SEMANTIC ARITHMETIC: A PREFACE John Corcoran Abstract Number theory, or pure arithmetic, concerns the natural numbers themselves, not the notation used, and in particular not the numerals. String theory, or pure syntax, concems the numerals as strings of «uninterpreted» characters without regard to the numbe~s they may be used to denote. Number theory is purely arithmetic; string theory is purely syntactical... in so far as the universe of discourse alone is considered. Semantic arithmetic is a broad subject which begins (...) when numerals are mentioned (not just used) and mentioned as names of numbers (not just as syntactic objects). Semantic arithmetic leads to many fascinating and surprising algorithms and decision procedures; it reveals in a vivid way the experiential import of mathematical propositions and the predictive power of mathematical knowledge; it provides an interesting perspective for philosophical, historical, and pedagogical studies of the growth of scientific knowledge and of the role metalinguistic discourse in scientific thought. (shrink)

Semantics plays a role in grammar in at least three guises. (A) Linguists seek to account for speakers‘ knowledge of what linguistic expressions mean. This goal is typically achieved by assigning a model theoretic interpretation in a compositional fashion. For example, *No whale flies* is true if and only if the intersection of the sets of whales and fliers is empty in the model. (B) Linguists seek to account for the ability of speakers to make various inferences based on (...) semantic knowledge. For example, *No whale flies* entails *No blue whale flies* and *No whale flies high*. (C) The wellformedness of a variety of syntactic constructions depends on morpho-syntactic features with a semantic flavor. For example, *Under no circumstances would a whale fly* is grammatical, whereas *Under some circumstances would a whale fly* is not, corresponding to the downward vs. upward monotonic features of the preposed phrases. It is usually assumed that once a compositional model theoretic interpretation is assigned to all expressions, its fruits can be freely enjoyed by inferencing and syntax. What place might proof theory have in this picture? (shrink)

Philosophical questions about minds and computation need to focus squarely on the mathematical theory of Turing machines (TM's). Surrogate TM's such as computers or formal systems lack abilities that make Turing machines promising candidates for possessors of minds. Computers are only universal Turing machines (UTM's)—a conspicuous but unrepresentative subclass of TM. Formal systems are only static TM's, which do not receive inputs from external sources. The theory of TM computation clearly exposes the failings of two prominent critiques, Searle's Chinese room (...) (1980) and arguments from Gödel's Incompleteness theorems (e.g., Lucas, 1961; Penrose, 1989), both of which fall short of addressing the complete TM model. Both UTM-computers and formal systems provide an unsound basis for debate. In particular, their special natures easily foster the misconception that computation entails intrinsically meaningless symbol manipulation. This common view is incorrect with respect to full-fledged TM's, which can process inputs non-formally, i.e., in a subjective and dynamically evolving fashion. To avoid a distorted understanding of the theory of computation, philosophical judgments and discussions should be grounded firmly upon the complete Turing machine model, the proper model for real computers. (shrink)

In this paper I submit that the “Chinese room” argument rests on the assumption that understanding a sentence necessarily implies being conscious of its content. However, this assumption can be challenged by showing that two notions of consciousness come into play, one to be found in AI, the other in Searle’s argument, and that the former is an essential condition for the notion used by Searle. If Searle discards the first, he not only has trouble explaining how we can learn (...) a language but finds the validity of his own argument in jeopardy. (shrink)

Turner argues that computer programs must have purposes, that implementation is not a kind of semantics, and that computers might need to understand what they do. I respectfully disagree: Computer programs need not have purposes, implementation is a kind of semantic interpretation, and neither human computers nor computing machines need to understand what they do.

The central claim of this paper is that surface-faithful word-by-word update is feasible and desirable, even in languages where word order is supposedly free. As a first step, in sections 1 and 2, I review an argument from Bittner 2001a that semantic composition is not a static process, as in PTQ, but rather a species of anaphoric bridging. But in that case the context-setting role of word order should extend from cross-sentential discourse anaphora to sentence-internal anaphoric composition. This can be (...) spelled out as a two-part hypothesis. First, in all languages anaphoric composition derives incremental updates based on the topological order rather than the syntactic hierarchy. And secondly, rigid vs. free word order is simply rigid vs. free mapping from syntax to topology. To formalize this hypothesis, I first present, in section 3, Sevensorted Logic of Change with Centering. This makes it possible, in section 4, to articulate a system of constraints on basic meanings in Kalaallisut — a polysynthetic language with free word order, ideally suited to test the hypothesis of incremental update. The key assumptions about topology as the input to anaphoric composition are spelled out in section 5, which concludes the development of a general formal framework. This formal framework then serves, in sections 6 through 8, t o explicate topologically based incremental updates for increasingly more complex samples of an actual Kalaallisut text. This reveals ubiquitous patterns of prominence-guided anaphora, in all semantic domains, t o increasingly more complex types of discourse referents. These anaphoric patterns show that the context-setting role of word order indeed does extend from discourse to word-to-word anaphora. And this, in turn, strongly supports the hypothesis of topologically based anaphoric composition. Finally, in section 9 I adduce evidence from English that this hypothesis also holds for languages with rigid word order, albeit the fixed mapping keeps the topology close to the syntax. I conclude that both free and rigid word orders receive a natural account if semantic composition is viewed as topologically based anaphoric bridging.. (shrink)

This paper is the twin of (Duží and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperprop- ositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary be- lieves that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible- world propositional contexts.) One (...) rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, sub- stitutivity of co-referential (as opposed to co-denoting or synony- mous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperinten- sions preserving transparency and compositionality in hyperinten- sional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichý’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyper- intension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hy- perintensions. (shrink)

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)

Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...) of true that attribution of being true to a given thing presupposes the thing is a sentence. Beta’s importance is further highlighted by the fact that alpha can be satisfied using the recursively definable concept of being satisfied by every infinite sequence, which Tarski explicitly rejects. Moreover, in Definition 23, the famous truth-definition, Tarski supplements “being satisfied by every infinite sequence” by adding the condition “being a sentence”. Even where truth is undefinable and treated by Tarski axiomatically, he adds as an explicit axiom a sentence to the effect that every truth is a sentence. Surprisingly, the sentence just before the presentation of Convention T seems to imply that alpha alone might be sufficient. Even more surprising is the sentence just after Convention T saying beta “is not essential”. Why include a condition if it is not essential? Tarski says nothing about this dissonance. Considering the broader context, the Polish original, the German translation from which the English was derived, and other sources, we attempt to determine what Tarski might have intended by the two troubling sentences which, as they stand, are contrary to the spirit, if not the letter, of several other passages in Tarski’s corpus. (shrink)

The question “what is an interpretation?” is often intertwined with the perhaps even harder question “what is a scientific theory?”. Given this proximity, we try to clarify the first question to acquire some ground for the latter. The quarrel between the syntactic and semantic conceptions of scientific theories occupied a large part of the scenario of the philosophy of science in the 20th century. For many authors, one of the two currents needed to be victorious. We endorse that such debate, (...) at least in the terms commonly expressed, can be misleading. We argue that the traditional notion of “interpretation” within the syntax/semantic debate is not the same as that of the debate concerning the interpretation of quantum mechanics. As much as the term is the same, the term “interpretation” as employed in quantum mechanics has its meaning beyond (pure) logic. Our main focus here lies on the formal aspects of the solutions to the measurement problem. There are many versions of quantum theory, many of them incompatible with each other. In order to encompass a wider variety of approaches to quantum theory, we propose a different one with an emphasis on pure formalism. This perspective has the intent of elucidating the role of each so-called “interpretation” of quantum mechanics, as well as the precise origin of the need to interpret it. (shrink)

The first aim of the paper is to show that under certain conditions generative syntax can be made suitable for Montague semantics, based on his type logic. One of the conditions is to make branching in the so-called X-bar syntax strictly binary, This makes it possible to provide an adequate semantics for Noun Phrases by taking them as referring to sets of collections of sets of entities ( type <ett,t>) rather than to sets of sets of (...) entities (ett). (shrink)

The paper develops some of the conclusions, reached in Floridi (2007), concerning the future developments of Information and Communication Technologies (ICTs) and their impact on our lives. The two main theses supported in that article were that, as the information society develops, the threshold between online and offline is becoming increasingly blurred, and that once there won't be any significant difference, we shall gradually re-conceptualise ourselves not as cyborgs but rather as inforgs, i.e. socially connected, informational organisms. In this paper, (...) I look at the development of the so-called Semantic Web and Web 2.0 from this perspective and try to forecast their future. Regarding the Semantic Web, I argue that it is a clear and well-defined project, which, despite some authoritative views to the contrary, is not a promising reality and will probably fail in the same way AI has failed in the past. Regarding Web 2.0, I argue that, although it is a rather ill-defined project, which lacks a clear explanation of its nature and scope, it does have the potentiality of becoming a success (and indeed it is already, as part of the new phenomenon of Cloud Computing) because it leverages the only semantic engines available so far in nature, us. I conclude by suggesting what other changes might be expected in the future of our digital environment. (shrink)

Many philosophers think that being in an intentional state is a matter of being related to a sentence in a mental language-a 'Language of Thought' (see especially Fodor 1975, 1987 Appendix; Field 1978). According to this view-which I shall call 'the LT hypothesis'-when anyone has a belief or a desire or a hope with a certain content, they have a sentence of this language, with that content, 'written' in their heads. The claim is meant quite literally: the mental representations that (...) make up the items of this language have semantic and syntactic properties. This is why, according to this view, cognitive psychology does, and should, treat that part of the mind which deals with intentional states as a semantic and a syntactic 'engine'. (shrink)

This paper highlights a small selection of cases where crosslinguistic insights have been important to big questions in the theory of semantics and the syntax/semantics interface. The selection includes (i) the role and representation of Speaker and Addressee in the grammar; (ii) mismatches between form and interpretation motivating high-placed silent operators for functional elements; and (iii) the explanation of semantic universals, including universals pertaining to inventories, in terms of learnability and the trade-off between informativeness and simplicity.

At the turn of the century, electronic mail emerged as a core mode of communication, fundamentally transforming the way individuals and organizations interact. In this digital age, one ubiquitous representational device is the email address. Given the importance of email addresses in our lives, it is natural to ask: what do email addresses represent? And how do they represent it? Given that email addresses have a semantic interpretation, and that they have a formal syntax, it is reasonable to assume (...) that they have a compositional semantics. Do they? If so, what is it? (shrink)

Many attempts to define depiction appeal to viewers' perceptual responses. Such accounts are liable to give a central role in determining depictive content to picture features responsible for the response, design. A different project is to give a compositional semantics for depictive content. Such attempts identify syntax: picture features systematically responsible for the content of the whole. Design and syntax are competitors. But syntax requires system, in how picture features contribute to content, that design does not. (...) By examining John Kulvicki's semantics for basic depictive content, I argue that the relevant systematicity is absent from the pictorial realm. (shrink)

I critically examine some provocative arguments that John Searle presents in his book The Rediscovery of Mind to support the claim that the syntactic states of a classical computational system are "observer relative" or "mind dependent" or otherwise less than fully and objectively real. I begin by explaining how this claim differs from Searle's earlier and more well-known claim that the physical states of a machine, including the syntactic states, are insufficient to determine its semantics. In contrast, his more (...) recent claim concerns the syntax, in particular, whether a machine actually has symbols to underlie its semantics. I then present and respond to a number of arguments that Searle offers to support this claim, including whether machine symbols are observer relative because the assignment of syntax is arbitrary, or linked to universal realizability, or linked to the sub-personal interpretive acts of a homunculus, or linked to a person's consciousness. I conclude that a realist about the computational model need not be troubled by such arguments. Their key premises need further support. (shrink)

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 paper argues that the idea of a computer is unique. Calculators and analog computers are not different ideas about computers, and nature does not compute by itself. Computers, once clearly defined in all their terms and mechanisms, rather than enumerated by behavioral examples, can be more than instrumental tools in science, and more than source of analogies and taxonomies in philosophy. They can help us understand semantic content and its relation to form. This can be achieved because they have (...) the potential to do more than calculators, which are computers that are designed not to learn. Today’s computers are not designed to learn; rather, they are designed to support learning; therefore, any theory of content tested by computers that currently exist must be of an empirical, rather than a formal nature. If they are designed someday to learn, we will see a change in roles, requiring an empirical theory about the Turing architecture’s content, using the primitives of learning machines. This way of thinking, which I call the intensional view of computers, avoids the problems of analogies between minds and computers. It focuses on the constitutive properties of computers, such as showing clearly how they can help us avoid the infinite regress in interpretation, and how we can clarify the terms of the suggested mechanisms to facilitate a useful debate. Within the intensional view, syntax and content in the context of computers become two ends of physically realizing correspondence problems in various domains. (shrink)

Like '&', '=' is no term; it represents no extrasentential property. It marks an atomic, nonpredicative, declarative structure, sentences true solely by codesignation. Identity (its necessity and total reflexivity, its substitution rule, its metaphysical vacuity) is the objectual face of codesignation. The syntax demands pure reference, without predicative import for the asserted fact. 'Twain is Clemens' is about Twain, but nothing is predicated of him. Its informational value is in its 'metailed' semantic content: the fact of codesignation (that 'Twain' (...) names Clemens) that explains what fact it asserts and why it is necessary. Critiques of concepts of rigidity and elimination of singular terms result. (shrink)

The paper presents Alfred Tarski’s debate with the semantic antinomies: the basic Liar Paradox, and its more sophisticated versions, which are currently discussed in philosophy: Strengthen Liar Paradox, Cyclical Liar Paradox, Contingent Liar Paradox, Correct Liar Paradox, Card Paradox, Yablo’s Paradox and a few others. Since Tarski, himself did not addressed these paradoxes—neither in his famous work published in 1933, nor in later papers in which he developed the Semantic Theory of Truth—therefore, We try to defend his concept of truth (...) against these antinomies. It is demonstrated that Tarskian theory of truth is resistant to the paradoxes and it is still the best solution to avoid the antinomies and remain within a classical logic, that is, accepting the laws of noncontradiction, excluded middle, and the principle of bivalence. Thus, the goal of the paper is double—firstly, to show that none of the versions of the Liar Paradox’s is a serious threat to Tarski’s concept of truth, and secondly, that Semantic Theory of Truth allows to remain within classical logic, and at the same time, avoid antinomies—which makes it the most attractive among classical theories of truth. (shrink)

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. In this paper, we present a model of a new type of intertheoretic relation, called 'Montague Reduction', which is assumed in Montague's framework for the analysis and interpretation of natural language syntax. To motivate the adoption of our new model, we show that this model (...) extends the scope of application of the Nagelian (or related) models, and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

In this article I present the conception of syntax emerging from the “dynamic approach” to syntax and semantics, developed in the last few decades, moving from the critic to the static theories of language, either those developed in the Chomskian framework or those based on Montague’s grammar. I will suggest that this view can be fruitfully compared with Saussure’s position on syntax.

It is commonly assumed that images, whether in the world or in the head, do not have a privileged analysis into constituent parts. They are thought to lack the sort of syntactic structure necessary for representing complex contents and entering into sophisticated patterns of inference. I reject this assumption. “Image grammars” are models in computer vision that articulate systematic principles governing the form and content of images. These models are empirically credible and can be construed as literal grammars for images. (...) Images can have rich syntactic structure, though of a markedly different form than sentences in language. (shrink)

In a series of recent works, Kit Fine, 605–631, 2003, 2007) has sketched a novel solution to Frege’s puzzle. Radically departing from previous solutions, Fine argues that Frege’s puzzle forces us to reject compositionality. In this paper we first provide an explicit formalization of the relational semantics for first-order logic suggested, but only briefly sketched, by Fine. We then show why the relational semantics alone is technically inadequate, forcing Fine to enrich the syntax with a coordination schema. (...) Given this enrichment, we argue, that that the semantics is compositional. We then examine the deep consequences of this result for Fine’s proposed solution to Frege’s puzzle. We argue that Fine has mis-diagnosed his own solution–his attempted solution does not deny compositionality. The correct characterization of Fine’s solution fits him more comfortably among familiar solutions to the puzzle. (shrink)

I review a widely accepted argument to the conclusion that the contents of our beliefs, desires and other mental states cannot be causally efficacious in a classical computational model of the mind. I reply that this argument rests essentially on an assumption about the nature of neural structure that we have no good scientific reason to accept. I conclude that computationalism is compatible with wide semantic causal efficacy, and suggest how the computational model might be modified to accommodate this possibility.

This paper presents an analysis of wh-complements in Montague Grammar. We will be concerned primarily with semantics, though some remarks on syntax are made in Section 4. Questions and wh-comple ments in Montague Grammar have been studied in Hamblin (1976), Bennett (1979), Karttunen (1977) and Hauser (1978) among others. These proposals will not be discussed explicitly, but some differences with Karttunen's analysis will be pointed out along the way.

This essay considers what it means to understand natural language and whether a computer running an artificial-intelligence program designed to understand natural language does in fact do so. It is argued that a certain kind of semantics is needed to understand natural language, that this kind of semantics is mere symbol manipulation (i.e., syntax), and that, hence, it is available to AI systems. Recent arguments by Searle and Dretske to the effect that computers cannot understand natural language (...) are discussed, and a prototype natural-language-understanding system is presented as an illustration. (shrink)

Semantic analysis in early analytic philosophy belongs to a long tradition of adopting geometrical methodologies to the solution of philosophical problems. In particular, it adapts Descartes’ development of formalization as a mechanism of analytic representation, for its application in natural language semantics. This article aims to trace the mathematical roots of Frege, Russel and Carnap’s analytic method. Special attention is paid to the formal character of modern analysis introduced by Descartes. The goal is to identify the particular conception of (...) “form” developed by the analytic tradition, from Descartes to early analytic philosophy, and to determine its relation to similar notions, like ‘function’ and ‘syntax’. Finally, I focus on how Frege, Russell and Carnap’s methods of semantic analysis fit the general characterization of formal analysis previously developed. (shrink)

Hypothesis: WFF(x) can be applied syntactically to the semantics of formalized declarative sentences such that: WFF(x) ↔ (x ↦ True) ∨ (x ↦ False) (see proof sketch below) For clarity we focus on simple propositions without binary logical connectives.

Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface Tista Bagchi National Institute of Science, Technology, and Development Studies (NISTADS) and the University of Delhi Since the proposal of Logical Form (LF) was put forward by Robert May in his 1977 MIT doctoral dissertation and was subsequently adopted into the overall architecture of language as conceived under Government-Binding Theory (Chomsky 1981), there has been a steady research effort to determine the nature of LF in language in light of structurally (...) diverse languages around the world, which has ultimately contributed to the reinterpretation of LF as a Conceptual-Intentional (C-I) interface level between the computational syntactic component of the faculty of language and one or more interpretive faculties of the human mind. While this has opened up further possibilities of research in phenomena such as quantifier scope and scope interactions between negation, quantification, and focus, it has also given rise to a few real challenges to linguistic theory as well. Some of these are: (i) the split between lexical meaning – a matter supposedly belonging to the phase-wise selection of lexical arrays – and issues of semantic interpretation that arise purely from binding and scope phenomena (Mukherji 2010); (ii) partially relatedly, the level at which theta role assignment can be argued to take place, an issue that is taken up by me in Bagchi (2007); and (iii) how supposedly “pure” scopal phenomena relating to quantifiers, negation, and emphasizing expressions such as only and even (comparable to, e.g., Urdu/Hindi hii and bhii, Bangla –i and –o) also have dimensions of both focus and discourse reference. While recognizing all of these challenges, this talk aims to highlight particularly challenge (iii), both in terms of scholarship in the past and for the rich prospects for research on languages of south Asia with the semantics of quantification, negation, and focus in view. The scholarship of the past that I seek to relate this issue to is where, parallel to (and largely independently of) the research on LF that had been happening, Barwise and Cooper were developing their influential view of noun phrases as generalized quantifiers, culminating in their key 1981 article “Generalized Quantifiers and Natural Language” while, independently, McCawley, in his 1981 book Everything that Linguists have Always Wanted to Know about Logic, established through argumentation that all noun phrases semantically behave like generalized quantified expressions (further elaborated by him in the second – 1994 – revised edition of his book). I seek to demonstrate, based on limited data analysis from selected languages of south Asia, that our current understanding of quantification, negation, and focus under the Minimalist view owes something significant to the two major, but now largely marginalized, works of scholarship, and that for the way forward it is essential to adopt a more formal-semantic approach as adopted by them and also by later works such as Denis Bouchard’s (1995) The Semantics of Syntax, Mats Rooth’s work on focus (e.g., Rooth 1996, “Focus” in Shalom Lappin’s Handbook of Contemporary Semantic Theory), Heim and Kratzer’s Semantics in Generative Grammar (1998), and Yoad Winter’s (2002) Linguistic Inquiry article on semantic number, to cite just a few instances. (shrink)

Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) (...) is not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary. (shrink)

The holism-reductionism debate, one of the classic subjects of study in the philosopy of science, is currently at the heart of epistemological concerns in ecology. Yet the division between holism and reductionism does not always stand out clearly in this field. In particular, almost all work in ecosystem ecology and landscape ecology presents itself as holistic and emergentist. Nonetheless, the operational approaches used rely on conventional reductionist methodology.From an emergentist epistemological perspective, a set of general 'transactional' principles inspired by the (...) work of J. Dewey and J.K. Feibleman are proposed in an effort to develop a coherent ontological and methodological semantics. (shrink)

Since the early 1980s, there has been a debate in the semantics literature pertaining to whether wh-interrogatives can be directly disjoined, as main clauses and as complements. Those who held that the direct disjunction of wh-interrogatives was in conflict with certain theoretical considerations proposed that they could be disjoined indirectly. Indirect disjunction proceeds by first lifting both wh-interrogatives and then disjoining them; it assigns matrix-level scope to OR. As we will see, the notorious theoretical need for indirect disjunction has (...) disappeared by today. But the factual question remains. Are wh-complements disjoined directly or indirectly? What is the fact of the matter? This paper argues that the case for indirect disjunction remains reasonably strong. (shrink)

ABSTRACT -/- A propositional attitude (PA) is a belief, desire, fear, etc., that x is the case. This dissertation addresses the question of the semantic content of a specific kind of PA-instance: an instance of a belief of the form all Fs are Gs. The belief that all bachelors are sports fans has this form, while the belief that Spain is a country in Eastern Europe do not. Unlike a state of viewing the color of an orange, a belief-instance is (...) semantically contentful because it has reference, a meaning, logical implications, or a truth-value. While the intrinsic semantics view holds that either concepts or abstract objects are the source of content for PAs, the extrinsic semantics view holds that symbols of a mental language provide this content. I argue that a successful theory of intentionality must explain: (1) the truth-preserving causal powers of PAs, (2) the failure of the deductive principle Substitutivity to preserve truth over sentences that ascribe PAs, and (3) the truth-evaluability of PAs. As an internalist version of the extrinsic semantics view, I first evaluate Fodor’s Computational Theory of Mind, which says the semantic ingredients of mental states are symbols governed by rules of a mental syntax. I argue that in order to meet (1), CTM would have to associate the causal patterns of each thought-type with the inferential relations of some proposition – in an arbitrary or question-begging way. I also evaluate Fodor’s causal theory, as an externalist version of the extrinsic semantics view. This view is that lawlike causal relations between mental symbols and objects determine the reference, and thus the truth-value, of a thought. I argue that Brian Loar’s circularity objection refutes the ability of this theory to meet (3); and I endorse the intrinsic semantics perspective. I evaluate Frege’s theory of abstract, mind-external, and intrinsically semantic objects (senses), as an attempt to meet condition (2). I conclude that mind-external universals are the source of the intrinsically semantic features of concepts. Finally, I put forth a theory called ‘Bare Property Intentionality’, which describes the features of intrinsically representative and semantic concepts that connect them to these universals. (shrink)

Natural recursion in syntax is recursion by linguistic value, which is not syntactic in nature but semantic. Syntax-specific recursion is not recursion by name as the term is understood in theoretical computer science. Recursion by name is probably not natural because of its infinite typeability. Natural recursion, or recursion by value, is not species-specific. Human recursion is not syntax-specific. The values on which it operates are most likely domain-specific, including those for syntax. Syntax seems to (...) require no more (and no less) than the resource management mechanisms of an embedded push-down automaton (EPDA). We can conceive EPDA as a common automata-theoretic substrate for syntax, collaborative planning, i-intentions, and we-intentions. They manifest the same kind of dependencies. Therefore, syntactic uniqueness arguments for human behavior can be better explained if we conceive automata-constrained recursion as the most unique human capacity for cognitive processes. (shrink)

This paper argues in the first place that nominalists are right in insisting against ontological realists that semantic universality does not require commitment to universal entities. However, Ockham, in his zeal to get rid of Scotus’s universal entities, swept under the carpet the issue of universal representational content of genuinely universal symbols, conflating it with the mere indifference of the information content of non-distinctive singular representations. Buridan did come up with an abstractionist theory of the formation of genuinely universal representational (...) content to solve the resulting issues, however, the paper argues further, his solution is committed to attributing the sort of “aspectuality” to universal absolute concepts that his Ockhamist semantics denies to them. The conclusion of the paper suggests how Aquinas’s “moderate realism” can provide a consistent solution without the ontological extravaganza of ontological realists, without conflating the mere indifference of singular representation with genuine universality, and without having to deny aspectuality to our quidditative universal concepts formed by abstraction. (shrink)

As formal theoretical linguistic methodology has matured, recent years have seen the advent of applying it to objects of study that transcend language, e.g., to the syntax and semantics of music (Lerdahl & Jackendoff 1983, Schlenker 2017a; see also Rebuschat et al. 2011). One of the aims of such extensions is to shed new light on how meaning is construed in a range of communicative systems. In this paper, we approach this goal by looking at narrative dance in (...) the form of Bharatanatyam. We argue that a semantic approach to dance can be modeled closely after the formal semantics of visual narrative proposed by Abusch (2013, 2014, 2021). A central conclusion is that dance not only shares properties of other fundamentally human means of expression, such as visual narrative and music, but that it also exhibits similarities to sign languages and the gestures of non-signers (see, e.g., Schlenker 2020) in that it uses space to track individuals in a narrative and performatively portray the actions of those individuals. From the perspective of general human cognition, these conclusions corroborate the idea that linguistic investigations beyond language (see Patel-Grosz et al. forthcoming) can yield insights into the very nature of the human mind and of the communicative devices that it avails. (shrink)

This squib begins with an argument emphasizing that the grammar of English makes a distinction between constituents that are focused and those that are merely new, hence not given. If the distinction is made via features, we need two features: one indicating focus and one indicating either given or new information. Which one of the two? Semantically, the choice doesn’t matter: whatever information is given is not new and the other way round. For the phonology, there is a difference, however. (...) If the prosody of all-new constituents is default prosody, but the prosody of given constituents is special, we would want to indicate givenness, rather than newness. (shrink)

Our aim here is to lay the groundwork for formal tree-ring analysis combining data from dendrochronology with formal techniques from semantics. We will present the basic syntax of, and basic compositional semantics of tree-ring structures.

Although most contemporary philosophers of language hold that semantics and pragmatics require separate study, there is surprisingly little agreement on where exactly the line should be drawn between these two areas, and why. In this paper I suggest that this lack of clarity is at least partly caused by a certain historical obfuscation of the roots of the founding three-way distinction between syntax, semantics and pragmatics in Charles Peirce’s pragmatist philosophy of language. I then argue for recovering (...) and revisiting these original roots, taking indexicality as a case-study of how certain questions connected with the distinction which are currently considered complex and difficult may be clarified by a ‘properly pragmatist pragmatics’. Such a view, I shall argue, upends a certain priority usually accorded to semantics over pragmatics, teaching that we do not work out what terms mean in some abstract overall sense and then work out to what use they are being put; rather, we must understand to what use terms are being put in order to understand what they mean. (shrink)

John Searle once said: "The Chinese room shows what we knew all along: syntax by itself is not sufficient for semantics. (Does anyone actually deny this point, I mean straight out? Is anyone actually willing to say, straight out, that they think that syntax, in the sense of formal symbols, is really the same as semantic content, in the sense of meanings, thought contents, understanding, etc.?)." I say: "Yes". Stuart C. Shapiro has said: "Does that make any (...) sense? Yes: Everything makes sense. The question is: What sense does it make?" This essay explores what sense it makes to say that syntax by itself is sufficient for semantics. (shrink)

: The Hamblin-Karttunen approach has led to many insights about questions in English. In this article the results of this rule-by-rule tradition are reconsidered from a crosslinguistic perspective. Starting from the type-driven XLS theory developed in Bittner (1994a, b), it is argued that evidence from simple questions (in English, Polish, Lakhota and Warlpiri) leads to certain revisions. The revised XLS theory then immediately generalizes to complex questions — including scope marking (Hindi), questions with quantifiers (English) and multiple wh-questions (English, Hindi, (...) Japanese). Eliminating language- and construction-specific information from the compositional rules, in favor of universal semantic filters, leads to analyses that not only generalize across unrelated languages but are also empirically more accurate, not less. (shrink)

A computer can come to understand natural language the same way Helen Keller did: by using “syntactic semantics”—a theory of how syntax can suffice for semantics, i.e., how semantics for natural language can be provided by means of computational symbol manipulation. This essay considers real-life approximations of Chinese Rooms, focusing on Helen Keller’s experiences growing up deaf and blind, locked in a sort of Chinese Room yet learning how to communicate with the outside world. Using the (...) SNePS computational knowledge-representation system, the essay analyzes Keller’s belief that learning that “everything has a name” was the key to her success, enabling her to “partition” her mental concepts into mental representations of: words, objects, and the naming relations between them. It next looks at Herbert Terrace’s theory of naming, which is akin to Keller’s, and which only humans are supposed to be capable of. The essay suggests that computers at least, and perhaps non-human primates, are also capable of this kind of naming. (shrink)

Formal thought disorder (FTD) is a clinical mental condition that is typically diagnosable by the speech productions of patients. However, this has been a vexing condition for the clinical community, as it is not at all easy to determine what “formal” means in the plethora of symptoms exhibited. We present a logic-based model for the syntax–semantics interface in semantic networking that can not only explain, but also diagnose, FTD. Our model is based on description logic (DL), which is (...) well known for its adequacy to model terminological knowledge. More specifically, we show how faulty logical form as defined in DL-based Conception Language (CL) impacts the semantic content of linguistic productions that are characteristic of FTD. We accordingly call this the dyssyntax model. (shrink)

Kripke (1977) presents an argument designed to show that the considerations in Donnellan (1966) concerning attributive and referential uses of (definite) descriptions do not, by themselves, refute Russell’s (1905) unitary theory of description sentences (RTD), which takes (utterances of) them to express purely general, quantificational, propositions. Against Kripke, Marga Reimer (1998) argues that the two uses do indeed reflect a semantic ambiguity (an ambiguity at the level of literal truth conditions). She maintains a Russellian (quantificational) analysis of utterances involving attributively (...) used descriptions but attempts to defend the following two claims about utterances involving referentially used descriptions (referential utterances) (1998, p. 89). (shrink)

In its January 20th, 2010 decision in Citizens United vs. Federal Election Commission, the United States Supreme Court ruled that certain restrictions on independent expenditures by corporations for political advocacy violate the First Amendment of the Constitution, which provides that “Congress shall make no law […] abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.” Justice Kennedy, writing for the 5-4 majority, (...) held that “[b]y suppressing the speech of manifold corporations, both for-profit and non-profit, the Government prevents their voices and view-points from reaching the public and advising voters on which person or entities are hostile to their interests” (Citizens United vs. Federal Election Commission 558 U.S. 38-9 (2010); emphasis added). Much of the language of the opinion, and some of its reasoning, as this passage illustrates, presupposes that corporations are agents capable of speech, and that it is (at least in part) in the light of this that limitations on political advocacy by corporations are prohibited by the Constitution. -/- While there are other strands in the argument, they are interwoven with the conception of the corporation as agent and speaker, with its voice and its viewpoints. The dissenters on the court objected on precisely this point (among others). Justice Stevens wrote sarcastically in his dissent, joined by Justices Ginsburg, Breyer, and Sotomayor, that “[u]nder the majority’s view, I suppose it may be a First Amendment problem that corporations are not permitted to vote, given that voting is, among other things, a form of speech” (558 U.S. 33 (2010)). Justice Sotomayor suggested in oral argument that the Court’s century-old practice of treating corporations as persons rests on a conceptual mistake. -/- My concern in this essay is not with the question whether the restrictions violate the Constitution. There are many issues that bear on this which will be outside the scope of my discussion. My concern is with the proper conceptual framework for understanding the agency of corporations and corporate speech, and the role that conceptions of these play in the background of the majority’s reasoning. The issue is legal, but it also has philosophical, conceptual and semantic aspects. It will be the latter aspects, and their potential to shed light on legal reasoning, that are my main focus. An adequate framework requires saying what properly speaking the corporation is, how agency is expressed through the corporation, whose agency it is, centrally whether the corporation is an agent or person in its own right, and in what sense it can be said to be capable of speech. I draw on recent work in collective action theory, particularly with respect to the semantics of collective action sentences (Ludwig 2007) and the analysis of the proxy agency in collective action (Ludwig 2014), to show (i) that corporations are neither genuine agents nor (therefore) capable of engaging in genuine speech, (ii) that consequently the First Amendment does not apply to corporations per se, and (iii) that a better understanding of the mechanisms of corporate agency casts doubt on more indirect arguments for extending the First Amendment to “corporate speech” as well. (shrink)

In this paper, I will argue that semantic holism is, inherently, a false claim. Semantic holism, here, being defined as the meaning of a word or expression in a given language (λ) is constructed by its relation to other words and expressions in said given language (λ) and its role in said given language (λ). The following premises and examples within the premises support the refutability of semantic holism, including linguistic relativity, culture and linguistic determinism.