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27925.53143
In the previous post, I offered a criticism of defining logical consequence by means of proofs. A more precise way to put my criticism would be:
Logical consequence is equally well defined by (i) tree-proofs or by (ii) Fitch-proofs. …
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29607.531528
In A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics [13], David Ellerman argues that the essence of the mathematics of quantum mechanics is the linearized Hilbert space version of the mathematics of partitions. In his article, Ellerman lays out the key mathematical concepts involved in the progression from logic, to logical information, to quantum theory—of distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability, which he argues run throughout the mathematics of quantum mechanics.
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33557.531544
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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33578.531551
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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37587.531557
There are two main accounts of ψ being a logical consequence of ϕ:
Inferentialist: there is a proof from ϕ to ψ
Model theoretic: every model of ϕ is a model of ψ. Both suffer from a related problem. On inferentialism, the problem is that there are many different concepts of proof all of which yield an equivalent relation of between ϕ and ψ. …
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40344.531562
Does science have any aim(s)? If not, does it follow that the debate about scientific progress is somehow misguided or problematically non-objective? These are two of the central questions posed in Rowbottom’s Scientific Progress. In this paper, I argue that we should answer both questions in the negative. Science probably has no aims, certainly not a single aim; but it does not follow from this that the debate about scientific progress is somehow misguided or problematically non-objective.
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40367.53158
This paper examines the tension between the growing algorithmic control in safety-critical societal contexts—motivated by human cognitive fallibility—and the rise of probabilistic types of AI, primarily in the form of Large Language Models (LLMs). Although both human cognition and LLMs exhibit inherent uncertainty and occasional unreliability, some futurist visions of the “Singularity” paradoxically advocate relinquishing control of the main societal processes–including critical ones–to these probabilistic AI agents, heightening the risks of a resulting unpredictable or “whimsical” governance. As an alternative, a “mediated control” framework is proposed here: a more prudent alternative wherein LLM-AGIs are strategically employed as “meta-programmers” to design sophisticated–but fundamentally deterministic–algorithms and procedures, or, in general, powerful rule-based solutions. It is these algorithms or procedures, executed on classical computing infrastructure and under human oversight, the systems to be deployed–based on human deliberative decision processes–as the actual controllers of critical systems and processes. This constitutes a way to harness AGI creativity for algorithmic innovation while maintaining essential reliability, predictability, and human accountability of the processes controlled by the algorithms so produced. The framework emphasizes a division of labor between the LLM-AGI and the algorithms it devises, a rigorous verification and validation protocols as conditions for safe algorithm generation, and a mediated application of the algorithms. Such an approach is not a guaranteed solution to the challenges of advanced AI, but–it is argued–it offers a more human-aligned, risk-mitigated, and ultimately more beneficial path towards integrating AGI into societal governance, possibly leading to a safer future, while preserving essential domains of human freedom and agency.
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40414.531586
In current philosophy of science, extrapolation is seen as an inference from a study to a distinct target system of interest. The reliability of such an inference is generally thought to depend on the extent to which study and target are similar in relevant respects, which is especially problematic when they are heterogeneous. This paper argues that this understanding is underdeveloped when applied to extrapolation in ecology. Extrapolation in ecology is not always well characterized as an inference from a model to a distinct target but often includes inferences from small-scale experimental systems to large-scale processes in nature, i.e., inferences across spatiotemporal scales. For this reason, I introduce a distinction between compositional and spatiotemporal variability. Whereas the former describes differences in entities and causal factors between model and target, the latter refers to the variability of a system over space and time. The central claim of this paper is that our understanding of heterogeneity needs to be expanded to explicitly include spatiotemporal variability and its effects on extrapolation across spatiotemporal scales.
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50652.531595
I’ve been watching the TV series “The Handmaid’s Tale” lately. The series is an adaptation of Margaret Atwood’s novel of the same title. For the readers who have never heard about it, this dystopia takes place in the context of worldwide infertility where the United States of America has disappeared following a civil war. …
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89668.5316
There is a certain kind of symmetry between praise and blame. We praise someone who incurs a cost to themselves by going above and beyond obligation and thereby benefitting another. We blame someone who benefits themselves by failing to fulfill an obligation and thereby harming another. …
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120355.531605
It seems very plausible that for any specific Turing machine M there is a fact of the matter about whether M would halt. We can just imagine running the experiment in an idealized world with an infinite future, and surely either it will halt or it won’t halt. …
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130966.53161
In a reference letter for Feyerabend’s application to UC Berkeley, Carl Hempel writes that ‘Mr. Feyerabend combines a forceful and penetrating analytic mind with a remarkably thorough training and high competence in theoretical physics and mathematics’ (Collodel and Oberheim, unpublished, 80). Similarly, Rudolf Carnap says of Feyerabend that he ‘knows both the physics and the philosophy thoroughly, and he is particularly well versed in the fundamental logical and epistemological problems of physics’ (83). These remarks echo a sentiment widely accepted amongst Feyerabend’s colleagues that his knowledge of physics was at an extremely high level. Feyerabend’s acumen in physics goes back to his youth, when, at the age of 13, he was offered a position as an observer at the Swiss Institute for Solar Research after building his own telescope (Feyerabend 1995, 27). It is unsurprising, therefore, that physics played an important and long-lasting role in Feyerabend’s work.
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132301.531616
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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138774.53162
According to the model of exchange as mutual assistance, an exchange can be perceived as a joint activity for mutual benefit – and needn’t involve any self-directed motives at all. This essay pushes back against this new defence of market motives. The essay develops an alternative ideal of production as caring solidarity, in which production is a joint activity of caring about one another. Points of overlap and difference are developed in some detail. The essay concludes by discussing the implications for an economics of caring solidarity, with discussion of the limitations of various market socialist strategies.
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155408.531628
For Karl Marx, ideological forms of consciousness are false, but how and in what respects? Ideologies must include some beliefs in order to be false, even if not all the beliefs that are inferentially related in the ideology are false, and even if there are (causally) related attitudes in the ideology that are neither true nor false. “Ideological” beliefs, however, are not simply false; their falsity has the specific property of not being in the interests of the agents who accept the ideology. One can make two kinds of mistakes about interests. One can mistake what is in one’s intrinsic interest or one can mistake what is in one’s extrinsic interest (that is, the means required to realize one’s intrinsic interests). Marx is mostly, but not exclusively, focused on mistakes about extrinsic interests; this is important in understanding how “morality” (which is not a matter of beliefs, but attitudes) can be ideological for Marx. I illustrate this analysis with some of Marx’s paradigmatic examples of ideological mistakes and offer an account of Marx’s conception of “interests.”
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188054.531635
Please enjoy Harvard’s Jacob Barandes and yours truly duking it out for 2.5 hours on YouTube about the interpretation of quantum mechanics, and specifically Jacob’s recent proposal involving “indivisible stochastic dynamics,” with Curt Jaimungal as moderator. …
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199428.53164
Attachment is deeply important to human life. When one person becomes ‘attached’ to another, their sense of security turns on their emotional, social, and physical engagement with that person. This kind of security-based attachment has been extensively studied in psychology. Yet attachment theory (in the specific sense studied by psychologists) has not received adequate attention in analytic theories of social justice. In this paper, we conceptualize attachment’s nature and value, addressing when and why attachments place justice-based claims on individuals and institutions, in an attempt to establish the centrality of attachment theory to liberal political philosophy. We first characterize security-based attachment and differentiate it from related phenomena (§1). We then explore its value, theorizing the connection between attachment, care, and companionship, drawing on the ethics of care (§2). We explain when and why security-based attachment generates claims of justice within liberal theory, noting some important difficulties (§3). Finally, we sketch some implications in three domains: the rights of those who have suffered pregnancy loss, the rights of grandparents vis-à-vis grandchildren, and the rights of attached friends to social and political recognition (§4).
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200818.531646
How grateful x should be to y for ϕing depends on:
The expected benefit to x
The actual benefit to x
The expected cost to y
The actual deontic status of y’ ϕing
The believed deontic status of y’s ϕing. …
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213377.531651
Although several accounts of scientific understanding exist, the concept of understanding in relation to technology remains underexplored. This paper addresses this gap by proposing a philosophical account of technological understanding—the type of understanding that is required for and reflected by successfully designing and using technological artefacts. We develop this notion by building on the concept of scientific understanding. Drawing on parallels between science and technology, and specifically between scientific theories and technological artefacts, we extend the idea of scientific understanding into the realm of technology. We argue that, just as scientific understanding involves the ability to explain a phenomenon using a theory, technological understanding involves the ability to use a technological artefact to realise a practical aim.
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213402.531656
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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213420.531662
This paper examines cases in which an individual’s misunderstanding improves the scientific community’s understanding via “corrective” processes that produce understanding from poor epistemic inputs. To highlight the unique features of valuable misunderstandings and corrective processes, we contrast them with other social-epistemological phenomena including testimonial understanding, collective understanding, Longino’s critical contextual empiricism, and knowledge from falsehoods.
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213444.531668
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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213464.531673
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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213482.531679
Whereas most scientists are highly critical of constructivism and relativism in the context of scientific knowledge acquisition, the dominant school of chemical education researchers appears to support a variety of such positions. By reference to the views of Herron, Spencer, and Bodner, I claim that these authors are philosophically confused, and that they are presenting a damaging and anti-scientific message to other unsuspecting educators. Part of the problem, as I argue, is a failure to distinguish between pedagogical con - structivism regarding students' understanding of science, and constructivism about the way that scientific knowledge is acquired by expert scientists.
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271189.531685
Shannon Vallor’s The AI Mirror is a useful introduction to the various moral, social, and political problems raised by arti cial intelligence (AI). There are many things that can be said to be arti cially intelligent. Vallor’s focus is a machine that learns using algorithmic, statistical mathematics to ‘produce novel outputs of the same general kind as their training data (such as images, sounds and sentences)’ (p. 19). This sort of intelligence is analogous to the intelligent ability of humans who, upon provision of limited input information, successfully generalize to unreported cases. For example, in learning colour language, humans need only a few cases for them to generalize successfully about colours in non-identical situations.
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271207.53169
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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271225.531697
There are two broad approaches to the publication emergency. Revolutionaries advocate abandoning the current system anonymous pre-publication peer review and editing in favour of open access archives and post-publication crowd-sourced peer review (Heesen and Bright [2021]; Copeland and Marin [2024]; Arvan et al. [2025]). Reformers acknowledge the many problems with the current system, but focus their e orts on improving journals: taking them open access, making them non-pro t, or improving their day-to-day administration. Levy’s sympathies seem to be with the reformers. He focuses on problems within the current publication system, including intellectual charity in peer review, how to handle hoaxes, and what attitude writers should take towards the claims they make in print.
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271243.531704
When is C a cause of E? Many traditional approaches to causation imply that the answer to this question must be of the form ‘C is a cause of E if and only if X’, where X is supposed to provide necessary and su cient conditions for C’s being a cause of E, while itself not relying on causal notions. This reductive approach to causation has led to various valuable insights. However, some philosophers have always been sceptical that such an analysis is possible and, especially in the last two decades, the hope that philosophers could eventually agree on a widely accepted reductive theory of causation has faded. Nevertheless, the literature on causation is ourishing, since causal notions are central to both philosophical and scienti c discourse and there is much to be said about them, even beyond attempts to provide a uni ed reductive analysis.
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271264.531709
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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271284.531715
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.