There are (at least) four numbers of physical and cosmological significance, whose inferred values, when expressed in mass units, cluster in a window below 1 eV. There are: the neutrino mass, the neutrino chemical potential, the cosmological constant, and the size of two extra dimensions (if the fundamental scale of gravity is 1–10 TeV). In this note, we imagine ways in which these four numbers could all be connected.

We define a new theory of concatenation WTC which is much weaker than Grzegorczyk's well-known theory TC. We prove that WTC is mutually interpretable with the weak theory of arithmetic R. The latter is, in a technical sense, much weaker than Robinson's arithmetic Q, but still essentially undecidable. Hence, as a corollary, WTC is also essentially undecidable.

Logical pluralism is the theory that there is more than one right logic. Logical instrumentalism is the view that a logic is a correct logic if it can be used to fruitfully pursue some deductive inquiry. Logical instrumentalism is a version of logical pluralism, since more than one logic can be used fruitfully. In this paper, I will show that a logical instrumentalist must accept linear logic as a correct logic, since linear logic is useful for studying natural language syntax. (...) I further show that this means that the logical instrumentalist must accept a wide range of connectives, in particular concatenation. I end by explaining why this is a feature rather than a bug. (shrink)

This paper presents a slightly modified version of the compositional semantics proposed in Events and Semantic Architecture (OUP 2005). Some readers may find this shorter version, which ignores issues about vagueness and causal constructions, easier to digest. The emphasis is on the treatments of plurality and quantification, and I assume at least some familiarity with more standard approaches.

In his paper "Undecidability without arithmetization," Andrzej Grzegorczyk introduces a theory of concatenation $\mathsf{TC}$. We show that pairing is not definable in $\mathsf{TC}$. We determine a reasonable extension of $\mathsf{TC}$ that is sequential, that is, has a good sequence coding.

We prove that a variant of Robinson arithmetic $\mathsf{Q}$ with nontotal operations is interpretable in the theory of concatenation $\mathsf{TC}$ introduced by A. Grzegorczyk. Since $\mathsf{Q}$ is known to be interpretable in that nontotal variant, our result gives a positive answer to the problem whether $\mathsf{Q}$ is interpretable in $\mathsf{TC}$. An immediate consequence is essential undecidability of $\mathsf{TC}$.

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.

Keystream sequences should look as random as possible, i.e. should present no logical pattern to be exploited in cryptographic attacks. The generalized self-shrinking generator, a sequence generator based on irregular decimation, produces a family of sequences with good cryptographic properties. In this work, we display a detailed analysis on the randomness of the sequences resulting from the concatenation of elements of this family. We apply the most important batteries of statistical and graphical tests providing powerful results and a new (...) method to construct sequences with good cryptographic properties. (shrink)

We consider weak theories of concatenation, that is, theories for strings or texts. We prove that the theory of concatenation WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, which is a weak subtheory of Grzegorczyk’s theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document}, is a minimal essentially undecidable theory, that is, the theory WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document} is essentially undecidable and if one omits an axiom scheme from (...) WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, then the resulting theory is no longer essentially undecidable. Moreover, we give a positive answer to Grzegorczyk and Zdanowski’s conjecture that ‘The theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document} is a minimal essentially undecidable theory’. For the alternative theories WTC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}}$$\end{document} and TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}}$$\end{document} which have the empty string, we also prove that the each theory without the neutrality of ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}$$\end{document} is to be such a theory too. (shrink)

The dynamical equations of relativistic quantum mechanics prescribe the motion of wave packets for sets of events which trace out the world lines of the interacting particles. Electromagnetic theory suggests thatparticle world line densities be constructed from concatenation of event wave packets. These sequences are realized in terms of conserved probability currents. We show that these conserved currents provide a consistent particle and antiparticle interpretation for the asymptotic states in scattering processes. The relation between current conservation and unitarity is (...) used to establish relations between pair production and annihilation amplitudes and scattering. The discrete symmetriesC, T, P are studied and it is shown that no Dirac sea (for fermions where such a construction is possible, or bosons where it is not) is required for consistency of the theory. These currents, furthermore, represent the discrete symmetries in a way consistent with their interpretation as particle currents. (shrink)

Paul M. Pietroski, University of Maryland For any sentence of a natural language, we can ask the following questions: what is its meaning; what is its syntactic structure; and how is its meaning related to its syntactic structure? Attending to these questions, as they apply to sentences that provide evidence for Davidsonian event analyses, suggests that we reconsider some traditional views about how the syntax of a natural sentence is related to its meaning.

In the language \(\lbrace 0, 1, \circ, \preceq \rbrace \), where 0 and 1 are constant symbols, \(\circ \) is a binary function symbol and \(\preceq \) is a binary relation symbol, we formulate two theories, \( \textsf {WD} \) and \( {\textsf {D}}\), that are mutually interpretable with the theory of arithmetic \( {\textsf {R}} \) and Robinson arithmetic \({\textsf {Q}} \), respectively. The intended model of \( \textsf {WD} \) and \( {\textsf {D}}\) is the free semigroup generated (...) by \(\lbrace {\varvec{0}}, {\varvec{1}} \rbrace \) under string concatenation extended with the prefix relation. The theories \( \textsf {WD} \) and \( {\textsf {D}}\) are purely universally axiomatised, in contrast to \( {\textsf {Q}} \) which has the \(\varPi _2\) -axiom \(\forall x \; [ \ x = 0 \vee \exists y \; [ \ x = Sy \ ] \ ] \). (shrink)

We show that we can interpret concatenation theories in arithmetical theories without coding sequences by identifying binary strings with \(2\times 2\) matrices with determinant 1.

The word “encyclopedia” comes to us from the Greek or, more precisely, is the deformed transcription, through Latin, of a erase in which we recognize a word composed of two elements, enkyklios and paideia, found in Quintilian in the ancient editions of De institutione oratoria (I, 10, 1). The expression itself, enkyklios paideia, appears only later, in the Hellenistic Age, under Roman domination, beginning with Dionysius of Halicarnassus (around the first century B.C.), but the concept goes back to the Eleatics, (...) especially to Hippias of Elis who, if we can believe the account in Plato's Dialogues, taught this total knowledge, later known with the term enkyklopaideia. (shrink)

For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. (...) It is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories. (shrink)

Is well-being the kind of thing that can be summed across individuals? This paper takes a measurement-theoretic approach to answering this question. To make sense of adding well-being, we would need to identify some natural "concatenation" operation on the bearers of well-being that satisfies the axioms of extensive measurement and can therefore be represented by the arithmetic operation of addition. I explore various proposals along these lines, involving the concatenation of segments within lives over time, of entire lives (...) led alongside one another or in sequence, and of evaluatively basic propositions via conjunction. All of these proposals turn out to carry highly controversial commitments about the good. I do not claim that these commitments are unacceptable. But they suggest that we cannot simply take for granted, as many philosophers do, that there is any such thing as the sum of well-being. (shrink)

We examine the Doubly Inflected Construction of Sicilian (DIC; Cardinaletti and Giusti 2001, 2003, Cruschina 2013), in which a motion verb V1 from a restricted set is followed by an event verb V2 and both verbs are inflected for the same person and tense features. The interpretation of DIC involves a complex event which behaves as a single, integrated event by linguistic tests. Based on data drawn from different sources, we argue that DIC is an asymmetrical serial verb construction (Aikhenvald (...) 2006). We propose an analysis of DIC in which V1 and V2 enter the semantic composition as lexical verbs, with V1 contributing a motion event and projecting a theme and a goal argument which are identified, respectively, with an agent and a location argument projected by V2. A morphosyntactic mechanism of feature-spread requires that the person and tense features be realized both on V1 and on V2, while, semantically, these features are interpreted only once, in a position from which they take scope over the complex predicate resulting from the combination of V1 and V2. The semantic analysis is based on an operation of event concatenation, defined over spatio-temporally contiguous events which share specific participants, and is implemented in a neo-Davidsonian framework (Parsons 1990). (shrink)

Kristiansen and Murwanashyaka recently proved that Robinson arithmetic, Q, is interpretable in an elementary theory of full binary trees, T. We prove that, conversely, T is interpretable in Q by producing a formal interpretation of T in an elementary concatenation theory QT+, thereby also establishing mutual interpretability of T with several well-known weak essentially undecidable theories of numbers, strings, and sets. We also introduce a “hybrid” elementary theory of strings and trees, WQT*, and establish its mutual interpretability with Robinson’s (...) weak arithmetic R, the weak theory of trees WT of Kristiansen and Murwanashyaka, and the weak concatenation theory WTCε of Higuchi and Horihata. (shrink)

This paper relates to Lyotard's philosophy of a différend. The paper has a dual purpose. The first is to explain what is meant by a différend and also a petit différend. The intention here is to preserve both the intrinsic validity and ethico-political value of the concept in cases where its legitimacy might easily be denied. This feeds into the second and main purpose of the paper, which is to testify to a petit différend in quality of care, so that (...) care may be taken in how the term ‘quality of care’ is actually used. It is here that the implications of a petit différend in quality of care are opened up from the perspective of cared-for and professional carers, respectively. It will be shown that the idea of quality of care is open to multiple interpretations, and therefore to disputes that judgement cannot resolve to the satisfaction of all parties. (shrink)

Concatenation, conjunction, and connection -- The sensitive infosphere -- Global skin : a trans-identitarian patchwork -- The aesthetic genealogy of globalization -- Language, limit, excess -- Avatars of the general intellect -- The swarm effect -- Social morphogenesis and neuroplasticity -- The transhuman -- The horizon of mutation -- Consciousness and evolution -- The end.

A concatenation of forces surrounded the rise of the photographic to the center of contemporary art practice. During the sixties the author-function was seriously critiqued. Roland Barthes announced the death of the author in 1967, and Michel Foucault answered his own question, what is an author? deconstructively in 1969, replacing what William Wimsatt and Monroe Beardsley had already termed the intentional fallacy with a model of the cultural constructedness of all notions of creative agency. At the same time, notions (...) of automatism generated by psychoanalytic models of mind and dada and surrealist conceptions of artistic and literary practice joined forces with sixties anticanonical, postexpressionist notions of the artwork as the deskilled, mechanical product of a consumerist society whose forces yielded the fantasy of individual will. Meanwhile, also during the sixties, painters such as Andy Warhol and Robert Rauschenberg began to use found photographs very overtly either as part and parcel of the generative process of their work or inside their work along with other kinds of materials. And thus the medium-specific boundaries between the photographic and the painterly, just to take the two, began to crumble for good, though the art-school disciplines and museum departments dedicated to these two media continued to hold sway. (shrink)

This thesis concerns alternative concatenating operations in extensive measurements and the degree to which concatenating operations are matter of convention. My arguments are directed against Ellis' claim that what prevents us from choosing alternative ways of combining extensive quantities is only convenience and simplicity and that the choice is not based on empirical reasons. ;My first argument is that, given certain relational theories of measurement, there can be no more than one concatenating operation per quantity; because combining operations are the (...) only conclusive distinguishing characteristic among distinct extensive measurements and thus the only thing that can serve as an indicator for the identity of a quantity. Rectangular and collinear concatenation, for example, cannot both be used as a way of combining lengths. However, rectangular concatenation could be used to measure some other extensive quantity since it fulfills the necessary conditions for adequate numerical assignment. ;For those that adopt theories of measurement which can support the claim that dinches measure length, I demonstrate, in the second argument, that rectangular concatenation would be a bad alternative and thus no alternative at all. Implementation of rectangular concatenation requires a new science; a science compatible with dinches violates present invariance principles and a new set must be provided, if possible. It is not clear that there is a set of invariance principles compatible with dinches which also gives basis for a science that explains the phenomena as well as the old one. Moreover, new invariance principles would be unintuitive and would require that certain fundamental concepts change their meaning. For these reasons the choice between them is guided by a number of empirical reasons and is not only a matter of convention. (shrink)

Two arguments apparently support the thesis that collective identity presupposes an Other: the recognition argument, according to which seeing myself as a self requires recognition by an other whom I also recognize as a self (Hegel); and the dialogic argument, according to which my sense of self can only develop dialogically (Taylor). But applying these arguments to collective identity involves a compositional fallacy. Two modern ideologies mask the particularist thesis’s falsehood. The ideology of indivisible state sovereignty makes sovereignty as such (...) appear particularistic by fusing “internal” with “external” sovereignty; nationalism imagines national identity as particularistic by linking it to sovereignty. But the concatenation of internal sovereignty, external sovereignty, and nation is contingent. Schmitt’s thesis that “the political” presupposes an other conflates internal and external sovereignty, while Mouffe’s neo-Schmittianism conflates difference (Derrida) with alterity. A shared global identity may face many obstacles, but metaphysical impossibility and conceptual confusion are not among them. (shrink)

Analytic philosophy is difficult to define since it is not so much a specific doctrine as a loose concatenation of approaches to problems. As well as having strong ties to scientism -the notion that only the methods of the natural sciences give rise to knowledge -it also has humanistic ties to the great thinkers and philosophical problems of the past. Moreover, no single feature characterizes the activities of analytic philosophers. Undaunted by these difficulties, Avrum Stroll investigates the "family resemblances" (...) between that impressive breed of thinkers known as analytic philosophers. In so doing, he grapples with the point and purpose of doing philosophy: What is philosophy? What are its tasks? What kind of information, illumination, and understanding is it supposed to provide if it is not one of the natural sciences? Imbued with clarity, liveliness, and philosophical sophistication, Stroll´s book presents a synoptic picture of the main developments in logic, philosophy of language, epistemology, and metaphysics in the past century. It does this by concentrating on the individual thinkers whose ideas have been most influential. Major themes in Twentieth-Century Analytic Philosophy include: · the innovation of mathematical logic by Gottlob Frege at the close of the nineteenth century and its independent development by Bertrand Russell; · the impact of advancements in science on the world of philosophy and its importance for understanding such doctrines as logical positivism, philosophy of language, philosophy of mind, and eliminative materialism; · the refusal by such thinkers as Wittgenstein, Moore, and Austin to treat logic as an ideal language superior to natural languages; and · a conjecture about which, if any, of the philosophers discussed in the book will enter the pantheon of philosophical gods. Along the way, Stroll also covers the theories of Rudolf Carnap, W. V. O. Quine, Gilbert Ryle, J. L. Austin, Hilary Putnam, Saul Kripke, John Searle, Ruth Marcus, and Patricia and Paul Churchland. Stroll´s approach to his subject treats the critical movements in analytic philosophy in terms of the philosophers who defined them. The notoriously complex realm of analytic philosophy emerges less as an abstract enterprise than as a domain of personalities and their competing methods and arguments. The book´s inventive presentations of complex logical doctrines relate them to the traditional problems of philosophy, seeking the continuity between them rather than polemical distinctions so as to bring the true differences of their respective achievements into sharper focus. (shrink)

[Edited from Conclusion section:] We have looked at various challenging issues to do with getting connectionism to cope with high-level cognitive activities such a reasoning and natural language understanding. The issues are to do with various facets of generalization that are not commonly noted. We have been concerned in particular with the special forms these issues take in the arena of propositional attitude processing. The main problems we have looked at are: (1) The need to construct explicit representations of generalizations, (...) not just generalize correctly to individual cases; (2) The need to be able to match two or more complex short-term information structures, to enable rapid generalization from recent examples rather than from long-term memories; (3) The need to represent and reason with anomalous combinations of concepts; (4) The need to perform embedded reasoning. This presents special problems for systems using non-concatenative representations (as in mainstream connectionist approaches). We also touched on vague quantification in attitude report complements. Neither this topic nor that of analogies between short-term structures (point 2) has been adequately addressed in the symbolic framework, let alone in connectionism. -/- The opportunities and problems covered are put forward as things worth being optimistic about or pessimistic about, respectively. They are not put forward as decisive arguments for or against connectionism. The hope is that this chapter contributes to a greater understanding of the connectionist/symbolist gap by presenting some unusual issues and by throwing new light on some well known ones. (shrink)

An elementary theory of concatenation,QT+, is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, quantifier-free part of Kirby’s finitary set theory, and Adjunctive Set Theory, with or without extensionality. The most basic arithmetic and simplest set theory thus turn out to be variants of string theory.