Extensive interpretation of legal provisions is in tension with the prohibition of reasoning by analogy in criminal law, for it is unclear what the difference is between the two. Some scholars claim that they differ from a theoretical point of view, since they do not have the same argumentative structure. On the other hand, the two come to the same result starting from the same legal materials: they justify the extension of a regulation to a case that is (...) not explicitly considered by the law. The paper deals with this issue discussing a recent Italian case and proposes an account of the distinction between the two based upon the principle of semantic tolerance and its inferential structure in legal argumentation. (shrink)

Arguments from fairness as described in Aristotle’s _Rhetoric_ are usually taken to aim at mitigating the strictness of the law or, in terms of procedure, to favour the defendant. This paper considers a more inclusive interpretation, that is, that arguments from fairness can work both ways. In the example given in the _Rhetoric,_ arguments from fairness are directed at a restrictive interpretation of the text. That may not be necessary however. Likewise, fairness may speak for the claimant. Two (...) examples may support this conclusion: a judicial speech by Hyperides, and the doctrine of issues appearing in Hellenistic school rhetoric. (shrink)

Contents Acknowledgements iii I. Royce and the Interpretation of His Contemporaries Introduction 1 1. Royce and Lotze 25 Introduction to Lotze. Lotze's ontology. Royce's response to Lotze. Successfull metaphysics renders experience broadly consistent without denying types of human experience. Logically testing metaphysical assumptions offers a promising methodology. The individual is not immediately given but realized through a process. The individual is not immediately given but realized through a process. Conclusion. 2. Royce and James 66 The friendship of James and (...) Royce. James's position. James summarized. Royce's response. The ‘abstract’ ideal has its pragmatic aspect. Logic can supplement pragmatism. Experience itself drives the unifying efforts of speculative philosophy. A more consistent pragmatism hypothesizes broader experience and allows an active and constructive process of response to that experience. Conclusion. 3. Royce and Bradley 108 Bradley's destruction of appearances. Bradley's construction? Royce's response - non-technical. Metaphysics is interpretively applicable to special experiential problems. In active willful attention the ethical complements the theoretical, rendering the relation of finite and absolute interpretable. Royce's response - technical development. Conclusion. 4. Royce and Whitehead 163 Statement of Whitehead's three primary presuppositions. Scheme of Whitehead's philosophy: the role of extended events. The building blocks of Whitehead's metaphysics. Process as an action within and upon experience. The process of concrescence. Consciousness and propositions in Whitehead's philosophy. Royce in comparison with Whitehead. Royce's cosmology in outline. Explicit contrast and comparison of Royce's and Whitehead's philosophies. Principles suggested by the contrast of Royce and Whitehead. II. An Extension of Royce’s Philosophy of Interpretation Preamble: The Need for a Re-Envisioned Philosophy of Interpretation 212 5. The Roycean Hypothetical Method and Its Prospects 226 The interpretation of Christianity. Metaphysical foundations of community. The synthesis and promise of Royce's insights. 6. Hyperthematics 269 Working definition. Some methodological considerations. Some general considerations. Some definitions. The foundational hypertheme and the derivatives. Hyperthematic expansion. The hyperthematic structure of the game. The hyperthematic structure of narrative. The hyperthematic structure of dance. The hyperthematic structure of music. Retrospect and prospect. 7. Hyperthematics Applied: The Corporation As a Hyperthematic Structure 339 Introduction. Restatement of the hyperthemes. The problematic of the corporation. Some exemplifications of the historical development of the corporation. Consideration of several prominent views regarding the purpose of commercial corporations. Consideration of consistency of the corporation as a hyperthematic structure. Hyperthematic reconstruction of the corporation as a community of epsionomic interpretation. Bibliography 412. (shrink)

In this paper we extend Wittgenstein’s notion of family resemblance to translation, interpretation, and comparison across traditions. There is no need for universals. This holds for everyday concepts such as green and qing 青, philosophical concepts such as emotion and qing 情, as well as philosophical categories such as form of life and dao 道. These notions as well as all other concepts from whatever tradition are family resemblance concepts. We introduce the notion of quasi-universal, which connects family resemblance (...) concepts from a limited number of traditions. The possibility and necessity of extending family resemblance concepts across traditions dissolves the false antinomy of universalism versus relativism. (shrink)

In this paper we study the combined structure of the relations of theory-extension and interpretability between theories for the case of finitely axiomatised theories. We focus on two main questions. The first is definability of salient notions in terms of the structure. We show, for example, that local tolerance, locally faithful interpretability and the finite model property are definable over the structure. The second question is how to think about ‘good’ properties of theories that are independent of implementation details and (...) of ‘bad’ properties that do depend on implementation details. Our degree structure is suitable to study this contrast, since one of our basic relations, to wit theory-extension, is dependent on implementation details and the other relation, interpretability, is not. Nevertheless, we can define new good properties using bad ones. We introduce a new notion of sameness of theories i-bisimilarity that is second-order definable over our structure. We define a notion of goodness in terms of this relation. We call this notion being capital. We illustrate that some intuitively good properties, like being a complete theory, are not capital. (shrink)

The purpose of this essay is exegesis. I explicate Nicolas Malebranche's (1674, 1678, 1688, 1714) concept of intelligible extension. I begin by detailing how the concept matured throughout Malebranche's work, and the new functions it took on within his metaphysical system. I then examine Gustav Bergmann's “axiomatic” interpretation, as well as the criticism of it offered by Daise Radner. I argue that Radner's criticism of the interpretation is only partly successful; some of her objections can be met; others (...) cannot. I then develop a novel interpretation of the concept, given insights from this dispute. I call it the “programmatic interpretation.” I argue that this interpretation coheres well with Malebranche's famous Vision in God thesis, as well as many of his other commitments. I conclude by considering a certain pertinent objection to my proposal, summarizing the dialectic, and forcefully restating my case. (shrink)

This article examines Wilfrid Sellars's views on the epistemic status of philosophical propositions. It suggests that according to Sellars philosophical propositions are normative and practically oriented. They do not form a theory for the description of reality; their function is, rather, that of motivating actions which aim at changing reality. The article argues that the role of philosophical propositions can be illuminated if they are understood as a special kind of (proposed) “material” rules of inference, provided that the latter are (...) construed as being firmly entrenched in practice. To this end, a distinction between “theoretical” and “practical” anomalies is drawn to better elucidate—and in some cases criticize and further expand—Sellars's position on the relation between the theoretical and practical dimensions of philosophical activity. In this connection, the Weberian notion of the “disenchantment of the world” is used to throw light on the relation between these two dimensions. (shrink)

There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski :891–939, 1951; 74:127–162, 1952). Another one The infinity project proceeding, Barcelona, 2012) comes from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as its main precursor. By a classical fact of general topology, the space of ultrafilters over a discrete space is (...) its largest compactification. The main result of Saveliev The infinity project proceeding, Barcelona, 2012), which confirms a canonicity of this extension, generalizes this fact to discrete spaces endowed with an arbitrary first-order structure. An analogous result for the former type of ultrafilter extensions was obtained in Saveliev. Results of such kind are referred to as extension theorems. After a brief introduction, we offer a uniform approach to both types of extensions based on the idea to extend the extension procedure itself. We propose a generalization of the standard concept of first-order interpretations in which functional and relational symbols are interpreted rather by ultrafilters over sets of functions and relations than by functions and relations themselves, and define ultrafilter models with an appropriate semantics for them. We provide two specific operations which turn ultrafilter models into ordinary models, establish necessary and sufficient conditions under which the latter are the two canonical ultrafilter extensions of some ordinary models, and obtain a topological characterization of ultrafilter models. We generalize a restricted version of the extension theorem to ultrafilter models. To formulate the full version, we propose a wider concept of ultrafilter models with their semantics based on limits of ultrafilters, and show that the former concept can be identified, in a certain way, with a particular case of the latter; moreover, the new concept absorbs the ordinary concept of models. We provide two more specific operations which turn ultrafilter models in the narrow sense into ones in the wide sense, and establish necessary and sufficient conditions under which ultrafilter models in the wide sense are the images of ones in the narrow sense under these operations, and also are two canonical ultrafilter extensions of some ordinary models. Finally, we establish three full versions of the extension theorem for ultrafilter models in the wide sense. The results of the first three sections of this paper were partially announced in Poliakov and Saveliev On two concepts of ultrafilter extensions of first-order models and their generalizations, Springer, Berlin, 2017). (shrink)

In ten essays, originally published 1987-91 and in some cases revised for the collection, Watson (philosophy, U. of Notre Dame) constructs a conception of rationality that moves between the extremes of the absolute and the ephemeral.

It will come as no surprise that I have a different interpretation of the four passages in which, McRae claims, Descartes “definitely includes extension and its modes in what is given through the senses”. In the first, Descartes includes extension, etc., among his ideas of corporeal bodies. This is not to say that he includes them among his adventitious ideas, though. All adventitious ideas are ideas of external bodies. But the converse is not true. Not all ideas of corporeal (...) bodies are ipso facto adventitious ideas, for, as I see it, the idea of the true and immutable nature of body is non-sensible and innate. McRae slides from “all adventitious ideas seem to be ideas of external bodies” to “all ideas of external bodies are adventitious”. (shrink)

In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows us to (...) recover the theorems of propositional classical logic within three sub-classical modal systems. (shrink)

Extensive measurement theory is developed in terms of theratio of two elements of an arbitrary (not necessarily Archimedean) extensive structure; thisextensive ratio space is a special case of a more general structure called aratio space. Ratio spaces possess a natural family of numerical scales (r-scales) which are definable in non-representational terms; ther-scales for an extensive ratio space thus constitute a family of numerical scales (extensive r-scales) for extensive structures which are defined in a non-representational manner. (...) This is interpreted as involving arelational theory of quantity which contrasts in certain respects with thequalitative theory of quantity implicit in standard representational extensive measurement theory. The representational properties of extensiver-scales are investigated, and found to coincide withweak extensive measurement in the sense of Holman. This provides support for the thesis (developed in a separate paper) that weak extensive measurement is a more natural model of actual physical extensive scales than is the standard model using strong extensive measurement. Finally, the present apparatus is applied to slightly simplify the existing necessary and sufficient conditions for strong extensive measurement. (shrink)

Andrzej Kisielewicz has proposed three systems of double extension set theory of which we have shown two to be inconsistent in an earlier paper. Kisielewicz presented an argument that the remaining system interprets ZF, which is defective: it actually shows that the surviving possibly consistent system of double extension set theory interprets ZF with Separation and Comprehension restricted to 0 formulas. We show that this system does interpret ZF, using an analysis of the structure of the ordinals.

We consider the extension of a (strict) preference over a set to its power set. Elements of the power set are non-resolute outcomes. The final outcome is determined by an “(external) chooser” which is a resolute choice function. The individual whose preference is under consideration confronts a set of resolute choice functions which reflects the possible behaviors of the chooser. Every such set naturally induces an extension axiom (i.e., a rule that determines how an individual with a given preference over (...) alternatives is required to rank certain sets). Our model allows to revisit various extension axioms of the literature. Interestingly, the Gärdenfors (1976) and Kelly (1977) principles are singled-out as the only two extension axioms compatible with the non-resolute outcome interpretation. (shrink)

. We start from the geometrical-logical extension of Aristotle’s square in [6,15] and [14], and study them from both syntactic and semantic points of view. Recall that Aristotle’s square under its modal form has the following four vertices: A is □α, E is , I is and O is , where α is a logical formula and □ is a modality which can be defined axiomatically within a particular logic known as S5 (classical or intuitionistic, depending on whether is involutive (...) or not) modal logic. [3] has proposed extensions which can be interpreted respectively within paraconsistent and paracomplete logical frameworks. [15] has shown that these extensions are subfigures of a tetraicosahedron whose vertices are actually obtained by closure of by the logical operations , under the assumption of classical S5 modal logic. We pursue these researches on the geometrical-logical extensions of Aristotle’s square: first we list all modal squares of opposition. We show that if the vertices of that geometrical figure are logical formulae and if the sub-alternation edges are interpreted as logical implication relations, then the underlying logic is none other than classical logic. Then we consider a higher-order extension introduced by [14], and we show that the same tetraicosahedron plays a key role when additional modal operators are introduced. Finally we discuss the relation between the logic underlying these extensions and the resulting geometrical-logical figures. (shrink)

Intuitionistic sentential logic is shown to be sound and complete with respect to a semantics centered around extensions of atomic bases (i.e. sets of inference rules for atomic sentences). The result is made possible through a non-standard interpretation of disjunction, whereby, roughly speaking, a disjunction is taken to hold just in case every atomic sentence that follows from each of the disjuncts separately holds; it is argued that this interpretation makes good sense provided that rules in atomic bases (...) are conceived of as being accepted hypothetically rather than categorically. (shrink)

The object of this paper is to examine half and full connexive extensions of the basic regular conditional logic CR. Extensions of this system are of interest because it is among the strongest well-known systems of conditional logic that can be augmented with connexive theses without inconsistency resulting. These connexive extensions are characterized axiomatically and their relations to one another are examined proof-theoretically. Subsequently, algebraic semantics are given and soundness, completeness, and decidability are proved for each system. The semantics is (...) also used to establish independence results. Finally, a deontic interpretation of one of the systems is examined and defended. (shrink)

This article presents an approach to the semantics of non-distributive propositional logics that is based on a lattice representation theorem that delivers a canonical extension of the lattice. Our approach supports both a plain Kripke-style semantics and, by restriction, a general frame semantics. Unlike the framework of generalized Kripke frames, the semantic approach presented in this article is suitable for modeling applied logics, as it respects the intended interpretation of the logical operators. This is made possible by restricting admissible (...) interpretations. (shrink)

Chung-ying Cheng’s onto-generative hermeneutical studies of the foundational philosophical texts of China and the Western philosophical traditions expand the horizon of comparative interpretative analyses. The origin of onto-generative hermeneutics is multifaceted, ranging from the Yijing 《易經》(the Book of Changes) and the Neo-Confucian text of Zhang Zai, Ximing《西銘》 (the Western Inscription) to the phenomenology of Husserl and Merleau-Ponty, and to the hermeneutics of Gadamer. Building on Cheng’s examination of the relation between phenomenology, hermeneutics, and the classical texts of Chinese philosophy, the (...) present discussion begins with an exploration of the origin and the continuation of phenomenology and hermeneutics in a comparative frame of reference of Chinese and Greek texts. (shrink)

Hilary Putnam's philosophical views have undergone extensive interpretation over many years. One such interpretive work is George Myerson's book Rhetoric, Reason and Society. Myerson's interest in dialogic rationalism leads him to examine the views of many theorists of rationality, philosophers and non-philosophers alike. As a prominent philosopher of rationality, Putnam is at the very center of this examination. Notwithstanding this fact, I contend that Myerson misinterprets the dialectical character of Putnam's philosophy in general and of Putnam's views on (...) rationality in particular. This misinterpretation, I argue, is revealing of an illusion of thought to which Myerson is subject, an illusion that makes it seem that it is possible to theorize intelligibly about rationality from a metaphysical standpoint. This same illusion, I claim, also makes it seem that Myerson's positive views on rationality are intelligible. Employing a close textual analysis of Myerson's book, I argue that neither scenario is the case. (shrink)

In Kant’s logical texts the reference of the form S is P to an “unknown = x” is well known, but its understanding still remains controversial. Due to the universality of all concepts, the subject as much as the predicate is regarded as predicate of the x, which, in turn, is regarded as the subject of the judgment. In the CPR, this Kantian interpretation of the S-P relationship leads to the question about the relations between intuition and concept in (...) judgment. In contrast to intuition, if no concept, due to its universality, refers immediately to an object, how should one understand the relations of S and P to one another, as well as their relations to intuition, which corresponds to the possible individuality of the object in general = x? To answer this question, it is necessary to understand Kant’s notion of extension, and to prove its irreducibility to the Port-Royal notion of extension as well as to the Fregean one. (shrink)

In proof-theoretic semantics, meaning is based on inference. It may seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems |$K$|⁠, |$KT$|⁠, |$K4$| (...) and |$S4$|⁠, with |$\square $| as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between |$\square $| and a natural presentation of |$\lozenge $|⁠. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases. (shrink)

Matthias Schirn has argued on a number of occasions against the interpretation of Frege's ``objects of a quite special kind'' (i.e., the objects referred to by names like `the concept F') as extensions of concepts. According to Schirn, not only are these objects not extensions, but also the idea that `the concept F' refers to objects leads to some conclusions that are counter-intuitive and incompatible with Frege's thought. In this paper, I challenge Schirn's conclusion: I want to try and (...) argue that the assumption that `the concept F' refers to the extension of F is entirely consistent with Frege's broader views on logic and language. I shall examine each of Schirn's main arguments and show that they do not support his claim. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...) seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist. (shrink)

We investigate an extension of the formalism of interpreted systems by Halpern and colleagues to model the correct behaviour of agents. The semantical model allows for the representation and reasoning about states of correct and incorrect functioning behaviour of the agents, and of the system as a whole. We axiomatise this semantic class by mapping it into a suitable class of Kripke models. The resulting logic, KD45n i-j, is a stronger version of KD, the system often referred to as Standard (...) Deontic Logic. We extend this formal framework to include the standard epistemic notions defined on interpreted systems, and introduce a new doubly-indexed operator representing the knowledge that an agent would have if it operates under the assumption that a group of agents is functioning correctly. We discuss these issues both theoretically and in terms of applications, and present further directions of work. (shrink)

This article provides a brief review of Saybrook Review, Vol 6, No. 1, Spring 1986. Special issue: Extensions in Human Science Methodology guest edited by Donald E. Polkinghorne. This issue contains articles written by four of the faculty of the Saybrook Institute, all of which examine "the consequences of extending the criteria of science beyond the traditional objectivism-relativism dichotomy." Polkinghorne's lead article is a compelling and clear historical characterization of the place of human science in today's academic world. The second (...) is an article by Anthony Stigliano that proposes "an ontology for the human sciences" where research would be grounded in a language of description that is "incomplete, discontinuous, dialogal, and interlaced with different 'levels' of discourse". Jurgen Kremer's article reviews prevailing views of reason and truth, and makes a proposal "for the development of narratives of truths...that consciously include moral and aesthetic dimensions." The final article is by Marcia Salner and is a piece that explores the question of validity in human science research, paying particular attention to "the central role of linguistic communication as a major data source, and to the role of communal negotiation and juridical rules for dealing with conflicting interpretations." Together these articles make a positive advance toward the understanding of the context as well as consequences of an epistemological position that stresses contextual relativism and embraces methodological pluralism. 2012 APA, all rights reserved). (shrink)

A recent no-go theorem gives an extension of the Wigner’s Friend argument that purports to prove the “Quantum theory cannot consistently describe the use of itself.” The argument is complex and thought provoking, but fails in a straightforward way if one treats QM as a statistical theory in the most fundamental sense, i.e. if one applies the so-called ensemble interpretation. This explanation is given here at an undergraduate level, which can be edifying for experts and students alike. A recent (...) paper has already shown that the no-go theorem is incorrect with regard to the de Broglie Bohm theory and misguided in some of its general claims. This paper’s contribution is three fold. It shows how the extended Wigner’s Friend argument fails in the ensemble interpretation. It also makes more evident how natural a consistent statistical treatment of the wave function is. In this way, the refutation of the argument is useful for bringing out the core statistical nature of QM. It, in addition, manifests the unnecessary complications and problems introduced by the collapse mechanism that is part of the Copenhagen interpretation. The paper uses the straightforwardness of the ensemble interpretation to make the no-go argument and its refutation more accessible. (shrink)

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie-Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a (...) general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified and often ambiguous picture that treats reduction simply as a matter of taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest's Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest's Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity. (shrink)

A natural language argument may be valid in at least two nonequivalent senses: it may be interpretationally or representationally valid (Etchemendy in The concept of logical consequence. Harvard University Press, Cambridge, 1990). Interpretational and representational validity can both be formally exhibited by classical first-order logic. However, as these two notions of informal validity differ extensionally and first-order logic fixes one determinate extension for the notion of formal validity (or consequence), some arguments must be formalized by unrelated nonequivalent formalizations in order (...) to formally account for their interpretational or representational validity, respectively. As a consequence, arguments must be formalized subject to different criteria of adequate formalization depending on which variant of informal validity is to be revealed. This paper develops different criteria that formalizations of an argument have to satisfy in order to exhibit the latter’s interpretational or representational validity. (shrink)

In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory—like Elementary Arithmetic EA, IΣ1, or the Gödel–Bernays theory of sets and classes GB—have suprema. This partially answers a question posed by Švejdar in his paper (Commentationes Mathematicae Universitatis Carolinae 19:789–813, 1978). The partial solution of Švejdar’s problem follows from a stronger fact: the convexity of the degree structure of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory in the degree (...) structure of the degrees of all finitely axiomatized sequential theories. In the paper we also study a related question: the comparison of structures for interpretability and derivability. In how far can derivability mimic interpretability? We provide two positive results and one negative result. (shrink)

This paper attempts to resolve the puzzle associated with the non-spatiality of monads by investigating the possibility that Leibniz employed a version of the extension of power doctrine, a Scholastic concept that explains the relationship between immaterial and material beings. As will be demonstrated, not only does the extension of power doctrine lead to a better understanding of Leibniz’ reasons for claiming that monads are non-spatial, but it also supports those interpretations of Leibniz’ metaphysics that accepts the real extension of (...) bodies. (shrink)

0. Introductory remarks. I assume that every serious theory of language must give some explicit account of the relationship between expressions in the language described and expressions in some interpreted language which spells out the semantics of the language.1 Let's call this relationship the translation relation. Theories differ as to how this relation is specified. In the Aspects theory of syntax, taken together with a Katz-Postal view of "semantic rules", it was assumed that the relation was defined on deep structures. (...) Serious problems led to modifications of this view in several directions. Chomsky's latest papers assume that a modified 'intermediate structure' is transformed by rules of interpretation to a level of representation called 'logical form'. Common to all of these approaches is the assumption that the translation rules are defined initially on syntactic structures of one sort or another. Let us call this assumption the configurational hypothesis: the translation rules all have the form: [183]. (shrink)

Philosophical accounts of quantum theory commonly suppose that the observables of a quantum system form a Type-I factor von Neumann algebra. Such algebras always have atoms, which are minimal projection operators in the case of quantum mechanics. However, relativistic quantum field theory and the thermodynamic limit of quantum statistical mechanics make extensive use of von Neumann algebras of more general types. This chapter addresses the question whether interpretations of quantum probability devised in the usual manner continue to apply in (...) the more general setting. Features of non-type I factor von Neumann algebras are cataloged. It is shown that these novel features do not cause the familiar formalism of quantum probability to falter, since Gleason's Theorem and the Lüders Rule can be generalized. However, the features render the problem of the interpretation of quantum probability more intricate. (shrink)

We obtain modal completeness of the interpretability logics IL $\!\!\textsf {P}_{\textsf {0}}$ and ILR w.r.t. generalised Veltman semantics. Our proofs are based on the notion of full labels [2]. We also give shorter proofs of completeness w.r.t. the generalised semantics for many classical interpretability logics. We obtain decidability and finite model property w.r.t. the generalised semantics for IL $\textsf {P}_{\textsf {0}}$ and ILR. Finally, we develop a construction that might be useful for proofs of completeness of extensions of ILW w.r.t. (...) the generalised semantics in the future, and demonstrate its usage with $\textbf {IL}\textsf {W}^\ast = \textbf {IL}\textsf {WM}_{\textsf {0}}$. (shrink)

Given a theoryTextending that of dense linear orders without endpoints, in a language ℒ ⊇ {<}, we are interested in extensionsT′ ofTin languages extending ℒ by unary relation symbols that are each interpreted in models ofT′ as sets that are both dense and codense in the underlying sets of the models.There is a canonically “wild” example, namelyT= Th andT′ = Th. Recall thatTis o-minimal, and so every open set definable in any model ofThas only finitely many definably connected components. But (...) it is well known that 〈ℝ, <, +, · ℚ 〉 defines every real Borel set, in particular, every open subset of any finite cartesian power of ℝ and every subset of any finite cartesian power of ℚ. To put this another way, the definable open sets in models ofTare essentially as simple as possible, whileT′ has a model where the definable open sets are as complicated as possible, as is the structure induced on the new predicate.In contrast to the preceding example, if ℝalgis the set of real algebraic numbers andT′ Th, then no model ofT′ defines any open set that is not definable in the underlying model ofT. (shrink)

The Extensive Continuum is most often seen as an empty form that awaits the accommodation of actuality. Contrary to this popular interpretation, I argue that extension is completely immanent to actual occasions and their prehensive relations. Whitehead's doctrine of internal relations entails that extension cannot be separated from actual occasions, just as actual occasions cannot be separated from extension. To prehend is to extend. Furthermore, any strict separation of form and actuality is shown to bifurcate nature into publicity (...) and privacy. Only with the immanence of extension is nature truly one. (shrink)

We show that monadic intuitionistic quantifiers admit the following temporal interpretation: “always in the future” (for$\forall $) and “sometime in the past” (for$\exists $). It is well known that Prior’s intuitionistic modal logic${\sf MIPC}$axiomatizes the monadic fragment of the intuitionistic predicate logic, and that${\sf MIPC}$is translated fully and faithfully into the monadic fragment${\sf MS4}$of the predicate${\sf S4}$via the Gödel translation. To realize the temporal interpretation mentioned above, we introduce a new tense extension${\sf TS4}$of${\sf S4}$and provide a full and (...) faithful translation of${\sf MIPC}$into${\sf TS4}$. We compare this new translation of${\sf MIPC}$with the Gödel translation by showing that both${\sf TS4}$and${\sf MS4}$can be translated fully and faithfully into a tense extension of${\sf MS4}$, which we denote by${\sf MS4.t}$. This is done by utilizing the relational semantics for these logics. As a result, we arrive at the diagram of full and faithful translations shown in Figure 1 which is commutative up to logical equivalence. We prove the finite model property (fmp) for${\sf MS4.t}$using algebraic semantics, and show that the fmp for the other logics involved can be derived as a consequence of the fullness and faithfulness of the translations considered. (shrink)

This article argues for a different outlook on the concept of extension, especially for the reference of general terms in scientific practice. Scientific realist interpretations of the two predominant theories of meaning, namely Descriptivism and Causal Theory, contend that a stable cluster of descriptions or an initial baptism fixes the extension of a general term such as a natural kind term. This view in which the meaning of general terms is presented as monosemantic and the referents as stable, homogeneous, and (...) unchangeable, however, does not reflect the various practices involved in the investigation of research materials and the related application of general terms in scientific practice. By drawing on the taxonomic diversity, particularly of structure-based classifications in chemical databases, this article illustrates the limited utility of such a concept of extension. Research materials often exhibit a plurality of material dimensions that, within different research contexts, allow for various and often equally significant taxonomic demarcations. In light of this, the extension of a general term cannot be uniquely determined by a supposedly independent nature of the referent but is relative to the model context under which the materials are investigated. This significance and plurality of the model context, I claim, needs to be mirrored in an account of meaning that is supposed to reflect scientific reality. On this account, the aim of this article is to present an alternative perspective on the concept of extension to accommodate the diverse material practices that determine the application of general terms in science. (shrink)

Using an interpreter in qualitative interviews: does it threaten validity?There is an extensive literature on the problem of translating scales for use across cultures, but very little is published on the problems of conducting qualitative interviews in another language with assistance of an interpreter. The aim of this paper is to describe and discuss threats to validity that arise when conducting qualitative interviews using an interpreter. Ten female student nurses in two cities in Lithuania were interviewed about how they (...) perceived their educational program. All interviews were conducted in English with an interpreter. When using an interpreter to conduct interviews, potential threats to validity arise at various points in the interview process. A threat arises when the researcher, whose first language is Swedish, addresses a question in English to the interpreter, another during the translation by the interpreter from English to Lithuanian, and again when the interpreter translates the interviewee’s Lithuanian responses to English. In the last situation, the researcher may not know whether the interpreter has summarized and/or modified the responses. To mitigate these problems, the interpreter should not only have the required linguistic abilities, but also be trained in the research field. The researcher has to be aware of these threats to validity and make efforts to meet and limit their effects. (shrink)

This paper is concerned with extensions of geometric stability theory to some nonelementary classes. We prove the following theorem:Theorem. Let [Formula: see text] be a large homogeneous model of a stable diagram D. Let p, q ∈ SD(A), where p is quasiminimal and q unbounded. Let [Formula: see text] and [Formula: see text]. Suppose that there exists an integer n < ω such that [Formula: see text] for any independent a1, …, an∈ P and finite subset C ⊆ Q, but (...) [Formula: see text] for some independent a1, …, an, an+1∈ P and some finite subset C ⊆ Q.Then [Formula: see text] interprets a group G which acts on the geometry P′ obtained from P. Furthermore, either [Formula: see text] interprets a non-classical group, or n = 1,2,3 and•If n = 1 then G is abelian and acts regularly on P′.•If n = 2 the action of G on P′ is isomorphic to the affine action of K ⋊ K* on the algebraically closed field K.•If n = 3 the action of G on P′ is isomorphic to the action of PGL2(K) on the projective line ℙ1(K) of the algebraically closed field K.We prove a similar result for excellent classes. (shrink)

Fitness apps on mobile devices are gaining popularity, as more people are engaging in self-tracking activities to record their status of fitness and exercise routines. These technologies also evolved from simply recording steps and offering exercise suggestions to an integrated lifestyle guide for physical wellbeing, thus exemplify a new era of "quantified self" in the context of health as individual responsibility. There is a considerable amount of literature in science, technology and society (STS) studies looking at this phenomenon from different (...) perspectives, linking it with the sociology of self-surveillance and neoliberal regimes of health. However, the human-technology interface, through which the micro- (behavioral) and macro- (social) aspects converge, still calls for extensive examination. This paper approaches this topic from the postphenomenological perspective, in combination with empirical studies of design analysis and interviews of fitness apps, to reveal the human-technology link between the design elements and people's perception through the direct experiences and interpretations of technology. It argues that the intentionality of self-tracking fitness app designs mediates the human-technology relations by "guiding" people into a quantified knowledge regime. It shapes the perceptions of fitness and health with representations of meanings about a "good life" of individual success and management. This paper also gives a critique of current individual, performance-oriented fitness app designs and offers the possibility of seeking alternatives through the multistable nature of human-technology relations—how altering interpretation and meaning of the design with a cultural or social context could change the form of technological embodiment. (shrink)

This is the first collection of essays to evaluate John Dewey's pragmatist philosophy from a feminist perspective. The variety of feminist interpretations offered here ranges from Jane Addams's praise for his collegial efforts to resolve the problems of the inner city to contemporary comparisons of his approach with Addams's own critique of capitalism as patriarchal. In between are essays assessing Dewey's contributions to feminist theory and practice both in his lifetime and in regard to contemporary feminist approaches to education, subjectivity, (...) objectivity and truth, and social and political philosophy. At a time when feminists are questioning and developing alternatives to the scientistic value-free inquiry advocated by logical positivism, the myth of detached observation informing the epistemological turn, rationalistic ethics, and the model of an unattached, nonrelational subject, this book reminds us of Dewey's early and passionate opposition to the same assumptions and his reconstruction of philosophy as a "method of moral and political diagnoses and prognosis." It has often been remarked that Dewey's pragmatism provides a genuine alternative to the usual masculinist biases of Western philosophy, and the various essays in this book develop this claim more extensively. Contributors, besides the editor, are Jane Addams, Ana M. Martínez Alemán, Paula Droege, Marilyn Fischer, Eugenie Gatens-Robinson, Judith M. Green, Lisa Heldke, Ellen Condliffe Lagemann, Erin McKenna, Marjorie C. Miller, Elizabeth Kamarck Minnich, and Shannon Sullivan. (shrink)

The formal methods of the representational theory of measurement (RTM) are applied to the extensive scales of physical science, with some modifications of interpretation and of formalism. The interpretative modification is in the direction of theoretical realism rather than the narrow empiricism which is characteristic of RTM. The formal issues concern the formal representational conditions which extensive scales should be assumed to satisfy; I argue in the physical case for conditions related to weak rather than strong (...) class='Hi'>extensive measurement, in the sense of Holman 1969 and Colonius 1978. The problem of justifying representational conditions is addressed in more detail than is customary in the RTM literature; this continues the study of the foundations of RTM begun in an earlier paper. The most important formal consequence of the present interpretation of physical extensive scales is that the basic existence and uniqueness properties of scales (representation theorem) may be derived without appeal to an Archimedean axiom; this parallels a conclusion drawn by Narens for representations of qualitative probability. It is concluded that there is no physical basis for postulation of an Archimedean axiom. (shrink)

We develop a timeout extension of propositional linear temporal logic to specify timing properties of timeout-based models of real-time systems. A timeout is used to model the execution of an action marking the end of a delay. With a view to expressing such timeout constraints, ToLTL uses a dynamic variable to abstract the timeout behaviour in addition to a variable which captures the global clock and some static timing variables which record time instances when discrete events occur. We propose a (...) corresponding timeout tableau for satisfiability checking of the ToLTL formulas. Further we prove that the validity checking for such an extended logic remains PSPACE-complete. Under discrete time semantics, with bounded timeout increments, the model-checking problem which verifies if a ToLTL-formula holds in a timeout Kripke structure is also shown to be PSPACE complete. We further prove that ToLTL, when interpreted over discrete time, can be embedded in the monadic second-order logic with.. (shrink)