We define a class of finite partial lattices which admit a notion of rank compatible with embedding constructions, and present a necessary and sufficient condition for the embeddability of a finite ranked partial lattice into the computably enumerable degrees.

We present a necessary and sufficient condition for the embeddability of a principally decomposable finite lattice into the computably enumerable degrees. This improves a previous result which required that, in addition, the lattice be ranked. The same condition is also necessary and sufficient for a finite lattice to be embeddable below every non-zero computably enumerable degree.

Martin [4, Theorems 1 and 2] proved that a Turing degree a is the degree of a maximal set if, and only if, a′ = 0″. Lachlan has shown that maximal sets have minimal many-one degrees [2, §1] and that every nonrecursive r.e. Turing degree contains a minimal many-one degree [2, Theorem 4]. Our aim here is to show that any r.e. Turing degree a of a maximal set contains an infinite number of maximal sets whose many-one degrees are pairwise (...) incomparable; hence such Turing degrees contain an infinite number of distinct minimal many-one degrees. This theorem has been proved by Yates [6, Theorem 5] in the case when a = 0′. The need for this theorem first came to our attention as a result of work done by the author [3, Theorem 2.3]. There we looked at the structure / obtained from the recursive functions of one variable under the equivalence relation f ~ g if, and only if, f(x) = g(x) a.e., that is, for all but finitely many x ∈, where M is a maximal set, and M is its complement. We showed that / 1 ≡ / 2 if, and only if, 1 = m 2, i.e., 1. and 2 have the same many-one degree. However, it might be possible that some Turing degree of a maximal set contains exactly one many-one degree of a maximal set. Theorem 1 was proved to show that this was not the case, and hence that the theory of / is not an invariant of Turing degree. (shrink)

Perceptual experience, that paradigm of subjectivity, constitutes our most immediate and fundamental access to the objective world. At least, this would seem to be so if commonsense realism is correct — if perceptual experience is (in general) an immediate awareness of mind-independent objects, and a source of direct knowledge of what such objects are like. Commonsense realism raises many questions. First, can we be more precise about its commitments? Does it entail any particular conception of the nature of perceptual experience (...) and its relation to perceived objects, or any particular view of the way perception yields knowledge? Second, what explains the apparent intuitive appeal of commonsense realism? Should we think of it as a kind of folk theory held by most human adults or is there a sense in which we are pre-theoretically committed to it — in virtue of the experience we enjoy or in virtue of the concepts we use or in virtue of the explanations we give? Third, is commonsense realism defensible, in the face of formidable challenges from epistemology, metaphysics and cognitive science? The project of the present volume is to advance our understanding of these issues and thus to shed light on the commitments and credentials of commonsense realism. As you may have guessed from the title, the volume also aims to highlight the key role the concept of causation plays in these debates. Central issues to be addressed include the status and nature of causal requirements on perception, the causal role of perceptual experience, and the relation between objective perception and causal thinking — issues that, as many chapters in the volume bring out, are inseparable from concerns with the very nature of causation. (shrink)

I first seriously contemplated writing a book on degree theory in 1976 while I was visiting the University of Illinois at Chicago Circle. There was, at that time, some interest in ann-series book about degree theory, and through the encouragement of Bob Soare, I decided to make a proposal to write such a book. Degree theory had, at that time, matured to the point where the local structure results which had been the mainstay of the earlier papers in the area (...) were finding a steadily increasing number of applications to global degree theory. Michael Yates was the first to realize that the time had come for a systematic study of the interaction between local and global degree theory, and his papers had a considerable influence on the content of this book. During the time that the book was being written and rewritten, there was an explosion in the number of global theorems about the degrees which were proved as applications of local theorems. The global results, in turn, pointed the way to new local theorems which were needed in order to make further progress. I have tried to update the book continuously, in order to be able to present some of the more recent results. It is my hope to introduce the reader to some of the fascinat ing combinatorial methods of Recursion Theory while simultaneously showing how to use these methods to prove some beautiful global theorems about the degrees. (shrink)

In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from RT, Ramsey's Theorem for Pairs. These principles tend to fall outside of the "big five" systems of reverse mathematics and a complicated picture of subsystems below RT has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that ADS is not equivalent to CAC and that EM is not equivalent to RT.

According to John McDowell and Bill Brewer, our experiences have the type of content which can be the content of judgements - content which is the result of the actualization of specific conceptual abilities. They defend this view by arguing that our experiences must have such content in order for us to be able to think about our environment. In this paper I show that they do not provide a conclusive argument for this view. Focusing on Brewer’s version of the (...) argument, I show that it rests on a questionable assumption - namely, that if a subject can recognize the normative bearing of a mental content upon what she should think and do, then this content must be the result of the actualization of conceptual capacities (and in this sense conceptual). I argue that considerations regarding the roles played by experience and concepts in our mental lives may require us to reject this assumption. (shrink)

We investigate homomorphisms of degree structures with various relations, functions and constants. Our main emphasis is on pseudolattices, i.e., partially ordered sets with a join operation and relations simulating the meet operation. We show that there are no finite quotients of the pseudolattice of degrees or of the pseudolattice of degrees 0′, but that many finite distributive lattices are pseudolattice quotients of the pseudolattice of computably enumerable degrees.

Both introspection and empirical studies suggest that visual attention can affect the phenomenology of our visual experience. However, the exact character of such effects is far from clear. My aim in this chapter is to spell out the main difficulties involved in attempting to achieve a clearer view of these effects, and to make some suggestions as to how we can make progress with this issue while avoiding tempting mistakes. I do this by discussing the question of whether there is (...) a sense in which attention to a seen object can be said to contribute to the object’s visual phenomenal salience. It is often suggested that focusing visual attention on a seen object renders the object phenomenally salient. I look at potential evidence for this suggestion, and consider what form, if any, of visual phenomenal salience it may support. (shrink)

This collection addresses a post-WWII shift in the hierarchy of scientific explanations, where the highest goal moves from reductionism towards some ...

In much of the current academic and public discussion, conspiracy theories are portrayed as a negative phenomenon, linked to misinformation, mistrust in experts and institutions, and political propaganda. Rather surprisingly, however, philosophers working on this topic have been reluctant to incorporate a negatively evaluative aspect when either analyzing or engineering the concept conspiracy theory. In this paper, we present empirical data on the nature of the concept conspiracy theory from five studies designed to test the existence, prevalence and exact form (...) of an evaluative dimension to the ordinary concept conspiracy theory. These results reveal that, while there is a descriptive concept of conspiracy theory, the predominant use of conspiracy theory is deeply evaluative, encoding information about epistemic deficiency and often also derogatory and disparaging information. On the basis of these results, we present a new strategy for engineering conspiracy theory to promote theoretical investigations and institutional discussions of this phenomenon. We argue for engineering conspiracy theory to encode an epistemic evaluation, and to introduce a descriptive expression—such as ‘conspiratorial explanation’—to refer to the purely descriptive concept conspiracy theory. (shrink)

This book presents a unifying framework for using priority arguments to prove theorems in computability. Priority arguments provide the most powerful theorem-proving technique in the field, but most of the applications of this technique are ad hoc, masking the unifying principles used in the proofs. The proposed framework presented isolates many of these unifying combinatorial principles and uses them to give shorter and easier-to-follow proofs of computability-theoretic theorems. Standard theorems of priority levels 1, 2, and 3 are chosen to demonstrate (...) the framework's use, with all proofs following the same pattern. The last section features a new example requiring priority at all finite levels. The book will serve as a resource and reference for researchers in logic and computability, helping them to prove theorems in a shorter and more transparent manner"--Provided by publisher. (shrink)

Contingency is the presence of non-actualized possibility in the world. Fatalism is a view of reality on which there is no contingency. Since it is contingency that permits agency, there has traditionally been much interest in contingency. This interest has long been embarrassed by the contention that simple and plausible assumptions about the world lead to fatalism. I begin with an Aristotelian argument as presented by Richard Taylor. Appreciation of this argument has been stultified by a question pertaining to the (...) source of necessity and possibility and a closely related one regarding the nature of metaphysics itself. Answering these questions reveals the crucial issue here, to wit, necessity and possibility in a temporal world. This issue is investigated through an important later criticism of Taylor by David Foster Wallace. Wallace’s critique is significant because it brings to the fore the pivotal notion for understanding contingency in a temporal world, that of synchronic possibility, the idea that incompatible states of affairs are possible at a single moment. This notion provides the basis of distinguishing two systematic accounts of truth, modality and time: two metaphysics of contingency. On one account, Taylor’s Aristotelian argument is straightforwardly valid and compelling; on the other, it is fallacious. In closing, I present reasons why the former account, supporting the Aristotelian views of time and truth, is correct and make some comments to ameliorate this conclusion. (shrink)

John McDowell (in Mind and World) and Bill Brewer (in Perception and Reason) argue that the content of our perceptual experience is conceptual in the following sense. It is of the type of content that could be the content of a judgement – that is, a content which results from the actualization of two (or more) conceptual abilities. Specifically, they suggest that the conceptual abilities actualized in experience are demonstrative abilities, and thus the resulting content is of the type we (...) may express by means of sentences of the form ‘this is thus’. In this paper I argue that we cannot construe experiential contents in this way. I first outline a construal of the ability to think about a thing being thus which is based on Brewer's discussion of conceptual experiential contents, and which I take to be the best construal available to the conceptualist. I then show that on this construal the demonstrative abilities that account for our experience of properties require intentional focused attention to the relevant properties. The conceptualist is thus committed to holding that we experience only the properties we are intentionally attending to, and I argue that this is implausible. The interest in examining Brewer's conceptualist construal of experiential content and pointing out its shortcoming is not limited merely to an interest in whether there is a workable conceptualist account of experiential content. I suggest that certain aspects of Brewer's construal capture important (and often neglected) aspects of our perceptual experience, and that understanding why the account fails can contribute to our understanding of both experiential content and demonstrative thought. (shrink)

The X-ray and bulk densities of PdIn alloys have been determined at ambient temperature on samples annealed at 1273 and 1373 K and quenched in water-ice mixtures. From these measurements the vacancy concentrations in this intermetallic phase have been obtained as a function of In concentration at these two temperatures. In addition, a generalized thermodynamic model is presented which considers the existence of antisite and vacancy defects on both sublattices without any dilute solution approximations. This model uses three energy parameters, (...) whose values have been obtained for PdIn using the measured vacancy concentrations and the chemical potentials of In. This model is able to describe all the available vacancy data and is suitable for calculating these values at compositions and temperatures when such data are not available. In addition, the model permits the calculation of the concentrations of the minority point defects. It is shown that dilute-solution approximations, which have invariably been used in this kind of modelling, are unsatisfactory. The present results and their analysis confirm that PdIn is a near-triple-defect type of intermetallic and not a near-Schottky type, as has been claimed recently. (shrink)

For the theorists of crisis, the revolutionary state comes into existence through violence, and due to its inability to provide an authoritative katechon (restrainer) against internal and external violence, it perpetuates violence until it self-destructs. Writing during extreme economic depression and growing social and political violence, the crisis theorists––Joseph de Maistre, Juan Donoso Cortés, and Carl Schmitt––each sought to blame the chaos of their time upon the Janus-faced postrevolutionary ideals of liberalism and socialism by urging a return to pre-revolutionary moral (...) and religious values. They are united by three counterrevolutionary principles, all of which are purported to remedy revolutionary violence: traditional constitutional fidelity, the philosophy of the decision, and opposition to bourgeois liberalism. This essay is followed by the first complete English translation and publication of Donoso’s letter of October 24, 1851, which contains Donoso’s only reference to the “discussing class,” a political entity later popularized by Schmitt in his 1922 work Political Theology. (shrink)

A choice set for a computable linear ordering is a set which contains one element from each maximal block of the ordering. We obtain a partial characterization of the computable linear order-types for which each computable model has a computable choice set, and a full characterization in the relativized case; Every model of the linear order-type α of degree ≤ d has a choice set of degree ≤ d iff α can written as a finite sum of order-types, each of (...) which either has finitely many blocks, or has order-type n · η for some integer n. (shrink)