This paper embeds the core part of Discourse Representation Theory in the classical theory of types plus a few simple axioms that allow the theory to express key facts about variables and assignments on the object level of the logic. It is shown how the embedding can be used to combine core analyses of natural language phenomena in Discourse Representation Theory with analyses that can be obtained in Montague Semantics.

Are there are normative reasons to have – or refrain from having – certain emotions? The dominant view is that there are. I disagree. In this paper, I argue for Strong Eliminativism – the view that there are no reasons for emotions. My argument for this claim has two premises. The first premise is that there is a deliberative constraint on reasons: a reason for an agent to have an attitude must be able to feature in that agent’s deliberation to (...) that attitude. My argument for this premise is that in order to have reasons for an attitude, we need to be able to exhibit some relevant form of control over this attitude, and this relevant form of control is deliberative control. The second premise is that no one can deliberate to any emotion. My argument for this premise turns on the claim that there is no deliberative question that is settled by forming (or giving up) an emotion. I contend that this is so due to the well-known phenomenon of recalcitrant emotions: for any deliberative question that can be settled, there is no guarantee that the relevant emotional state will follow (or be revised). Strong Eliminativism follows from these two premises. (shrink)

In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic.

A logic is called higher order if it allows for quantification over higher order objects, such as functions of individuals, relations between individuals, functions of functions, relations between functions, etc. Higher order logic began with Frege, was formalized in Russell [46] and Whitehead and Russell [52] early in the previous century, and received its canonical formulation in Church [14].1 While classical type theory has since long been overshadowed by set theory as a foundation of mathematics, recent decades have shown remarkable (...) comebacks in the fields of mechanized reasoning (see, e.g., Benzm¨. (shrink)

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it (...) is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of (...) this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization. (shrink)

In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent logics once the right (...) set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s [4] and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants. (shrink)

The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is non-directional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators.

In this paper we discuss a new perspective on the syntax-semantics interface. Semantics, in this new set-up, is not ‘read off’ from Logical Forms as in mainstream approaches to generative grammar. Nor is it assigned to syntactic proofs using a Curry-Howard correspondence as in versions of the Lambek Calculus, or read off from f-structures using Linear Logic as in Lexical-Functional Grammar (LFG, Kaplan & Bresnan [9]). All such approaches are based on the idea that syntactic objects (trees, proofs, fstructures) are (...) somehow prior and that semantics must be parasitic on those syntactic objects. We challenge this idea and develop a grammar in which syntax and semantics are treated in a strictly parallel fashion. The grammar will have many ideas in common with the (converging) frameworks of categorial grammar and LFG, but its treatment of the syntax-semantics interface is radically different. Also, although the meaning component of the grammar is a version of Montague semantics and although there are obvious affinities between Montague’s conception of grammar and the work presented here, the grammar is not compositional, in the sense that composition of meaning need not follow surface structure. (shrink)

This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable.

The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which finite sequences of lambda terms are the basic data structures, (...) pairs of terms syntax, semantics for example. These sequences then combine with the help of simple generalizations of the usual abstraction and application operations. This theory, which I call Lambda Grammars and which is closely related to the independently formulated theory of Abstract Categorial Grammars (de Groote, 2001; de Groote, 2002), in fact is an implementation of Curry’s ideas: the level of tectogrammar is encoded by the sequences of lambda-terms and their ways of combination, while the syntactic terms in those sequences constitute the phenogrammatical level. In de Groote’s formulation of the theory, tectogrammar is the level of abstract terms, while phenogrammar is the level of object terms. (shrink)

This contribution focuses on three aspects of Nietzsche’s art of living that have become relevant today especially in the United States (but not only here): first, regarding some facets of the economic-political conditions of any contemporary art of living; second, the widespread adoption of Nietzsche’s notion of self-overcoming and artistic self-design in entrepreneurship and individual’s lives; and third, how his notion of ‘incorporation’ has been further developed in current approaches to habit design. Eventually I will show via the example of (...) Anthony Robbins that some notions of Nietzsche’s art of living have become most popular outside of academia, namely in the commercial industries of what has been called ‘self-growth’ or ‘self-development.’. (shrink)

In "Making Sense of Animal Disenhancement" Adam Henschke provides a framework for fully understanding and evaluating animal disenhancement. His conclusion is that animal disenhancement is neither morally nor pragmatically justified. In this paper I argue that Henschke misapplies his own framework for understanding disenhancement, resulting in a stronger conclusion than is justified. In diagnosing his misstep, I argue that the resources he has provided us, combined with my refinements, result in two new avenues for inquiry: an application of concepts from (...) political theory to disenhancement, and an inquiry in to the mode of valuation that underlies industrial animal agriculture and disenhancement proposals. (shrink)

This essay investigates, via the concepts of the philosophy of orientation, Annie Duke’s decision-making theory in "Thinking in Bets" and scrutinizes as to what extent one can universalize the 'orientation skill' of decision-making with regard to our everyday and professional life.

Vector models of language are based on the contextual aspects of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, the denotations of phrases, and their compositional properties. In the latter approach the denotation of a sentence determines its truth conditions and can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In this short paper, we develop a vector semantics for language based (...) on the simply typed lambda calculus. Our semantics uses techniques familiar from the truth conditional tradition and is based on a form of dynamic interpretation inspired by Heim's context updates. (shrink)

We present Logical Description Grammar (LDG), a model ofgrammar and the syntax-semantics interface based on descriptions inelementary logic. A description may simultaneously describe the syntacticstructure and the semantics of a natural language expression, i.e., thedescribing logic talks about the trees and about the truth-conditionsof the language described. Logical Description Grammars offer a naturalway of dealing with underspecification in natural language syntax andsemantics. If a logical description (up to isomorphism) has exactly onetree plus truth-conditions as a model, it completely specifies thatgrammatical (...) object. More common is the situation, corresponding tounderspecification, in which there is more than one model. A situation inwhich there are no models corresponds to an ungrammatical input. (shrink)

This essay proposes that Socrates practiced various spiritual exercises, including meditation, and that this Socratic practice of meditation was habitual, aimed at cultivating emotional self-control and existential preparedness. Contemporary research in neurobiology supports the view that intentional mental actions, including meditation, have a profound impact on brain activity, neuroplasticity, and help engender emotional self-control. This impact on brain activity is confirmed via technological developments, a prime example of how technology benefits humanity. Socrates attains the balanced emotional self-control that Alcibiades describes (...) in the Symposium because of the sustained mental effort he exerts that directly impacts his brain and his emotional and philosophical life. The essay concludes that Socratic meditative practices aimed at manifesting true dignity as human beings within the complexities of a technological world offer a promising model of self-care worthy of embracing today. (shrink)

In this paper it is shown how simple texts that can be parsed in a Lambek Categorial Grammar can also automatically be provided with a semantics in the form of a Discourse Representation Structure in the sense of Kamp [1981]. The assignment of meanings to texts uses the Curry-Howard-Van Benthem correspondence.

There are two kinds of semantic theories of anaphora. Some, such as Heim’s File Change Semantics, Groenendijk and Stokhof’s Dynamic Predicate Logic, or Muskens’ Compositional DRT (CDRT), seem to require full coindexing of anaphora and their antecedents prior to interpretation. Others, such as Kamp’s Discourse Representation Theory (DRT), do not require this coindexing and seem to have an important advantage here. In this squib I will sketch a procedure that the first group of theories may help themselves to so that (...) they can interleave interpretation and coindexing in DRT’s way. (shrink)

Nietzsche and Shaw are famous and infamous: famous for their innovative and influential forms of writing, but infamous for their apparent support of totalitarianism and Nazism. However, while it has long been shown that Nietzsche’s provocative language about “breeding” and “masters and slaves” was intended to enhance culture through competition, it is still an open question how and when Shaw supported biological eugenics. Via Nietzsche’s “philosophical breeding,” this article presents a new reading of Shaw’s Man and Superman: on the one (...) hand, it contrasts Nietzsche’s philosophical Übermensch with Shaw’s eugenic Superman; and on the other hand, it connects Nietzsche’s agonistic enhancement of culture with Shaw’s philosophical reflections in “Don Juan in Hell.” In contrast to Tanner’s support of eugenic breeding in his Revolutionist’s Handbook, Shaw’s Don Juan remarkably resembles Nietzsche’s notion of “philosophical breeding” toward a more competent, truthful, and autonomous orientation that is needed in increasingly complex global politics. (shrink)

Ambiguities in natural language can multiply so fast that no person or machine can be expected to process a text of even moderate length by enumerating all possible disambiguations. A sentence containing $n$ scope bearing elements which are freely permutable will have $n!$ readings, if there are no other, say lexical or syntactic, sources of ambiguity. A series of $m$ such sentences would lead to $(n!)^m$ possibilities. All in all the growth of possibilities will be so fast that generating readings (...) first and testing their acceptability afterwards will not be feasible. -/- This insight has led a series of researchers to adopt a level of representation at which ambiguities remain unresolved. The idea here is not to generate and test many possible interpretations but to first generate one `underspecified' representation which in a sense represents all its complete specifications and then use whatever information is available to further specify the result. -/- One central hypothesis in the paper will be that the relation between an underspecified representation and its full representations is not so much the relation between one structure and a set of other structures but is in fact the relation between a description (a set of logical sentences) and its models. (shrink)

This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation . It is explained how making this distinction obviates the need for directed types in type-theoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a lambda term representing its manifestation, (...) but also to a lambda term representing its semantics. (shrink)

Kant said that existence is not a predicate and Russell agreed, arguing that a sentence such as ‘The king of France exists’, which seems to attribute existence to the king of France, really has a logical form that is not reflected in the surface structure of the sentence at all. While the surface form of the sentence consists of a subject and a predicate, the underlying logical form, according to Russell, is the formula given in. This formula obviously has no (...) subjectpredicate form and in fact has no single constituent that corresponds to the verb phrase ‘exists’ in the surface sentence. ∃x∀y The importance of Russell’s analysis becomes clear when we consider ‘The king of France does not exist’. If this sentence would attribute non-existence to the king it should entail that there is someone who does not exist, just as ‘Mary doesn’t like bananas’ entails that there is someone who doesn’t like bananas. Thus the idea that all sentences have subject-predicate form has led some philosophers to the view that there are objects that lack existence. This embarrassing position can be avoided once Russell’s analysis is accepted: if ‘The king of France does not exist’ is formalised as the negation of formula, no unwanted consequences follow. (shrink)

During the last years of his life, the mathematician Karl Menger worked on a biography of his father, the economist and founder of the Austrian School of Economics, Carl Menger. The younger Menger never finished the work. While working in the Menger collections at Duke University’s David M. Rubenstein Rare Book and Manuscript Library, we discovered draft chapters of the biography, a valuable source of information given that relatively little is known about Carl Menger’s life nearly a hundred years after (...) his death. The unfinished biography covers Carl Menger’s family background and his life through early 1889. In this article, we discuss the biography and the most valuable new insights it provides into Carl Menger’s life, including Carl Menger’s family, his childhood, his student years, his time working as a journalist and newspaper editor, his early scientific career, and his relationship with Crown Prince Rudolf. (shrink)

An attractive way to model the relation between an underspecified syntactic representation and its completions is to let the underspecified representation correspond to a logical description and the completions to the models of that description. This approach, which underlies the Description Theory of Marcus et al. 1983 has been integrated in Vijay-Shanker 1992 with a pure unification approach to Lexicalized Tree-Adjoining Grammars (Joshi et al. 1975, Schabes 1990). We generalize Description Theory by integrating semantic information, that is, we propose to (...) tackle both syntactic and semantic underspecification using descriptions. (shrink)

Standard approaches to proper names, based on Kripke's views, hold that the semantic values of expressions are (set-theoretic) functions from possible worlds to extensions and that names are rigid designators, i.e.\ that their values are \emph{constant} functions from worlds to entities. The difficulties with these approaches are well-known and in this paper we develop an alternative. Based on earlier work on a higher order logic that is \emph{truly intensional} in the sense that it does not validate the axiom scheme of (...) Extensionality, we develop a simple theory of names in which Kripke's intuitions concerning rigidity are accounted for, but the more unpalatable consequences of standard implementations of his theory are avoided. The logic uses Frege's distinction between sense and reference and while it accepts the rigidity of names it rejects the view that names have direct reference. Names have constant denotations across possible worlds, but the semantic value of a name is not determined by its denotation. (shrink)

The Common Core State Standards are an initiative to adopt a uniform set of kindergarten through 12th-grade mathematics and English educational standards throughout the United States. Many Christian schools are also voluntarily adopting Common Core standards. This article examines whether such a practice is truly in the best interest of students and parents by considering the compatibility of Common Core with a classical Christian philosophy of education. This article begins with an analysis of Common Core standards to identify the foundational (...) philosophy of education inherent in Common Core. This philosophy of education is then contrasted with the classical Christian philosophy of education to discern whether Common Core is compatible with the Christian core that should be at the heart of every Christian school. (shrink)

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms (...) of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the 20th century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory. (shrink)

This article explains Blumenberg's reluctance to make humankind the saviour of nature, and the implied scepticism towards environmental politics.

Logic has its roots in the study of valid argument, but while traditional logicians worked with natural language directly, modern approaches first translate natural arguments into an artificial language. The reason for this step is that some artificial languages now have very well developed inferential systems. There is no doubt that this is a great advantage in general, but for the study of natural reasoning it is a drawback that the original linguistic forms get lost in translation. An alternative approach (...) would be to develop a general theory of the natural logic behind human reasoning and human information processing by studying formal logics that operate directly on linguistic representations. That this is possible we will try to make plausible in this paper. It will turn out that one level of representation, that of Logical Form, can meaningfully be identified with the language of an existing and well-understood logic, a restricted form of the theory of types. It is not difficult to devise inference systems for this language, and it is thus possible to study reasoning systems that are based directly on language. (shrink)

In mathematical languages and in predicate logic coreferential terms can be interchanged in any sentence without altering the truth value of that sentence. Replacing 3 + 5 by 12 − 4 in any formula of arithmetic will never lead from truth to falsity or from falsity to truth. But natural languages are different in this respect. While in some contexts it is always allowed to interchange coreferential terms, other contexts do not admit this. An example of the first sort of (...) context is likes bananas: for any two coreferential noun phrases A and B the sentence A likes bananas is true if and only if B likes bananas is. A context that does not allow intersubstitution of coreferents is The Ancients knew that appears at dawn. If we fill the hole with the noun phrase the Morning Star we get the true (1a), while if we plug in the Evening Star we get the false (1b). Yet the Morning Star and the Evening Star both refer to the planet Venus and are thus coreferential. (shrink)

In this paper it is shown how a formal theory of interpretation in Montague’s style can be reconciled with a view on meaning as a social construct. We sketch a formal theory in which agents can have their own theory of interpretation and in which groups can have common theories of interpretation. Frege solved the problem how different persons can have access to the same proposition by placing the proposition in a Platonic realm, independent from all language users but accessible (...) to all of them. Here we explore the alternative of letting meaning be socially constructed. The meaning of a sentence is accessible to each member of a linguistic community because the way the sentence is to be interpreted is common knowledge among the members of that community. Misunderstandings can arise when the semantic knowledge of two or more individuals is not completely in sync. (shrink)

In a recent paper we have defined an analytic tableau calculus PL_16 for a functionally complete extension of Shramko and Wansing's logic based on the trilattice SIXTEEN_3. This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic---such as the relations |=_t, |=_f, and |=_i that each correspond to a lattice order in SIXTEEN_3; and |=, the intersection of |=_t and |=_f,. -/- It turns out that our method of characterising these semantic relations---as (...) intersections of auxiliary relations that can be captured with the help of a single calculus---lends itself well to proving interpolation. All entailment relations just mentioned have the interpolation property, not only when they are defined with respect to a functionally complete language, but also in a range of cases where less expressive languages are considered. For example, we will show that |=, when restricted to L_{tf}, the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano. (shrink)

Der Titel des Bandes greift eine Frage auf, die im alltäglichen Umgang aufkam: die Frage nach analytischer Philosophie, vom Rücksitz eines Autos gestellt. Dieser Kontext bot den Anlass, eine Herangehensweise zu wählen, die bislang nicht üblich war: auszuprobieren, was eine Einbeziehung des Alltags und Umgangs erbringen könnte, ohne auf Komplexität zu verzichten. -/- Diese Öffnung hat zu überraschenden Ergebnissen geführt, die eine Weiterentwicklung der analytischen Philosophie erlauben, auch und in besonderer Weise theoretisch: Die Beachtung von umgangsprachlichem Verhalten kann dabei behilflich (...) sein, Sprache besser zu verstehen, als dies eine traditionelle wissenschaftsphilosophische Ausrichtung ermöglichen würde. -/- Die Beiträge zu diesem Band haben Kathrina Talmi, Reinhard Matern und Kai Pege eingebracht. (shrink)

This book offers the first comprehensive collection of essays on the key concepts of Kitaro Nishida (1870-1945), the father of modern Japanese philosophy and founder of the Kyoto School. The essays analyze several of the major philosophical concepts in Nishida, including pure experience, absolute will, place, and acting intuition. They examine the meaning and positioning of Nishida’s philosophy in the history of philosophy, as well as in the contemporary world, and discuss the relevance of his philosophy in the present context. (...) The book next looks at the significance of Nishida’s philosophy in the wider contexts of science, arts, and religion. The book includes a glossary of key terms that have been translated in a unified manner throughout the volume. (shrink)

The battle of Little Bighorn in 1876 marked the beginning of the end of conflict between the U.S. and its military against the various Native American tribes west of the Mississippi River. Historians have given us various ideas of why Lieutenant Colonel Custer met with defeat. But none have noted, in connection with the November 3rd “secret meeting” between Grant and his generals, a movement of troops away from the Black Hills even before decisions were supposedly made to no longer (...) keep miners out of that sacred land. When we study attitude and orders in conjunction with what we know about these events, the idea emerges that the government knew that they couldn’t get the Indians to break the Fort Laramie Treaty unless they were attacked. Here, then, is a presentation of the possibility of deliberate defeat by the U.S. government and its military in order to take the Black Hills. (shrink)

Die Erörterung über Zivilisationen und die Goldenen Regeln ist zentral ein sprachliches Projekt, das dazu dienen soll, eine angemessene Bedeutung und mittels dieser einen möglichen Bezug zu finden. Reinhard Matern sucht und entwickelt ein Kriterium, um zivilisierte von unzivilisierten Gesellschaften zu differenzieren und nutzt dabei die weltweit entstandenen Goldenen Regeln, die er im Plural anführt, weil sich die überlieferten Formulierungen konkret unterscheiden. Es sind jedoch nicht die Unterschiede, sondern es ist das Gemeinsame, das ihn auf dem Weg zu einem (...) allgemeinen Kriterium interessiert. -/- Primär im ersten Jahrtausend vor unserer Zeitrechnung werden Spruchweisheiten notiert, über deren Ursprünge nichts bekannt ist. Die Goldenen Regel erlauben gegenüber dem formalisierten Vergeltungsrecht eine grundsätzlich andere Herangehenweise an menschliches Verhalten, ist auf Gleichbehandlung ausgerichtet. Diese vergleichsweise moderne Haltung ermöglicht es, ein allgemeines Kriterium zu bilden. Empirisch ist Gleichbehandlung in heutigen Gesellschaften jedoch immer noch nicht vollzogen, eine Zivilisation deshalb noch nicht erlangt. -/- Zum Abschluss findet sich ein Ausblick, der eine Erweiterung der Perspektive aufgrund zukünftiger Entwicklungen anstrebt: die Integration von humanoiden Robotern. (shrink)

Russell's a priori postulates of empirist theories of knowledge. Kurze Darstellung von Russells Postulaten als Ermöglichung einer empiristischen Erkenntnistheorie.

I want to show that truth is an important concept, and that it can be explained. However, we must deal with what are called ‘deflationist’ concepts of truth first. Deflationism is the view that there is nothing more to be said about truth once a semantic theory for the truth-predicate (such as Tarski's) has been provided.

We discuss two models of virtue cultivation that are present throughout the Republic: the self-mastery model and the harmony model. Schultz (2013) discusses them at length in her recent book, Plato’s Socrates as Narrator: A Philosophical Muse. We bring this Socratic distinction into conversation with two modes of intentional regulation strategies articulated by James J. Gross. These strategies are expressive suppression and cognitive reappraisal. We argue that that the Socratic distinction helps us see the value in cognitive reappraisal and that (...) the contemporary neurological research supports the wide range of attitudes toward the value of emotional experience that mirror those found in the Republic. (shrink)

This is a short reminder that Bertrand Russell suggested a number of a priori postulates which are to serve as foundation for an empiricist philsophy.

Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In the vector models, (...) the degree of co-occurrence of words in context determines how similar the meanings of words are. In this paper, we put these two models together and develop a vector semantics for language based on the simply typed lambda calculus models of natural language. We provide two types of vector semantics: a static one that uses techniques familiar from the truth conditional tradition and a dynamic one based on a form of dynamic interpretation inspired by Heim’s context change potentials. We show how the dynamic model can be applied to entailment between a corpus and a sentence and provide examples. (shrink)

The article gives a short characterization of Russell's solution to Hume's problem: empirical postulates.

This paper uses classical logic for a simultaneous description of the syntax and semantics of a fragment of English and it is argued that such an approach to natural language allows procedural aspects of linguistic theory to get a purely declarative formulation. In particular, it will be shown how certain construction rules in Discourse Representation Theory, such as the rule that indefinites create new discourse referents and definites pick up an existing referent, can be formulated declaratively if logic is used (...) as a metalanguage for English. In this case the declarative aspects of a rule are highlighted when we focus on the model theory of the description language while a procedural perspective is obtained when its proof theory is concentrated on. Themes of interest are Discourse Representation Theory, resolution of anaphora, resolution of presuppositions, and underspecification. (shrink)