We are used to the idea that computers operate on numbers, yet another kind of data is equally important: the syntax of formal languages, with variables, binding, and alpha-equivalence. The original application of nominal techniques, and the one with greatest prominence in this paper, is to reasoning on formal syntax with variables and binding. Variables can be modelled in many ways: for instance as numbers (since we usually take countably many of them); as links (since they may `point' (...) to a binding site in the term, where they are bound); or as functions (since they often, though not always, represent `an unknown'). None of these models is perfect. In every case for the models above, problems arise when trying to use them as a basis for a fully formal mechanical treatment of formal language. The problems are practical—but their underlying cause may be mathematical. The issue is not whether formal syntax exists, since clearly it does, so much as what kind of mathematical structure it is. To illustrate this point by a parody, logical derivations can be modelled using a Gödel encoding (i.e., injected into the natural numbers). It would be false to conclude from this that proof-theory is a branch of number theory and can be understood in terms of, say, Peano's axioms. Similarly, as it turns out, it is false to conclude from the fact that variables can be encoded e.g., as numbers, that the theory of syntax-with-binding can be understood in terms of the theory of syntax-without-binding, plus the theory of numbers (or, taking this to a logical extreme, purely in terms of the theory of numbers). It cannot; something else is going on. What that something else is, has not yet been fully understood. In nominal techniques, variables are an instance of names, and names are data. We model names using urelemente with properties that, pleasingly enough, turn out to have been investigated by Fraenkel and Mostowski in the first half of the 20th century for a completely different purpose than modelling formal language. What makes this model really interesting is that it gives names distinctive properties which can be related to useful logic and programming principles for formal syntax. Since the initial publications, advances in the mathematics and presentation have been introduced piecemeal in the literature. This paper provides in a single accessible document an updated development of the foundations of nominal techniques. This gives the reader easy access to updated results and new proofs which they would otherwise have to search across two or more papers to find, and full proofs that in other publications may have been elided. We also include some new material not appearing elsewhere. (shrink)

An explanation for the uncertain progress of formalist linguistics is sought in an examination of the concept of syntax. The idea of analyzing language formally was made possible by developments in 20th century logic. It has been pointed out by many that the analogy between natural language and a formal system may be imperfect, but the objection made here is that the very concept of syntax, when applied to any non-abstract system of communication, is flawed as it (...) is commonly used. Syntax is properly defined with respect to an individual transformation rule that might be applied to some message. Collections of syntax rules, however, are inevitably due to categories imposed by an observer, and do not correspond to functional features found in non-abstract systems. As such, these categories should not be relied upon as aids to understanding any natural system. (shrink)

An explanation for the uncertain progress of formalist linguistics is sought in an examination of the concept of syntax. The idea of analyzing language formally was made possible by developments in 20th century logic. It has been pointed out by many that the analogy between natural language and a formal system may be imperfect, but the objection made here is that the very concept of syntax, when applied to any non-abstract system of communication, is flawed as it (...) is commonly used. Syntax is properly defined with respect to an individual transformation rule that might be applied to some message. Collections of syntax rules, however, are inevitably due to categories imposed by an observer, and do not correspond to functional features found in non-abstract systems. As such, these categories should not be relied upon as aids to understanding any natural system. (shrink)

The Craig Interpolation Theorem is a fundamental property of rst order logic L!!. What happens if we strengthen rst order logic? Second order logic L 2 satises Craig for trivial reasons but on the other hand, L 2 is not very interesting from a fundational point of view.

A central debate in the cognitive sciences surrounds the nature of adult speakers' linguistic representations: Are they purely syntactic (a traditional and widely held view; e.g., Branigan & Pickering, ), or are they semantically structured? A recent study (Ambridge, Bidgood, Pine, Rowland, & Freudenthal, ) found support for the latter view, showing that adults' acceptability judgments of passive sentences were significantly predicted by independent semantic “affectedness” ratings designed to capture the putative semantics of the construction (e.g., Bob was pushed by (...) Wendy is rated as more acceptable than Bob was liked by Wendy, as Bob is more affected in the former). However, because English lacks a separate topicalization construction which provides an alternative means of highlighting the patient (e.g., BOB, Wendy kicked), these findings have a possible alternative explanation: that highly affected entities are more likely to be topicalized, rather than passivized per se. Here we show that, in fact, Ambridge et al.'s () finding replicates in Indonesian, a language with a topicalization construction. The present study therefore provides particularly compelling evidence that grammatical representations have semantic structure. (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 groundbreaking book offers a new and compelling perspective on the structure of human language. The fundamental issue it addresses is the proper balance between syntax and semantics, between structure and derivation, and between rule systems and lexicon. It argues that the balance struck by mainstream generative grammar is wrong. It puts forward a new basis for syntactic theory, drawing on a wide range of frameworks, and charts new directions for research. In the past four decades, theories of syntactic (...) structure have become more abstract, and syntactic derivations have become ever more complex. Peter Culicover and Ray Jackendoff trace this development through the history of contemporary syntactic theory, showing how much it has been driven by theory-internal rather than empirical considerations. They develop an alternative that is responsive to linguistic, cognitive, computational, and biological concerns. At the core of this alternative is the Simpler Syntax Hypothesis: the most explanatory syntactic theory is one that imputes the minimum structure necessary to mediate between phonology and meaning. A consequence of this hypothesis is a far richer mapping between syntax and semantics than is generally assumed. Through concrete analyses of numerous grammatical phenomena, some well studied and some new, the authors demonstrate the empirical and conceptual superiority of the Simpler Syntax approach.Simpler Syntax is addressed to linguists of all persuasions. It will also be of central interest to those concerned with language in psychology, human biology, evolution, computational science, and artificial intellige. (shrink)

Abstract It is widely assumed that the meaning of at least some types of expressions involves more than their reference to objects, and hence that there may be co-referential expressions which differ in meaning. It is also widely assumed that ?syntax does not suffice for semantics?, i.e. that we cannot account for the fact that expressions have semantic properties in purely syntactical or computational terms. The main goal of the paper is to argue against a third related assumption, (...) namely that what is responsible for a difference in meaning between co-referential expressions is the computational difference in the cognitive functioning of the expressions. ?Intentional aspects? of expressions?those features which their meanings involve in addition to reference?cannot be syntacticized, since they are individuated not in terms of any cognitive feature, but rather in terms of those properties of the referents through which the expressions refer to them, and cognitive features cannot determine such properties in exactly the same sense as they cannot determine reference. (shrink)

During the last thirty years, most linguists and philosophers have assumed that meaning can be represented symbolically and that the mental processing of language involves the manipulation of symbols. Scholars have assembled strong evidence that there must be linguistic representations at several abstract levels--phonological, syntactic, and semantic--and that those representations are related by a describable system of rules. Because meaning is so complex, linguists often posit an equally complex relationship between semantic and other levels of grammar. The Semantics of (...) Syntax is an elegant and powerful analysis of the relationship between syntax and semantics. Noting that meaning is underdetermined by form even in simple cases, Denis Bouchard argues that it is impossible to build knowledge of the world into grammar and still have a describable grammar. He thus proposes simple semantic representations and simple rules to relate linguistic levels. Focusing on a class of French verbs, Bouchard shows how multiple senses can be accounted for by the assumption of a single abstract core meaning along with background information about how objects behave in the world. He demonstrates that this move simplifies the syntax at no cost to the descriptive power of the semantics. In two important final chapters, he examines the consequences of his approach for standard syntactic theories. (shrink)

Fitch's basic logic is an untyped illative combinatory logic with unrestricted principles of abstraction effecting a type collapse between properties (or concepts) and individual elements of an abstract syntax. Fitch does not work axiomatically and the abstraction operation is not a primitive feature of the inductive clauses defining the logic. Fitch's proof that basic logic has unlimited abstraction is not clear and his proof contains a number of errors that have so far gone undetected. This paper corrects these (...) errors and presents a reasonably intuitive proof that Fitch's system K supports an implicit abstraction operation. Some general remarks on the philosophical significance of basic logic, especially with respect to neo-logicism, are offered, and the paper concludes that basic logic models a highly intensional form of logicism. (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)

In the recent literature of the philosophy of science, much space has been given to the problem of analyzing theories of the deductive and natural sciences in a way which makes explicit some of the syntactic and semantic features which seem to be implicitly present in their structures. This pa- per is concerned with the same problem; however, some other problems of syntax and semantics are touched upon along the way. After some prelim- inaries, a very general method of (...) constructing symbolic languages is intro- duced. The resulting languages are interpreted in either empty or non- empty sets and so in a way which permits them to contain terms which stand for nothing at all and an existence predicate which is not applicable to all terms. Also, certain variable binders are interpreted in a way which leaves open the possibility of interpreting them modally and a semantic operation of degree of truth for arbitrary formulas is introduced. An axiomless logic commensurate with a semantics of this kind and so one which contains a new treatment of definite descriptions is then constructed and shown to be both sound and semantically complete. Finally, theories and various concepts pertaining to theories are defined on the basis of this syntax and semantics. Among the concepts are operations which assign degrees of confirmation, explanatory powers, degrees of deductive simplic- ity, and degrees of adequacy to theories, relations and concreteness and abstractness for expressions, a relation of significance for theories, and operations which assign denotations and meanings to expressions. (shrink)

For various reasons several authors have enriched classical first order syntax by adding a predicate abstraction operator. “Conservatives” have done so without disturbing the syntax of the formal quantifiers but “revisionists” have argued that predicate abstraction motivates the universal quantifier’s re-classification from an expression that combines with a variable to yield a sentence from a sentence, to an expression that combines with a one-place predicate to yield a sentence. My main aim is to advance the cause of predicate (...) abstraction while cautioning against revisionism. In so doing, however, I shall pursue a secondary aim by conveying mixed blessings to those who hold the view that in the logical sense of “existence” some existing object is such as to exist contingently. Advocates of this view must concede Williamson’s recent contention that the domain of unrestricted objectual quantification could not have been narrower than it is actually, but predicate abstraction affords them some hope of accommodating this concession. (shrink)

All accounts of language acquisition agree that, by around age 4, children’s knowledge of grammatical constructions is abstract, rather than tied solely to individual lexical items. The aim of the present research was to investigate, focusing on the passive, whether children’s and adults’ performance is additionally semantically constrained, varying according to the distance between the semantics of the verb and those of the construction. In a forced‐choice pointing study (Experiment 1), both 4‐ to 6‐year olds (N = 60) and (...) adults (N = 60) showed support for the prediction of this semantic construction prototype account of an interaction such that the observed disadvantage for passives as compared to actives (i.e., fewer correct points/longer reaction time) was greater for experiencer‐theme verbs than for agent‐patient and theme‐experiencer verbs (e.g., Bob was seen/hit/frightened by Wendy). Similarly, in a production/priming study (Experiment 2), both 4‐ to 6‐year olds (N = 60) and adults (N = 60) produced fewer passives for experiencer‐theme verbs than for agent‐patient/theme‐experiencer verbs. We conclude that these findings are difficult to explain under accounts based on the notion of A(rgument) movement or of a monostratal, semantics‐free, level of syntax, and instead necessitate some form of semantic construction prototype account. (shrink)

In this paper we first give a survey of reductive cut-elimination methods in classical logic. In particular we describe the methods of Gentzen and Schütte-Tait from the abstract point of view of proof reduction. We also present the method CERES which we classify as a semi-semantic method. In a further section we describe the so-called semantic methods. In the second part of the paper we carry the proof analysis further by generalizing the CERES method to CERESD . In the (...) generalized version CERESD we admit general elimination rules which are based on the mere semantical truth of sentences. We construct complete cut-free LK-derivations originating from derivations potentially containing unproven lemmas. Finally we give a comparison of reductive methods and CERESD by presenting a general simulation result. (shrink)

We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the Bernays postulates for quantifiers and the comprehension schemata of ZF and other set theories. We prove that it is consistent in any finite Boolean subset lattice. We investigate the antinomies of Russell, Cantor, Burali-Forti, and others, and discuss the relationship of the system to other set-theoretic (...) systems ZF, NBG, and NF. We discuss two methods of axiomatizing higher order quantification and abstraction, and then very briefly discuss the application of one of these methods to areas of mathematics outside of logic. (shrink)

Previous research has linked the concept of number and other ordinal series to space via a spatially oriented mental number line. In addition, it has been shown that in visual scene recognition and production, speakers of a language with a left-to-right orthography respond faster to and tend to draw images in which the agent of an action is located to the left of the patient. In this study, we aim to bridge these two lines of research by employing a novel (...) method that measures the spatial bias produced by transitive sentences that use a wide variety of abstract and concrete verbs. Across four experiments, participants read sentences and then responded to probe words appearing on either the left or right sides of the screen. Probe words consisted of agents, patients, other words in the sentence, or newly encountered words. We found consistent lateral biases to responding to agents and patients, which appears to be independent of order of mention in the sentence but which does reflect a correspondence between position in the sentence and role in the causal sequence of the action. Our results also show that this spatial bias is driven by the use of the hands in two different ways: The left hand shows a greater sensitivity to the spatial effect than the right hand, and vocal responses produce no spatial effect. (shrink)

The distinction between syntactic and semantic techniques in linguistic theory is by now sufficiently clear. What is often debated is the extent to which syntactic and semantic considerations should be used in analyzing a given phenomenon. An empirical domain where the division of labour between syntax and semantics is especially problematic is the case of ``non-overt'' scope, or what I prefer to call the..

Discussion of Searle's case against strong AI has usually focused upon his Chinese Room thought-experiment. In this paper, however, I expound and then try to refute what I call his abstract argument against strong AI, an argument which turns upon quite general considerations concerning programs, syntax, and semantics, and which seems not to depend on intuitions about the Chinese Room. I claim that this argument fails, since it assumes one particular account of what a program is. I suggest (...) an alternative account which, however, cannot play a role in a Searle-type argument, and argue that Searle gives no good reason for favoring his account, which allows the abstract argument to work, over the alternative, which doesn't. This response to Searle's abstract argument also, incidentally, enables the Robot Reply to the Chinese Room to defend itself against objections Searle makes to it. (shrink)

Recent work on mood choice considers fine-grained semantic differences among desire predicates (notably, ‘want’ and ‘hope’) and their consequences for the distribution of indicative and subjunctive complement clauses. In that vein, this paper takes a close look at ‘intend’. I show that cross-linguistically, ‘intend’ accepts nonfinite and subjunctive complements and rejects indicative complements. This fact poses difficulties for recent approaches to mood choice. Toward a solution, a broad aim of this paper is to argue that—while ‘intend’ is loosely in the (...) family of desire predicates—it differs from ‘want’ and ‘hope’ in that it has a causative component, and this is relevant to its mood choice behavior, given that causative predicates also systematically reject indicative complements. More concretely, my analysis has three ingredients: (i) following related proposals in philosophy, intention reports have causally self-referential content; (ii) encoding causal self-reference requires abstraction over the complement clause’s eventuality argument; and (iii) nonfinite and subjunctive clauses enable such abstraction but indicative clauses do not. Aside from causative predicates, independent support for the proposal comes from the syntax of belief-/intention-hybrid attitude predicates like ‘decide’ and ‘convince’, anankastic conditional antecedents, aspectual predicates, and memory and perception reports. Synthesizing this result with that of previous literature, the emergent generalization is that subjunctive mood occurs in attitude reports that involve either comparison or eventuality abstraction. Toward a unified theory of mood choice, I suggest that both comparison and eventuality abstraction represent departures from the clausal semantics of unembedded assertions and consequently that subjunctive mood signals such a departure. (shrink)

Mandarin Chinese, along with Japanese, Yorùbá, Mòoré, and Samoan, has been argued to lack ‘degree abstraction’, a configuration at LF involving lambda abstraction over a degree variable. These languages are claimed to have a negative setting for a hypothesized ‘Degree Abstraction Parameter’. Recent work, however, has argued for degree abstraction in Japanese and Yorùbá, and degree abstraction has been detected in a number of additional languages. Could it in fact be universal? Here, we focus on the case of Mandarin, and (...) argue that Mandarin has degree abstraction too. We offer three arguments in favor of degree abstraction in Mandarin, based on attributive comparatives, comparatives with embedded predicates, and scope interactions with modals. We also rebut prior arguments for the lack of degree abstraction in Mandarin, considering degree questions, measure phrases, and negative island effects. Taken together, these results show that degree abstraction is not a parameter along which Mandarin and English vary, and suggest rather that degree abstraction may be universally available. (shrink)

Abstract: In this brief commentary, I focus on two issues, first on Moltmann’s proposed Davidsonian event semantics for transitive verb attitude predicates, and second on the import of what she calls ‘the underspecification of content’ for the proper semantic interpretation of that-clauses. With respect to the first of these issues, I question the empirical justification of her proposed semantics, suggesting that she needs a syntactic rationale for her semantics. With respect to the second issue, I question whether, as she (...) claims, the that-clauses in transitive verb attitude predicates specify (or even partially specify) the truth or satisfaction conditions for the attributed attitudes. (shrink)

There is a widespread assumption in Construction Grammar that the meanings of verbs correlate with or even determine their complementation forms and patterns. There is much less research on noun complementation, however, although this category is even more interesting for a number of reasons such as the potential for valency reduction, nominal topicalization constructions, and additional complementation options, e.g.of-PPs and existential constructions.In this paper we focus on the class of nouns reporting commissive illocutionary acts, and address the question of whether (...) there is a correlation between the meaning of these nouns and their preferred complementation patterns, and between their semantic similarity and their similarity in the distribution of complementation patterns.We report the results of a study of a set of 17 commissive nouns chosen from a wider collection of illocutionary nouns. Two types of analysis were carried out in order to compare the semantic and grammatical characteristics of these nouns. The semantic analysis was based on insights from speech act theory and the philosophy of language. We developed a framework for a systematic comparative description of the nouns in our word field. The results were tallied with a corpus-based grammatical analysis. Two hundred tokens of each noun type were randomly sampled from the Corpus of Contemporary American English. Using these data, the 17 nouns were subjected to an analysis of the relative frequencies of their complementation patterns.Results indicate a general match between noun meanings and complementation patterns. More specifically, however, they indicate that the closeness of this match depends on the prototypicality of nouns as members of the class of commissives.The study, then, contributes to our understanding of the relation between lexis and syntax. At the same time, it confirms the need for a close semantic analysis to account for the great extent to which item-specific information, i.e. properties of individual nouns, have to be taken into consideration at the expense of large-scale generalizations. (shrink)

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice. This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued (...) today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)

I will defend a purely structural account of the different readings arising from the German adverb wieder ÒagainÓ. We will be concerned with the so-called repetitive/restitutive ambiguity. The claim is that the ambiguity can be resolved entirely in terms of syntactic scope. The theory assumes a rather abstract syntax. In particular, abundant use is made of KratzerÕs (1994) voice phrase, which plays a central role for the derivation of repetitive readings. One of the leading ideas of the analysis (...) is that the structural accusative position has wide scope with respect to the agent relation expressed by the head of the voice phrase. If wieder precedes an accusative object, a repetitive reading is obligatory. If wieder follows the accusative object, two readings are available due to two possible positions of wieder. The analysis is an improvement of the proposal of Stechow (1995). It solves a number of questions left open there and considers a range of new data. (shrink)

In this paper, I outline a grammar of lifting (i.e., resistance training) and compare it to that of language. I approach lifting as a system of generating complex meaning–form correspondences from regularized elements and describe the levels of mental representations and relationships between them that are involved in full command of this system. To be able to do so, I adopt a goal-based conception of meaning, which allows us to talk about mappings from complex goals to complex surface outputs in (...) systems of intentional action, signaling and non-signaling, interactive and non-interactive, in a unified way, and show how it applies in lifting. I then proceed to argue that the grammar of lifting is architecturally very similar to that of language. First, I show that both involve stable (idiomatized/lexicalized) pairings of regularized forms with regularized meanings. Second, I argue that in both lifting and language, meaning–form mapping is mediated by syntax, which, crucially, operates on non-linearized hierarchical structures of abstract objects that include both content morphemes and functional morphemes. I conclude, following and expanding on some insights from prior literature and offering further evidence for them, that neither of these architectural phenomena (idiomatized meaning–form pairings and abstract syntax) is specific to language, with both of them likely emerging in skilled action that does not necessarily involve social interaction, due to considerations of repeatability and reusability of elements in new contexts. (shrink)

In this paper, we propose a framework capable of dealing with anaphora and ellipsis which is both general and algorithmic. This generality is ensured by the compination of two general ideas. First, we use a dynamic semantics which reperent effects using a monad structure. Second we treat scopes flexibly, extending them as needed. We additionally implement this framework as an algorithm which translates abstract syntax to logical formulas. We argue that this framework can provide a unified account of (...) a large number of anaphoric phenomena. Specifically, we show its effectiveness in dealing with pronominal and VP-anaphora, strict and lazy pronouns, lazy identity, bound variable anaphora, e-type pronouns, and cataphora. This means that in particular we can handle complex cases like Bach–Peters sentences, which require an account dealing simultaneously with several phenomena. We use Haskell as a meta-language to present the theory, which also consitutes an implementation of all the phenomena discussed in the paper. To demonstrate coverage, we propose a test suite that can be used to evaluate computational approaches to anaphora. (shrink)

Nominal logic is a variant of first-order logic in which abstract syntax with names and binding is formalized in terms of two basic operations: name-swapping and freshness. It relies on two important principles: equivariance (validity is preserved by name-swapping), and fresh name generation ("new" or fresh names can always be chosen). It is inspired by a particular class of models for abstract syntax trees involving names and binding, drawing on ideas from Fraenkel-Mostowski set theory: finite-support models (...) in which each value can depend on only finitely many names. Although nominal logic is sound with respect to such models, it is not complete. In this paper we review nominal logic and show why finite-support models are insufficient both in theory and practice. We then identify (up to isomorphism) the class of models with respect to which nominal logic is complete: ideal-supported models in which the supports of values are elements of a proper ideal on the set of names. We also investigate an appropriate generalization of Herbrand models to nominal logic. After adjusting the syntax of nominal logic to include constants denoting names, we generalize universal theories to nominal-universal theories and prove that each such theory has an Herbrand model. (shrink)

Although a number of authors have used diagrams extensively in their studies of Navya-Nyāya, they have done so to explain and illustrate concepts, not with the goal of reasoning with the diagrams themselves. Adherents of diagrammatic reasoning have made claims for its potential by pointing to key structural correspondences between diagrams and logical concepts, arguably lacking in sentential representations, and describing these relations using concepts such as “well matchedness” and “iconicity”. A canonical example of this iconicity is the use of (...) Euler diagrams to depict categorical syllogisms. Since the meaning of expressions in Indian logic differs in so many important ways from logic in the Western tradition, the use or adaptation of diagrams developed in the latter would seem to preclude iconicity. Thus, the development of diagrams which reflect the nature of inference in Navya-Nyāya, which centres on the anumāna inference schema, is motivated. In this paper we extend Ganeri’s method of depicting the Vaiśeṣika ontology with graphs to include syntax intended to expose the nature of anumāna. The diagrams are given a formal basis: i.e. abstract syntax, inference rules defined abstractly and a graph-theoretic semantics. These are the first formalised logical diagrams that aim to reflect the nature of the anumāna inference. This paper lays the way for further work in extending the formalism to cover more of Navya-Nyāya, and in exploring a dialogue between properties of the formalism and of Navya-Nyāya. (shrink)

This book examines the hypothesis of "direct compositionality", which requires that semantic interpretation proceed in tandem with syntactic combination. Although associated with the dominant view in formal semantics of the 1970s and 1980s, the feasibility of direct compositionality remained unsettled, and more recently the discussion as to whether or not this view can be maintained has receded. The syntax-semantics interaction is now often seen as a process in which the syntax builds representations which, at the abstract level (...) of logical form, are sent for interpretation to the semantics component of the language faculty. In the first extended discussion of the hypothesis of direct compositionality for twenty years, this book considers whether its abandonment might have been premature and whether in fact direct compositionality is not after all a simpler and more effective conception of the grammar than the conventional account of the syntax-semantics interface in generative grammar. It contains contributions from both sides of the debate, locates the debate in the setting of a variety of formal theories, and draws on examples from a range of languages and a range of empirical phenomena. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Testimony of Sense: Empiricism and the Essay from Hume to Hazlitt by Tim MilnesMargaret WatkinsTim Milnes. The Testimony of Sense: Empiricism and the Essay from Hume to Hazlitt. Oxford: Oxford University Press, 2019. Pp. viii + 278. Hardback. ISBN: 9780198812739. $91.00.In his brief autobiography, “My Own Life,” Hume reports that “almost all [his] life has been spent in literary pursuits and occupations” (E-MOL: xxxi). This is (...) one of at least ten places in this brief work in which he associates himself with “letters” or “literature”—as compared to at most four associations with philosophy. The moral to be inferred is not that Hume considered himself not to be a philosopher. Rather, he conceived of philosophy as a kind of literature. The Treatise was itself a “literary attempt.” Indeed, opposition between the “literary” and “philosophical” aspects of a text would have been foreign to Hume and his contemporaries—a notion for a later age, despite his occasional loose distinction between the relevant genres, as in his list of writings “historical, philosophical, or literary” in “My Own Life” (E-MOL: xxxvi).Yet despite Hume’s own understanding of the continuity between philosophy and literature, broadly conceived, it is still common for contemporary philosophers to ignore literary questions in their examination of Hume’s work, or to presume that one can easily distinguish the “philosophical” parts from the “literary” ones. Tim Milnes’s The Testimony of Sense is therefore a welcome addition to the Hume literature (pun intended). With a particular focus on the essay—a genre of great importance to Hume—Milnes contributes to the small set of engagements with Hume from the disciplinary perspective of English literature. With training in both philosophy and literature, as well as established expertise on Romanticism and its own essays, Milnes is well-qualified for the task. The Testimony of Sense includes sustained engagement with Hume’s contemporaries and successors, but for the purposes of this review, I engage the book primarily as a Hume scholar for Hume scholars.Milnes’s story plays out in three acts. The first establishes the need for public trust created by a skeptical crisis, itself a product of Hume’s criticism of the epistemic program of thinkers in the Cartesian and Lockean traditions. The second explains how the essays of the long eighteenth century constitute a response to that need in various ways. The third reveals in detail how the Romantic essayists, particularly William Hazlitt and Charles Lamb, both respond to and deviate from the “neoclassical” essayists, typified by Hume and Samuel Johnson.The first chapter, “Self and Intersubjectivity,” lays the groundwork by articulating how Hume, Adam Smith, Thomas Reid, and Dugald Stewart identify the need for what we now call intersubjectivity. Milnes describes the common thread as a kind of “natural transcendentalism.” In what sense are these thinkers properly understood as [End Page 175] transcendentalists? The central idea seems to be that all posit things other than reason as “conditions of meaningful thought” (72). For Hume, it is the social, linguistic experience of a community of virtuous judges. The intricate relations between self and other essential to such a community get “internalized within the specular drama of the impartial spectator” (72) in Smith’s writing, which itself takes part in the drama through his “halting, qualified syntax” that mimics “everyday speech” (44). Reid posits a “prescience” of trust, which grounds our reliance on both human testimony and the uniformity of nature, itself undergirded by the design of a benevolent God. Stewart, who posits axiomatic truths that help constitute the “stamina of intellect,” goes furthest, actually calling these truths transcendental (55). This chapter also puts these eighteenth-century thinkers in conversation with twentieth-century theorists, including Habermas, Davidson, and Rorty.Chapter 2, “The Subject of Trust,” deepens the analysis by situating these “natural transcendentalisms” in the broader enlightenment context. In contrast to Descartes, Bacon, and Locke, who were suspicious of our reliance on the opinions of others, the eighteenth-century thinkers understand trust as prior to reason in various ways—though not prior to solidarity. The particulars in each case depend on their responses to skepticism and their accounts of the relation between... (shrink)

• Lisp programs are Lisp data—abstract syntax. Programming languages need functions for their abstract • English is important for its semantics—not its syntax • The largest piece of cake—Kleene µ operator • An elephant never forgets and is faithful. • Resolution considered harmful. • Special provers are just strategies—Davis-Putnam • Programs as logical formulas—Algol 48 and Algol..

In The Dynamics of Meaning , Gennaro Chierchia tackles central issues in dynamic semantics and extends the general framework. Chapter 1 introduces the notion of dynamic semantics and discusses in detail the phenomena that have been used to motivate it, such as "donkey" sentences and adverbs of quantification. The second chapter explores in greater depth the interpretation of indefinites and issues related to presuppositions of uniqueness and the "E-type strategy." In Chapter 3, Chierchia extends the dynamic approach to the domain (...) of syntactic theory, considering a range of empirical problems that includes backwards anaphora, reconstruction effects, and weak crossover. The final chapter develops the formal system of dynamic semantics to deal with central issues of definites and presupposition. Chierchia shows that an approach based on a principled enrichment of the mechanisms dealing with meaning is to be preferred on empirical grounds over approaches that depend on an enrichment of the syntactic apparatus. Dynamics of Meaning illustrates how seemingly abstract stances on the nature of meaning can have significant and far-reaching linguistic consequences, leading to the detection of new facts and influencing our understanding of the syntax/semantics/pragmatics interface. (shrink)

The interaction between syntax and its semantics is one which has been well studied in categorical logic. The results of this particular study are employed to understand how the brain is able to create meanings. To emphasize the toy character of the proposed model, we prefer to speak of the homunculus brain rather than the brain per se. The homunculus brain consists of neurons, each of which is modeled by a category, and axons between neurons, which are modeled by (...) functors between the corresponding neuron-categories. Each neuron has its own program enabling its working, i.e. a theory of this neuron. In analogy to what is known from categorical logic, we postulate the existence of a pair of adjoint functors, called Lang and Syn, from a category, now called BRAIN, of categories, to a category, now called MIND, of theories. Our homunculus is a kind of “mathematical robot”, the neuronal architecture of which is not important. Its only aim is to provide us with the opportunity to study how such a simple brain-like structure could “create meanings” and perform abstraction operations out of its purely syntactic program. The pair of adjoint functors Lang and Syn model the mutual dependencies between the syntactical structure of a given theory of MIND and the internal logic of its semantics given by a category of BRAIN. In this way, a formal language and its meanings are interwoven with each other in a manner corresponding to the adjointness of the functors Lang and Syn. Higher cognitive functions of abstraction and realization of concepts are also modelled by a corresponding pair of adjoint functors. The categories BRAIN and MIND interact with each other with their entire structures and, at the same time, these very structures are shaped by this interaction. (shrink)

By logical foundations of language syntax ontology we understand here the construction of formalized linguistic theories based on widely conceived mathematical logic and dependent on two trends in language ontology. The formalization includes exclusively the syntactic aspect of logical analysis of language characterized categorially according to Ajdukiewicz's approach [1935, 1960]. Any categorial language L is characterized formally on two levels: on one of them it concerns the language of expression-tokens, on the other one - that of expression-types. Accepting the (...) view that expression-concretes, that is expression-tokens - thus, physical objects are fundamental language layer, whereas the secondary layer for L are expression-abstracts, that is expression-types - thus, ideal objects, it is the nominalistic, concretistic philosophical view on the ontological nature of language entities that is adhered to. Supporting the view that expression-types are the basic language layer, while expression-concretes are the secondary one, we take the opposite standpoint - platonizing one. We prove that the two dual approaches towards the two-level syntax theory of language are logically eqivalent. In the scope of language syntax, both conceptions deriving from two different existential assumption are equivalent. This statement is philosophical significance, since it proves that in syntactical studies on language the assumption of the existence of abstract language beings (interpreted as classes equiform tokens) can be neglected. The idea was signalized by author in ealier paper "On the type-token relationships'' [1986) and than, in a slighly diffrent form in English "On the eliminatibility of ideal linguistic entities, Studia Logica 48,no 4 (1989), pp. 587-615. (shrink)