This book provides linguists with a clear, critical, and comprehensive overview of theoretical and experimental work on information structure. Leading researchers survey the main theories of information structure in syntax, phonology, and semantics as well as perspectives from psycholinguistics and other relevant fields. Following the editors' introduction the book is divided into four parts. The first, on theories of and theoretical perspectives on information structure, includes chapters on topic, prosody, and implicature. Part 2 covers a range of current issues in (...) the field, including focus, quantification, and sign languages, while Part 3 is concerned with experimental approaches to information structure, including processes involved in its acquisition and comprehension. The final part contains a series of linguistic case studies drawn from a wide variety of the world's language families. This volume will be the standard guide to current work in information structure and a major point of departure for future research. (shrink)

Classically, weak König's lemma and Brouwer's fan theorem for detachable bars are equivalent. We give a direct constructive proof that the former implies the latter.

精神障害の分類と診断が難しいなか、哲学や精神医学は精神障害とどのように向きあうのか。思考吹入や妄想についての哲学的考察に加え、現象学的精神病理学や精神分析の現状、そして現代の精神医学のさまざまなアプロ ーチの到達点を総観する。.

In this essay I present the philosophy of Nishida Kitarō, the father of the Kyoto School tradition, as an alternative version of transcendental philosophy. While following the steps of Kant and Husserl in important ways, Nishida attempts to take the transcendental approach even further, finally leaving us with a different view of reality that is neither realist nor idealist, but, rather, radically realist. I call this radical transcendental position, “awakened realism”. Due to word limitations, I can only set the stage (...) for further discussion on what kind of implication this may have for transcendental philosophy. But if I succeed in making my presentation clear enough, it should naturally ignite discussion on how far we can radicalize transcendental philosophy without making it into something else. (shrink)

The Dedekind cuts in an ordered set form a set in the sense of constructive Zermelo—Fraenkel set theory. We deduce this statement from the principle of refinement, which we distill before from the axiom of fullness. Together with exponentiation, refinement is equivalent to fullness. None of the defining properties of an ordering is needed, and only refinement for two—element coverings is used. In particular, the Dedekind reals form a set; whence we have also refined an earlier result by Aczel and (...) Rathjen, who invoked the full form of fullness. To further generalise this, we look at Richman's method to complete an arbitrary metric space without sequences, which he designed to avoid countable choice. The completion of a separable metric space turns out to be a set even if the original space is a proper class; in particular, every complete separable metric space automatically is a set. (shrink)

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to prove that the (...) Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. (shrink)

We present statements equivalent to some fragments of the principle of non-deterministic inductive definitions (NID) by van den Berg (2013), working in a weak subsystem of constructive set theory CZF. We show that several statements in constructive topology which were initially proved using NID are equivalent to the elementary and finitary NIDs. We also show that the finitary NID is equivalent to its binary fragment and that the elementary NID is equivalent to a variant of NID based on the notion (...) of biclosed subset. Our result suggests that proving these statements in constructive topology requires genuine extensions of CZF with the elementary or finitary NID. (shrink)

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We deal with principles which are equivalent to the statements "every mapping is sequentially nondiscontinuous", "every sequentially nondiscontinuous mapping is sequentially continuous", and "every sequentially continuous mapping is continuous". As corollaries, we show that every mapping of a complete separable space is continuous in constructive recursive mathematics (the Kreisel-Lacombe-Schoenfield-Tsejtin theorem) and in intuitionism.

We will overview the results in an informal approach to constructive reverse mathematics, that is reverse mathematics in Bishop’s constructive mathematics, especially focusing on compactness properties and continuous properties.

We will overview the results in an informal approach to constructive reverse mathematics, that is reverse mathematics in Bishop’s constructive mathematics, especially focusing on compactness properties and continuous properties.

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We show that every mapping is sequentially continuous if and only if it is sequentially nondiscontinuous and strongly extensional, and that "every mapping is strongly extensional", "every sequentially nondiscontinuous mapping is sequentially continuous", and a weak version of Markov's principle are equivalent. Also, assuming a consequence of Church's thesis, we prove a version of the Kreisel-Lacombe-Shoenfield-Tsĕitin theorem.

We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis.

ZusammenfassungIm Mittelpunkt des Beitrags steht die Übertragung ausgewählter Kapitel aus den 1955 niedergelegten autobiographischen Erinnerungen des japanischen Bakteriologen Taichi Kitashima, in denen Kitashima stark persönlich gefärbt über seinen Aufenthalt in Marburg berichtet. Wie andere japanische Mediziner seiner Generation verbrachte Kitashima mehrere Jahre in Deutschland, um dort bei dem Serumforscher Emil von Behring zu arbeiten und sich weiterzubilden. Der Kontakt war über Kitashimas Lehrer Shibasaburô Kitasato zustande gekommen, mit dem Behring in Berlin über Fragen der Immunologie geforscht hatte. Im „Kommentar“ wird (...) diskutiert, inwieweit die von Kitashima in der zeitlichen Distanz von 50 Jahren getroffene Einschätzung des Deutschlandaufenthalts als „vergeudete Zeit“ als zutreffend anzusehen ist, welche Vorteile ihm aus den europäischen Kontakten, zu denen auch Begegnungen im Pariser Pasteur-Institut gehörten, erwuchsen und aus welchen Gründen sie im Nationalsozialismus wiederbelebt wurden. (shrink)

Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. Furthermore, (...) we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum. (shrink)

We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space $\mathcal{D} (\mathbb{R})$ of test functions is equivalent to the principle BD-N which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.

In this note, we prove that certain theories of (many‐sorted) intuitionistic predicate logic are closed under the independence of premiss rule (IPR). As corollaries, we show that and extended by some non‐classical axioms and non‐constructive axioms are closed under IPR.

Consider the problem which set V of propositional variables suffices for whenever, where, and ⊢c and ⊢i denote derivability in classical and intuitionistic implicational logic, respectively. We give a direct proof that stability for the final propositional variable of the (implicational) formula A is sufficient; as a corollary one obtains Glivenko's theorem. Conversely, using Glivenko's theorem one can give an alternative proof of our result. As an alternative to stability we then consider the Peirce formula. It is an easy consequence (...) of the result above that adding a single instance of the Peirce formula suffices to move from classical to intuitionistic derivability. Finally we consider the question whether one could do the same for minimal logic. Given a classical derivation of a propositional formula not involving ⊥, which instances of the Peirce formula suffice as additional premises to ensure derivability in minimal logic? We define a set of such Peirce formulas, and show that in general an unbounded number of them is necessary. (shrink)

We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space $\mathcal{D} (\mathbb{R})$ of test functions is equivalent to the principle BD-N which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.

We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval ) is equivalent to weak König lemma ) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to \ for convex trees, in the framework of constructive reverse mathematics.

We give a variant of the Gödel-Gentzen-negative translation, and a syntactic characterization which entails conservativity result for formulas.

How are the various classically equivalent definitions of compactness for metric spaces constructively interrelated? This question is addressed with Bishop-style constructive mathematics as the basic system – that is, the underlying logic is the intuitionistic one enriched with the principle of dependent choices. Besides surveying today's knowledge, the consequences and equivalents of several sequential notions of compactness are investigated. For instance, we establish the perhaps unexpected constructive implication that every sequentially compact separable metric space is totally bounded. As a by-product, (...) the fan theorem for detachable bars of the complete binary fan proves to be necessary for the unit interval possessing the Heine-Borel property for coverings by countably many possibly empty open balls. (shrink)

We extend the concept of apartness spaces to the concept of quasi-apartness spaces. We show that there is an adjunction between the category of quasi-apartness spaces and the category of neighbourhood spaces, which indicates that quasi-apartness is a more natural concept than apartness. We also show that there is an adjoint equivalence between the category of apartness spaces and the category of Grayson’s separated spaces.

The standard construction of quotient spaces in topology uses full separation and power sets. We show how to make this construction using only the predicative methods available in constructive type theory and constructive set theory.

Consistency with the formal Church’s thesis, for short CT, and the axiom of choice, for short AC, was one of the requirements asked to be satisfied by the intensional level of a two-level foundation for constructive mathematics as proposed by Maietti and Sambin From sets and types to topology and analysis: practicable foundations for constructive mathematics, Oxford University Press, Oxford, 2005). Here we show that this is the case for the intensional level of the two-level Minimalist Foundation, for short MF, (...) completed in 2009 by the second author. The intensional level of MF consists of an intensional type theory à la Martin-Löf, called mTT. The consistency of mTT with CT and AC is obtained by showing the consistency with the formal Church’s thesis of a fragment of intensional Martin-Löf’s type theory, called \, where mTT can be easily interpreted. Then to show the consistency of \ with CT we interpret it within Feferman’s predicative theory of non-iterative fixpoints \ by extending the well known Kleene’s realizability semantics of intuitionistic arithmetics so that CT is trivially validated. More in detail the fragment \ we interpret consists of first order intensional Martin-Löf’s type theory with one universe and with explicit substitution rules in place of usual equality rules preserving type constructors -rule which is not valid in our realizability semantics). A key difficulty encountered in our interpretation was to use the right interpretation of lambda abstraction in the applicative structure of natural numbers in order to model all the equality rules of \ correctly. In particular the universe of \ is modelled by means of \-fixpoints following a technique due first to Aczel and used by Feferman and Beeson. (shrink)

We investigate separation properties for neighbourhood spaces in some details within a framework of constructive mathematics, and define corresponding separation properties for quasi-apartness spaces. We also deal with separation properties for spaces with inequality.

We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic $\mathbf {IQC}$ and first-order arithmetic $\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic $\mathbf {IPC}$. To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata in (...) $\mathbf {IQC}$ and a separation theorem of a sentence from a set of schemata in $\mathbf {HA}$. We see several examples which give us separations among omniscience principles. (shrink)

In this paper, I argue that later Nishida's analysis of self-awareness (jikaku) provides a new perspective on the nature of self-awareness as understood in the philosophical literature today. I argue that the contemporary literature deals with two kinds of self-awareness; the higher-order theory understands self-awareness to be an objectified awareness and the phenomenological tradition generally understands self-awareness to be, at least primarily, a non-objectified awareness. In light of this, I first give an account of Nishida's ?acting-intuition? with reference to the (...) ?historical body.? Then I argue that later Nishida's analysis of self-awareness depicts the inadequacy of the two kinds of self-awareness as both being stuck in the subject-object dichotomy which, according to Nishida, is but one mode of experience, namely the mode of difference. Nishida provides an account that ultimately foregrounds the experiential mode of unity that negates any sense of differentiation between the subject and object. (shrink)

In this paper we introduce effectiveness into model theory of intuitionistic logic. The main result shows that any computable theory T of intuitionistic predicate logic has a Kripke model with decidable forcing such that for any sentence φ, φ is forced in the model if and only if φ is intuitionistically deducible from T.

Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.

We deal with a restricted form WC-N' of the weak continuity principle, a version BT' of Baire's theorem, and a boundedness principle BD-N. We show, in the spirit of constructive reverse mathematics, that WC-N'. BT' + ¬LPO and BD-N + ¬LPO are equivalent in a constructive system, where LPO is the limited principle of omniscience.

In this paper, we deal with compact operators on a Hilbert space, within the framework of Bishop's constructive mathematics. We characterize the compactness of a bounded linear mapping of a Hilbert space into C n , and prove the theorems: Let A and B be compact operators on a Hilbert space H , let C be an operator on H and let α ϵ C . Then α A is compact, A + B is compact, A ∗ is compact, CA (...) is compact and if C ∗ exists, then AC is compact; An operator on a Hilbert space has an adjoint if and only if it is weakly compact. (shrink)