We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, or Schnorr random reals. (...) We show that Low(ML, Kurtz) coincides with the non-DNR degrees, while both Low(CR, Kurtz) and Low(Schnorr, Kurtz) are exactly the non-high, non-DNR degrees. (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)

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call 1/2-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the K-trivial sets. We characterize 1/2-bases as the sets computable from both halves of Chaitin’s Ω, and as the sets that obey the cost function c(x,s)=Ωs−Ωx−−−−−−−√. Generalizing these results yields a dense hierarchy of (...) subideals in the K-trivial degrees: For k<n, let Bk/n be the collection of sets that are below any k out of n columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be Ω. Furthermore, the corresponding cost function characterization reveals that Bk/n is independent of the particular representation of the rational k/n, and that Bp is properly contained in Bq for rational numbers p<q. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the K-trivial sets; we can calculate from the family which Bp it characterizes. We finish by studying the union of Bp for p<1; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic81(3) (2016) 1028–1046], who showed that it is a proper subclass of the K-trivial sets. We prove that all such sets are robustly computable from Ω, and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a Σ03 subideal of the K-trivial sets. (shrink)

We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle.

There is a perfect thin class whose upward closure in the Turing degrees has full measure . Thus, in the Muchnik lattice of classes, the degree of 2-random reals is comparable with the degree of some perfect thin class. This solves a question of Simpson [S. Simpson, Mass problems and randomness, Bulletin of Symbolic Logic 11 1–27].

The hippocampal formation is a structure critical to navigation and many forms of memory. In mammals, the firing of place cells is widely regarded as the fundamental unit of HF information processing. Supporting homology between the avian and mammalian HF, context-specific patterns of Egr1 have been reported in birds that are comparable to those produced by place cell firing in mammals. Recent electrophysiological data, however, suggest that many avian species lack place cells, potentially undermining the correspondence between Egr1 and place (...) cell-related firing in the avian brain. To clarify this, the current study examines Egr1 expression in Japanese quail under conditions known to elicit only weakly spatially modulated firing patterns and report robust context-dependent Egr1 expression. These data confirm that context-dependent expression of Egr1 is not dependent on precise place fields and provide insight into how these birds are able to perform complex spatial tasks despite lacking mammalian-like place cells. (shrink)

EveryK-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem.

A real is called properly n-generic if it is n-generic but not n+1-generic. We show that every 1-generic real computes a properly 1-generic real. On the other hand, if m > n ≥ 2 then an m-generic real cannot compute a properly n-generic real.

We define the Scott complexity of a countable structure to be the least complexity of a Scott sentence for that structure. This is a finer notion of complexity than Scott rank: it distinguishes between whether the simplest Scott sentence is $\Sigma _{\alpha }$, $\Pi _{\alpha }$, or $\mathrm {d-}\Sigma _{\alpha }$. We give a complete classification of the possible Scott complexities, including an example of a structure whose simplest Scott sentence is $\Sigma _{\lambda + 1}$ for $\lambda $ a limit (...) ordinal. This answers a question left open by A. Miller.We also construct examples of computable structures of high Scott rank with Scott complexities $\Sigma _{\omega _1^{CK}+1}$ and $\mathrm {d-}\Sigma _{\omega _1^{CK}+1}$. There are three other possible Scott complexities for a computable structure of high Scott rank: $\Pi _{\omega _1^{CK}}$, $\Pi _{\omega _1^{CK}+1}$, $\Sigma _{\omega _1^{CK}+1}$. Examples of these were already known. Our examples are computable structures of Scott rank $\omega _1^{CK}+1$ which, after naming finitely many constants, have Scott rank $\omega _1^{CK}$. The existence of such structures was an open question. (shrink)

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)

Despite the supreme political and economic significance of boundaries--and ongoing challenges to existing national boundaries--scant attention has been paid to their ethics. This volume explores how diverse ethical traditions understand the political and property rights reflected in territorial and jurisdictional boundaries. It is the first book to bring together thinkers from a range of traditions, both religious and secular, to discuss the ethics of boundaries. Each contributor represents a tradition's views on questions surrounding the use of boundaries to delimit property (...) and political rights. What does it mean to own something? What resources should not be privately owned? What justifies the erection of political boundaries between one people and another? How ''hard'' should such boundaries be? What rights extend to minorities within a state? Should territorial boundaries coincide with social ones? Does national autonomy have an ethical basis, or is it an aspect of modern power politics? Should we aim for a more inclusive community than that afforded by modern nation-states? Cross-chapter dialogue and a substantive conclusion draw out similarities and differences among the traditions represented, traditions that include Christianity, classical liberalism, Confucianism, international law, Islam, Judaism, liberal egalitarianism, and natural law. In addition to the editors, the contributors are Nigel Biggar, Joseph Boyle, Joseph Chan, Russell Hardin, Will Kymlicka, Loren Lomasky, Robert McCorquodale, Richard B. Miller, David Novak, Sulayman Nyang, Michael Nylan, Raul C. Pangalangan, Daniel Philpott, Jeremy Rabkin, Hillel Steiner, M. Raquibuz Zaman, and Noam J. Zohar. (shrink)

Review by: Johanna N. Y. Franklin The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 115-118, March 2013.

This book is an outstanding contribution to the philosophical study of language and mind, by one of the most influential thinkers of our time. In a series of penetrating essays, Chomsky cuts through the confusion and prejudice which has infected the study of language and mind, bringing new solutions to traditional philosophical puzzles and fresh perspectives on issues of general interest, ranging from the mind-body problem to the unification of science. Using a range of imaginative and deceptively simple linguistic analyses, (...) Chomsky defends the view that knowledge of language is internal to the human mind. He argues that a proper study of language must deal with this mental construct. According to Chomsky, therefore, human language is a 'biological object' and should be analyzed using the methodology of the sciences. His examples and analyses come together in this book to give a unique and compelling perspective on language and the mind. (shrink)

From interpreting the world to changing it, this book is a synthesis of Chomsky's early work on philosophy, linguistics, and politics.

Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

Attempts to indentify the fundamental concepts of language, argues that the study of language reveals hidden facts about the mind, and looks at the impact of propaganda.

World politics, international relations, representative government. Author's works in demand.

Featuring an essay by the author on the role of intellectuals in society and government, a fascinating volume sheds light on the relation between language, mind ...

This Introduction introduces readers to the concepts of political philosophy: authority, democracy, freedom and its limits, justice, feminism, multiculturalism, and nationality. Accessibly written and assuming no previous knowledge of the subject, it encourages the reader to think clearly and critically about the leading political questions of our time. THe book first investigates how politcial philosophy tackles basic ethical questions such as 'how should we live together in society?' It furthermore looks at political authority, discusses the reasons society needs politics in (...) the first place, explores the limitations of politics, and asks if there are areas of life that shouldn't be governed by politics. Moreover, the book explores the connections between political authority and justice, a constant theme in political philosophy, and the ways in which social justice can be used to regulate rather than destroy a market economy. In his travels through this realm, Miller covers why nations ar the natural units of government and wonders if the rise of multiculturalism and transnational co-operation will change all this, and asks in the end if we will ever see the formation of a world government. (shrink)

Chomsky proposes a reformulation of the theory of transformational generative grammar that takes recent developments in the descriptive analysis of particular ...

A single-volume compendium of seminal writings by a forefront philosopher and critic includes selections from such best-selling works as Manufacturing Consent, Hegemony or Survival, and Failed States, in an anthology that explores such subjects as the media, human rights, and intellectual freedom. 20,000 first printing.

When attempting to generalize recursion theory to admissible ordinals, it may seem as if all classical priority constructions can be lifted to any admissible ordinal satisfying a sufficiently strong fragment of the replacement scheme. We show, however, that this is not always the case. In fact, there are some constructions which make an essential use of the notion of finiteness which cannot be replaced by the generalized notion of $\alpha$-finiteness. As examples we discuss bothcodings of models of arithmetic into the (...) recursively enumerable degrees, and non-distributive lattice embeddings into these degrees. We show that if an admissible ordinal $\alpha$ is effectively close to $\omega$ (where this closeness can be measured by size or by cofinality) then such constructions maybe performed in the $\alpha$-r.e. degrees, but otherwise they fail. The results of these constructions can be expressed in the first-order language of partially ordered sets, and so these results also show that there are natu. (shrink)

In Rules and Representations, first published in 1980, Noam Chomsky lays out many of the concepts that have made his approach to linguistics and human cognition so instrumental to our understanding of language.Chomsky arrives at his well-known position that there is a universal grammar, structured in the human mind and common to all human languages. Based on Chomsky's 1978 Woodbridge Lectures, this edition contains revised versions of the lectures and two new essays.

Arthur I. Miller is a historian of science whose approach has been strongly influenced by current work in cognitive science, and in this book he shows how the two fields might be fruitfully linked to yield new insights into the creative process.

The book from which these sections are excerpted is concerned with the prospects for assimilating the study of human intelligence and its products to the natural sciences through the investigation of cognitive structures, understood as systems of rules and representations that can be regarded as “mental organs.” These mental structui′es serve as the vehicles for the exercise of various capacities. They develop in the mind on the basis of an innate endowment that permits the growth of rich and highly articulated (...) structures along an intrinsically determined course under the triggering and partially shaping effect of experience, which fixes parameters in an intricate system of predetermined form. It is argued that the mind is modular in character, with a diversity of cognitive structures, each with its specific properties arid principles. Knowledge of language, of the behavior of objects, and much else crucially involves these mental structures, and is thus not characterizable in terms of capacities, dispositions, or practical abilities, nor is it necessarily grounded in experience in the standard sense of this term.Various types of knowledge and modes of knowledge acquisition are discussed in these terms. Some of the properties of the language faculty are investigated. The basic cognitive relation is “knowing a grammar”; knowledge of language is derivative and, correspondingly, raises further problems. Language as commonly understood is not a unitary phenomenon but involves a number of interacting systems: the “computational” system of grammar, which provides the representations of sound and meaning that permit a rich range of expressive potential, is distinct from a conceptual system with its own properties; knowledge of language must be distinguished from knowledge of how to use a language; and the various systems that enter into the knowledge and use of language must be further analyzed into their specific subcomponents. (shrink)

The book from which these sections are excerpted is concerned with the prospects for assimilating the study of human intelligence and its products to the natural sciences through the investigation of cognitive structures, understood as systems of rules and representations that can be regarded as These mental structui′es serve as the vehicles for the exercise of various capacities. They develop in the mind on the basis of an innate endowment that permits the growth of rich and highly articulated structures along (...) an intrinsically determined course under the triggering and partially shaping effect of experience, which fixes parameters in an intricate system of predetermined form. It is argued that the mind is modular in character, with a diversity of cognitive structures, each with its specific properties arid principles. Knowledge of language, of the behavior of objects, and much else crucially involves these mental structures, and is thus not characterizable in terms of capacities, dispositions, or practical abilities, nor is it necessarily grounded in experience in the standard sense of this term. (shrink)

At its core, this exhilarating collection of essays, interviews, and correspondence spanning the years 1988 through 2018, and reaching back a decade or more previous is about the simple concept that ideas matter. And not only that ideas matter. But that ideas in this case, through the lens of two engaged intellectuals mutate, inform, inspire, and ultimately provide more fuel for thought, the actions that follow such thought, and for carrying on, and doing the work.

This chapter centers around law's capacity to constitute practical reasons. In discussing this theme, consideration is given to law's artifactual character. The discussion falls into two main parts. In Section 1, I critically examine a skeptical line of thought about law's capacity to constitute reasons for action, which draws, in part, on law's artifactuality. I argue for a somewhat less skeptical (but still qualified) stance, according to which the fact that a legal directive has been issued can (notwithstanding the artifactuality (...) involved) be a reason for action, yet one that is underpinned by bedrock values which (under certain conditions and constraints) law is apt to serve. In Section 2, I consider whether, and in what sense, law can acquire an even more 'robust' status as a source of practical reasons. I focus particularly on Joseph Raz's position about the normative force of (legitimate) legal authority and on an alternative position I have proposed and advocated elsewhere. (shrink)

This chapter outlines the main ideas of my book National responsibility and global justice. It begins with two widely held but conflicting intuitions about what global justice might mean on the one hand, and what it means to be a member of a national community on the other. The first intuition tells us that global inequalities of the magnitude that currently exist are radically unjust, while the second intuition tells us that inequalities are both unavoidable and fair once national responsibility (...) is allowed to operate. This conflict might be resolved either by adopting a cosmopolitan theory of justice (which leaves no room for national responsibility) or by adopting a ?political? theory of justice (which denies that questions of distributive justice can arise beyond the walls of the sovereign state). Since neither resolution is satisfactory, the chapter defends the idea of national responsibility and proposes a new theory of global justice, whose main elements are the protection of basic human rights worldwide, and fair terms of interaction between independent political communities. (shrink)

People increasingly form beliefs based on information gained from automatically filtered Internet ‎sources such as search engines. However, the workings of such sources are often opaque, preventing ‎subjects from knowing whether the information provided is biased or incomplete. Users’ reliance on ‎Internet technologies whose modes of operation are concealed from them raises serious concerns about ‎the justificatory status of the beliefs they end up forming. Yet it is unclear how to address these concerns ‎within standard theories of knowledge and justification. (...) To shed light on the problem, we introduce a ‎novel conceptual framework that clarifies the relations between justified belief, epistemic responsibility, ‎action, and the technological resources available to a subject. We argue that justified belief is subject to ‎certain epistemic responsibilities that accompany the subject’s particular decision-taking circumstances, ‎and that one typical responsibility is to ascertain, so far as one can, whether the information upon which ‎the judgment will rest is biased or incomplete. What this responsibility comprises is partly determined by ‎the inquiry-enabling technologies available to the subject. We argue that a subject’s beliefs that are ‎formed based on Internet-filtered information are less justified than they would be if she either knew how ‎filtering worked or relied on additional sources, and that the subject may have the epistemic ‎responsibility to take measures to enhance the justificatory status of such beliefs.‎. (shrink)

Exploring materialism and social relationships in modern culture Material Culture and Mass Consumption offers an in-depth exploration of objects, objectification, ideology, and materialism in modern society. Drawing from Hegel, Marx, Munn, and Simmel, the discussion delves into the physicality of the material world and attempts to understand materialism as a form of cultural expression. Targeting mass production as the root of mass consumption, rather than the result, this book positions material goods at odds with genuine social interaction and questions these (...) relationships from the abstract to the intensely specific. (shrink)

Scientific consensus is widely deferred to in public debates as a social indicator of the existence of knowledge. However, it is far from clear that such deference to consensus is always justified. The existence of agreement in a community of researchers is a contingent fact, and researchers may reach a consensus for all kinds of reasons, such as fighting a common foe or sharing a common bias. Scientific consensus, by itself, does not necessarily indicate the existence of shared knowledge among (...) the members of the consensus community. I address the question of under what conditions it is likely that a consensus is in fact knowledge based. I argue that a consensus is likely to be knowledge based when knowledge is the best explanation of the consensus, and I identify three conditions—social calibration, apparent consilience of evidence, and social diversity, for knowledge being the best explanation of a consensus. (shrink)

In a recent paper, Barry Loewer attempts to defend Humeanism about laws of nature from a charge that Humean laws are not adequately explanatory. Central to his defense is a distinction between metaphysical and scientific explanations: even if Humeans cannot offer further metaphysical explanations of particular features of their “mosaic,” that does not preclude them from offering scientific explanations of these features. According to Marc Lange, however, Loewer’s distinction is of no avail. Defending a transitivity principle linking scientific explanantia to (...) their metaphysical grounds, Lange argues that a charge of explanatory inadequacy resurfaces once this intuitive principle is in place. This paper surveys, on behalf of the Humean, three strategies for responding to Lange’s criticism. The ready availability of these strategies suggests that Lange’s argument may not bolster anti-Humean convictions, since the argument rests on premises that those not antecedently sharing these convictions may well reject. The three strategies also correspond to three interesting ways of thinking about relations of grounding linking Humean laws and their instances, all of which are consistent with theses of Humean supervenience, and some of which have been heretofore overlooked. (shrink)

La obra compuesta de dos (2) partes, permite conocer acerca de los avances de la linguística contemporánea, en diversos aspectos de investigación sobre la mente humana, en que medida la mente y el le nguaje se cosideran fenómenos naturales, profundización en lo supuestos e implicaciones del programa minimalista y temas relacionados.

The elections of 1994 are described as a "political earthquake," a "triumph of conservatism" that reflects the continuing "drift to the right" on the part of the American population. The victorious Gingrich army of welltrained, well-funded "conservatives" call for a Contract with America that will finally "get government off our backs" so that we can return to the happy days when the free market reigned. They will restore "family values," ridding us of "the excesses of the welfare state" and the (...) other residues of the failed "big government" policies of New Deal liberalism and Johnson's "Great Society." By dismantling the "nanny state" they will succeed, where the Democrats have failed, to achieve the shared goal of all elite and leadership elements: to "create jobs for Americans" and win security and freedom for the "middle class." And they will take over and successfully lead the crusade to establish the American Dream of free market democracy, worldwide. (shrink)