While second-order quantifiers have long been known to admit nonstandard, or interpretations, first-order quantifiers (when properly viewed as predicates of predicates) also allow a kind of interpretation that does not presuppose the full power-set of that interpretationgeneral” interpretations for (unary) first-order quantifiers in a general setting, emphasizing the effects of imposing various further constraints that the interpretation is to satisfy.

Many biologists appeal to the so-called Krogh principle when justifying their choice of experimental organisms. The principle states that “for a large number of problems there will be some animal of choice, or a few such animals, on which it can be most conveniently studied”. Despite its popularity, the principle is often critiqued for implying unwarranted generalizations from optimal models. We argue that the Krogh principle should be interpreted in relation to the historical and scientific contexts in which it has (...) been developed and used. We interpret the Krogh Principle as a heuristic, i.e., as a recommendation to approach biological problems through organisms where a specific trait or physiological mechanism is expected to be most distinctively displayed or most experimentally accessible. We designate these organisms “Krogh organisms.” We clarify the differences between uses of model organisms and non-standard Krogh organisms. Among these is the use of Krogh organisms as “negative models” in biomedical research, where organisms are chosen for their dissimilarity to human physiology. Importantly, the representational scope of Krogh organisms and the generalizability of their characteristics are not fixed or assumed but explored through experimental studies. Research on Krogh organisms is steeped in the comparative method characteristic of zoology and comparative physiology, in which studies of biological variation produce insights into general physiological constraints. Accordingly, we conclude that the Krogh principle exemplifies the advantages of studying biological variation as a strategy to produce generalizable insights. (shrink)

Interactionism holds that explanatory and interpretive projects are mutually enriching. If so, then the evolutionary and cognitive science of religions’ explanatory theories should aid interpretive projects concerning religious meaning. Although interpretive accounts typically focus on the local and the particular, interpreters over the past century have construed Freud and Marx as offering general interpretive theories. So, precedent for general interpretive theorizing exists. 4E cognitive science, which champions how cognition is embedded in natural and cultural settings, extended into external structures, enacted (...) via motor routines, and embodied via representations rooted in human bodily form, has encouraged interpretive researchers. Theories of embodied cognition especially have embraced a sweeping view of meaning that attends to the emotions’ role and to their evolutionary origins. That inspires a 6E cognitive science that attends to the emotional and evolved dimensions of cognition too and opens up the possibility of general interpretive theories of broadly Darwinian character. Evolved cognitive systems qualify as maturationally natural cognition, which exhibits a distinctive constellation of features. The by-product theory holds that religious representations’ engagement of maturationally natural cognition fosters religions’ success. Representations with some minimal violation of intuitive expectations concerning some ontological category grab attention, stick in memory, and preserve the many automatic inferences accompanying the category. The empirical evidence for this and other elaborations of the by-product view suggests that it discloses dynamics of evolved cognition and associated emotions that tend to guide the pursuit of religious meanings systematically toward well-worn grooves in the semantic landscape. (shrink)

We draw on Short’s work on Peirce’s theory of signs to propose a new general definition of interpretation. Short argues that Peirce’s semiotics rests on his naturalised teleology. Our proposal extends Short’s work by modifying his definition of interpretation so as to make it more generally applicable to putatively interpretative processes in biological systems. We use our definition as the basis of an account of different kinds of misinterpretation and we discuss some questions raised by the definition by (...) reference to parallel problems in the field of teleosemantics. We propose that interpretative responses fulfilling the criteria of our definition may be made by relatively simple molecular entities and we suggest two specific empirical applications of the definition to experimental work in the field of origin of life research. Our wider aim is to suggest that a well formulated naturalistic definition of interpretation will allow a re-evaluation of the role of semiotic phenomena in biological systems, including the generation of empirically testable hypotheses. (shrink)

Although generalization is universally relied on in all scientific thought and is prerequisite to it, many students of scientific methods have neglected to analyze generalizing behavior. This is understandable in view of the fact that generalizing thought begins early in childhood and continues at simple or complex levels through the years of elementary school, high school and college. Most such generalization is clearly pre-critical, following the patterns of parents, playmates and teachers by means of suggestion, imitation and insight. (...) In spite of its universality, however, the process of generalization deserves careful analysis in order that it be fully understood and that errors in interpretation of experience due to faulty generalizing may be avoided. (shrink)

In one of his papers, JC Beall advanced a new and interesting interpretation of Weak Kleene logic, in terms of on-topic/off-topic. In brief, Beall suggests to read the third value as _off-topic_, whereas the two classical values are read as _true and on-topic_ and _false and on-topic_. Building on Beall’s new interpretation, the aim of this paper is threefold. First, we discuss two motivations to enrich Beall’s interpretation, and offer an alternative semantic framework that reflects our motivations. (...) Second, by making use of our new framework, we will offer a new interpretation of the logic of Catuskoti which combines Beall’s proposal of having _FDE_ as the correct logic with the on-topic/off-topic divide. Finally, we will offer a general result that will allow us to make sense of a family of infectious logics in terms of Beall’s on-topic/off-topic reading. (shrink)

This chapter is based on a presentation I gave at a conference on General Education. It provides an overview of a course I teach on (Jungian) dream interpretation, focusing especially on the assessment criteria that make it possible to grade students' interpretations of their own dreams in a highly objective manner.

In this paper I critically discuss and, in the end, reject Morgan’s Canon, a popular principle in comparative psychology. According to this principle we should always prefer explanations of animal behavior in terms of lower psychological processes over explanations in terms of higher psychological processes, when alternative explanations are possible. The validity of the principle depends on two things, a clear understanding of what it means for psychological processes to be higher or lower relative to each other and a justification (...) of a general preference for explanations that refer to lower psychological abilities. However, I argue that we cannot spell out the idea of a psychological scale in a way that claim is satisfied. I start with the discussion of different interpretations of the notion of a psychological scale. In Sect. 3, I discuss different possible strategies to justify any of those interpretations and argue that all of them fail. Finally, in Sect. 4, I generalize the argument for all possible interpretations of Morgan’s Canon and propose an alternative strategy: We should base our interpretations of animal behavior on more general principles such as evidential support and explanatory power, as followed in other scientific domains. (shrink)

Dzhaparidze, G., A generalized notion of weak interpretability and the corresponding modal logic, Annals of Pure and Applied Logic 61 113-160. A tree Tr of theories T1,...,Tn is called tolerant, if there are consistent extensions T+1,...,T+n of T1,...,Tn, where each T+i interprets its successors in the tree Tr. We consider a propositional language with the following modal formation rule: if Tr is a tree of formulas, then Tr is a formula, and axiomatically define in this language the decidable logics TLR (...) and TLRω. It is proved that TLR yields exactly the schemata of PA-provable sentences, if Tr is understood as “Tr is tolerant”. In fact, TLR axiomatizes a considerable fragment of provability logic with quantifiers over ∑1-sentences, and many relations that have been studied in the literature can be expressed in terms of tolerance. We introduce and study two more relations between theories: cointerpretability and cotolerance which are, in a sense, dual to interpretability and tolerance. Cointerpretability is a characterization of ∑1-conservativity for essentially reflexive theories in terms of translations. (shrink)

The article investigates the relations between Hausdorff and non-Hausdorff manifolds as objects of general relativity. We show that every non-Hausdorff manifold can be seen as a result of gluing together some Hausdorff manifolds. In the light of this result, we investigate a modal interpretation of a non-Hausdorff differential manifold, according to which it represents a bundle of alternative space-times, all of which are compatible with a given initial data set.

At the beginning of the pandemic, many music ensembles had to stop their activities due to the confinement. While some found creative ways to start making music again with the help of technologies, the transition from “real” rehearsals to “online” rehearsals was challenging, especially among older amateur musicians. The aim of this case study was to examine the effects of this transition on three community band conductors and three older amateur musicians. Specific objectives were to explore intergenerational relationships to support (...) online group music-making; digital literacy and access in later life; and online music-making in a COVID-19 context. Semi-structured interviews were conducted and theoretical thematic analysis was undertaken. Results were analyzed from the conductors’ and older musicians’ perspectives, and common trends were combined to facilitate interpretation. The first theme showed that being part of an intergenerational ensemble contributed positively to the learning experience online. The second theme demonstrated that because both conductors and musicians were new to the online rehearsals, it contributed to attenuate the age-related digital divide that may have been observed in other studies. Regarding access in later-life, older musicians reported benefits associated with rehearsing online, specifically in terms of distance/commute, time, energy, and cost. However, for those who did not already have internet and electronic devices, the cost of acquiring all the necessary equipment to make music online could have been too high. Finally, the third theme revealed that musicians appreciated the opportunity to make music online and indicated that it was definitely better than having nothing, especially for its social aspects. In conclusion, while participants noted several challenges associated with online music-making, they were also appreciative of the opportunity to continue making music at a time when in-person rehearsals were not possible. Pedagogical implications are discussed, specifically the importance of the support network, of meeting people where they are, of learning to adapt, and of collaborative teaching. (shrink)

In this paper, we provide a re-interpretation of qualitative and quantitative modeling from a representationalist perspective. In this view, both approaches attempt to construct abstract representations of empirical relational structures. Whereas quantitative research uses variable-based models that abstract from individual cases, qualitative research favors case-based models that abstract from individual characteristics. Variable-based models are usually stated in the form of quantified sentences. This syntactic structure implies that sentences about individual cases are derived using deductive reasoning. In contrast, case-based models (...) are usually stated using context-dependent existential sentences. This syntactic structure implies that sentences about other cases are justifiable by inductive reasoning. We apply this representationalist perspective to the problems of generalization and replication. Using the analytical framework of modal logic, we argue that the modes of reasoning are often not only applied to the context that has been studied empirically, but also on a between-contexts level. Consequently, quantitative researchers mostly adhere to a top-down strategy of generalization, whereas qualitative researchers usually follow a bottom-up strategy of generalization. Depending on which strategy is employed, the role of replication attempts is very different. In deductive reasoning, replication attempts serve as empirical tests of the underlying theory. Therefore, failed replications imply a faulty theory. From an inductive perspective, however, replication attempts serve to explore the scope of the theory. Consequently, failed replications do not question the theory per se, but help to shape its boundary conditions. We conclude that quantitative research may benefit from a bottom-up generalization strategy as it is employed in most qualitative research programs. Inductive reasoning forces us to think about the boundary conditions of our theories and provides a framework for generalization beyond statistical testing. In this perspective, failed replications are just as informative as successful replications, because they help to explore the scope of our theories. (shrink)

We generalize the modal interpretation of quantum mechanics so that it may be applied to composite systems represented by arbitrary density operators. We discuss the interpretation these density operators receive and relate this to the discussion about the interpretation of proper and improper mixtures in the standard interpretation.

Logics for ‘generally’ are intended to express some vague notions, such as ‘generally’, ‘several’, ‘many’, ‘most’, etc., by means of the new generalized quantifier ∇ and to reason about assertions with ‘generally’ . We introduce the idea of functional interpretation for ‘generally’ and show that representative functions enable elimination of ∇ and reduce consequence to classical theories. Thus, one can use proof procedures and theorem provers for classical first-order logic to reason about assertions involving ‘generally’.

There is a widespread impression that General Relativity, unlike Quantum Mechanics, is in no need of an interpretation. I present two reasons for thinking that this is a mistake. The first is the familiar hole argument. I argue that certain skeptical responses to this argument are too hasty in dismissing it as being irrelevant to the interpretative enterprise. My second reason is that interpretative questions about General Relativity are central to the search for a quantum theory of gravity. I (...) illustrate this claim by examining the interpretative consequences of a particular technical move in canonical quantum gravity. (shrink)

I argue that, contrary to the recent claims of physicists and philosophers of physics, general relativity requires no interpretation in any substantive sense of the term. I canvass the common reasons given in favor of the alleged need for an interpretation, including the difficulty in coming to grips with the physical significance of diffeomorphism invariance and of singular structure, and the problems faced in the search for a theory of quantum gravity. I find that none of them shows (...) any defect in our comprehension of general relativity as a physical theory. I conclude by comparing general relativity with quantum mechanics, a theory that manifestly does stand in need of an interpretation in an important sense. Although many aspects of the conceptual structure of general relativity remain poorly understood, it suffers no incoherence in its formulation as a physical theory that only an ‘interpretation’ could resolve. *Received November 2007; revised February 2009. †To contact the author, please write to: Center for Philosophy of Science, University of Pittsburgh, 817 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: [email protected] . When science starts to be interpretive it is more unscientific even than mysticism. (D. H. Lawrence, “Self‐Protection”). (shrink)

Abstractabstract:Malebranche claims that God always, or nearly always, acts by general volitions. However, two possible interpretations of this claim have led to competing understandings of Malebranche's occasionalism. The General Content interpretation (GC) holds that God forms as few volitions as possible, and that aside from a limited number of particular volitions, God's normal mode of action consists simply in willing the general laws themselves. The Particular Content interpretation (PC) affirms that God forms a distinct volition for each event (...) or state of affairs, but that those volitions count as general when they are issued "in accordance with" some general law. This essay examines five lines of evidence that purport to reveal Malebranche's commitment to PC and explains why they all fail. As a result, GC emerges unscathed as a consistent and viable interpretation, and, at the same time, much of the case for PC is undermined. (shrink)

The subject of research in this article is the question of the possibility of formalizing the general theory of systems, that is, turning it into a language for describing systems of any nature with unambiguously defined lexical units and rules. To answer this question, the author considers the phenomenon of semantic indeterminacy of languages, which ensures the flexibility of formed lexical constructions due to the multivalence of lexical units. Also the subject of the research is the practice of quoting out (...) of context – a phenomenon, the admissibility of which is conditioned by the isomorphism of lexical constructions, as well as by the creative nature of the cognitive process, in which the result of cognition is unknown in advance, and thus the change of interpretation of the used concepts is inevitable. The conducted research allows us to state that the general theory of systems cannot be exclusively an applied theory, but should be supplemented with an ontological component. In this case, it becomes a philosophical theory, for which full formalization is impossible without loss of functionality. As a result, general systems theory must inevitably retain a certain semantic uncertainty. This uncertainty, however, can be reduced by translation into universality and generalization of concepts. Besides, it is possible and in some cases necessary to formalize separate components of the general theory of systems, in particular, its ontological component - the metaphysics of material existence. (shrink)

A geometric interpretation of gravitation is given using general relativity. The law of gravitation is taken in the formR 44=0, whereR 44is the component of the contracted Riemann-Christoffel (Ricci) tensor representing the curvature of time. The remaining curvature components of the contracted Riemann-Christoffel tensor may or may not vanish. All that is required in addition toR 44=0 is that the Gaussian curvatureR be nowhere infinite. The conditionR 44=0 yields a nonlinear wave equation. One of the static degenerate solutions represents (...) the gravitational field surrounding a static gravitational point singularity. It is found that for this solution, the three famous predictions of general relativity are obtained in the weak-field approximation. In addition, it is found that there is a correction to the Kepler period of revolution for an orbit. (shrink)

The English pronoun _it_ can anaphorically take on the meaning of a salient generalized quantifier when it occurs in subject position followed by an elided Verb Phrase and (optionally) a VP-level operator. The extent to which theories of pronoun interpretation will have to be altered to take account of this finding will depend on whether the phenomenon is unique to English or part of a crosslinguistic pattern.

We discuss generalized pobabilistic models for which states not necessarily obey Kolmogorov's axioms of probability. We study the relationship between properties and probabilistic measures in this setting, and explore some possible interpretations of these measures.

The paper reviews links between Bernard Lonergan's theory of innovative economic growth and cycles, and the ideas of Friedrich Hayek, John Maynard Keynes, and Joseph Schumpeter. They were contemporary economists, who remain influential today. For Lonergan, although markets define what is bought and sold in an exchange economy, production decisions are more fundamental. These decisions are choices about the direction of development, the standard of living, and variations in the distribution of wealth in a modern society. The paper shows how (...) Lonergan's pure cycle theory extends mainstream theory to include a broader view of human behaviour and choice. (shrink)

This paper advances an interpretation of what Hume called ‘the general rules’: natural principles of belief-formation that nevertheless can be augmented via reflection. According to Hume, reflection is, in part, what separates the wise from the vulgar. In this paper, I argue that for Hume being wise must therefore be, to some degree, voluntary. Hume faced a significant problem in attempting to reconcile his epistemic normativity, i.e. his claims about what we ought to believe, with his largely involuntarist theory (...) of the mind. Reflection on the General Rules, and an interpretation of that reflection as voluntary, helps explain not only Hume's theory of belief, but also how he hoped to reconcile epistemic normativity with naturalism about the mental. (shrink)

It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields (...) to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details. (shrink)

The problem of motion in general relativity is about how exactly the gravitational field equations, the Einstein equations, are related to the equations of motion of material bodies subject to gravitational fields. This article compares two approaches to derive the geodesic motion of matter from the field equations: the ‘T approach’ and the ‘vacuum approach’. The latter approach has been dismissed by philosophers of physics because it apparently represents material bodies by singularities. I argue that a careful interpretation of (...) the approach shows that it does not depend on introducing singularities at all and that it holds at least as much promise as the T approach. (shrink)

Peano arithmetic cannot serve as the ground of mathematics for it is inconsistent to infinity, and infinity is necessary for its foundation. Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at least one (logical) axiomatics consistent to infinity. That is nothing else than a new reading at issue and comparative interpretation of Gödel’s papers (1930; 1931) meant here. Peano arithmetic admits anyway generalizations consistent to infinity and thus to some addable axiom(s) of infinity. The (...) most utilized example of those generalizations is the complex Hilbert space. Any generalization of Peano arithmetic consistent to infinity, e.g. the complex Hilbert space, can serve as a foundation for mathematics to found itself and by itself. (shrink)

Philosophical Studies, Vol. 34 (August, 1978), pp. 207-211.