A set of integers A is computably encodable if every infinite set of integers has an infinite subset computing A. By a result of Solovay, the computably encodable sets are exactly the hyperarithmetic ones. In this article, we extend this notion of computable encodability to subsets of the Baire space, and we characterize the Π10-encodable compact sets as those which admit a nonempty Σ11-subset. Thanks to this equivalence, we prove that weak weak König’s lemma is not strongly computably reducible to (...) Ramsey’s theorem. This answers a question of Hirschfeldt and Jockusch. (shrink)

The infinite pigeonhole principle for 2-partitions asserts the existence, for every set A, of an infinite subset of A or of its complement. In this paper, we study the infinite pigeonhole pr...

We study genericity and randomness with respect to ITTMs, continuing the work initiated by Carl and Schlicht. To do so, we develop a framework to study randomness in the constructible hierarchy. We then answer several of Carl and Schlicht’s question. We also ask a new question one the equality of two classes of randoms. Although the natural intuition would dictate that the two classes are distinct, we show that things are not as simple as they seem. In particular we show (...) that the categorical analogues of these two classes coincide, in contradiction with the natural intuition. Even though we are not able to answer the question for randomness in this article, we delineate and sharpen its contour and outline. (shrink)

There exist two main notions of typicality in computability theory, namely, Cohen genericity and randomness. In this article, we introduce a new notion of genericity, called partition genericity, which is at the intersection of these two notions of typicality, and show that many basis theorems apply to partition genericity. More precisely, we prove that every co-hyperimmune set and every Kurtz random is partition generic, and that every partition generic set admits weak infinite subsets, for various notions of weakness. In particular, (...) we answer a question of Kjos-Hanssen and Liu by showing that every Kurtz random admits an infinite subset which does not compute any set of positive effective Hausdorff dimension. Partition genericity is a partition regular notion, so these results imply many existing pigeonhole basis theorems. (shrink)

A mass problem is a set of functions $\omega \to \omega $. For mass problems ${\mathcal {C}}, {\mathcal {D}}$, one says that ${\mathcal {C}}$ is Muchnik reducible to ${\mathcal {D}}$ if each function in ${\mathcal {C}}$ is computed by a function in ${\mathcal {D}}$. In this paper we study some highness properties of Turing oracles, which we view as mass problems. We compare them with respect to Muchnik reducibility and its uniform strengthening, Medvedev reducibility.For $p \in [0,1]$ let ${\mathcal {D}}$ (...) be the mass problem of infinite bit sequences y such that for each computable bit sequence x, the bit sequence $ x {\,\leftrightarrow\,} y$ has asymptotic lower density at most p = y$ ). We show that all members of this family of mass problems parameterized by a real p with $0 p$ for each computable set x. We prove that the Medvedev complexity of the mass problems ${\mathcal {B}}$ is the same for all $p \in $, by showing that they are Medvedev equivalent to the mass problem of functions bounded by ${2^{2}}^{n}$ that are almost everywhere different from each computable function.Next, together with Joseph Miller, we obtain a proper hierarchy of the mass problems of type $\text {IOE}$ : we show that for any order function g there exists a faster growing order function $h $ such that $\text {IOE}$ is strictly above $\text {IOE}$ in the sense of Muchnik reducibility.We study cardinal characteristics in the sense of set theory that are analogous to the highness properties above. For instance, ${\mathfrak {d}} $ is the least size of a set G of bit sequences such that for each bit sequence x there is a bit sequence y in G so that $\underline \rho >p$. We prove within ZFC all the coincidences of cardinal characteristics that are the analogs of the results above. (shrink)

If lay theories associate moral intuitions with deeply held values, people should feel uncomfortable relying on deliberative thinking when judging violations of personal taboos. In two preliminary studies, participants with siblings of the opposite sex were particularly troubled when evaluating a sibling incest scenario under instructions to think slowly and rationally, or when the scenario was presented in a hard-to-read font forcing them to employ deliberative processing. This suggests that we may be intuitive intuitionists, and opens the door for investigations (...) of people’s preferred modes of moral judgment. (shrink)

Quantification has been constitutive of psychology since its inception and is core to its scientific status. The adoption of qualitative methods eschewing inferential statistics is therefore unlikely to obtain. Rather than discarding useful tools because of improper use, we recommend highlighting how inferential statistics can be more thoughtfully applied.

For Knobe, observers evaluate mental states by comparing agents' statements with the attitudes they are expected to hold. In our analysis, Knobe's model relies primarily on what agents should think, and little on expectancies of what they would think. We show the importance and complexity of including descriptive and prescriptive norms if one is to take expectancies seriously.

We investigate the role of continuous reductions and continuous relativization in the context of higher randomness. We define a higher analogue of Turing reducibility and show that it interacts well with higher randomness, for example with respect to van Lambalgen’s theorem and the Miller–Yu/Levin theorem. We study lowness for continuous relativization of randomness, and show the equivalence of the higher analogues of the different characterizations of lowness for Martin-Löf randomness. We also characterize computing higher [Formula: see text]-trivial sets by higher (...) random sequences. We give a separation between higher notions of randomness, in particular between higher weak 2-randomness and [Formula: see text]-randomness. To do so we investigate classes of functions computable from Kleene’s [Formula: see text] based on strong forms of the higher limit lemma. (shrink)

We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is -random, then A is K-trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of K-triviality and answering a question of Yu. We also prove that if A is K-trivial, then for all Y such that Ω is Y-random, ≡LRY. This answers a question of Merkle and Yu. The other direction is immediate, so (...) we have the second characterization of K-triviality.The proof of the first characterization uses a new cupping result. We prove that if A≰LRB, then for every set X there is a B-random set Y such that X is computable from Y⊕A. (shrink)

PIERRE-YVES MONIN. — Que dit la chanson?JULIETTE. — La chanson ne dit rien. Et la chanson peut tout dire. Cela doit dépendre de la bouche qui la fredonne et l’invente. Elle reflète peut-être le monde, la société qui l’a vue naître. Elle reflète peut-être aussi la Vérité, la vraie, celle qui sort, toute nue, de son puits. Mais elle...

It is clear enough that utilitarianism contributed to the softening of many penal systems in the world by arguing that very cruel punishments should be excluded every time a less cruel one would be just as effective. But does utilitarianism as such oppose the death penalty ? It is well known that Beccaria and Bentham criticized capital punishment on utilitarian grounds. But the fact that John Stuart Mill held a speech in favour of the death penalty at the House of (...) Commons in 1868 suggests that there is no necessity for a utilitarian thinker to oppose it. Otherwise, it would be possible to claim that John Stuart Mill betrayed, so to speak, the principle of utility by defending such a punishment. But nothing, it seems, allows us to say so. On the contrary, we would like to suggest that Mill’s disagreement with Bentham and Beccaria originates from his own empirical judgement on the following question : is death penalty the most cruel punishment for murder ? In other words, whether we like it or not, there is no way we can hold that Mill was less faithful than Beccaria and Bentham to the principle of utility when supporting the death penalty. (shrink)

Uniformism is the view that one and the same epistemology should apply for all modal knowledge. I argue that, whether or not all modal knowledge can be accounted for in terms of knowledge of essences, uniformism about knowledge of essences is untenable. I do this by showing that, while some essences are empirically discoverable, others are not. I then argue that the uniquely realisable–non-uniquely realisable distinction is a better metaphysical candidate for grounding this epistemic difference than the concrete–abstract distinction. I (...) conclude by suggesting that the task of philosophy is to identify non-empirically discoverable essences. (shrink)

The last sentence of Chapter 10 of the Analects describes a brief encounter between Confucius and a hen-pheasant, and it does so in puzzling terms, ridden with lexical difficulties. At the same time, intertextual references insert this fragment into the context of Confucius’ life mission as well as of Chinese mythological narratives. This contribution assesses the fragment’s meaning and significance: Confucius’ reaction to the hen-pheasant unveils his evolving understanding of the Heavenly Mandate bestowed upon him. The fragment thus forcefully concludes (...) the chapter in which it is inserted. Additionally, I put forward a hypothesis: the focus of this narrative, coupled with its positioning at the end of Chapter 10, induce us to postulate that it may have been purposefully located at the very center of the Analects, a proposition that reverberates on the way we look at the composition of the book. (shrink)

My main aim in this paper is to contribute to the elucidation of the nature of non-religious faith. I start by summarising several well-known arguments that belief is neither necessary nor sufficient for faith. I then try to identify the nature of the positive cognitive attitude towards p that is involved in having faith that p. After dismissing some candidates for the role, I explore the idea that faith and hope are similar attitudes. On this basis, I then advance a (...) new characterisation of faith. Finally, I turn to the question of the rationality of faith. I argue that faith is intrinsically irrational because it is an intrinsically incoherent propositional attitude, but that there is nonetheless a sense in which faith is neither intrinsically epistemically irrational nor intrinsically practically irrational. (shrink)

La présente étude rassemble les passages de l’Ab Vrbe condita de Tite-Live où un terme lié au rire est associé à un discours ou à une parole rapportée, afin de les confronter aux vues exprimées par Cicéron et Quintilien sur le rire en contexte rhétorique. Si tous les passages étudiés s’insèrent très bien dans la conception rhétorique du rire, l’historien latin s’appuie sur celle-ci pour offrir une répartition originale entre usages acceptables et formes abusives du rire qui participe à la (...) construction des portraits personnages et de l’œuvre. (shrink)

Throughout the manuscript of the Pensées and in other writings, Pascal crisscrosses his research on what the art of writing achieves and entails, on the one hand, and on the way to read and interpret the Holy Scriptures, on the other hand. Reading and writing practices are critically interwoven. This article offers a synthesis on Pascal’s reflexive account of such practices. After a summary of previous findings on the subject, it examines Pascal’s approach to (a) the rules that govern scriptural (...) interpretation; (b) the techniques of persuasion; and (c) the way to ground an instituted body, an expression by which we refer to a textual corpus, a political society, or a community of believers. (shrink)

Répondre à la question de savoir comment comprendre un être dépourvu de langage implique de savoir quels types d’attitudes intentionnelles, et avec quels contenus, il est possible de lui attribuer. On examinera ici trois réponses « différentialistes » à cette dernière question, d’après lesquelles une différence de catégorie ou de nature sépare, s’agissant de ces attitudes et de leurs contenus, les êtres pourvus de langage, tels les humains, et ceux qui en sont dépourvus, tels les animaux. On discutera en particulier (...) du plus solide des arguments de Donald Davidson en faveur d’un différentialisme fort : l’argument de l’indétermination, d’après lequel de notre incapacité à attribuer un contenu déterminé à toute croyance animale supposée il suit qu’il ne faudrait pas attribuer aux animaux la moindre croyance. En s’appuyant sur les analyses wittgensteiniennes de Peter Hacker, on rejettera l’une des trois prémisses de cet argument tout en défendant les deux autres, ce qui conduira à avancer un différentialisme modéré. (shrink)

My aim in this article is to elucidate the nature of a form of intellectual and practical neutrality that is not covered by existing accounts of suspension of judgment. After rejecting some inadequate characterizations of this attitude of neutrality, I provide a positive characterization of it: it is a successful effort to resist certain tendencies that are part of the dispositional profile of the doxastic state one is in on a given issue. I conclude by saying a few words about (...) the reasons for which this effort can be made, and by answering in the negative the question of whether all the attitudes that can be characterized as attitudes of committed neutrality are of the same type. (shrink)

This paper deals with the philosophical purpose of the Gorgias. I argue that this dialogue, both in its form and content, yields a dramatic demonstration that the success of the Socratic inquiry depends on the character of his interlocutors and their sense of what is shameful or not. To read the Gorgias is to inquire whether Socrates’ refutations have demonstrated anything. Although there is no definition of justice, happiness or the art of rhetoric, the dialogue nevertheless shows that justice and (...) trustworthiness concern both the practitioners of rhetoric and those of dialectic. (shrink)

Combining insights from two of the most influential approaches in linguistics, Construction Grammar and Relevance Theory, this book furthers our understanding of how meaning comes about. This title is part of the Flip it Open Programme and may also be available Open Access. Check our website Cambridge Core for details.

Gallicagram est un nouvel outil de lexicométrie, fondé notamment sur les archives océrisées de la Bibliothèque nationale de France et sur celles du journal Le Monde ; il dénombre dans le corpus choisi et pour une période donnée les occurrences d’un mot ou d’un syntagme, et offre différents modes de visualisation des données obtenues. Ce logiciel mérite à plusieurs titres d’être investi par les chercheurs : outre le volume des données qu’il exploite, suffisant pour fonder des analyses lexicométriques depuis le (...) XVIIe siècle jusqu’à nos jours, Gallicagram a sur son concurrent immédiat, Ngram Viewer, l’avantage d’une transparence très supérieure et d’une structure plus constante au cours du temps. L’article présente Gallibase, son extension qui lui applique les outils de la statistique textuelle – en particulier les analyses factorielles et arborées. Il illustre son potentiel et insiste sur l’intérêt spécifique des corpus de presse, qui permettent des études sur périodes courtes. (shrink)

This article examines algorithmic content moderation, using the moderation of violent extremist content as a specific case. In recent years, algorithms have increasingly been mobilized to perform essential moderation functions for online social media platforms such as Facebook, YouTube, and Twitter, including limiting the proliferation of extremist speech. Drawing on Katherine Hayles’ concept of “cognitive assemblages” and the Critical Security Studies literature, we show how algorithmic regulation operates within larger assemblages of humans and non-humans to influence the surveillance and regulation (...) of information flows. We argue that the dynamics of algorithmic regulation are more liquid, cobbled together and distributed than it appears. It is characterized by a set of shifting human and machine entities, which mix traditional surveillance methods with more sophisticated tools, and whose linkages and interactions are transient. The processes that enable the consolidation of knowledge about risky profiles and contents are, therefore, collective and distributed among humans and machines. This allows us to argue that the cognitive assemblages involved in content moderation become a cobbled space of preemptive calculation. (shrink)

Via a hermeneutics focused on Chinese numerology and concentric arrangements, the book offers a novel construal of the textual universe proper to early China writings. The author lays bare distinguishable patterns of textual composition while relating them to corresponding patterns of thinking. He differentiates rhetorical variants through detailed studies of the Zhuangzi's Inner chapters, the Laozi, the Analects, and the Huainanzi. The philosophical depth and relevance of the Chinese ancient worldview appear in a fresh light when one unearths the patterns (...) into which its content is embedded. The focus on textual patterns and rhetorical arrangements also facilitates the reading of Chinese classics alongside other traditions. The book will be a valuable reference for scholars and graduate students studying Chinese literary criticism, Chinese philosophy, and comparative philosophy. (shrink)

« L’animal » n’est pas une notion au programme de philosophie, et pourtant combien nous la rencontrons dans nos cours : interpellés par les élèves, souvent moins au fait des nouveautés de l’éthologie que l’on pourrait le croire ; ou en mobilisant l’animal à l’occasion du traitement de notions. Cet article vise principalement à mettre au jour les problématiques et les références classiques et récentes qui permettent de traiter cette question en évoquant le statut de l’animalité et de l’humanité, le (...) rapport aux hypothèses nouvelles concernant les cultures animales, l’inclusion d’une pensée de l’animalité dans la conception du vivant, et enfin les perspectives non seulement morales mais politiques de l’animalité. (shrink)

En quel sens le scepticisme causal de Hume permet-il la solution qu’il revendique au problème de la liberté et de la nécessité? D’abord, on soutient qu’une interprétation épistémologique (et non sémantique) de ce scepticisme suffit au nécessitarisme proposé. Ensuite, on soutient que, parce qu’il s’accompagne d’une explication naturaliste de l’inférence, ce scepticisme rend raison de l’imputation morale requise par la défense d’un compatibilisme. Le caractère sceptique de ce naturalisme permet de qualifier l’ensemble du propos humien de solution sceptique de réconciliation.

The progressive dominance of historical-critical methods in the reading of ancient Chinese classics has led scholars to privilege micro levels of textual analysis. Consequently, the question as to whether laws of composition could be identified in this corpus has often been ignored, or considered irrelevant. Working on Chinese number symbolism as well as on rules governing “ring composition” in other cultural contexts, this article aims at fashioning anew the question of the possibility of an ancient Chinese “structural rhetoric” and at (...) envisioning the patterns that might have governed it. It specifically applies the approach it propounds to Huainanzi 淮南子, showing how numerology frames its structure and argument, the text being built after the image of the “roundness” of the Way and of the Ruler. It then endeavors to apply these results to the unearthing of “inter-structural” patterns that would help us to locate Huainanzi, Lüshi Chunqiu 呂氏春秋, the versions at hand of Zhuangzi 莊子, Lunyu 論語, or yet Laozi 老子 into a textual universe that shares correlated rhetorical features. (shrink)

In this book, Benoît Dubreuil explores the creation and destruction of hierarchies in human evolution. Combining the methods of archaeology, anthropology, cognitive neuroscience and primatology, he offers a natural history of hierarchies from the point of view of both cultural and biological evolution. This volume explains why dominance hierarchies typical of primate societies disappeared in the human lineage and why the emergence of large-scale societies during the Neolithic period implied increased social differentiation, the creation of status hierarchies, and, eventually, (...) political centralisation. (shrink)