Recent studies have shown that the brain functional connectome constitutes a unique fingerprint that allows the identification of individuals from a group. However, what information encoded in the brain that makes us unique remains elusive. Here, we addressed this issue by examining how individual identifiability changed along the language hierarchy. Subjects underwent fMRI scanning during rest and when listening to short stories played backward, scrambled at the sentence level, and played forward. Identification for individuals was performed between two (...) scan sessions for each task as well as between the rest and task sessions. We found that individual identifiability tends to increase along the language hierarchy: the more complex the task is, the better subjects can be distinguished from each other based on their whole-brain functional connectivity profiles. A similar principle is found at the functional network level: compared to the low-order network (the auditory network), the high-order network is more individualized (the frontoparietal network). Moreover, in both cases, the increase in individual identifiability is accompanied by the increase in inter-subject variability of functional connectivities. These findings advance the understanding of the source of brain individualization and have potential implications for developing robust connectivity-based biomarkers. (shrink)

Roman Ingarden offered a strong criticism of the verifiability principle in his talk delivered at the 8th International Congress in Prague in 1934. Ingarden argued that this principle either violates itself or smuggles a hidden sense. In this paper I show that Ingarden-like arguments about smuggled (but this pejorative qualification is skipped) meaning apply not only to the criteria of sense, but also to other semantic assertions within language-hierarchies in Tarski’s sense.

This article argues that the English-language nonsense words “foo,” “bar,” “baz,” and others in a more or less standardized sequence of so-called metasyntactic variables commonly used in computer programming ought to be understood as meta-abstractive, re-representing a linguistically derived code’s abstraction of language and the abstraction of the programming language hierarchy itself, making it legible in a manner that rewards culturally oriented study: for example, of programming as a culture and of cultures of software development or (...) engineering. (shrink)

This article argues that the English-language nonsense words “foo,” “bar,” “baz,” and others in a more or less standardized sequence of so-called metasyntactic variables commonly used in computer programming ought to be understood as meta-abstractive, re-representing a linguistically derived code’s abstraction of language and the abstraction of the programming language hierarchy itself, making it legible in a manner that rewards culturally oriented study: for example, of programming as a culture and of cultures of software development or (...) engineering. (shrink)

This article argues that the English-language nonsense words “foo,” “bar,” “baz,” and others in a more or less standardized sequence of so-called metasyntactic variables commonly used in computer programming ought to be understood as meta-abstractive, re-representing a linguistically derived code’s abstraction of language and the abstraction of the programming language hierarchy itself, making it legible in a manner that rewards culturally oriented study: for example, of programming as a culture and of cultures of software development or (...) engineering. (shrink)

This article argues that the English-language nonsense words “foo,” “bar,” “baz,” and others in a more or less standardized sequence of so-called metasyntactic variables commonly used in computer programming ought to be understood as meta-abstractive, re-representing a linguistically derived code’s abstraction of language and the abstraction of the programming language hierarchy itself, making it legible in a manner that rewards culturally oriented study: for example, of programming as a culture and of cultures of software development or (...) engineering. (shrink)

The thesis focuses on a quite recent research field lying in between Descriptive Set Theory and Automata Theory (for infinite objects). In both areas, one is often concerned with subsets of the Cantor space or of its homeomorphic copies. In Descriptive Set Theory, such subsets are usually stratified in topological hierarchies, like the Borel hierarchy, the Wadge hierarchy and the difference hierarchy; in Automata Theory, such sets are studied in terms of regularity, that is, the property of (...) being recognised by an automaton or, equivalently, of being expressible in Monadic Second-Order Logic. This double point of view leads to many interesting questions about the interplay and relationship between topological complexity and regularity. While we have a complete picture of what happens in the case of automata on words, the case of automata on trees is still a terra incognita. Some results have already been obtained for particular classes of languages, like Buchi languages, deterministic languages, ¨ and unambiguous languages. In this thesis we instead drop any restriction and prove some new results concerning arbitrary regular tree languages which belong to low levels of the Borel hierarchy and of the Wadge hierarchy. (shrink)

We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and (...) Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (shrink)

We examine some assumptions about the nature of 'levels of reality' in the light of examples drawn from physics. Three central assumptions of the standard view of such levels (for instance, Oppenheim and Putnam 1958) are (i) that levels are populated by entities of varying complexity, (ii) that there is a unique hierarchy of levels, ranging from the very small to the very large, and (iii) that the inhabitants of adjacent levels are related by the parthood relation. Using examples (...) from physics, we argue that it is more natural to view the inhabitants of levels as the behaviors of entities, rather than entities themselves. This suggests an account of reduction between levels, according to which one behavior reduces to another if the two are related by an appropriate limit relation. By considering cases where such inter-level reduction fails, we show that the hierarchy of behaviors differs in several respects from the standard hierarchy of entities. In particular, while on the standard view, lower-level entities are 'micro' parts of higher-level entities, on our view, a system's macro-level behavior can be seen as a ('non-spatial') part of its micro-level behavior. We argue that this second hierarchy is not really in conflict with the standard view and that it better suits examples of explanation in science. (shrink)

Gödel claimed that Zermelo-Fraenkel set theory is 'what becomes of the theory of types if certain superfluous restrictions are removed'. The aim of this paper is to develop a clearer understanding of Gödel's remark, and of the surrounding philosophical terrain. In connection with this, we discuss some technical issues concerning infinitary type theories and the programme of developing the semantics for higher-order languages in other higher-order languages.

Hierarchies abound to help us organize our world. A hierarchy places items into a general order, where more ‘general’ is also more ‘abstract’. The etymology of hierarchy is grounded in notions of religious and social rank. This article, after a historical review, focuses on knowledge systems, an interloper of the term hierarchy since at least the 1800s. Hierarchies in knowledge systems include taxonomies, classification systems, or thesauri in information science, and systems for representing information and knowledge to (...) computers, notably ontologies and knowledge representation languages. Hierarchies are the logical underpinning of inference and reasoning in these systems, as well as the scaffolding for classification and inheritance. Hierarchies in knowledge systems express subsumption relations that have flexible variants, which we can represent algorithmically, and thus computationally. This article dissects that variability, leading to a proposed typology of hierarchies useful to knowledge systems. The article argues through a perspective informed by Charles Peirce that natural hierarchies are real, can be logically determined, and are the appropriate basis for knowledge systems. Description logics and semantic language standards reflect this perspective, importantly through their open-world logic and vocabularies for generalized subsumption hierarchies. Recent research suggests possible mechanisms for the emergence of natural hierarchies. (shrink)

The general notions of object- and metalanguage are discussed and as a special case of this relation an arbitrary first order language with an infinite model is expanded by a predicate symbol T0 which is interpreted as truth predicate for . Then the expanded language is again augmented by a new truth predicate T1 for the whole language plus T0. This process is iterated into the transfinite to obtain the Tarskian hierarchy of languages. It is shown (...) that there are natural points for stopping this process. The sets which become definable in suitable hierarchies are investigated, so that the relevance of the Tarskian hierarchy to some subjects of philosophy of mathematics are clarified. (shrink)

The Liar paradox is an obstacle to a theory of truth, but a Liar sentence need not contain a semantic predicate. The Pinocchio paradox, devised by Veronique Eldridge-Smith, was the first published paradox to show this. Pinocchio’s nose grows if, and only if, what Pinocchio is saying is untrue. What happens if Pinocchio says that his nose is growing? Eldridge-Smith and Eldridge-Smith : 212-5, 2010) posed the Pinocchio paradox against the Tarskian-Kripkean solutions to the Liar paradox that use language (...) hierarchies. Eldridge-Smith : 306-8, 2011) also set the Pinocchio paradox against semantic dialetheic solutions to the Liar. Beall argued the Pinocchio story was just an impossible story. Eldridge-Smith : 749-752, 2012b) responded that unless the T-schema is a necessary truth of some sort, the Pinocchio principle is possible. Luna : 77–86, 2016) argues that the Pinocchio contradiction proves the principle is false. D’Agostini & Ficara discuss a more plausible physical truth-tracking trait, the Blushing Liar, and argue that the Pinocchio contradiction is not a metaphysical dialetheia. I respond to Luna, and D’Agostini & Ficara, and prove that the Pinocchio paradox is a counterexample to hierarchical solutions to the Liar. (shrink)

Many logics considered in finite model theory have a natural notion of an arity. The purpose of this article is to study the hierarchies which are formed by the fragments of such logics whose formulae are of bounded arity.Based on a construction of finite graphs with a certain property of homogeneity, we develop a method that allows us to prove that the arity hierarchies are strict for several logics, including fixed-point logics, transitive closure logic and its deterministic version, variants of (...) the database language Datalog, and extensions of first-order logic by implicit definitions.Furthermore, we show that all our results already hold on the class of finite graphs. (shrink)

For a Euclidean space , let L n denote the modal logic of chequered subsets of . For every n 1, we characterize L n using the more familiar Kripke semantics, thus implying that each L n is a tabular logic over the well-known modal system Grz of Grzegorczyk. We show that the logics L n form a decreasing chain converging to the logic L of chequered subsets of . As a result, we obtain that L is also a logic (...) over Grz, and that L has the finite model property. We conclude the paper by extending our results to the modal language enriched with the universal modality. (shrink)

For a Euclidean space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{R}^n $$ \end{document}, let Ln denote the modal logic of chequered subsets of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{R}^n $$ \end{document}. For every n ≥ 1, we characterize Ln using the more familiar Kripke semantics, thus implying that each Ln is a tabular logic over the well-known modal system Grz of Grzegorczyk. We show that the logics Ln form a decreasing chain (...) converging to the logic L∞ of chequered subsets of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{R}^\infty $$ \end{document}. As a result, we obtain that L∞ is also a logic over Grz, and that L∞ has the finite model property. We conclude the paper by extending our results to the modal language enriched with the universal modality. (shrink)

Although the two volumes of _Logic, Language, and Meaning_ can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions. Volume 1, _Introduction to Logic_, begins with a historical overview and then offers a thorough introduction to standard propositional and first-order predicate logic. It provides both a syntactic and a semantic approach to inference (...) and validity, and discusses their relationship. Although language and meaning receive special attention, this introduction is also accessible to those with a more general interest in logic. In addition, the volume contains a survey of such topics as definite descriptions, restricted quantification, second-order logic, and many-valued logic. The pragmatic approach to non-truthconditional and conventional implicatures are also discussed. Finally, the relation between logic and formal syntax is treated, and the notions of rewrite rule, automation, grammatical complexity, and language hierarchy are explained. (shrink)

The paper provides a new argument against the classical invariance criterion for logical terms: if all terms with a permutation invariant extension qualify as logical, then for any arbitrary true contingent sentence K of the meta-language, there would be a logically true object-language sentence 'φ' such that K follows from the sentence 'φ is true'. Thus, many logically true sentences would be a posteriori. To prevent this fatal consequence, we propose to alter the invariance criterion: not only the (...) term's extension, but also its semantic clause must satisfy certain invariance conditions. The paper ends with the observation that the new criterion makes explicit the dependency of the classification of terms into logical and non-logical ones at the different levels of the Tarskian hierarchy of languages. (shrink)

To understand – intuitively and analytically both – that man is a „being of light” created as a perfect „face and alikeness” and, implicitly, as a becoming measure of the cosmic „wave patterns”, is the main purpose of the present paper. To recuperate the language of the religion by the privilege of a new „living fields” science (biophotonics) means to realize rationally the millenary expectancy of the ESSENTIAL UNITY: man, cosmos, and divinity, harmoniously together.

The classification of grammars that became known as the Chomsky hierarchy was an exploration of what kinds of regularities could arise from grammars that had various conditions imposed on their structure. Intersubstitutability is closely related to the way different levels on the Chomsky hierarchy correspond to different kinds of memory. This chapter deals with the general concept of a string‐rewriting grammar, which provides the setting in which the Chomsky hierarchy can be formulated. An unrestricted rewriting grammar works (...) with a specified set of nonterminal symbols, and specified set of terminal symbols. From the very outset there were doubts about about whether context‐free grammars (CFGs) could form the basis of a theory of natural language syntax. The grammar's rewrite rules correspond to the automaton's transitions. Chomsky argued that even if the generative capacity of CFGs turned out to be sufficient for English, the resulting grammars would be unreasonably complex. (shrink)

This book begins with the question 'Who am I?' and immediately sets off in an astonishingly original direction. Why didn't anyone before Harding think of responding to this question like this? It's so obvious, once you see it. Harding presents a new vision of our place in the universe that uses the scientific method of looking to see what is true. It turns out that the truth about ourselves is not only true but also very good, and breathtakingly beautiful. We (...) live in a sacred, many-layered, living universe - or rather it lives in us. Though it was completed in 1950, this book is still ahead of its time. One day it will surely be widely recognised for its greatness: its all-encompassing vision, its originality and freshness, its depth of insight, its wide-ranging knowledge, the clarity and poetry of its language, its humanity. It is a world-view not dependent on local culture or religion, but on universally verifiable facts. It is also a world-view that respects our manifest differences whilst celebrating our underlying unity - the unity not just of oneself with other people but with all of life, indeed with the whole universe. Harding died in 2007 aged 97, leaving behind him an impressive body of work. He was a highly creative person who was passionate about - he was in love with - this living universe and the immortal treasure that abides at its centre - at our centre. "A work of the highest genius." C. S. Lewis. (shrink)

Quine’s way of dealing with the semantical paradoxes (Ways of Paradox, pp. 9-10) is criticized. The criticism is based on three premises: (1) no learnable language has infinitely many semantical primitives; (2) any language of which Quine’s theory is true has infinitely many semantical primitives; (3) English is a learnable language. The conclusion drawn is that Quine’s theory is not true of English.

3rd ed, 2021. A circumscription of the classical theory of computation building up from the Chomsky hierarchy. With the usual topics in formal language and automata theory.

Mates’s Puzzle has flown below many philosophers’ radar, despite its relations to both Frege’s Puzzle and the Paradox of Analysis. We explain the relations amongst these puzzles on the way to arguing that Mates’s Puzzle suggests a generalization of Frege’s Puzzle, and of the sense-reference distinction itself, in the form of hierarchy of senses. We explain how Mates’s Puzzle and the hierarchy, to different degrees, illuminate each other, and how their connection is missed in the literature. However, we (...) argue that the potential of Mates’s Puzzle to illuminate the hierarchy is yet to be fully actualised. We suggest that in order to do better, we need to formulate Mates’s Puzzle as a puzzle in the philosophy of thought and not as puzzle in the philosophy of language. What is needed, to which the present paper is a precursor, is an account of the cognitive significance of higher-order senses. (shrink)

There is a perennial philosophical dream of a certain natural order for the natural kinds. The name of this dream is ‘the hierarchy requirement’. According to this postulate, proper natural kinds form a taxonomy which is both unique and traditional. Here I demonstrate that complex scientific objects exist: objects which generate different systems of scientific classification, produce myriad legitimate alternatives amongst the nonetheless still natural kinds, and make the hierarchical dream impossible to realize, except at absurdly great cost. Philosophical (...) hopes for a certain order in nature cannot be fulfilled. Natural kinds crosscut one another, ubiquitously so, and this crosscutting spells the end of the hierarchical dream. (shrink)

This book begins with the question 'Who am I?' and immediately sets off in an astonishingly original direction. Why didn't anyone before Harding think of responding to this question like this? It's so obvious, once you see it. Harding presents a new vision of our place in the universe that uses the scientific method of looking to see what is true. It turns out that the truth about ourselves is not only true but also very good, and breathtakingly beautiful. We (...) live in a sacred, many-layered, living universe - or rather it lives in us. Though it was completed in 1950, this book is still ahead of its time. One day it will surely be widely recognised for its greatness: its all-encompassing vision, its originality and freshness, its depth of insight, its wide-ranging knowledge, the clarity and poetry of its language, its humanity. It is a world-view not dependent on local culture or religion, but on universally verifiable facts. It is also a world-view that respects our manifest differences whilst celebrating our underlying unity - the unity not just of oneself with other people but with all of life, indeed with the whole universe. Harding died in 2007 aged 97, leaving behind him an impressive body of work. He was a highly creative person who was passionate about - he was in love with - this living universe and the immortal treasure that abides at its centre - at our centre. "A work of the highest genius." C. S. Lewis. (shrink)

Prominence hierarchy effects such as the animacy hierarchy and definiteness hierarchy have been a puzzle for formal treatments of case since they were first described systematically in Silverstein 1976. Recently, these effects have received more sustained attention from generative linguists, who have sought to capture them in treatments grounded in well-understood mechanisms for case assignment cross-linguistically. These efforts have taken two broad directions. In the first, Aissen 1999, 2003 has integrated the effects elegantly into a competition model (...) of grammar using OT formalisms, where iconicity effects emerge from constraint conjunctions between constraints on fixed universal hierarchies (definiteness, animacy, person, grammatical role) and a constraint banning overt morphological expression of case. The second direction grows out of the work of Jelinek and Diesing, and is found most articulated in Jelinek 1993, Jelinek and Carnie 2003, and Carnie 2005. This work takes as its starting point the observation that word order is sometimes correlated with the hierarchies as well, and works backwards from that to conclusions about phrase structure geometries. In this paper, I propose a particular implementation of this latter direction, and explore its consequences for our understanding of the nature of case assignment. If hierarchy effects are due to positional differences in phrase structures, then, I argue, the attested cross-linguistic differences fall most naturally out if the grammars of these languages countenance polyvalent case—that is, assignment of more than one case value to a single nominal phrase. (shrink)

Sociology originated in the mid-nineteenth century from a new confidence in the power of science to explain the world on a mathematical foundation. Both mathematics and sociology transformed over the ensuing century, inverting the hierarchical relationship from sociology as a mathematics-based science of complex human configurations to mathematics as a complex science based on social institutions. That is, where sociology began as the hard case for mathematics, it became possible to see mathematics as the hard case for sociology. In this (...) light, we examine a number of motivations and provocations for the sociology of mathematics, from language and social cognition to Marxist and materialist skepticism of ideology, and sample the evidence and arguments brought to bear on the sociology of mathematics at a range of scales. (shrink)

When people describe motion events, their path expressions are biased toward inclusion of goal paths (e.g., into the house) and omission of source paths (e.g., out of the house). In this paper, we explored whether this asymmetry has its origins in people’s non-linguistic representations of events. In three experiments, 4-year-old children and adults described or remembered manner of motion events that represented animate/intentional and physical events. The results suggest that the linguistic asymmetry between goals and sources is not fully rooted (...) in non-linguistic event representations: linguistic descriptions showed the goal bias for both kinds of events, whereas non-linguistic memory for events showed the goal bias only for events involving animate, goal-directed motion. The findings are discussed in terms of the mapping between non-linguistic representations of goals and sources in language, focusing on the role that linguistic principles play in producing a more absolute goal bias from more gradient non-linguistic representations of paths. (shrink)

What is the point of language? If we begin with that abstract question, we may be tempted towards a high-minded answer: “People say things to get other people to come to know things that they didn't know before” (Stalnaker, 2002, 703). The point is truth, knowledge, communication. If we begin with a concrete question, “What has language to do with race?” we find a different point: to attack, spread hatred, create racial hierarchy. The mere practice of racial (...) categorization is controversial: are race terms natural or social kind terms? What does categorization do to the categorized? (Outlaw, 1990; Omi and Winant, 1994; Appiah, 1996; Andreason, 1998; Kitcher, 1999; Zack, 2002; Haslanger, 2008; Glasgow, 2009). But there is worse than mere categorization to contend with. (shrink)

The aim of this paper is to point out the equivalence between three notions respectively issued from recursion theory, computational complexity and finite model theory. One the one hand, the rudimentary languages are known to be characterized by the linear hierarchy. On the other hand, this complexity class can be proved to correspond to monadic second‐order logic with addition. Our viewpoint sheds some new light on the close connection between these domains: We bring together the two extremal notions by (...) providing a direct logical characterization of rudimentary languages and a representation result of second‐order logic into these languages. We use natural arithmetical tools, and our proofs contain no ingredient from computational complexity. (shrink)

A common objection to hierarchical approaches to truth is that they fragment the concept of truth. This paper defends hierarchical approaches in general against the objection of fragmentation. It argues that the fragmentation required is familiar and unprob-lematic, via a comparison with mathematical proof. Furthermore, it offers an explanation of the source and nature of the fragmentation of truth. Fragmentation arises because the concept exhibits a kind of failure of closure under reflection. This paper offers a more precise characterization of (...) the reflection involved, first in the setting of formal theories of truth, and then in a more general setting. (shrink)

Several writers have assumed that when in “Outline of a Theory of Truth” I wrote that “the orthodox approach” – that is, Tarski’s account of the truth definition – admits descending chains, I was relying on a simple compactness theorem argument, and that non-standard models must result. However, I was actually relying on a paper on ‘pseudo-well-orderings’ by Harrison. The descending hierarchy of languages I define is a standard model. Yablo’s Paradox later emerged as a key to interpreting the (...) result. (shrink)

Formulas of the propositional modal language with the unary modal operators □, Σ1, 1, Σ2, 2,… are considered as schemata of sentences of arithmetic , where □A is interpreted as “A is PA-provable”, ΣnA as “A is PA-equivalent to a Σn-sentence” and nA as “A is PA-equivalent to a Boolean combination of Σn-sentences”. We give an axiomatization and show decidability of the sets of the modal formulas which are schemata of: PA-provable, true arithmetical sentences.

This monograph explores how seven prominent German and Austrian novelists of the twentieth century—Franz Kafka, Thomas Mann, Anna Seghers, Uwe Johnson, Ingeborg Bachmann, Wolfgang Hilbig, and Marlene Steeruwitz—conveyed their literary figures' time spent waiting. By presenting states of waiting as emblematic of human existence in the turbulent twentieth century, these writers criticized hierarchical power structures in various historical contexts. Killing Time presents fresh readings of seven German-language novels, while providing insights into how and why German and Austrian writers repeatedly (...) turned to the waiting motif to expose the injustices inherent in interpersonal, political, and social hierarchies. In investigating the treatment of waiting in literary texts, William reexamines how prominent philosophers of metaphor and time influenced German and Austrian writers of the past century. This study is underpinned in part by the work of cultural and social theorists who have emphasized how the liminal status of the subjugated within social hierarchies ensures that they are kept perpetually waiting. (shrink)