This chapter contains sections titled: Introduction On Foundations Properties, Sums, Plurality, and Reality Mereological Property Theory Foundations of Mathematics.

This paper shows that species are individuals with respect to evolutionary theory in the sense that the laws of the theory deal with species as irreducible wholes rather than as sets of organisms. 'Species X' is an instantiation of a primitive term of the theory. I present a sketch of a proof that it cannot be defined within the theory as a set of organisms; the proof relies not on details of my axiomatization but rather on a generally accepted property (...) of speciation; hence the same argument should work for any axiomatization which captures this generally accepted property of speciation. (shrink)

In the last decade, Systems Biology has emerged as a conceptual and explanatory alternative to reductionist-based approaches in molecular biology. However, the foundations of this new discipline need to be fleshed out more carefully. In this paper, we claim that a relational ontology is a necessary tool to ground both the conceptual and explanatory aspects of Systems Biology. A relational ontology holds that relations are prior—both conceptually and explanatory—to entities, and that in the biological realm entities are defined primarily (...) by the context they are embedded within—and hence by the web of relations they are part of. (shrink)

In 1908 the German mathematician Ernst Zermelo gave an axiomatization of the concept of set. His axioms remain at the core of what became to be known as Zermelo-Fraenkel set theory. There were two axioms that received diverse criticisms at the time: the axiom of choice and the axiom of separation. This paper centers around one question this latter axiom raised. The main purpose is to show how this question might be solved with the aid of another, more recent mathematical (...) theory of sets which, like Zermelo’s, has numerous philosophical underpinnings. Keywords: properties of sets, foundations of mathematics, axiom of separation, subobject classifier, truth values. (shrink)

The theoretical foundations of the social structure of the society and the historical forms of ownership were discussed in the article. The presence of many types of property is a necessary condition for its normal functioning in society. As a result of these types of property, the needs and activities of every person in society are fully satisfied. From ancient times to the present day, attitudes towards property issues have developed in different ways in different regimes. Even before the (...) creation of society, people generally, used and took advantage of collective property. Over time, as a result of a number of events occurring in the world and in nature, collective property began to lose its relevance. After property inequality began to emerge, stratification among people began to form, which acted as a driving force for the creation of other forms of property. The collective form of property gradually changed and began to be replaced by individual and other forms of property. Modern production is conditioned by the transformation of economic, social and other spheres, which, in turn, creates the basis for the formation of new types of social systems and requires the reconsideration of property as the main category of private-legal relations. Since property is multi-subject, it not only expands and complicates the internal structure of property subjects, but also means the formation of new social classes according to the place they occupy (the functions they perform) in property relations.The modern structure of property relations is formed as a complex multi-level system: the close contact of individual and common beginnings, levels of ownership, the specificity of various sociаl fields creates the opportunity and demand for the formation of various forms of property, determines their dynamics and transformation in advance. Different classes and groups of owners, territorial associations, state, national groups and monopolies become the subjects of property relations. (shrink)

We present a conceptual analysis of the notions of actual physical property and potential physical property as used by theoretical physicists/mathematicians working in the domain of operational quantum logic. We investigate how these notions are being used today and what role they play in the specified field of research. In order to do so, we will give a brief introduction to this area of research and explain it as a part of the discipline known as “mathematical metascience”. An in depth (...) analysis of Aristotle’s use of the notions of “actuality” and “potentiality” is presented in order to point out exactly how much of the Aristotelian connotations are embedded in the contemporary use of the concepts under investigation. Although we will not focus in depth on all the drawbacks in the early historical development of physics due to the overwhelming influence of Aristotle’s writings, our analysis does touch upon some aspects of the Aristotelian theory of movement that are often overthrown nowadays. (shrink)

The Evolutionary Synthesis is often seen as a unification process in evolutionary biology, one which provided this research area with a solid common theoretical foundation. As such, neo-Darwinism is believed to constitute from this time onward a single, coherent, and unified movement offering research guidelines for investigations. While this may be true if evolutionary biology is solely understood as centred around evolutionary mechanisms, an entirely different picture emerges once other aspects of the founding neo-Darwinists’ views are taken into consideration, aspects (...) potentially relevant to the elaboration of an evolutionary worldview: the tree of life, the ontological distinctions of the main cosmic entities , the inherent properties of self-organizing matter, evolutionary ethics, and so on. Profound tensions and inconsistencies are immediately revealed in the neo-Darwinian movement once this broader perspective is adopted. This pluralism is such that it is possible to identify at least three distinct and quasi-incommensurable epistemological/metaphysical frameworks as providing a proper foundation for neo-Darwinism. The analysis of the views of Theodosius Dobzhansky, Bernhard Rensch, and Ernst Mayr will illustrate this untenable pluralism, one which requires us to conceive of the neo-Darwinian research agenda as being conducted in more than one research programme or research tradition at the same time. (shrink)

What is a minimal proof-theoretical foundation of logic? Two different ways to answer this question may appear to offer themselves: reduce the whole of logic either to the relation of inference, or else to the property of incompatibility. The first way would involve defining logical operators in terms of the algebraic properties of the relation of inference—with conjunction $$\hbox {A}\wedge \hbox {B}$$ A ∧ B as the infimum of A and B, negation $$\lnot \hbox {A}$$ ¬ A as the minimal (...) incompatible of A, etc. The second way involves introducing logical operators in terms of the relation of incompatibility, such that X is incompatible with $$\{\lnot \hbox {A}\}$$ { ¬ A } iff every Y incompatible with X is incompatible with {A}; and X is incompatible with $$\{\hbox {A}\!\wedge \!\hbox {B}\}$$ { A ∧ B } iff X is incompatible with {A,B}; etc. Whereas the first route leads us naturally to intuitionistic logic, the second leads us to classical logic. The aim of this paper is threefold: to investigate the relationship of the two approaches within a very general framework, to discuss the viability of erecting logic on such austere foundations, and to find out whether choosing one of the ways we are inevitably led to a specific logical system. (shrink)

In addition to its main theme of freedom, Hegel’s political philosophy addresses the problem of poverty. This article proposes a theoretical foundation for a Hegelian welfare state by demonstrating how its rationale and concepts are derived from Hegel’s political philosophy. Poverty constitutes a fundamental deficiency in the modern liberal state focused on the self-actualization of its citizens. This poverty is not an accidental but a structural factor of modern market society, resulting from economic contingencies. The poor rabble is deprived of (...) the opportunities for self-actualization that market society provides. Therefore, the main task of a Hegelian welfare state is to secure the right of subsistence as a condition of the possibility of self-actualization. Without subsistence citizens are unable to develop and actualize their free will through property formation in market society. Derived from Hegel’s right of necessity and the guiding principle of freedom, the right of subsistence is paramount to the legitimacy of the state. Therefore, it cannot be left to the contingent morality of private charity. The right of subsistence does not only guarantee mere survival, but also includes a minimum of property needed to participate in market society. (shrink)

In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency (_LFI_) a more appealing formalism for reasoning under uncertainty, it is important to develop the proof theory of the first-order versions of such _LFI_s. Here, we intend to make a first step in this direction. On the other hand, the logic _Ciore_ was developed to provide new logical systems in the study of inconsistent databases from the point of view of _LFI_s. (...) An interesting fact about _Ciore_ is that it has a _strong_ consistency operator, that is, a consistency operator which (forward/backward) propagates inconsistency. Also, it turns out to be an algebraizable logic (in the sense of Blok and Pigozzi) that can be characterized by means of a 3-valued logical matrix. Recently, a first-order version of _Ciore_, namely _QCiore_, was defined preserving the spirit of _Ciore_, that is, without introducing unexpected relationships between the quantifiers. Besides, some important model-theoretic results were obtained for this logic. In this paper we study some proof–theoretic aspects of both _Ciore_ and _QCiore_ respectively. In first place, we introduce a two-sided sequent system for _Ciore_. Later, we prove that this system enjoys the cut-elimination property and apply it to derive some interesting properties. Later, we extend the above-mentioned system to first-order languages and prove completeness and cut-elimination property using the well-known Shütte’s technique. (shrink)

With the rapidly growing amounts of information, visualization is becoming increasingly important, as it allows users to easily explore and understand large amounts of information. However the field of information visualiza- tion currently lacks sufficient theoretical foundations. This article addresses foundational questions connecting information visualization with computing and philosophy studies. The idea of multiscale information granula- tion is described based on two fundamental concepts: information (structure) and computation (process). A new information processing paradigm of Granular Computing enables stepwise increase (...) of granulation/aggregation of information on different levels of resolution, which makes possible dynamical viewing of data. Information produced by Google Earth is an illustration of visualization based on clustering (granulation) of information on a succession of layers. Depending on level, specific emergent properties become visible as a result of different ways of aggregation of data/information. As information visualization ultimately aims at amplifying cognition, we discuss the process of simulation and emulation in relation to cognition, and in particular visual cognition. (shrink)

This paper presents a type-free property-theoretic system in the spirit of a framework proposed by Menzel and then supplements it with a theory of truth and exemplification. The notions of a truth-relevantly complex (simple) sentence and of a truth-relevant subsentence are introduced and then used in order to motivate the proposed theory. Finally, it is shown how the theory avoids Russell's paradox and similar problems. Some potential applications to the foundations of mathematics and to natural language semantics are sketched (...) in the introduction. (shrink)

In The Foundations of Private Law James Gordley argues that the modern private law in common and civil law jurisdictions is best explained on the basis of a neo-Aristotelian theory first developed by a group of 16th century Spanish thinkers known as the ‘late scholastics’. The concepts of distributive and commutative justice that, according to Gordley, lay at core of the scholastics’ theory and that explain, respectively, modern property law and the law of obligations , though ignored and disparaged (...) for much of the 19th and 20th centuries, are today familiar to most private law scholars . Yet Gordley’s understanding of these concepts and, in particular, of their relationship both to one another and to the apex idea of ‘living a distinctively human life’ is unique, setting his account apart not just from utilitarian and other ‘modern’ accounts of private law, but also from other neo-Aristotelian theories . In Gordley’s presentation, commutative justice is derived from distributive justice and distributive justice is derived from the idea of the distinctively human life. Confidently traversing a wide range of historical, comparative and theoretical materials, the book’s argument is at once ambitious, learned, and elegantly presented. But as a theoretical account of the foundations of the modern private law it is unpersuasive. The book’s own account of property law suggests that in practice the idea of distributive justice does little, if any, work in explaining the rules we actually have. Nor is it clear how, if at all, distributive justice flows from the allegedly foundational idea of the ‘distinctively human life’. As for commutative justice, it is not clear why, if is derived from distributive justice in the way Gordley believes, the courts should care about it. Finally, but perhaps most significantly, Gordley’s conception of commutative justice is unable to account for central features of the law of obligations. (shrink)

Classical first-order logic \ is commonly used to study logical connections between statements, that is sentences that in every context have an associated truth-value. Inquisitive first-order logic \ is a conservative extension of \ which captures not only connections between statements, but also between questions. In this paper we prove the disjunction and existence properties for \ relative to inquisitive disjunction Open image in new window and inquisitive existential quantifier \. Moreover we extend these results to several families of theories, (...) among which the one in the language of \. To this end, we initiate a model-theoretic approach to the study of \. In particular, we develop a toolkit of basic constructions in order to transform and combine models of \. (shrink)

This dissertation has three parts. Part I, comprising chapters 1 and 2, addresses some basic commitments which must be presupposed in theorizing about concepts. Concepts, to a first approximation, are mental representations that are constituents of thoughts. Chapter 1 attempts to clarify the notion of representing. Chapter 2 reconstructs arguments in the work of Frege against the mental nature of thoughts and (by the same token) of concepts, arguing that they are confused and leave the notion of concepts as mental (...) representations unscathed. Part II, comprising chapters 3 to 5, pursues the aim of closing in on concepts in light of the widely shared understanding that concepts form a more specific class than just any kind of subpropositional mental representations. This part, if successful, should also help clarify the interrelations among a certain cluster of ideas which are customarily connected to the property of being a concept. Chapter 3 advocates storage in long-term memory as a basic, explanatorily principled criterion of delimiting concepts from nonconceptual mental representations. In leading up to this criterion, the chapter subjects to methodological critique the typical manner in which philosophers justify their assumption of a conceptual/nonconceptual-distinction. Chapter 4 investigates the idea that concepts are, in some sense, mental representations under which we categorize things in the world. Two versions of this idea of categorizing mental representations are distinguished, one metaphysical, the other psychological in kind. Both of these ideas, it is claimed, are inadequate to capture concepthood as such. Chapter 5 continues on the positive side, reconnecting to an earlier introduced idea which places concepts, other than sensory-perceptual events, in the realm of so-called high-level cognition. Concepts are not only stored in long-term memory, they are also capable of entering into cognitive processes that are “flexible”, rather than “hardwired”. Subdistinctions and explanations are provided that hopefully make the relevant notions workably precise. Part III of the dissertation moves on to engage in more specific debates in the theory of concepts. In one way or another, all three chapters in this part take as their points of departure the influential compositionality arguments against prototype theory often reiterated by Fodor, until recently the agenda-setting concept theorist in the philosophy of psychology. The chapters jointly aim to identify and correct a number of errors committed in the context of this debate: in the basic, generally accepted, presuppositions of these arguments (chapter 6); in the topography of concept-theoretical positions assumed by Fodor and adopted by subsequent commentators (chapter 7); and in the followup comments with which Fodor has intended to support and supplement these arguments (chapter 8). (shrink)

An ab-initio foundation for relativistic spacetime is given, which is a conservative extension of Zermelo’s set theory with urelemente. Primitive entities are worldlines rather than spacetime points. Spacetime points are sets of intersecting worldlines. By the proper axioms, they form a manifold. Entities known in differential geometry, up to a metric, are defined and have the usual properties. A set-realistic point of view is adopted. The intended ontology is a set-theoretical hierarchy with a broad base of the empty set and (...) urelemente. Sets generated from the empty set are mathematically interpreted, all other sets are physically interpreted. (shrink)

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we (...) calculate a canonical characteristic fomula H of S (char(S)) so that ⊢G ∼ H → (∼S) and ⊢GL-LIN ∼ H, and the complexity σ of ∼ H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of ∼ H with H = char(S) and σ(∼ H) = d(S, G). (shrink)

The issue of the emergence of formal axiomatic logical systems due to the emergence of logical antinomies in formal axiomatic systems, specifically the issue of developing formal logical axiomatics in the calculus of considerations was investigated in the considered research. At the same time, in order to determine the characteristics of the implementation of the logical-methodological principles and provisions of the deductive reasoning obviously, conceptual-logical foundations of the calculus of considerations was studied and the main propositions of the calculus (...) of considerations and the analysis of the initial logical operations on them were given in the study. The basic laws of logic and the expression of one logical act with another one were also explained in the research work by giving the concepst of proportional form and tautology in the calculus of considerations. At the same time, main properties and the procedure of setting of the formal deductive theory in the calculus of considerations were studied in the article. In order to provide an adequate characterization of the conceptual and methodological bases of the calculus of considerations in the research work, the basic logical laws of the calculus of considerations developed by the German mathematician and thinker P. Hilbert were also given. In addition, the main principles and methodological provisions of the deductive method were investigated, and the rules of deriving new conclusions from the axioms were interpreted. At the end of the reviewed article, the main principles and methods of the formal axiomatic mathematical systems built on a deductive basis, specifically the calculus of considerations, were studied and a logical-methodological analysis of the calculus of considerations was carried out on this basis. In this framework, the syntactic and semantic analysis of formalized language in formal axiomatic logical systems was carried out separately, the constituent parts of those systems, including the construction scheme, were given. (shrink)

In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACSs A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures (...) with tipically logical properties of the sentential logic S. The main algebraic properties we consider are the closure of FGModS under substructures and under reduced products, and the property that for any A the lattice FACSs A is a complete sublattice of the lattice of all algebraic closed-set systems over A. The logical properties are the existence of a fully adequate Gentzen system for S, the Local Deduction Theorem and the Deduction Theorem for S. Some of the results are established for arbitrary deductive systems, while some are found to hold only for deductive systems in more restricted classes like the protoalgebraic or the weakly algebraizable ones. The paper ends with a section on examples and counterexamples. (shrink)

A sequent calculus methodology for systems of agency based on branching-time frames with agents and choices is proposed, starting with a complete and cut-free system for multi-agent deliberative STIT; the methodology allows a transparent justification of the rules, good structural properties, analyticity, direct completeness and decidability proofs.

This paper explores proof-theoretic aspects of hybrid type-logical grammars, a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also present both a sequent and a proof net calculus for hybrid type-logical grammars. In addition to clarifying the logical foundations of hybrid type-logical grammars, the current study opens the way to variants and extensions of the original system, including but not limited to a non-associative version (...) and a multimodal version incorporating structural rules and unary modes. (shrink)

Let \ be a class of formulas. We say that a theory T in classical logic has the \-disjunction property if for any \ sentences \ and \, either \ or \ whenever \. First, we characterize the \-disjunction property in terms of the notion of partial conservativity. Secondly, we prove a model theoretic characterization result for \-disjunction property. Thirdly, we investigate relationships between partial disjunction properties and several other properties of theories containing Peano arithmetic. Finally, we investigate unprovability of (...) formalized partial disjunction properties. (shrink)

This article takes up Marilyn Strathern’s formulation of a law/culture ‘duplex’ – her term for the complementarity of anthropology and law as means to each other’s ends. She draws attention to the limitations of the duplex, and urges us to consider ethnography as (in part) a project of unwinding its entwinement. As a step toward that end, the article returns to classic texts by Emile Durkheim and Bronislaw Malinowski – texts that were foundational to the emergence of anthropology, and to (...) the establishment of law as an object of study for the social sciences. Re-read in light of Strathern’s insight, what has been widely taken as their relativism emerges instead as their defense of political community as a subject for ethnography, and (accordingly) the basis for a theoretical check on law conceived globally – within states or as colonial overrule. The article concludes with a discussion of the contemporary relevance of that position. (shrink)

The physical, mathematical, and philosophical foundations of the quantum theory of free Bose fields in fixed general relativistic spacetimes are examined. It is argued that the theory is logically and mathematically consistent whereas semiclassical prescriptions for incorporating the back-reaction of the quantum field on the geometry lead to inconsistencies. Still, the relations and heuristic value of the semiclassical approach to canonical and covariant schemes of quantum gravity-plus-matter are assessed. Both conventional and rigorous formulations of the theory and of its (...) principal predictions, cosmological particle creation and horizon radiation, are expounded and compared. Special attention is devoted to spacetime properties needed for the existence or uniqueness of the relevant theoretical elements , renormalization of the stress tensor). The emergence of unitarily inequivalent representations in a single dynamical context is used as motivation for the introduction of the abstract $\rm C\sp{\*}$-algebraic axiomatic formalism. The operationalist and conventionalist claims of the original abstract algebraic program are criticized in favor of its tempered outgrowth, local quantum physics. The interpretation of the theory as a wave mechanics of classical field configurations, deriving from the Schrodinger representations of the abstract algebra, is discussed and is found superior, at least on the level of analogy, to particle or harmonic oscillator interpretations. Further, it is argued that the various detector results and the Fulling nonuniqueness problem do not undermine the particle concept in the ways commonly claimed. In particular, arguments are offered against the attribution of particle status to the Rindler quanta, against the physical realizability of the Rindler vacuum, and against the more general notion of observer-dependence as to the definition of 'particle' or 'vacuum'. However, the question of the ontological status of particles is raised in terms of the consistency of quantum field theory with non-reductive realism about particles, the latter being conceived as entities exhibiting attributes of discreteness and localizability. Two arguments against non-reductive realism about particles, one from axiomatic algebraic local quantum theory in Minkowski spacetime and one from quantum field theory in curved spacetime, are developed. (shrink)

The dominant school of logic, semantics, and the foundation of mathematics construct its theories within the framework of set theory. There are three strategies by means of which a member of this school might attempt to justify his ontology of sets. One strategy is to show that sets are already included in the naturalistic part of our everyday ontology. If they are, then one may assume that whatever justifies the everyday ontology justifies the ontology of sets. Another strategy is to (...) show that set theory is already part of logic. In this case, the ontology of sets would be justified in the sam way logic is justified. The third strategy is to show that set theory plays some unique role in theoretical work. If it does, then its ontology would be justified pragmatically. In this paper it is shown that none of these strategies is successful. One properly constructs foundations, not within set theory. bit within an intensional logic that takes properties, relations, propositions as basic. (shrink)

The present paper reveals (non-relativistic) quantum mechanics as an emergent property of otherwise classical ergodic systems embedded in a stochastic vacuum or zero-point radiation field (zpf). This result provides a theoretical basis for understanding recent numerical experiments in which a statistical analysis of an atomic electron interacting with the zpf furnishes the quantum distribution for the ground state of the H atom. The action of the zpf on matter is essential within the present approach, but it is the ergodic demand (...) what ultimately leads to the matrix formulation of quantum mechanics. The paper thus represents a step forward in the quest for an elucidation of the fundamentals of quantum mechanics. (shrink)

This Thesis engages with contemporary philosophical controversies about the nature of dispositional properties or powers and the relationship they have to their non-dispositional counterparts. The focus concerns fundamentality. In particular, I seek to answer the question, ‘What fundamental properties suffice to account for the manifest world?’ The answer I defend is that fundamental categorical properties need not be invoked in order to derive a viable explanation for the manifest world. My stance is a field-theoretic view which describes the world as (...) a single system comprised of pure power, and involves the further contention that ‘pure power’ should not be interpreted as ‘purely dispositional’, if dispositionality means potentiality, possibility or otherwise unmanifested power or ability bestowed upon some bearer. The theoretical positions examined include David Armstrong’s Categoricalism, Sydney Shoemaker’s Causal Theory of Properties, Brian Ellis’s New Essentialism, Ullin Place’s Conceptualism, Charles Martin’s and John Heil’s Identity Theory of Properties and Rom Harré’s Theory of Causal Powers. The central concern of this Thesis is to examine reasons for holding a pure-power theory, and to defend such a stance. This involves two tasks. The first requires explaining what plays the substance role in a pure-power world. This Thesis argues that fundamental power, although not categorical, can be considered ontologically-robust and thus able to fulfil the substance role. A second task—answering the challenge put forward by Richard Swinburne and thereafter replicated in various neo-Swinburne arguments—concerns how the manifestly qualitative world can be explained starting from a pure-power base. The Light-like Network Account is put forward in an attempt to show how the manifest world can be derived from fundamental pure power. (shrink)

The integration of reasoning and computation services across system and language boundaries has been mostly treated from an engineering perspective. In this paper we take a foundational point of view. We identify the following form of integration problems: an informal (mathematical; i.e, logically underspecified) specification has multiple concrete formal implementations between which queries and results have to be transported. The integration challenge consists in dealing with the implementation-specific details such as additional constants and properties. We pinpoint their role in safe (...) and unsafe integration schemes and propose a proof-theoretic solution based on modular theory-graphs that include the meta-logical foundations. This also gives a clean conceptual basis for earlier attempts that explain integration via “content/semantic markup”. (shrink)

The standard interpretation of quantum physics (QP) and some recent generalizations of this theory rest on the adoption of a rerificationist theory of truth and meaning, while most proposals for modifying and interpreting QP in a “realistic” way attribute an ontological status to theoretical physical entities (ontological realism). Both terms of this dichotomy are criticizable, and many quantum paradoxes can be attributed to it. We discuss a new viewpoint in this paper (semantic realism, or briefly SR), which applies both to (...) classical physics (CP) and to QP. and is characterized by the attempt of giving up verificationism without adopting ontological realism. As a first step, we construct a formalized observative language L endowed with a correspondence truth theory. Then, we state a set of axioms by means of L which hold both in CP and in QP. and construct a further language Lv which can express bothtestable andtheoretical properties of a given physical system. The concepts ofmeaning andtestability do not collapse in L and Le hence we can distinguish between semantic and pragmatic compatibility of physical properties and define the concepts of testability and conjoint testability of statements of L and Le. In this context a new metatheoretical principle (MGP) is stated, which limits the validity of empirical physical laws. By applying SR (in particular. MGP) to QP, one can interpret quantum logic as a theory of testability in QP, show that QP is semantically incomplete, and invalidate the widespread claim that contextuality is unavoidable in QP. Furthermore. SR introduces some changes in the conventional interpretation of ideal measurements and Heisenberg’s uncertainty principle. (shrink)

A theoretical device, which incorporates the functions of clock, rod, nonrotating platform, and accelerometer, and whose operation depends on the properties of light rays and free particles, is defined. The device, which we call a metrosphere, is simple enough that it can be introduced at the starting point of relativity theory and versatile enough that it can serve as an aid in the development and conceptualization of the theory. Relative to an inertial frame, a moving metrosphere undergoes a Lorentz-Fitzgerald contraction (...) and the associated clock exhibits a Lorentz-Larmor rate retardation. From this fact and the assumption that there exists one inertial frame, it is possible to generate the kinematical results of special relativity. A metrosphere provides an observer with a local frame of reference, hence it is well adapted to the needs of general relativity, allows the equivalence principle to be introduced in a straightforward manner, and permits a smooth transition from special relativity to general relativity. (shrink)

The crossing property is perhaps the most subtle aspect of the particle-field relation. Although it is not difficult to state its content in terms of certain analytic properties relating different matrixelements of the S-matrix or formfactors, its relation to the localization- and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT. This paper presents a recent account based on new ideas derived (...) from “modular localization” including a mathematic appendix on this subject. Its main achievement is the proof of the crossing property from a two-algebra generalization of the KMS condition.The main content is an in-depth criticism of the dual model and its string theoretic extension. The conceptual flaws of these models are closely related to misunderstandings of crossing. The correct interpretation of string theory is that of a dynamic infinite component one particle space where “dynamic” means that, unlike a mere collection of independent free fields, the formalism contains also operators which communicate between the different irreducible Poincaré representations and set the mass/spin spectrum. Whereas in pre-string times there were unsuccessful attempts to achieve this in analogy to the O(4,2) hydrogen spectrum by the use of higher noncompact groups, the superstring in d=9+1, which uses instead (bosonic/fermionic) oscillators obtained from multicomponent chiral currents, is the only known solution of the dynamical infinite component pointlike field (or pointlike generated wave function) project. (shrink)

The still unsettled decision problem for the restricted purely universal formulae 0-formulae) of the first order set-theoretic language based over =, ∈ is discussed in relation with the adoption or rejection of the axiom of foundation. Assuming the axiom of foundation, the related finite set-satisfiability problem for the very significant subclass of the 0-formulae consisting of the formulae involving only nested variables of level 1 is proved to be semidecidable on the ground of a reflection property over the hereditarily finite (...) sets, and various extensions of this result are obtained. When variables are restricted to range only over sets, in universes with infinitely many urelements the set-satisfiability problem is shown to be solvable provided the axiom of foundation is assumed; if it is not, then the decidability of a related derivability problem still holds. That, in turn, suggests the alternative adoption of an antifoundation axiom under which the set-satisfiability problem is also solvable . Turning to set theory without urelements, assuming a form of Boffa's antifoundation axiom, the complement of the set-satisfiability problem for the full class of Δ0-formulae is shown to be semidecidable; a result that is known not to hold, for the set-satisfiability problem itself, even for a very restricted subclass of the Δ0-formulae. (shrink)

In the last years, the surprising bosonic behavior that a many-fermion system may acquire has raised interest because of theoretical and practical reasons. This trans-statistical behavior is usually considered to be the result of approximation modeling methods generally employed by physicists when faced with complexity. In this paper, we take a tensor product structure and an ontology of properties approach and provide two versions of a toy model in order to argue that trans-statistical behavior allows for a realistic interpretation.

The constraint formalism of classical mechanics is extended to field theories with gauge groups. Explicit examples of Klein-Gordon and Maxwell fields are presented. The symmetry properties of the Maxwell fields have the unexpcted feature in this formalism of forming a first-class algebra which is not Lie, a situation already encountered in the general theory of relativity.

The difficulties of relativistic particle theories formulated by means of canonical quantization, such as those of Klein–Gordon and Dirac, ultimately led theoretical physicists to turn to quantum field theory to model elementary particle physics. In order to overcome these difficulties, the theories of the present approach are developed deductively from the physical principles that specify the system, without making use of canonical quantization. For a free particle these starting assumptions are invariance of the theory and covariance of position with respect (...) to Poincaré transformations. In pursuing the approach, the effectiveness of group theoretical methods is exploited. The coherent development of our program has shown that robust classes of representations of the Poincaré group, discarded by the known particle theories, can in fact be taken as bases for perfectly consistent theories. For massive spin zero particles, six inequivalent theories have been determined, two of which do not correspond to any of the current ones; all of these theories overcome the difficulties of Klein–Gordon one. The present lack of the explicit transformation properties of position with respect to boosts prevents the complete determination of non zero spin particle theories. In the past a particular form of these transformation properties was adopted by Jordan and Mukunda. We check its consistency within the present approach and find that for spin \ particles there is only one consistent theory, which is unitarily related to Dirac’s; yet, once again, it requires classes of irreducible representations previously discarded. (shrink)

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers. This paper sets out the case for support for this effort. The focus of the transformative research program proposal is biology-centric. We admit that biology to date has been more fact-oriented (...) and less theoretical than physics. However, the key leverageable idea is that careful extension of the science of living systems can be more effectively applied to some of our most vexing modern problems than the prevailing scheme, derived from abstractions in physics. While these have some universal application and demonstrate computational advantages, they are not theoretically mandated for the living. A new set of mathematical abstractions derived from biology can now be similarly extended. This is made possible by leveraging new formal tools to understand abstraction and enable computability. [The latter has a much expanded meaning in our context from the one known and used in computer science and biology today, that is "by rote algorithmic means", since it is not known if a living system is computable in this sense (Mossio et al., 2009).] Two major challenges constitute the effort. The first challenge is to design an original general system of abstractions within the biological domain. The initial issue is descriptive leading to the explanatory. There has not yet been a serious formal examination of the abstractions of the biological domain. What is used today is an amalgam; much is inherited from physics (via the bridging abstractions of chemistry) and there are many new abstractions from advances in mathematics (incentivized by the need for more capable computational analyses). Interspersed are abstractions, concepts and underlying assumptions “native” to biology and distinct from the mechanical language of physics and computation as we know them. A pressing agenda should be to single out the most concrete and at the same time the most fundamental process-units in biology and to recruit them into the descriptive domain. Therefore, the first challenge is to build a coherent formal system of abstractions and operations that is truly native to living systems. Nothing will be thrown away, but many common methods will be philosophically recast, just as in physics relativity subsumed and reinterpreted Newtonian mechanics. -/- This step is required because we need a comprehensible, formal system to apply in many domains. Emphasis should be placed on the distinction between multi-perspective analysis and synthesis and on what could be the basic terms or tools needed. The second challenge is relatively simple: the actual application of this set of biology-centric ways and means to cross-disciplinary problems. In its early stages, this will seem to be a “new science”. This White Paper sets out the case of continuing support of Information and Communication Technology (ICT) for transformative research in biology and information processing centered on paradigm changes in the epistemological, ontological, mathematical and computational bases of the science of living systems. Today, curiously, living systems cannot be said to be anything more than dissipative structures organized internally by genetic information. There is not anything substantially different from abiotic systems other than the empirical nature of their robustness. We believe that there are other new and unique properties and patterns comprehensible at this bio-logical level. The report lays out a fundamental set of approaches to articulate these properties and patterns, and is composed as follows. -/- Sections 1 through 4 (preamble, introduction, motivation and major biomathematical problems) are incipient. Section 5 describes the issues affecting Integral Biomathics and Section 6 -- the aspects of the Grand Challenge we face with this project. Section 7 contemplates the effort to formalize a General Theory of Living Systems (GTLS) from what we have today. The goal is to have a formal system, equivalent to that which exists in the physics community. Here we define how to perceive the role of time in biology. Section 8 describes the initial efforts to apply this general theory of living systems in many domains, with special emphasis on crossdisciplinary problems and multiple domains spanning both “hard” and “soft” sciences. The expected result is a coherent collection of integrated mathematical techniques. Section 9 discusses the first two test cases, project proposals, of our approach. They are designed to demonstrate the ability of our approach to address “wicked problems” which span across physics, chemistry, biology, societies and societal dynamics. The solutions require integrated measurable results at multiple levels known as “grand challenges” to existing methods. Finally, Section 10 adheres to an appeal for action, advocating the necessity for further long-term support of the INBIOSA program. -/- The report is concluded with preliminary non-exclusive list of challenging research themes to address, as well as required administrative actions. The efforts described in the ten sections of this White Paper will proceed concurrently. Collectively, they describe a program that can be managed and measured as it progresses. (shrink)

In this paper, non-additivity of a set function is interpreted as a method to express relations between sets which are not modeled in a set theoretic way. Drawing upon a concept called “quasi-analysis” of the philosopher Rudolf Carnap, we introduce a transform for sets, functions, and set functions to formalize this idea. Any image-set under this transform can be interpreted as a class of (quasi-)components or (quasi-)properties representing the original set. We show that non-additive set functions can be represented as (...) signed σ-additive measures defined on sets of quasi-components. We then use this interpretation to justify the use of non-additive set functions in various applications like for instance multi criteria decision making and cooperative game theory. Additionally, we show exemplarily by means of independence, conditioning, and products how concepts from classical measure and probability theory can be transfered to the non-additive theory via the transform. (shrink)

Twenty-first century science faces a dilemma. Two of its well-verified foundation stones - relativity and quantum theory - have proven inconsistent. Resolution of the conflict has resisted improvements in experimental precision leaving some to believe that some fundamental understanding in our world-view may need modification or even radical reform. Employment of the wave-front model of electrodynamics, as a propagation process with a Markov property, may offer just such a clarification.

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...) and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers. This paper sets out the case for support for this effort. The focus of the transformative research program proposal is biology-centric. We admit that biology to date has been more fact-oriented (...) and less theoretical than physics. However, the key leverageable idea is that careful extension of the science of living systems can be more effectively applied to some of our most vexing modern problems than the prevailing scheme, derived from abstractions in physics. While these have some universal application and demonstrate computational advantages, they are not theoretically mandated for the living. A new set of mathematical abstractions derived from biology can now be similarly extended. This is made possible by leveraging new formal tools to understand abstraction and enable computability. [The latter has a much expanded meaning in our context from the one known and used in computer science and biology today, that is "by rote algorithmic means", since it is not known if a living system is computable in this sense (Mossio et al., 2009).] Two major challenges constitute the effort. The first challenge is to design an original general system of abstractions within the biological domain. The initial issue is descriptive leading to the explanatory. There has not yet been a serious formal examination of the abstractions of the biological domain. What is used today is an amalgam; much is inherited from physics (via the bridging abstractions of chemistry) and there are many new abstractions from advances in mathematics (incentivized by the need for more capable computational analyses). Interspersed are abstractions, concepts and underlying assumptions “native” to biology and distinct from the mechanical language of physics and computation as we know them. A pressing agenda should be to single out the most concrete and at the same time the most fundamental process-units in biology and to recruit them into the descriptive domain. Therefore, the first challenge is to build a coherent formal system of abstractions and operations that is truly native to living systems. Nothing will be thrown away, but many common methods will be philosophically recast, just as in physics relativity subsumed and reinterpreted Newtonian mechanics. -/- This step is required because we need a comprehensible, formal system to apply in many domains. Emphasis should be placed on the distinction between multi-perspective analysis and synthesis and on what could be the basic terms or tools needed. The second challenge is relatively simple: the actual application of this set of biology-centric ways and means to cross-disciplinary problems. In its early stages, this will seem to be a “new science”. This White Paper sets out the case of continuing support of Information and Communication Technology (ICT) for transformative research in biology and information processing centered on paradigm changes in the epistemological, ontological, mathematical and computational bases of the science of living systems. Today, curiously, living systems cannot be said to be anything more than dissipative structures organized internally by genetic information. There is not anything substantially different from abiotic systems other than the empirical nature of their robustness. We believe that there are other new and unique properties and patterns comprehensible at this bio-logical level. The report lays out a fundamental set of approaches to articulate these properties and patterns, and is composed as follows. -/- Sections 1 through 4 (preamble, introduction, motivation and major biomathematical problems) are incipient. Section 5 describes the issues affecting Integral Biomathics and Section 6 -- the aspects of the Grand Challenge we face with this project. Section 7 contemplates the effort to formalize a General Theory of Living Systems (GTLS) from what we have today. The goal is to have a formal system, equivalent to that which exists in the physics community. Here we define how to perceive the role of time in biology. Section 8 describes the initial efforts to apply this general theory of living systems in many domains, with special emphasis on crossdisciplinary problems and multiple domains spanning both “hard” and “soft” sciences. The expected result is a coherent collection of integrated mathematical techniques. Section 9 discusses the first two test cases, project proposals, of our approach. They are designed to demonstrate the ability of our approach to address “wicked problems” which span across physics, chemistry, biology, societies and societal dynamics. The solutions require integrated measurable results at multiple levels known as “grand challenges” to existing methods. Finally, Section 10 adheres to an appeal for action, advocating the necessity for further long-term support of the INBIOSA program. -/- The report is concluded with preliminary non-exclusive list of challenging research themes to address, as well as required administrative actions. The efforts described in the ten sections of this White Paper will proceed concurrently. Collectively, they describe a program that can be managed and measured as it progresses. (shrink)

We show that a theory of autonomous iterated Ramseyness based on second order arithmetic (SOA) is proof-theoretically equivalent to ${\Pi^1_2}$ -comprehension. The property of Ramsey is defined as follows. Let X be a set of real numbers, i.e. a set of infinite sets of natural numbers. We call a set H of natural numbers homogeneous for X if either all infinite subsets of H are in X or all infinite subsets of H are not in X. X has the property (...) of Ramsey if there exists a set which is homogeneous for X. The property of Ramsey is considered in reverse mathematics to compare the strength of subsystems of SOA. To characterize the system of ${\Pi^1_2}$ -comprehension in terms of Ramseyness we introduce a system of autonomous iterated Ramseyness, called R-calculus. We augment the language of SOA with additional set terms (called R-terms) ${R\vec{x}X\phi(\vec{x},X)}$ for each first order formula ${\phi(\vec{x},X)}$ (where φ may contain further R-terms). The R-calculus is a system which comprises comprehension for all first order formulas (which may contain R-terms or other set parameters) and defining axioms for the R-terms which claim that for each ${\vec{x}}$ , we can remove finitely many elements from the set ${R\vec{x}X\phi(\vec{x},X)}$ such that the remaining set is homogeneous for ${\{{X}{\phi(\vec{x},X)\}}}$ . We show that the R-calculus proves the same ${\Pi^1_1}$ -sentences as the system of ${\Pi^1_2}$ -comprehension. (shrink)

This investigation of time and space is motivated by gaps in our current understanding: by the lack of definitions, by our failure to appreciate the nature of these entities, by our inability to pin down their properties. The author's approach is based on two key ideas: The first idea is to seek the geo-historical origins of time and space concepts. A thorough investigation of a diversified archaeological corpus, allows him to draft coherent definitions; it furthermore gives clues as to whether (...) time and space were discovered or invented. The second idea is to define the units before trying to define space and time. The results presented here are unexpected: Time and space were not discovered in nature, but they were invented; time is not a phenomenon and space has no materiality; they are only concepts. This runs contrary to the opinion of most scientific and the philosophical authorities, although one would seek in vain for a theoretical validation of the conventional position. This book will provide much food for thought for philosophers and scientists, as well as interested general readers. (shrink)

In this book Harry Heft examines the historical and theoretical foundations of James J. Gibson's ecological psychology in 20th century thought, and in turn, integrates ecological psychology and analyses of sociocultural processes. A thesis of the book is that knowing is rooted in the direct experience of meaningful environmental objects and events present in individual-environment processes and at the level of collective, social settings. Ecological Psychology in Context: *traces the primary lineage of Gibson's ecological approach to William James's philosophy (...) of radical empiricism; *illuminates how the work of James's student and Gibson's mentor, E.B. Holt, served as a catalyst for the development of Gibson's framework and as a bridge to James's work; *reveals how ecological psychology reciprocally can advance Jamesian studies by resolving some of the theoretical difficulties that kept James from fully realizing a realist philosophy; *broadens the scope of Gibson's framework by proposing a synthesis between it and the ecological program of Roger Barker, who discovered complex systems operating at the level of collective, social processes; *demonstrates ways in which the psychological domain can be extended to properties of the environment rendering its features meaningful, publicly accessible, and distributed across person-environment processes; and *shows how Gibson's work points the way toward overcoming the gap between experimental psychology and the humanities. Intended for scholars and students in the areas of ecological and environmental psychology, theoretical and historical psychology, cognitive science, developmental psychology, anthropology, and philosophy. (shrink)

So-called grand or paradigmatic theories—structural functionalism, psychoanalysis, Marxism, rational-choice theory—provide their proponents with a conceptual vocabulary and syntax that allows for the classification and configuring of wide ranges of phenomena. Advocates for any particular “analytical grammar” are accordingly prone to conflating the internal coherence of their paradigm—its integrated complex of definitions, axioms, and inferences—with a corresponding capacity for representational verisimilitude. The distinction between Theory-as-heuristic and Theory-as-imposition is of course difficult to negotiate in practice, given that empirical observation and measurement are (...) not entirely “theory neutral” or independent of prior analytical conceptualization. Nonetheless, the scientific cogency of any theory is ultimately evaluated by the substantive realism of its foundational assumptions and categorical designations; that is, the accuracy with which it identifies and tracks the determinant properties and processes of the phenomena to be explicated. The paradigm of sociocultural evolutionism—despite extensive revamping by contemporary proponents—does not carry warrant in this regard, as its recourse to an analytical grammar fashioned and derived from another discipline raises doubts about its empirical veridicality. This article revisits the contentious issue of remodeling social phenomena in accordance with biological categories and offers both a theoretical and a substantive critique of the “selectionist” paradigm. The transdisciplinary program of historical social science is affirmed by way of counterpoint. (shrink)

In the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem.Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this gap, (...) we present in this paper a theory for representing ontologies in a dependently typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' (...) perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

This article proposes a conceptual mapping to outline salient properties and relations that allow for a knowledge transfer from the well-established greenwashing phenomenon to the more recent machinewashing. We account for relevant dissimilarities, indicating where conceptual boundaries may be drawn. Guided by a “reasoning by analogy” approach, the article addresses the structural analogy and machinewashing idiosyncrasies leading to a novel and theoretically informed model of machinewashing. Consequently, machinewashing is defined as a strategy that organizations adopt to engage in misleading behavior (...) about ethical Artificial Intelligence /algorithmic systems. Machinewashing involves misleading information about ethical AI communicated or omitted via words, visuals, or the underlying algorithm of AI itself. Furthermore, and going beyond greenwashing, machinewashing may be used for symbolic actions such as lobbying and prevention of stricter regulation. By outlining diverse theoretical foundations of the established greenwashing domain and their relation to specific research questions, the article proposes a machinewashing model and a set of theory-related research questions on the macro, meso, and micro-level for future machinewashing research. We conclude by stressing limitations and by outlining practical implications for organizations and policymakers. (shrink)

Context: Constructivist approaches to cognition have mostly been descriptive, and now face the challenge of specifying the mechanisms that may support the acquisition of knowledge. Departing from cognitivism, however, requires the development of a new functional framework that will support causal, powerful and goal-directed behavior in the context of the interaction between the organism and the environment. Problem: The properties affecting the computational power of this interaction are, however, unclear, and may include partial information from the environment, exploration, distributed processing (...) and aggregation of information, emergence of knowledge and directedness towards relevant information. Method: We posit that one path towards such a framework may be grounded in these properties, supported by dynamical systems. To assess this hypothesis, we describe computational models inspired from swarm intelligence, which we use as a metaphor to explore the practical implications of the properties highlighted. Results: Our results demonstrate that these properties may serve as the basis for complex operations, yielding the elaboration of knowledge and goal-directed behavior. Implications: This work highlights aspects of interaction that we believe ought to be taken into account when characterizing the possible mechanisms underlying cognition. The scope of the models we describe cannot go beyond that of a metaphor, however, and future work, theoretical and experimental, is required for further insight into the functional role of interaction with the environment for the elaboration of complex behavior. Constructivist content: Inspiration for this work stems from the constructivist impetus to account for knowledge acquisition based on interaction. (shrink)

This paper reconstructs the conceptual foundations of Locke’s unilateralist theory of original appropriation through a critical comparison with the rival compact theories of Grotius and Pufendorf. Much of the normative and conceptual framework of Locke’s theory is common to theirs. Integrating his innovative doctrines on labour and natural self-proprietorship into this received theoretical framework logically required Locke to make several conceptual amendments. I highlight three all but overlooked revisions: (i) an unusually broad conception of labour; (ii) a reduction of (...) mere use-rights to property rights; and (iii) a novel non-self-preservationist interpretation of the divine authorization to use natural resources in common. The reconceptualization of ‘labour’ is theoretically the most fundamental, underpinning the other two. My contextual reconstruction enhances our grasp of the structure of Locke’s theory of original appropriation. It also reveals Locke’s main objection to compact theories to be an external one, hinging on idiosyncratic conceptualizations of key notions. (shrink)

By formalizing recent syntactic theories for natural languages Stabler shows how their complexity can be handled without guesswork or oversimplification. By formalizing recent syntactic theories for natural languages in the tradition of Chomsky's Barriers, Stabler shows how their complexity can be handled without guesswork or oversimplification. He introduces logical representations of these theories together with special deductive techniques for exploring their consequences that will provide linguists with a valuable tool for deriving and testing theoretical predictions and for experimenting with alternative (...) formulations of grammatical principles. Stabler's novel approach allows results to be deduced with straightforward calculations and provides a systematic framework for tackling the problem of how speakers can infer the properties of an utterance from principles of the grammar. The special treatment of equality, induction principles, and inclusion of a general method for collecting structures from proofs means that sophisticated linguistic arguments can be carried out in detail, giving a rich perspective to issues in linguistic theory and parsing. (shrink)