A union ultrafilter is an ultrafilter over the finite subsets of ω that has a base of sets of the form ${\text{FU}}\left$, where X is an infinite pairwise disjoint family and ${\text{FU}} = \left\{ {\bigcup {F|F} \in [X]^{ < \omega } \setminus \{ \emptyset \} } \right\}$. The existence of these ultrafilters is not provable from the $ZFC$ axioms, but is known to follow from the assumption that ${\text{cov}}\left = \mathfrak{c}$. In this article we obtain various models of $ZFC$ that (...) satisfy the existence of union ultrafilters while at the same time ${\text{cov}}\left = \mathfrak{c}$. (shrink)

In the context of [Formula: see text], we analyze a version of Hindman’s finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the [Formula: see text].

For any ordinal $\Lambda$, we can define a polymodal logic $\mathsf{GLP}_\Lambda$, with a modality $[\xi]$ for each $\xi < \Lambda$. These represent provability predicates of increasing strength. Although $\mathsf{GLP}_\Lambda$ has no Kripke models, Ignatiev showed that indeed one can construct a Kripke model of the variable-free fragment with natural number modalities, denoted $\mathsf{GLP}^0_\omega$. Later, Icard defined a topological model for $\mathsf{GLP}^0_\omega$ which is very closely related to Ignatiev's. In this paper we show how to extend these constructions for arbitrary $\Lambda$. (...) More generally, for each $\Theta,\Lambda$ we build a Kripke model $\mathfrak I^\Theta_\Lambda$ and a topological model $\mathfrak T^\Theta_\Lambda$, and show that $\mathsf{GLP}^0_\Lambda$ is sound for both of these structures, as well as complete, provided $\Theta$ is large enough. (shrink)

Ordinal functions may be iterated transfinitely in a natural way by taking pointwise limits at limit stages. However, this has disadvantages, especially when working in the class of normal functions, as pointwise limits do not preserve normality. To this end we present an alternative method to assign to each normal function f a family of normal functions Hyp[f]=〈fξ〉ξ∈OnHyp[f]=〈fξ〉ξ∈On, called its hyperation, in such a way that f0=idf0=id, f1=ff1=f and fα+β=fα∘fβfα+β=fα∘fβ for all α, β.Hyperations are a refinement of the Veblen hierarchy (...) of f. Moreover, if f is normal and has a well-behaved left-inverse g called a left adjoint, then g can be assigned a cohyperationcoH[g]=〈gξ〉ξ∈OncoH[g]=〈gξ〉ξ∈On, which is a family of initial functions such that gξgξ is a left adjoint to fξfξ for all ξ. (shrink)

We introduce the logics GLP Λ, a generalization of Japaridze’s polymodal provability logic GLP ω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP ω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP Λ and the decidability of GLP Λ for recursive orderings Λ. Further, we give a restricted axiomatization of the variable-free fragment (...) of GLP Λ. (shrink)

Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use $[\lambda |X]_T^{\rm{\Lambda }}\varphi$ as a formalization of “φ is provable from T and an oracle for the set X, using ω-rules of nesting depth at most λ”.For a set of formulas Γ, define predicative oracle reflection for T over Γ ) to be the schema that asserts that, if X ⊆ ℕ, Λ is a well-order and φ ∈ Γ, then$$\forall \,\lambda (...) < {\rm{\Lambda }}\,.$$In particular, define predicative oracle consistency ) as Pred–O–RFN{0=1}.Our main result is as follows. Let ATR0 be the second-order theory of Arithmetical Transfinite Recursion, ${\rm{RCA}}_0^{\rm{*}}$ be Weakened Recursive Comprehension and ACA be Arithmetical Comprehension with Full Induction. Then,$${\rm{ATR}}_0 \equiv {\rm{RCA}}_0^{\rm{*}} + {\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - RFN}}\,_{{\bf{\Pi }}_2^1 } \left.$$We may even replace ${\rm{RCA}}_0^{\rm{*}}$ by the weaker ECA0, the second-order analogue of Elementary Arithmetic.Thus we characterize ATR0, a theory often considered to embody Predicative Reductionism, in terms of strong reflection and consistency principles. (shrink)

A key aim in biology and psychology is to identify fundamental principles underpinning the behavior of animals, including humans. Analyses of human language and the behavior of a range of non-human animal species have provided evidence for a common pattern underlying diverse behavioral phenomena: Words follow Zipf's law of brevity (the tendency of more frequently used words to be shorter), and conformity to this general pattern has been seen in the behavior of a number of other animals. It has been (...) argued that the presence of this law is a sign of efficient coding in the information theoretic sense. However, no strong direct connection has been demonstrated between the law and compression, the information theoretic principle of minimizing the expected length of a code. Here, we show that minimizing the expected code length implies that the length of a word cannot increase as its frequency increases. Furthermore, we show that the mean code length or duration is significantly small in human language, and also in the behavior of other species in all cases where agreement with the law of brevity has been found. We argue that compression is a general principle of animal behavior that reflects selection for efficiency of coding. (shrink)

Darwinism, Democracy, and Race examines the development and defence of an argument that arose at the boundary between anthropology and evolutionary biology in twentieth-century America. In its fully articulated form, this argument simultaneously discredited scientific racism and defended free human agency in Darwinian terms. The volume is timely because it gives readers a key to assessing contemporary debates about the biology of race. By working across disciplinary lines, the book's focal figures--the anthropologist Franz Boas, the cultural anthropologist Alfred Kroeber, the (...) geneticist Theodosius Dobzhansky, and the physical anthropologist Sherwood Washburn--found increasingly persuasive ways of cutting between genetic determinist and social constructionist views of race by grounding Boas's racially egalitarian, culturally relativistic, and democratically pluralistic ethic in a distinctive version of the genetic theory of natural selection. Collaborators in making and defending this argument included Ashley Montagu, Stephen Jay Gould, and Richard Lewontin. Darwinism, Democracy, and Race will appeal to advanced undergraduates, graduate students, and academics interested in subjects including Philosophy, Critical Race Theory, Sociology of Race, History of Biology and Anthropology, and Rhetoric of Science. (shrink)

Indirect speech acts—responding “I forgot to wear my watch today” to someone who asked for the time—are ubiquitous in daily conversation, but are understudied in current neurobiological models of language. To comprehend an indirect speech act like this one, listeners must not only decode the lexical-semantic content of the utterance, but also make a pragmatic, bridging inference. This inference allows listeners to derive the speaker’s true, intended meaning—in the above dialog, for example, that the speaker cannot provide the time. In (...) the present work, we address this major gap by asking non-aphasic patients with behavioral variant frontotemporal dementia and brain-damaged controls with amnestic mild cognitive impairment to judge simple question-answer dialogs of the form: “Do you want some cake for dessert?” “I’m on a very strict diet right now,” and relate the results to structural and diffusion MRI. Accuracy and reaction time results demonstrate that subjects with bvFTD, but not MCI, are selectively impaired in indirect relative to direct speech act comprehension, due in part to their social and executive limitations, and performance is related to caregivers’ judgment of communication efficacy. MRI imaging associates the observed impairment in bvFTD to cortical thinning not only in traditional language-associated regions, but also in fronto-parietal regions implicated in social and executive cerebral networks. Finally, diffusion tensor imaging analyses implicate white matter tracts in both dorsal and ventral projection streams, including superior longitudinal fasciculus, frontal aslant, and uncinate fasciculus. These results have strong implications for updated neurobiological models of language, and emphasize a core, language-mediated social disorder in patients with bvFTD. (shrink)

In this Open Peer Commentary, we draw on our clinical experience to argue that instrumental paternalism carves a pathway to competent refusal of medical intervention. Whether C successfully navigat...

These eighty-seven memoirs, anecdotes, and informal recollections by a broad range of reporters reflect both the reality and the myths surrounding this legendary figure. Together, they cover the entire span of Nietzsche's life and yield new insights into Nietzsche as a thinker and as a commentator on his times, recounting his views on religion, philosophy, women, literature, arts, and some of the great thinkers and historical figures.

The future of higher education is in question as universities struggle to remain relevant to the present and future needs of society. The context in which learning occurs is rapidly changing and those engaged and interested in the place and position of university education need to figure out to adapt. This book embodies a vision for higher education where graduate attributes and proficiencies are at the core of the academic project, where degree programs move beyond disciplinary content and where students (...) are encouraged to be Citizen Scholars. Through a series of cross-disciplinary and contextual cases, the contributors to this book articulate how this vision can be achieved in our pedagogical environments, future proofing higher education. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Books ReceivedAndrianou, Dimitra. The Furniture and Furnishings of Ancient Greek Houses and Tombs. Cambridge: Cambridge University Press, 2009. xvi + 213 pp. 24 black-and-white figs. Cloth, $80.Andrisano, Angela Maria, and Paolo Fabbri, eds. La favola di Orfeo: Letteratura, immagine, performance. Ferrara: UnifePress, 2009. 255 pp. 41 black-and-white figs. Paper, €15.Bartsch, Shadi, and David Wray, eds. Seneca and the Self. Cambridge: Cambridge University Press, 2009. ix + 304 pp. (...) 1 black-and-white ill. Cloth, $99.Bers, Victor. Genos Dikanikon: Amateur and Professional Speech in the Courtrooms of Classical Athens. Hellenic Studies 33. Washington, D.C.: Center for Hellenic Studies, 2009. Dist. by Harvard University Press. ix + 159 pp. Paper, $15.95.Bowie, Ewen, and Jaś Elsner, eds. Philostratus. Greek Culture in the Roman World. Cambridge: Cambridge University Press, 2009. xii + 401 pp. 14 black-and-white ills. Cloth, $135.Bowlby, Rachel. Freudian Mythologies: Greek Tragedy and Modern Identities. Oxford: Oxford University Press, 2009. viii + 251 pp. Paper, $49.95.Calame, Claude. Poetic and Performative Memory in Ancient Greece: Heroic Reference and Ritual Gestures in Time and Space. Hellenic Studies 18. Washington, D.C.: Center for Hellenic Studies, 2009. Dist. by Harvard University Press. xii + 267 pp. 9 black-and-white figs. Paper, $19.95Collins, Paul. Assyrian Palace Sculptures. With photographs by Lisa Baylis and Sandra Marshall. Austin: University of Texas Press, 2009. 144 pp. Numerous color ills. Cloth, $45.Coltman, Viccy. Classical Sculpture and the Culture of Collecting in Britain Since 1870. Classical Presences. Oxford: Oxford University Press, 2009. xiv + 315 pp. 85 black-and-white figs., 32 color plates. Cloth, $99.Comoth, Katharina. Gott selbst und die Idee. Beiträge zur Philosophie. Heidelberg: Universitätsverlag Winter, 2009. 86 pp. 2 black-and-white ills. Paper, €10.Connelly, Joan Breton. Portrait of a Priestess: Women and Ritual in Ancient Greece. Princeton, N.J.: Princeton University Press, 2007. xv + 421 pp. Numerous black-and-white figs., 27 color plates, 3 maps. Paper, $35. [End Page 345]Eezzuduemhoi, James. I. A. A Fundamental Greek Course. Ed. Glenn Storey. Lanham, Md.: University Press of America, 2009. xxxv + 547 pp. Paper, $65.Erskine, Andrew, ed. A Companion to Ancient History. Blackwell Companions to the Ancient World. Malden, Mass.: Wiley-Blackwell, 2009. xxxvii + 693 pp. 27 black-and-white figs., 5 maps. Cloth, $199.95.Flower, Harriet I. Roman Republics. Princeton, N.J.: Princeton University Press, 2010. xv + 204 pp. Cloth, $29.95.Föllinger, Sabine. Aischylos: Meister der griechischen Tragödie. Munich: C. H. Beck, 2009. 224 pp. 5 black-and-white ills. Cloth, €24.90.Goldhill, Simon, and Edith Hall, eds. Sophocles and the Greek Tragic Tradition. Cambridge: Cambridge University Press, 2009. xvi + 336 pp. Cloth, $99.Grethlein, Jonas, and Antonios Rengakos, eds. Narratology and Interpretation. Trends in Classics 4. Berlin: Walter de Gruyter, 2009. vii + 630 pp. Cloth, €93.41.Haziza, Typhaine. Le Kaléidoscope hérodotéen: Images, imaginaire et représentations de l'Égypte à travers le livre II d'Hérodote. Études anciennes 142. Paris: Les Belles Lettres, 2009. 393 pp. 7 black-and-white figs. Paper, €45.Jouanna, Jacques, and Franco Montanari, eds. Eschyle: À l'aube du théâtre occidental. Entretiens Hardt 55. Geneva: Fondation Hardt, 2009. Dist. by Vandoeuvres. xi + 510 pp. Cloth: SFr 85.Johnson, Mark J. The Roman Imperial Mausoleum in Late Antiquity. Cambridge: Cambridge University Press, 2009. xviii + 296 pp. Numerous black-and-white figs., 16 color plates. Cloth, $95.Kronenberg, Leah. Allegories of Farming from Greece and Rome: Philosophical Satire in Xenophon, Varro, and Virgil. Cambridge: Cambridge University Press, 2009. xi + 223 pp. Cloth, $99.Loukopoulou, Louisa D., and Selene Psoma, eds. Thrakika Zetemata. Vol. 1. In collaboration with Athéna Iakovidou. Meletemata 58. Athens: Research Centre for Greek and Roman Antiquity of the National Hellenic Research Foundation, 2008. Dist. by Boccard. 175 pp. Numerous black-and-white figs. Paper, price not stated.Lowrie, Michèle, ed. Horace: Odes and Epodes. Oxford Readings in Classical Studies. Oxford: Oxford University Press, 2009. viii + 472 pp. Cloth, $199; paper, $75.Martin, Gunther. Divine Talk: Religious Argumentation in Demosthenes. Oxford Classical Mongraphs. Oxford: Oxford University Press, 2009. ix + 345 pp. Cloth, $125. [End Page 346]Mendoni, Lina G., and Sophia B... (shrink)

[This is an edited version of a keynote talk at the conference on Neural Information Processing Systems (NeurIPS) on November 28, 2022, with some minor additions and subtractions.] -/- There has recently been widespread discussion of whether large language models might be sentient or conscious. Should we take this idea seriously? I will break down the strongest reasons for and against. Given mainstream assumptions in the science of consciousness, there are significant obstacles to consciousness in current models: for example, their (...) lack of recurrent processing, a global workspace, and unified agency. At the same time, it is quite possible that these obstacles will be overcome in the next decade or so. I conclude that while it is somewhat unlikely that current large language models are conscious, we should take seriously the possibility that successors to large language models may be conscious in the not-too-distant future. (shrink)

Is there progress in philosophy? A glass-half-full view is that there is some progress in philosophy. A glass-half-empty view is that there is not as much as we would like. I articulate a version of the glass-half-empty view, argue for it, and then address the crucial question of what explains it.

In the carefully argued central chapters of Adapting Minds, Buller scrutinizes several of evolutionary psychology's most highly publicized "...

Diderot is widely praised as a master of lively, dramatic and original dialogue. This book studies the developing role of dialogue in his early writings (1745 to 1754). Diderot's earlier experiments with the dialogue form, meticulously charted and analysed by D. J. Adams, opened the way to the exploration of human communication and cooperation which lies at the heart of the Encyclopédie. At first for Diderot dialogue ended in the triumph of monologue, with one speaker reducing another to silence. But (...) one of his central problems was precisely that of solipsism. Is it possible for people to communicate effectively with each other? By engaging with this problem in his early writings Diderot gradually came to realise the epistemological importance of true dialogue as an escape from the solipsistic trap; and, slowly and hesitantly, he developed the form of communicative dialogue which was to flourish in the masterpieces of his later years. (shrink)

Does consciousness collapse the quantum wave function? This idea was taken seriously by John von Neumann and Eugene Wigner but is now widely dismissed. We develop the idea by combining a mathematical theory of consciousness (integrated information theory) with an account of quantum collapse dynamics (continuous spontaneous localization). Simple versions of the theory are falsified by the quantum Zeno effect, but more complex versions remain compatible with empirical evidence. In principle, versions of the theory can be tested by experiments with (...) quantum computers. The upshot is not that consciousness-collapse interpretations are clearly correct, but that there is a research program here worth exploring. (shrink)

There are two versions of the language-of-thought hypothesis (LOT): Representational LOT (roughly, structured representation), introduced by Ockham, and computational LOT (roughly, symbolic computation) introduced by Fodor. Like many others, I oppose the latter but not the former. Quilty-Dunn et al. defend representational LOT, but they do not defend the strong computational LOT thesis central to the classical-connectionist debate.

Mechanistic interpretability is the program of explaining what AI systems are doing in terms of their internal mechanisms. I analyze some aspects of the program, along with setting out some concrete challenges and assessing progress to date. I argue for the importance of propositional interpretability, which involves interpreting a system’s mechanisms and behav- ior in terms of propositional attitudes: attitudes (such as belief, desire, or subjective probabil- ity) to propositions (e.g. the proposition that it is hot outside). Propositional attitudes are (...) the central way that we interpret and explain human beings and they are likely to be central in AI too. A central challenge is what I call thought logging: creating systems that log all of the rel- evant propositional attitudes in an AI system over time. I examine currently popular methods of interpretability (such as probing, sparse auto-encoders, and chain of thought methods) as well as philosophical methods of interpretation (including those grounded in psychoseman- tics) to assess their strengths and weaknesses as methods of propositional interpretability. (shrink)

Does the capacity to think require the capacity to sense? A lively debate on this topic runs throughout the history of philosophy and now animates discussions of artificial intelligence. Many have argued that AI systems such as large language models cannot think and understand if they lack sensory grounding. I argue that thought does not require sensory grounding: there can be pure thinkers who can think without any sensory capacities. As a result, the absence of sensory grounding does not entail (...) that large language models cannot think or understand. I also consider to what extent quasi-sensory grounding can at least boost the performance of a language model. (shrink)

The turn to narrative in biomedicine has been one of the most important alternatives to traditional approaches to bioethics. Rather than using ethical theories and principles to guide behavior, narrative ethics uses the moral imagination to cultivate and expand one’s capacities for empathy. This paper argues that by themselves narratives do not, and cannot, fully capture the range of the illness experience. But more than that, the emphasis on narrative often obscures how dominant forms of narrative discourse often operate to (...) marginalize those whose narratives fall outside the parameters of traditional narrative forms or whose stories are occluded by structural violence and oppression. Rather, by focusing on forms of embodiment that are irreducible to narrative discursivity, this paper highlights forms of selfhood that exist outside of the narrative self. (shrink)

THE SELF, THE INDIVIDUAL AND THE COMMUNITY: LIBERALISM IN THE POLITICAL THOUGHT OF F. A. HAYEK AND SIDNEY AND BEATRICE WEBB by Brian Lee Crowley New York: Oxford University Press, 1987. 310 pp., $59.00.