenal chain that transmits information from a system A to a system B, rather than to any subjective lack of knowledge. It is shown that, under such conditions, the probabilities accessible to a real observer are necessarily conditioned by decidability and obey a non-commutative algebra, formally equivalent to the fundamental postulates of quantum mechanics.
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985618.492011
In the 1960s and 1970s a series of observations and theoretical developments highlighted the presence of several anomalies which could, in principle, be explained by postulating one of the following two working hypotheses: (i) the existence of dark matter, or (ii) the modification of standard gravitational dynamics in low accelerations. In the years that followed, the dark matter hypothesis as an explanation for dark matter phenomenology attracted far more attention compared to the hypothesis of modified gravity, and the latter is largely regarded today as a non-viable alternative. The present article takes an integrated history and philosophy of science approach in order to identify the reasons why the scientific community mainly pursued the dark matter hypothesis in the years that followed, as opposed to modified gravity. A plausible answer is given in terms of three epistemic criteria for the pursuitworthiness of a hypothesis: (a) its problem-solving potential, (b) its compatibility with established theories and the feasibility of incorporation, and (c) its independent testability. A further comparison between the problem of dark matter and the problem of dark energy is also presented, explaining why in the latter case the situation is different, and modified gravity is still considered a viable possibility.
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1071999.492019
This article revisits Taurek’s famous question: Should the greater number be saved in situations of resource scarcity? At the heart of this debate lies a central issue in normative ethics—whether numerical superiority can constitute a moral pro tanto reason. Engaging with this question helps to illuminate core principles of normative theory. Welfarismmin presents a pro-number position. The article first outlines Taurek’s original argument. It then examines non-welfarist responses and explains why they remain unsatisfactory. Finally, it identifies the main shortcomings of the hybrid welfarismmin approach and suggests a possible alternative for more adequately addressing the Taurek problem.
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1158109.492031
The epistemic projection approach (EPA) is an intermediate approach to value management in science. It recognizes that there are sometimes good reasons to make research responsive to contextual values, but it achieves this responsiveness via the careful formulation of a research problem in the problem-selection stage of investigation. EPA is thus an approach that could be acceptable to some parties on both sides of the debate over the value-free ideal. Independent of this, EPA provides practitioners with concrete guidance on how to make research responsive to contextual values. This is illustrated with an example involving air pollution.
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1158131.492042
Key elements of the recent dialectic surrounding the hole argument in the philosophy of general relativity are clarified by close attendance to the nature of scientific representation. I argue that a structuralist account of representation renders the purported haecceitistic differences between target systems irrelevant to the representational role of models of general relativity. Framing the hole argument in this way helps resolve the impasse in the literature between Weatherall and Pooley and Read.
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1266766.492053
In this paper I develop a view of token causation that is inspired by Anscombe’s Causality and Determination, and is likely what she meant by “causality consists in the derivativeness of an effect from its causes”. On this view, token causation is not a logical relation, even in a very broad sense, and so is very different from logical consequence, conditional probability, and counterfactual dependence. Instead, causation is a kind of ontological dependence, so that to cause something means to confer existence on it. Causation is thus absent from physics, but I argue that recognising this absence enables us to make sense of the direction of time and the stability of physical probabilities.
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1331153.492064
Achilles and the tortoise compete in a race where the beginning (the start) is at point O and end (the finish) is at point P. At all times the tortoise can run at a speed that is a fraction of Achilles' speed at most (with being a positive real number lower than 1, 0 < < 1), and both start the race at t = 0 at O. If the trajectory joining O with P is a straight line, Achilles will obviously win every time. It is easy to prove that there is a trajectory joining O and P along which the tortoise has a strategy to win every time, reaching the finish before Achilles.