In the TACITUS project for using commonsense knowledge in the understanding of texts about mechanical devices and their failures, we have been developing various commonsense theories that are needed to mediate between the way we talk about the behavior of such devices and causal models of their operation. Of central importance in this effort is the axiomatization of what might be called commonsense metaphysics. This includes a number of areas that figure in virtually every domain of discourse, such as granularity, (...) scales, time, space, material, physical objects, shape, causality, functionality, and force. Our effort has been to construct core theories of each of these areas, and then to define, or at least characterize, a large number of lexical items in terms provided by the core theories. In this paper we discuss our methodological principles and describe the key ideas in the various domains we are investigating. (shrink)

In ‘The Pregnancy Rescue Case: why abortion is immoral’, Hendricks presents The Pregnancy Rescue Case. In this reply I argue that even if it would be better (i.e., less bad) for the abortion to be prevented in The Pregnancy Rescue Case, that does not mean that typical abortions are impermissible. I also argue that there is a possible explanation, consistent with the pro-choice view and empirically testable, as to why people would think it better for the abortion to be prevented (...) in The Pregnancy Rescue Case. (shrink)

I argue that contrary to their own intentions Casser and Schiller should think that their pain-in-mouth argument is invalid. I cast doubt on whether a hole must be in a host of it but show that the crux of Casser and Schiller’s proposal does not depend on this.

In the last forty years Dummett, Hanks, Künne, and Bobzien have claimed that when Frege wrote ‘Über Sinn und Bedeutung’, he thought that the sense of a sentence-question [Satzfrage] was not a thought [Gedanke] ((Dummett 1981: 307–308); (Hanks 2007: 142–143); (Künne 2010: 427–429); (Bobzien 2021: 163–164)). Recently, Textor has claimed that when Frege wrote ‘Über Sinn und Bedeutung’, he thought that the sense of a sentence-question was not a question [Frage] (Textor 2021: 227 fn.2). I think it is possible that (...) when Frege wrote ‘Über Sinn und Bedeutung’, he thought that the sense of a sentence-question was a question and a thought. To show that this possibility should not be overlooked, I have written a dialogue in which Frege responds to Dummett, Hanks, Künne, Bobzien, and Textor. -/- Bobzien seems to think that when Frege wrote ‘Die Verneinung’, he thought that the sense of a sentence-question was not a question (Bobzien 2021: 163–165). I think it is possible that when Frege wrote ‘Die Verneinung’, he thought that the sense of a sentence-question was a question and a thought. Hence, I have also written the dialogue to show that this possibility should not be overlooked either. (shrink)

In (Owesen 2022), Owesen purportedly argues that pains are activations of nociceptors. In these comments I show that much of what Owesen says is consistent with pains being nociceptors themselves.

Georgalis claimed that when Frege wrote ‘Über Sinn und Bedeutung’ Frege thought that the indirect [ungerade] sense of an expression was identical to its normal [gewöhnlich] sense (Georgalis 2022: e.g. 4, 5, 13). In this paper, I present five arguments for the falsity of Georgalis’ claim which are based on three pieces of apparent counterevidence: a passage from Frege’s letter to Russell dated 28.12.1902; a passage from Frege’s letter to Russell dated 20.10.1902; and a passage from ‘Über Sinn und Bedeutung’. (...) I outline possible counter-arguments and responses. (shrink)

This is a research report in which we present examples which should be of interest to those working on clausal embedding and dubitative verbs. Examples are presented which are relevant to the evaluation of claims and arguments in: (Karttunen 1977), (Uegaki 2021), (Huddleston 1994), (Biezma & Rawlins 2012), (Roelofsen; Herbstritt; & Aloni 2019), (Suñer 1993), and (Rawlins 2008). The examples are mostly from English, but we also present some examples from Italian, Spanish, and German.

I draw attention to two questions which arise from: Frege’s underlining in a letter to Russell, some of his remarks in ‘Meine grundlegenden logischen Einsichten’/‘My basic logical insights’, and a plausible thesis regarding indirect Bedeutungen. Addressing these questions is necessary for a proper understanding of Frege’s account of „dass“-sentences/“that”-clauses.

This paper is about the work of a long forgotten philosopher and his views which have surprising relevance to discussions in present-day philosophy of mind and cognitive science. I argue that, far from being a traditional idealist, Mitchell advanced a very subtle position best seen as marking a transition from idealist views and later materialist accounts, the latter popularly attributed to Australian philosophers in the second half of the 20th century.

This article is a rebuttal to Robert G. Cavin and Carlos A. Colombetti’s article, “Assessing the Resurrection Hypothesis: Problems with Craig’s Inference to the Best Explanation,” which argues that the Standard Model of current particle physics entails that non-physical things (like a supernatural God or a supernaturally resurrected body) can have no causal contact with the physical universe. As such, they argue that William Lane Craig’s resurrection hypothesis is not only incompatible with the notion of Jesus physically appearing to (...) the disciples, but the resurrection hypothesis is significantly limited in both its explanatory scope and explanatory power. This article seeks to demonstrate why their use of the Standard Model does not logically entail a rejection of the physical resurrection of Jesus when considering the scope and limitations of science itself. (shrink)

Kalam cosmological arguments have recently been the subject of criticisms, at least inter alia, by physicists---Paul Davies, Stephen Hawking---and philosophers of science---Adolf Grunbaum. In a series of recent articles, William Craig has attempted to show that these criticisms are “superficial, iII-conceived, and based on misunderstanding.” I argue that, while some of the discussion of Davies and Hawking is not philosophically sophisticated, the points raised by Davies, Hawking and Grunbaum do suffice to undermine the dialectical efficacy of kalam cosmological arguments.

“Critical thinking in higher education” is a phrase that means many things to many people. It is a broad church. Does it mean a propensity for finding fault? Does it refer to an analytical method? Does it mean an ethical attitude or a disposition? Does it mean all of the above? Educating to develop critical intellectuals and the Marxist concept of critical consciousness are very different from the logician’s toolkit of finding fallacies in passages of text, or the practice of (...) identifying and distinguishing valid from invalid syllogisms. Critical thinking in higher education can also encompass debates about critical pedagogy, i.e., political critiques of the role and function of education in society, critical feminist approaches to curriculum, issues related to what has become known as critical citizenship, or any other education-related topic that uses the appellation “critical”. Equally, it can, and usually does, refer to the importance and centrality of developing general skills in reasoning—skills that we hope all graduates possess. Yet, despite more than four decades of dedicated scholarly work “critical thinking” remains as elusive as ever. As a concept, it is, as Raymond Williams has noted, a ‘most difficult one’ (Williams, 1976, p. 74). (shrink)

English version of collaborative text with Bruno Varela on his film La máquina de futuro (2024), published in the catalog of Umbrales experimental film section of the FICUNAM film festival.

Spanish version of collaborative essay with Oaxaca-based Mexican experimental filmmaker Bruno Varela on his found footage project La máquina de futuro. Published on the website Los Experimentos together with the release of Varela's diptych Anáhuac contra los robots, consisting of the films La máquina de futuro and La ranura en el tiempo.

We respond to Stephen T. Davis’ criticism of our earlier essay, “Assessing the Resurrection Hypothesis.” We argue that the Standard Model of physics is relevant and decisive in establishing the implausibility and low explanatory power of the Resurrection hypothesis. We also argue that the laws of physics have entailments regarding God and the supernatural and, against Alvin Plantinga, that these same laws lack the proviso “no agent supernaturally interferes.” Finally, we offer Bayesian arguments for the Legend hypothesis and against the (...) Resurrection hypothesis. (shrink)

In response to Stephen Davis’s criticism of our previous essay, we revisit and defend our arguments that the Resurrection hypothesis is logically incompatible with the Standard Model of particle physics—and thus is maximally implausible—and that it cannot explain the sensory experiences of the Risen Jesus attributed to various witnesses in the New Testament—and thus has low explanatory power. We also review Davis’s reply, noting that he evades our arguments, misstates their conclusions, and distracts the reader with irrelevancies regarding, e.g., what (...) natural laws are, what a miracle is, and how “naturalism” and “supernaturalism” differ as worldviews. Contrary to what Davis claims (even in his abstract), we do not argue that “if the Standard Model of particle physics is true, then the resurrection of Jesus did not occur and physical things can only causally interact with other physical things.” Davis distorts our claims and criticizes straw men of his own creation. (shrink)

WILLIAM DAVIS HAS MAINTAINED THAT A SUPER PLEASURE HELMET COULD IN PRINCIPLE SATISFY ALL HUMAN NEEDS, BUT THAT SUCH A MACHINE IS PROBABLY A PRACTICAL IMPOSSIBILITY. I ARGUE THAT THE SUPER PLEASURE HELMET IS CONCEPTUALLY IMPOSSIBLE BY ARGUING THAT A PERSON'S NEEDS CANNOT BE SATISFIED JUST BY BRINGING ABOUT CERTAIN PSYCHOLOGICAL STATES IN THAT PERSON.

This paper begins with a fairly careful and detailed discussion of the conditions under which someone who presents an argument ought to be prepared to concede that the argument is unsuccessful. The conclusions reached in this discussion are then applied to William Lane Craig’s defense of what he calls “the kalam cosmological argument.” Perhaps unsurprisingly, the chief contention of the paper is that Craig ought to be prepared to concede that “the kalam cosmological argument” is not a successful argument. (...) The paper pays particular attention to Craig’s recent criticisms of Adolf Grünbaum’s contention that “the kalam cosmological argument” presupposes “the normalcy of nothingness”; and it also addresses some methodological issues raised by Craig’s response to my previous criticisms of his replies to critiques of “the kalam cosmological argument” provided by Grünbaum, Hawking, and Davies. (shrink)

Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. -/- ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, scope, Tarski (Alfred), tautology, universe of discourse. -/- The entire work is available online free at more than (...) one website. Paste the whole URL. http://archive.org/stream/RobertiAudi_The.Cambridge.Dictionary.of.Philosophy/Robert.Audi_The.Cambrid ge.Dictionary.of.Philosophy -/- The 2015 third edition will be available soon. Before you think of buying it read some reviews on Amazon and read reviews of its competition: For example, my review of the 2008 Oxford Companion to Philosophy, History and Philosophy of Logic,29:3,291-292. URL: http://dx.doi.org/10.1080/01445340701300429 -/- Some of the entries have already been found to be flawed. For example, Tarski’s expression ‘materially adequate’ was misinterpreted in at least one article and it was misused in another where ‘materially correct’ should have been used. The discussion provides an opportunity to bring more flaws to light. -/- Acknowledgements: Each of these entries was presented at meetings of The Buffalo Logic Dictionary Project sponsored by The Buffalo Logic Colloquium. The members of the colloquium read drafts before the meetings and were generous with corrections, objections, and suggestions. Usually one 90-minute meeting was devoted to one entry although in some cases, for example, “axiomatic method”, took more than one meeting. Moreover, about half of the entries are rewrites of similarly named entries in the 1995 first edition. Besides the help received from people in Buffalo, help from elsewhere was received by email. We gratefully acknowledge the following: José Miguel Sagüillo, John Zeis, Stewart Shapiro, Davis Plache, Joseph Ernst, Richard Hull, Concha Martinez, Laura Arcila, James Gasser, Barry Smith, Randall Dipert, Stanley Ziewacz, Gerald Rising, Leonard Jacuzzo, George Boger, William Demopolous, David Hitchcock, John Dawson, Daniel Halpern, William Lawvere, John Kearns, Ky Herreid, Nicolas Goodman, William Parry, Charles Lambros, Harvey Friedman, George Weaver, Hughes Leblanc, James Munz, Herbert Bohnert, Robert Tragesser, David Levin, Sriram Nambiar, and others. -/- . (shrink)

Chapter 1: "Reason for Hope " by Michael J. Murray Chapter 2: "Theistic Arguments" by William C. Davis Chapter 3: "A Scientific Argument for the Existence of God: The Fine- Tuning Design Argument" by Robin Collins Chapter 4: "God, Evil and Suffering" by Daniel Howard Snyder Chapter 5: "Arguments for Atheism" by John O'Leary Hawthorne Chapter 6: "Faith and Reason" by Caleb Miller Chapter 7: "Religious Pluralism" by Timothy O'Connor Chapter 8: "Eastern Religions" by Robin Collins Chapter 9: "Divine (...) Providence and Human Freedom" by Scott A. Davison Chapter 10: "The Incarnation and the Trinity" by Thomas D. Senor Chapter 11: "The Resurrection of the Body and the Life Everlasting" by Trenton Merricks Chapter 12: "Heaven and Hell" by Michael J. Murray Chapter 13: "Religion and Science" by W. Christopher Stewart Chapter 14: "Miracles and Christian Theism" by J. A. Cover Chapter 15: "Christianity and Ethics" by Frances Howard-Snyder Chapter 16: "The Authority of Scripture" by Douglas Blount. (shrink)

Recent progress in artificial intelligence (AI) has drawn attention to the technology’s transformative potential, including what some see as its prospects for causing large-scale harm. We review two influential arguments purporting to show how AI could pose catastrophic risks. The first argument — the Problem of Power-Seeking — claims that, under certain assumptions, advanced AI systems are likely to engage in dangerous power-seeking behavior in pursuit of their goals. We review reasons for thinking that AI systems might seek power, that (...) they might obtain it, that this could lead to catastrophe, and that we might build and deploy such systems anyway. The second argument claims that the development of human-level AI will unlock rapid further progress, culminating in AI systems far more capable than any human — this is the Singularity Hypothesis. Power-seeking behavior on the part of such systems might be particularly dangerous. We discuss a variety of objections to both arguments and conclude by assessing the state of the debate. (shrink)

The psychological literature now differentiates between two types of psychopath:successful (with little or no criminal record) and unsuccessful (with a criminal record). Recent research indicates that earlier findings of reduced autonomic activity, reduced prefrontal grey matter, and compromised executive activity may only be true of unsuccessful psychopaths. In contrast, successful psychopaths actually show autonomic and executive function that exceeds that of normals, while having no difference in prefrontal volume from normals. We argue that many successful psychopaths are legally responsible for (...) their actions, as they have the executive capacity to choose not to harm (and thus are legally rational). However, many unsuccessful psychopaths have a lack of executive function that should at least partially excuse them from criminal culpability. Although a successful psychopath's increased executive function may occur in conflict with, rather than in consonance with their increased autonomic activity - producing a cognitive style characterized by self deception and articulate-sounding, but unsound reasoning - they may be capable of recognizing and correcting their lack of autonomic data, and thus can be held responsible. (shrink)

Agent-based models have played a prominent role in recent debates about the merits of democracy. In particular, the formal model of Lu Hong and Scott Page and the associated “diversity trumps ability” result has typically been seen to support the epistemic virtues of democracy over epistocracy (i.e., governance by experts). In this paper we first identify the modeling choices embodied in the original formal model and then critique the application of the Hong-Page results to philosophical debates on the relative merits (...) of democracy. In particular we argue that the “best-performing agents” in Hong-Page model should not be interpreted as experts. We next explore a closely related model in which best-performing agents are more plausibly seen as experts and show that the diversity trumps ability result fails to hold. However, with changes in other parameters (such as the deliberation dynamic) the diversity trumps ability result is restored. The sensitivity of this result to parameter choices illustrates the complexity of the link between formal modeling and more general philosophical claims; we use this debate as a platform for a more general discussion of when and how agent-based models can contribute to philosophical discussions. (shrink)

Philosophers have rightly condemned lookism—that is, discrimination in favor of attractive people or against unattractive people—in education, the justice system, the workplace and elsewhere. Surprisingly, however, the almost universal preference for attractive romantic and sexual partners has rarely received serious ethical scrutiny. On its face, it’s unclear whether this is a form of discrimination we should reject or tolerate. I consider arguments for both views. On the one hand, a strong case can be made that preferring attractive partners is bad. (...) The idea is that choosing partners based on looks seems essentially similar to other objectionable forms of discrimination. (In particular, the preference for attractive partners is arguably both unfair and harmful to a significant degree.) One can try to resist this conclusion in several ways. I consider three possible replies. The first has to do with the possibility of controlling our partner preferences. The second pertains to attractiveness and “good genes”. The last attempts to link certain aspects of attractiveness to a prospective partner’s personality and values. I argue that the first two replies fail conclusively, while the third only amounts to a limited defense of a particular kind of attractiveness preference. So the idea that we should often avoid preferring attractive partners is compelling. (shrink)

Organization figures centrally in the understanding of biological systems advanced by both new mechanists and proponents of the autonomy framework. The new mechanists focus on how components of mechanisms are organized to produce a phenomenon and emphasize productive continuity between these components. The autonomy framework focuses on how the components of a biological system are organized in such a way that they contribute to the maintenance of the organisms that produce them. In this paper we analyze and compare these two (...) accounts of organization and argue that understanding biological organisms as cohesively integrated systems benefits from insights from both. To bring together the two accounts, we focus on the notions of control and regulation as bridge concepts. We start from a characterization of biological mechanisms in terms of constraints and focus on a specific type of mechanism, control mechanisms, that operate on other mechanisms on the basis of measurements of variables in the system and its environment. Control mechanisms are characterized by their own set of constraints that enable them to sense conditions, convey signals, and effect changes on constraints in the controlled mechanism. They thereby allow living organisms to adapt to internal and external variations and to coordinate their parts in such a manner as to maintain viability. Because living organisms contain a vast number of control mechanisms, a central challenge is to understand how they are themselves organized. With the support of examples from both unicellular and multicellular systems we argue that control mechanisms are organized heterarchically, and we discuss how this type of control architecture can, without invoking top-down and centralized forms of organizations, succeed in coordinating internal activities of organisms. (shrink)

This is my main contribution to P. Gould (ed.) Beyond the Control of God?: Six Views on the Problem of God and Abstract Objects Bloomsbury. (The other contibutors to this work are: Keith Yandell; Paul Gould and Rich Davis; Greg Welty; William Lane Craig; and Scott Shalkowski.) I argue that, when it comes to a comparative assessment of the merits of theism and atheism, it makes no difference whether one opts for realism or fictionalism concerning abstract objects.

Apresentação da tradução para o português de três textos póstumos do filósofo e historiador escocês David Hume (1711-1776): os ensaios “Da imortalidade da alma” e “Do suicídio”, e a autobiografia “Minha vida”. O livro Inclui também a tradução dois relatos sobre os últimos dias de Hume: a “Carta a William Strahan”, de Adam Smith, e a “Última entrevista com David Hume”, de James Boswell. - Hume, David. Da imortalidade da alma e outros textos póstumos. Tradução: Jaimir Conte, Davi de (...) Souza e Daniel Murialdo. Ijuí:Editora Unijuí, 2006. (Coleção filosofia; 12). ISBN: 85-7429-558-2. (shrink)

Living organisms act as integrated wholes to maintain themselves. Individual actions can each be explained by characterizing the mechanisms that perform the activity. But these alone do not explain how various activities are coordinated and performed versatilely. We argue that this depends on a specific type of mechanism, a control mechanism. We develop an account of control by examining several extensively studied control mechanisms operative in the bacterium E. coli. On our analysis, what distinguishes a control mechanism from other mechanisms (...) is that it relies on measuring one or more variables, which results in setting constraints in the control mechanism that determine its action on flexible constraints in other mechanisms. In the most basic arrangement, the measurement process directly determines the action of the control mechanism, but in more complex arrangements signals mediate between measurements and effectors. This opens the possibility of multiple responses to the same measurement and responses based on multiple measurements. It also allows crosstalk, resulting in networks of control mechanisms. Such networks integrate the behaviors of the organism but also present a challenge in tailoring responses to particular measurements. We discuss how integrated activity can still result in differential, versatile, responses. (shrink)

The field of AI safety aims to prevent increasingly capable artificially intelligent systems from causing humans harm. Research on moral alignment is widely thought to offer a promising safety strategy: if we can equip AI systems with appropriate ethical rules, according to this line of thought, they'll be unlikely to disempower, destroy or otherwise seriously harm us. Deontological morality looks like a particularly attractive candidate for an alignment target, given its popularity, relative technical tractability and commitment to harm-avoidance principles. I (...) argue that the connection between moral alignment and safe behavior is more tenuous than many have hoped. In general, AI systems can possess either of these properties in the absence of the other, and we should favor safety when the two conflict. In particular, advanced AI systems governed by standard versions of deontology need not be especially safe. (shrink)

This article seeks the origin, in the theories of Ibn al-Haytham (Alhazen), Descartes, and Berkeley, of two-stage theories of spatial perception, which hold that visual perception involves both an immediate representation of the proximal stimulus in a two-dimensional ‘‘sensory core’’ and also a subsequent perception of the three dimensional world. The works of Ibn al-Haytham, Descartes, and Berkeley already frame the major theoretical options that guided visual theory into the twentieth century. The field of visual perception was the first area (...) of what we now call psychology to apply mathematics, through geometrical models as used by Euclid, Ptolemy, Ibn al-Haytham, and Descartes (among others). The article shows that Kepler’s discovery of the retinal image, which revolutionized visual anatomy and entailed fundamental changes in visual physiology, did not alter the basic structure of theories of spatial vision. These changes in visual physiology are advanced especially in Descartes' Dioptrics and his L'Homme. Berkeley develops a radically empirist theory vision, according to which visual perception of depth is learned through associative processes that rely on the sense of touch. But Descartes and Berkeley share the assertion that there is a two-dimensional sensory core that is in principle available to consciousness. They also share the observation that we don't usually perceived this core, but find depth and distance to be phenomenally immediate, a point they struggle to accommodate theoretically. If our interpretation is correct, it was not a change in the theory of the psychology of vision that engendered the idea of a sensory core, but rather the introduction of the theory into a new metaphysical context. (shrink)

According to proponents of the extended mind, bio-external resources, such as a notebook or a smartphone, are candidate parts of the cognitive and mental machinery that realises cognitive states and processes. The present chapter discusses three areas of ethical concern associated with the extended mind, namely mental privacy, mental manipulation, and agency. We also examine the ethics of the extended mind from the standpoint of three general normative frameworks, namely, consequentialism, deontology, and virtue ethics.

We discuss potential biorisks from large language models (LLMs). AI assistants based on LLMs such as ChatGPT have been shown to significantly reduce barriers to entry for actors wishing to synthesize dangerous, potentially novel pathogens and chemical weapons. The harms from deploying such bioagents could be further magnified by AI-assisted misinformation. We endorse several policy responses to these dangers, including prerelease evaluations of biomedical AIs by subject-matter experts, enhanced surveillance and lab screening procedures, restrictions on AI training data, and access (...) controls on biomedical AI. We conclude with a suggestion about future research directions in bioethics. (shrink)

The new mechanists and the autonomy approach both aim to account for how biological phenomena are explained. One identifies appeals to how components of a mechanism are organized so that their activities produce a phenomenon. The other directs attention towards the whole organism and focuses on how it achieves self-maintenance. This paper discusses challenges each confronts and how each could benefit from collaboration with the other: the new mechanistic framework can gain by taking into account what happens outside individual mechanisms, (...) while the autonomy approach can ground itself in biological research into how the actual components constituting an autonomous system interact and contribute in different ways to realize and maintain the system. To press the case that these two traditions should be constructively integrated we describe how three recent developments in the autonomy tradition together provide a bridge between the two traditions: (1) a framework of work and constraints, (2) a conception of function grounded in the organization of an autonomous system, and (3) a focus on control. (shrink)

According to a widespread view in metaphysics and philosophy of science, all explanations involve relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans. I argue that a family of mathematical cases, which I call “viewing-as explanations”, are incompatible with the Dependence Thesis. These cases, I claim, feature genuine explanations that aren’t supported by ontic dependence relations. Hence the thesis isn’t true in general. The first part of the paper defends this claim (...) and discusses its significance. The second part of the paper considers whether viewing-as explanations occur in the empirical sciences, focusing on the case of so-called fictional models. It’s sometimes suggested that fictional models can be explanatory even though they fail to represent actual worldly dependence relations. Whether or not such models explain, I suggest, depends on whether we think scientific explanations necessarily give information relevant to intervention and control. Finally, I argue that counterfactual approaches to explanation also have trouble accommodating viewing-as cases. (shrink)

For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...) is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories. (shrink)

Defense of an account of intrinsic properties in terms of (what is now called) grounding rather than naturalness.

In a recent letter, Dillion et. al (2023) make various suggestions regarding the idea of artificially intelligent systems, such as large language models, replacing human subjects in empirical moral psychology. We argue that human subjects are in various ways indispensable.

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...) of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences. (shrink)

Mathematicians often describe the importance of well-developed intuition to productive research and successful learning. But neither education researchers nor philosophers interested in epistemic dimensions of mathematical practice have yet given the topic the sustained attention it deserves. The trouble is partly that intuition in the relevant sense lacks a usefully clear characterization, so we begin by offering one: mature intuition, we say, is the capacity for fast, fluent, reliable and insightful inference with respect to some subject matter. We illustrate the (...) role of mature intuition in mathematical practice with an assortment of examples, including data from a sequence of clinical interviews in which a student improves upon initially misleading covariational intuitions. Finally, we show how the study of intuition can yield insights for philosophers and education theorists. First, it contributes to a longstanding debate in epistemology by undermining epistemicism, the view that an agent’s degree of objectual understanding is determined exclusively by their knowledge, beliefs and credences. We argue on the contrary that intuition can contribute directly and independently to understanding. Second, we identify potential pedagogical avenues towards the development of mature intuition, highlighting strategies including adding imagery, developing associations, establishing confidence and generalizing concepts. (shrink)

Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...) and Eisenstein, and a sophisticated proof using algebraic number theory, due to Hilbert. Philosophers have yet to look carefully at such explanatory disagreements in mathematics. I do so here. According to the view I defend, there are two important explanatory virtues—depth and transparency—which different proofs (and other potential explanations) possess to different degrees. Although not mutually exclusive in principle, the packages of features associated with the two stand in some tension with one another, so that very deep explanations are rarely transparent, and vice versa. After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, I draw some morals about the nature of mathematical explanation. (shrink)

Explanatory pluralism holds that the sorts of comprehensive theoretical and ontological economies, which microreductionists and New Wave reductionists envision and which antireductionists fear, offer misleading views of both scientific practice and scientific progress. Both advocates and foes of employing reductionist strategies at the interface of psychology and neuroscience have overplayed the alleged economies that interlevel connections (including identities) justify while overlooking their fundamental role in promoting scientific research. A brief review of research on visual processing provides support for the explanatory (...) pluralist=s general model of cross-scientific relations and discloses the valuable heuristic role hypothetical identities play in cross-scientific research. That model also supplies grounds for hesitation about the correlation objection to the psycho-physical identity theory and complaints about an explanatory gap in physicalist accounts of consciousness. These takes on psycho-neural connections miss both the sorts of considerations that motivate hypothetical identities in science and their fundamental contribution to progressive research. Thus, their focus on the contributions of research at multiple levels of analysis does not bar explanatory pluralists from considering heuristic identity theory (HIT). Arguably, it encourages it. (shrink)

We defend a noetic account of intramathematical explanation. On this view, a piece of mathematics is explanatory just in case it produces understanding of an appropriate type. We motivate the view by presenting some appealing features of noeticism. We then discuss and criticize the most prominent extant version of noeticism, due to Inglis and Mejía Ramos, which identifies explanatory understanding with the possession of well-organized cognitive schemas. Finally, we present a novel noetic account. On our view, explanatory understanding arises from (...) meeting specific explanatory objectives. We defend a cluster-concept account of explanatory objectives and identify four important subfamilies within the relevant network of resemblance relations. The resulting view is objectivist (in the sense that it takes explanatory success to be a matter of observer-independent fact), broader in scope than why-question-based accounts, compatible with empirical findings on experts’ explanatory judgments, and capable of generalizing (with appropriate provisos) to scientific explanation as a whole. It thus fulfills Friedman’s half-century-old demand for a general and objectivist theory which accounts for the link between explanation and understanding. (shrink)

False belief tasks have enjoyed a monopoly in the research on children’s development of a theory of mind. They have been granted this status because they promise to deliver an unambiguous assessment of children’s understanding of the representational nature of mental states. Their poor cousins, true belief tasks, have been relegated to occasional service as control tasks. That this is their only role has been due to the universal assumption that correct answers on true belief tasks are inherently ambiguous regarding (...) the level of the child’s understanding of mental states. It has also been due to the universal assumption that nothing in the child’s developing theory of mind would lead to systematically incorrect answers on true belief tasks. We review new findings that 4- and 5-year-olds do err, systematically and profoundly, on the true belief versions of all the extant belief tasks. This reveals an intermediate level of understanding in the development of children’s theory of mind. Researchers have been unaware of this intermediate level because it produces correct answers in false belief tasks. A simple two-task battery—one true belief task and one false belief task—is sufficient to remove the ambiguity from each task. The new findings show that children do not acquire an understanding of beliefs, and hence a representational theory of mind, until after 6 years of age, or 2 years later than most developmental psychologists have concluded. This raises the question of how to interpret other new findings that infants are able to pass false belief tasks. We review these new infant studies, as well as recent studies on chimpanzees, in light of older children’s failure on true belief tasks, and end with some speculation about how all of these new findings might be reconciled. (shrink)

Iglesias et al. (2025) argue that “some of the aims or ostensible goods of person-span expansion could plausibly be fulfilled in part by creating a digital doppelgänger”—that is, an AI system desig...

This chapter makes the case for strong longtermism: the claim that, in many situations, impact on the long-run future is the most important feature of our actions. Our case begins with the observation that an astronomical number of people could exist in the aeons to come. Even on conservative estimates, the expected future population is enormous. We then add a moral claim: all the consequences of our actions matter. In particular, the moral importance of what happens does not depend on (...) when it happens. That pushes us toward strong longtermism. We then address a few potential concerns, the first of which is that it is impossible to have any sufficiently predictable influence on the course of the long-run future. We argue that this is not true. Some actions can reasonably be expected to improve humanity’s long-term prospects. These include reducing the risk of human extinction, preventing climate change, guiding the development of artificial intelligence, and investing funds for later use. We end by arguing that these actions are more than just extremely effective ways to do good. Since the benefits of longtermist efforts are large and the personal costs are comparatively small, we are morally required to take up these efforts. (shrink)

Racist beliefs express value judgments. According to an influential view, value judgments are subjective, and not amenable to rational adjudication. In contrast, we argue that the value judgments expressed in, for example, racist beliefs, are false and objectively so. Our account combines a naturalized, philosophical account of meaning inspired by Donald Davidson, with a prominent social-psychological theory of values pioneered by the social-psychologist Milton Rokeach. We use this interdisciplinary approach to show that, just as with beliefs expressing descriptive judgments, beliefs (...) expressing value judgments have empirical content, or can be inferentially linked to beliefs that do; the truth or falsity of that content can be objectively assigned; and that assignment is amenable to rational assessment. While versions of this objective view of value judgments have been defended by moral realists of various metaphysical stripes, our argument has the virtue of appealing, instead, to accounts that are as naturalistically informed as possible. And, unlike the influential subjective view of value judgments, and racist beliefs more particularly, our arguments are better able to account for instances where rational, persuasive strategies have been effective in reducing the ubiquity of racism in American culture. (shrink)

SNePS, the Semantic Network Processing System 45, 54], has been designed to be a system for representing the beliefs of a natural-language-using intelligent system (a \cognitive agent"). It has always been the intention that a SNePS-based \knowledge base" would ultimatelybe built, not by a programmeror knowledge engineer entering representations of knowledge in some formallanguage or data entry system, but by a human informing it using a natural language (NL) (generally supposed to be English), or by the system reading books or (...) articles that had been prepared for human readers. Because of this motivation, the criteria for the development of SNePS have included: it should be able to represent anything and everything expressible in NL; it should be able to represent generic, as well as speci c information; it should be able to use the generic and the speci c information to reason and infer information implied by what it has been told; it cannot count on any particular order among the pieces of information it is given; it must continue to act reasonably even if the information it is given includes circular de nitions, recursive rules, and inconsistent information. (shrink)

This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".

The Repugnant Conclusion served an important purpose in catalyzing and inspiring the pioneering stage of population ethics research. We believe, however, that the Repugnant Conclusion now receives too much focus. Avoiding the Repugnant Conclusion should no longer be the central goal driving population ethics research, despite its importance to the fundamental accomplishments of the existing literature.