The Ecclesiastical History of Orderic Vitalis has been called `the greatest of all medieval chronicles'. Written in Normandy between 1114 and 1141, it is a detailed history of the Norman people and their conquests, full of vivid, often penetrating portraits of the lives and characters of kings and queens, lords and bishops, simple knights, and humble villagers. The chronicle gives a unique, authentic picture of feudal society during a period of rapid change in church and state which saw the emergence (...) of the Anglo-Norman realm, the spread of new forms of monasticism, and the launching of the Crusades. Published in 1968, volume II of Marjorie Chibnall's six-volume edition of the Ecclesiastical History is now available for the first time in paperback. `a superbly edited Latin text and a unique English translation of the work of a major historian' American Historical Review `Mrs Chibnall is giving us... her edition of a classical medieval text which will itself become a classic of medieval scholarship.' Times Literary Supplement. (shrink)

Betrifft die Handschrift Cod. 555 der Burgerbibliothek Bern.

Edited with a facing-page English translation from the Latin text by: Chibnall, Marjorie.

After the three families divided up the state of Jin and the Tian family took over Qi, the political situation in the fourth century B.C.E. appeared even more chaotic. Wei conquered Chu's Luyang and Qin's Xihe, Qin defeated Wei at Shimen , and again at Shaoliang , and Wei moved its capital to Daliang. During the mid-Warring States period, Qin became dominant in the west, Qi in the east, Chu in the south, and Wei in the center. Rapid changes occurred (...) one after another; trickery and conflict were rampant. However, the shi , the intelligentsia, actually managed to expand their spheres of existence and activity accordingly in this state of tension between countries, states, and men. A few major states assembled quite a number of literati; and those men of the villages, who had in earlier times merely waited passively for opportunities to fall into their laps, crisscrossed the various feudal states; literati who previously had no cause to use military force became, one by one, the honored guests of the feudal lords. With the breakdown of the previously simple and obvious order, the gradually dismantling of the common body of the ancestral clan of the past, and the increasing complexities of social relationships after the dissolution of blood ties, social order became a matter of concern. Or, to reword this most practical issue: How could this universally chaotic society go from disorder to order? (shrink)

This fascinating study in the sociology of science explores the way scientists conduct, and draw conclusions from, their experiments. The book is organized around three case studies: replication of the TEA-laser, detecting gravitational rotation, and some experiments in the paranormal. "In his superb book, Collins shows why the quest for certainty is disappointed. He shows that standards of replication are, of course, social, and that there is consequently no outside standard, no Archimedean point beyond society from which we can lever (...) the intellects of our fellows. "- -Donald M. McCloskey, Journal of Economic Psychology "Collins is one of the genuine innovators of the sociology of scientific knowledge.... Changing Order is a rich and entertaining book. "- - Isis "The book gives a vivid sense of the contingent nature of research and is generally a good read. "- -Augustine Brannigan, Nature "This provocative book is a review of [Collins's] work, and an attempt to explain how scientists fit experimental results into pictures of the world.... A promising start for new explorations of our image of science, too often presented as infallibly authoritative. "- -Jon Turney, New Scientist. (shrink)

Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this.In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the (...) system QS4M+BF+FIN. It corresponds to the class of transitive, reflexive and final frames. With borderlineness defined logically as usual, it then follows that something is borderline precisely when it is higher-order borderline, and that a predicate is vague precisely when it is higher-order vague.Like Williamson's, the theory proposed here has no clear borderline cases in Sorites sequences. I argue that objections that there must be clear borderline cases ensue from the confusion of two notions of borderlineness—one associated with genuine higher-order vagueness, the other employed to sort objects into categories—and that the higher-order vagueness paradoxes result from superimposing the second notion onto the first. Lastly, I address some further potential objections. (shrink)

We discuss the differences between first-order set theory and second-order logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if second-order logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if it is given a weak semantics, it loses its power in expressing concepts categorically. First-order set theory and second- (...) class='Hi'>order logic are not radically different: the latter is a major fragment of the former. (shrink)

I argue against such "Relation Intentionalist" theories of consciousness as the higher-order thought and inner sense views on the grounds that they understand a subject's awareness of his or her phenomenal characters to be intentional, like seeming-seeing, rather than "direct", like seeing. The trouble with such views is that they reverse the order of explanation between phenomenal character and intentional awareness. A superior theory of consciousness, based on views expressed by Russell and Price, takes the relation of awareness (...) to be a nonintentional "acquaintance". (shrink)

A sentence of first-order logic is satisfiable if it is true in some structure, and finitely satisfiable if it is true in some finite structure. The question arises as to whether there exists an algorithm for determining whether a given formula of first-order logic is satisfiable, or indeed finitely satisfiable. This question was answered negatively in 1936 by Church and Turing (for satisfiability) and in 1950 by Trakhtenbrot (for finite satisfiability).In contrast, the satisfiability and finite satisfiability problems are (...) algorithmically solvable for restricted subsets---or, as we say, fragments---of first-order logic, a fact which is today of considerable interest in Computer Science. This book provides an up-to-date survey of the principal axes of research, charting the limits of decision in first-order logic and exploring the trade-off between expressive power and complexity of reasoning. Divided into three parts, the book considers for which fragments of first-order logic there is an effective method for determining satisfiability or finite satisfiability. Furthermore, if these problems are decidable for some fragment, what is their computational complexity? Part I focusses on fragments defined by restricting the set of available formulas. Topics covered include the Aristotelian syllogistic and its relatives, the two-variable fragment, the guarded fragment, the quantifier-prefix fragments and the fluted fragment. Part II investigates logics with counting quantifiers. Starting with De Morgan's numerical generalization of the Aristotelian syllogistic, we proceed to the two-variable fragment with counting quantifiers and its guarded subfragment, explaining the applications of the latter to the problem of query answering in structured data. Part III concerns logics characterized by semantic constraints, limiting the available interpretations of certain predicates. Taking propositional modal logic and graded modal logic as our cue, we return to the satisfiability problem for two-variable first-order logic and its relatives, but this time with certain distinguished binary predicates constrained to be interpreted as equivalence relations or transitive relations. The work finishes, slightly breaching the bounds of first-order logic proper, with a chapter on logics interpreted over trees. (shrink)

George Boolos's employment of plurals to give an ontologically innocent interpretation of monadic higher‐order quantification continues and extends a minority tradition in thinking about quantification and ontological commitment. An especially prominent member of that tradition is Stanislaw Leśniewski, and shall first draw attention to this work and its relation to that of Boolos. Secondly I shall stand up briefly for plurals as logically respectable expressions, while noting their limitations in offering ontologically deflationary accounts of higher‐order quantification. Thirdly I (...) shall focus on the key idea of ontological commitment and investigate its connection with the idea of truth‐making. Fourthly I shall consider how different interpretations of quantification may sideline Boolos's work, but finally I shall largely support his analysis of quantification involving nominal expressions, while arguing, in the spirit of Arthur Prior, that non‐nominal quantification is non‐committing. (shrink)

Theories of what it is for a mental state to be conscious must answer two questions. We must say how we're conscious of our conscious mental states. And we must explain why we seem to be conscious of them in a way that's immediate. Thomas Natsoulas distinguishes three strategies for explaining what it is for mental states to be conscious. I show that the differences among those strategies are due to the divergent answers they give to the foregoing questions. Natsoulas (...) finds most promising the strategy that amounts to the higher-order-thought hypothesis that I've defended elsewhere. But he raises a difficulty for it, which he thinks probably can be met only by modifying that strategy. I argue that this is unnecessary. The difficulty is a special case of a general question, the answer to which is independent of any issues about consciousness. So it's no part of a theory of consciousness to address the problem, much less solve it. Moreover, the difficulty seems to have intuitive force only given the picture that underlies the other two explanatory strategies, which both Natsoulas and I reject. (shrink)

In this paper we introduce the notion of a first order topological structure, and consider various possible conditions on the complexity of the definable sets in such a structure, drawing several consequences thereof.Our aim is to develop, for a restricted class of unstable theories, results analogous to those for stable theories. The “material basis” for such an endeavor is the analogy between the field of real numbers and the field of complex numbers, the former being a “nicely behaved” unstable (...) structure and the latter the archetypal stable structure. In this sense we try here to situate our work ono-minimal structures [PS] in a general topological context. Note, however, that thep-adic numbers, and structures definable therein, will also fit into our analysis.In the remainder of this section we discuss several ways of studying topological structures model-theoretically. Eventually we fix on the notion of a structure in which the topology is “explicitly definable” in the sense of Flum and Ziegler [FZ]. In §2 we introduce the hypothesis that every definable set is a Boolean combination of definable open sets. In §3 we introduce a “dimension rank” on definable sets. In §4 we consider structures on which this rank is defined, and for which also every definable set has a finite number of definably connected definable components. We show that prime models over sets exist under such conditions. (shrink)

It is shown that a formula of modal propositional logic has precisely the same models as a sentence of the first-order language of a single dyadic predicate iff its class of models is closed under ultraproducts. as a corollary, any modal formula definable by a set of first-order conditions is always definable by a single such condition. these results are then used to show that the formula (lmp 'validates' mlp) is not first-order definable.

This paper investigates the claim that the second-order consequence relation is intractable because of the incompleteness result for SOL. The opponents’ claim is that SOL cannot be proper logic since it does not have a complete deductive system. I argue that the lack of a completeness theorem, despite being an interesting result, cannot be held against the status of SOL as a proper logic.

It is well known that a degree-of-belief function P is coherent if and only if it satisfies the probability calculus. In this paper, we show that the notion of coherence can be extended to higher order probabilities such as P(P(h)=p)=q, and that a higher order degree-of-belief function P is coherent if and only if it satisfies the probability calculus plus the following axiom: P(h)=p iff P(P(h)=p)=1. Also, a number of lemmata which extend an incomplete probability function to a (...) complete one are established. (shrink)

Introduction.--Aristotle.--The seventeenth century.--The eighteenth century.--Biology.--Nature.--Evolution.--The problem.--The three elements.--The teleological order.--Appendix: Clerk Maxwell on determinism and free will. Fechner on the tendency to stability.

R. Sorensen’s argument to the effect that ’vague’ is a vague predicate has been used by D. Hyde to infer that vague predicates suffer from higher-order vagueness. M. Tye has objected (convincingly) that this is too strong: all that follows from Sorensen’s result is that there are some border border cases, but not necessarily border border cases of every vague predicate. I argue that this is still too strong: Sorensen’s proof presupposes the existence of border border cases, hence cannot (...) be used to establish that fact on pain of circularity. (shrink)

In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal (...) properties of "quantifying into" epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for finite games with mixed strategies. (shrink)

We study second order generalized quantifiers on finite structures. One starting point of this research has been the notion of definability of Lindström quantifiers. We formulate an analogous notion for second order generalized quantifiers and study definability of second order generalized quantifiers in terms of Lindström quantifiers.

The cognitive critique of the goals and desires that are input into the implicit calculations that result in instrumental rationality is one aspect of what has been termed broad rationality (Elster, 1983). This cognitive critique involves, among other things, the search for rational integration (Nozick, 1993)—that is, consistency between first-order and second-order preferences. Forming a second-order preference involves metarepresentational abilities made possible by mental decoupling operations. However, these decoupling abilities are separable from the motive that initiates the (...) cognitive critique itself. I argue that Velleman (1992) has identified that motive (“the desire to act in accordance with reasons”), and that it might be operationalisable as a thinking disposition at a very superordinate cognitive level. This thinking disposition, the Master Rationality Motive, is likely to be of particular importance in explaining individual differences in the tendency to seek rational integration. Preliminary research on related constructs suggests that this construct is measurable. (shrink)

In three experiments, we examined priming effects where primes were formed by transposing the first and last phoneme of tri‐phonemic target words (e.g., /byt/ as a prime for /tyb/). Auditory lexical decisions were found not to be sensitive to this transposed‐phoneme priming manipulation in long‐term priming (Experiment 1), with primes and targets presented in two separated blocks of stimuli and with unrelated primes used as control condition (/mul/‐/tyb/), while a long‐term repetition priming effect was observed (/tyb/‐/tyb/). However, a clear transposed‐phoneme (...) priming effect was found in two short‐term priming experiments (Experiments 2 and 3), with primes and targets presented in close temporal succession. The transposed‐phoneme priming effect was found when unrelated prime‐target pairs (/mul/‐/tyb/) were used as control and more important when prime‐target pairs sharing the medial vowel (/pys/‐/tyb/) served as control condition, thus indicating that the effect is not due to vocalic overlap. Finally, in Experiment 3, a transposed‐phoneme priming effect was found when primes sharing the medial vowel plus one consonant in an incorrect position with the targets (/byl/‐/tyb/) served as control condition, and this condition did not differ significantly from the vowel‐only condition. Altogether, these results provide further evidence for a role for position‐independent phonemes in spoken word recognition, such that a phoneme at a given position in a word also provides evidence for the presence of words that contain that phoneme at a different position. (shrink)

The system whose only predicate is identity, whose only nonlogical vocabulary is the abstraction operator, and whose axioms are all first-order instances of Frege's Axiom V is shown to be undecidable.

This paper is an attempt to develop the many-valued first-order fuzzy logic. The set of its truth, values is supposed to be either a finite chain or the interval 0, 1 of reals. These are special cases of a residuated lattice L, , , , , 1, 0. It has been previously proved that the fuzzy propositional logic based on the same sets of truth values is semantically complete. In this paper the syntax and semantics of the first-order (...) fuzzy logic is developed. Except for the basic connectives and quantifiers, its language may contain also additional n-ary connectives and quantifiers. Many propositions analogous to those in the classical logic are proved. The notion of the fuzzy theory in the first-order fuzzy logic is introduced and its canonical model is constructed. Finally, the extensions of Gödel's completeness theorems are proved which confirm that the first-order fuzzy logic is also semantically complete. (shrink)

Meehan finds fault with a number of my arguments, and proposes that better solutions to the problems I was addressing are available if we adopt a higher-order theory of consciousness. I start with some general remarks on theories of this sort. I connect what I had to say about the A-thesis with different forms of higher-order sense theories, and explain why I ignored higher-order thought theories altogether: there are compelling grounds for thinking they cannot provide a viable (...) account of phenomenal unity in phenomenal terms. Meehan. (shrink)

This chapter examines order effects on moral judgments and general moral principles in an attempt to analyze if philosophical expertise can be strengthened by moral reasoning, and then comparing such reasoning with the non-philosophers'. The chapter cites three moral principles in light of its investigation: the _doctrine of the double effect_, the principle of _moral luck_, and the concept of _action and omission_. It concludes that philosophical judgments can indeed be affected by psychological factors derived from ordinary people's conflicting (...) judgments. However, these factors can also strongly influence the general principles professional philosophers endorse. (shrink)

The Language of First-Order Logic is a complete introduction to first-order symbolic logic, consisting of a computer program and a text. The program, an aid to learning and using symbolic notation, allows one to construct symbolic sentences and possible worlds, and verify that a sentence is well formed. The truth or falsity of a sentence can be determined by playing a deductive game with the computer.

We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.

The notion of order as a universal and fundamental conceptual category is discussed as being based on sets of similar differences and different similarities. A discussion of relationships between order and disorder is followed by a proposal for a mathematical theory based on non-ordinality which could also have relevance for indistinguishables in physics.

O'Brien & Opie's position is consistent with the existence of implicit learning and subliminal perception below a subjective threshold but it is inconsistent with various other findings in the literature. The main problem with the theory is that it attributes consciousness to too many things. Incorporating the higher order thought theory renders their position more plausible.

This paper makes a comparison between naturalist and non-naturalist theories of consciousness with respect to their explanatory merits. It focuses on David Rosenthal's higher-order thought theory, arguing that the motives for higher-order theories are based on a confusion of three distinct meanings of the term 'intrinsic'. The explanatory power of HOT theories is compared with that of an alternative nonrepresentational theory, offered as an example of a naturalistic account. The latter is found overall to have more virtues and (...) less shortcomings that the higher-order theory. (shrink)

A continuum is here a primitive notion intended to correspond precisely to a path-connected subset of the usual euclidean space. In contrast, however, to the traditional treatment, we treat here continua not as pointsets, but as irreducible entities equipped only with a partial ordering ≤ interpreted as parthood. Our aim is to examine what basic topological and geometric properties of continua can be expressed in the language of ≤, and what principles we need in order to prove elementary facts (...) about them. Surprisingly enough ≤ suffices to formulate the very heart of continuity (=jumpless and gapless transitions) in a general setting. Further, using a few principles about ≤ (together with the axioms of ZFC), we can define points, joins, meets and infinite closeness. Most important, we can develop a dimension theory based on notions like path, circle, line (=one-dimensional continuum), simple line and surface (=two-dimensional continuum), recovering thereby in a rigorous way Poincaré's well-known intuitive idea that dimension expresses the ways in which a continuum can be torn apart. We outline a classification of lines according to the number of circles and branching points they contain. The ordering (C,≤) is a topped and bottomed, atomic, almost dense and complete partial ordering, weaker than a lattice. Continuous transformations from C to C are also defined in a natural way and results about them are proved. (shrink)