Armstrong holds the Supervenience Theory of instantiation, namely that the instantiation of universals by particulars supervenes upon what particulars and what universals there are, where supervenience is stipulated to be explanatory or dependent supervenience. I begin by rejecting the Supervenience Theory of instantiation. Having done so it is then tempting to take instantiation as primitive. This has, however, an awkward consequence, undermining one of the main advantages universals have over tropes. So I examine another account hinted at by (...) Armstrong. This is the Operator Theory of instantiation, by which I mean the theory that universals are operators, and that a particular instantiates a monadic universal because the universal operates on the particular, resulting in the state of affairs. On this theory the state of affairs supervenes on the instantiation rather than vice versa. In the second part of the paper I develop this theory of universals as operators, including an account of structural universals, which are useful for accounts of modality and of mathematics. (shrink)

The proposed heavy dependence on Pavlovian conditioning to account for social behavior confounds phylogenically and ontogenically selected behavior patterns and ignores the extension of the principle of selection by consequences from biological to learning theory. Instead of acknowledging operant relations, Domjan et al. construct vaguely specified mechanisms based upon anticipatory cost-benefit considerations that are not supported by the Pavlovian conditioning literature.

The research Nevin & Grace report is impressive in its integrative power, but it also shows the current limits of operant theory: There is tremendous concentration on understanding how existing behavioral relations are modulated in rate or time allocation, but little on dealing with the origin of the behavioral relations themselves. Specifying what should count as a behavioral unit will require source principles sensitive to the composition of the units being related.

Attempts to define life should focus on the transition from molecules to cells and the “closure” aspects of this event. Rather than classifying existing objects into living and non-living entities I believe the challenge is to understand how the transition from non-life to life can take place, that is, the how the closure in Jagers op Akkerhuis’s hierarchical classification of operators, comes about.

Current, prevalent models of the food system, including complex-adaptive systems theories and commodity-as-relation thinking, have usefully analyzed the food system in terms of its elements and relationships, confronting persistent questions about a system’s identity and leverage points for change. Here, inspired by Heldke’s analysis, we argue for another approach to the “system-ness” of food that carries those key questions forward. Drawing on Niklas Luhmann’s systems theory, we propose a model of the food system defined by the relational process of (...) feeding itself; that is, the food system is made of feeding and only feeding, and system structures are produced by the coupling of that process to its various contexts. We argue that this approach moves us away from understandings of the food system that take structures and relations as given, and sees them instead as contingent, thereby helping to identify leverage points for food system change. The new approach we describe also prompts us as critical agrifood scholars to be constantly reflexive about how our analyses are shaped by our own assumptions and subjectivities. (shrink)

This article explores how researchers in a scientific research lab co-operate with each other and value these co-operations, using a case study of a life sciences lab as an illustrative example. It explores how researchers within the lab co-operate in three main ways: through their ideas, methods and resources. A core contention of this article is that the values researchers attach to these different ways of co-operating can be assessed on two dimensions: goals and ways of understanding. The goals dimension (...) moves from group goals, manifested in the vision of the lab defined by its principal investigator, to the goals of individual researchers within the lab, often achieved through work on individual projects. Individual goals were more highly valued by researchers in this case study. The ways of understanding dimension moves from theory-based and theory-building research activities, to craft-based activities related to the research lab’s experiments. Theoretical ways of understanding are more highly valued by researchers in this case study. Combined, these two dimensions mean that researchers will value co-operations that support individual goals and theoretical ways of understanding more highly. Idea-based collaborations, individualistic and theoretical in nature, were the most highly valued. Collaborations based on resources, communal and craft-centered, were the least valued in this case study. (shrink)

In this paper we review the general framework of operational probabilistic theories, along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.

Fara and Williamson (Mind, 2005) argue that counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.

In Ref. 1 we have considered the finite-dimensional quantum mechanics. There the quantum mechanical space of states wasV=C r. It is known that the second quantization of this space is the space of square-summable functions of finite number of variables(L 2(Rr,dx)) (Segal isomorphism). Creation and annihilation operators were introduced in Ref. 1, and the former coincided with the usual position and momentum operators in the conventional quantum mechanics. In this paper we shall investigate the spectral properties of field operators. We (...) shall show that the isomorphism between the exponential ofV andL 2(Rr,dx) can be understood as the decomposition by generalized eigenvectors of field operators (“Fourier transform”). (shrink)

This paper deals with Boolean algebras supplied with an additional binary operation, calledB-algebras for short.The aim of the paper is to generalize some theorems concerning topological Boolean algebras to more comprehensive classes ofB-algebras, to formulate fundamental properties ofB-algebras, and to find more important relationships of these algebras to other known algebras.

Constructive set theory a' la Myhill-Aczel has been extended in (Cantini and Crosilla 2008, Cantini and Crosilla 2010) to incorporate a notion of (partial, non--extensional) operation. Constructive operational set theory is a constructive and predicative analogue of Beeson's Inuitionistic set theory with rules and of Feferman's Operational set theory (Beeson 1988, Feferman 2006, Jaeger 2007, Jaeger 2009, Jaeger 1009b). This paper is concerned with an extension of constructive operational set theory (Cantini and Crosilla 2010) by (...) a uniform operation of Transitive Closure, \tau. Given a set a, \tau produces its transitive closure \tau a. We show that the theory ESTE of (Cantini and Crosilla 2010) augmented by \tau is still conservative over Peano Arithmetic. (shrink)

The general aim of this book is to provide an elementary exposition of some basic concepts in terms of which both classical and non-dassicallogirs may be studied and appraised. Although quantificational logic is dealt with briefly in the last chapter, the discussion is chiefly concemed with propo gjtional cakuli. Still, the subject, as it stands today, cannot br covered in one book of reasonable length. Rather than to try to include in the volume as much as possible, I have put (...) emphasis on some selected topics. Even these could not be roverrd completely, but for each topic I have attempted to present a detailed and precise t’Xposition of several basic results including some which are non-trivial. The roots of some of the central ideas in the volume go back to J. Luka siewicz’s seminar on mathematicallogi. (shrink)

We introduce an operational set theory in the style of [5] and [16]. The theory we develop here is a theory of constructive sets and operations. One motivation behind constructive operational set theory is to merge a constructive notion of set ([1], [2]) with some aspects which are typical of explicit mathematics [14]. In particular, one has non-extensional operations (or rules) alongside extensional constructive sets. Operations are in general partial and a limited form of self{application is (...) permitted. The system we introduce here is a fully explicit, nitely axiomatised system of constructive sets and operations, which is shown to be as strong as HA. (shrink)

(2003). Berkeley's theory of operative language in the Manuscript Introduction. British Journal for the History of Philosophy: Vol. 11, No. 2, pp. 271-301. doi: 10.1080/09608780320001047877.

I present a general theory of abstraction operators which treats them as variable-binding term- forming operators, and provides a reasonably uniform treatment for definite descriptions, set abstracts, natural number abstraction, and real number abstraction. This minimizing, extensional and relational theory reveals a striking similarity between definite descriptions and set abstracts, and provides a clear rationale for the claim that there is a logic of sets (which is ontologically non- committal). The theory also treats both natural and real (...) numbers as answering to a two-fold process of abstraction. The first step, of conceptual abstraction, yields the object occupying a particular position within an ordering of a certain kind. The second step, of objectual abstraction, yields the number sui generis, as the position itself within any ordering of the kind in question. (shrink)

We study constructive set theories, which deal with operations applying both to sets and operations themselves. Our starting point is a fully explicit, finitely axiomatized system ESTE of constructive sets and operations, which was shown in 10 to be as strong as PA. In this paper we consider extensions with operations, which internally represent description operators, unbounded set quantifiers and local fixed point operators. We investigate the proof theoretic strength of the resulting systems, which turn out to be impredicative . (...) © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as (...) mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence. (shrink)

In this paper, we investigate the constitutive problems and other several aspects of what a research entitled 'formal epistemology' should be. The interest in this subject has to do with the possibility of reaching a privileged point of view or axis of research - i.e., the 'formal' one - that would allow, a better grasp of the richness and variety of the facts and problems tackled by precise (local) epistemology of theories (for example, in physics). This approach is likely to (...) enable one to hold the main structural lines that organize those theories according to a more com prehensive, unifying and synthetic intelligibilit. By the same token, it would eventually allow a better handling of the changes required in the organization of knowledge, putting emphasis on its main directions, drawing up a rational inventory of this knowledge, and perhaps anticipating others. At first, we deal with the `thought of changes' that no approach of the 'form' can afford to leave aside, since the meaning of this concept is inseparable from the contents that come with constructions and modifications. We examine then the notion of 'epistemic operation' as an instrument to create new forms on the theoretical as well as on the meta-theoretical levels. ln the wake of it, we analyze the characteristics of the form and of the formal, as well as their relationship with the contents of knowledge. We also take the notion of object into account, since it depends upon the decision of a subject and upon conventional choices. We finally inquire about the link between `epistemic operations' as specified above and algorithmic functions for knowledge statements, and emphasize the risk of reductionism that might follow from a naturalistic conception of representation. (shrink)

In this paper we develop an abstract theory of adequacy. In the same way as the theory of consequence operations is a general theory of logic, this theory of adequacy is a general theory of the interactions and connections between consequence operations and its sound and complete semantics. Addition of axioms for the connectives of propositional logic to the basic axioms of consequence operations yields a unifying framework for different systems of classical propositional logic. We (...) present an abstract model-theoretical semantics based on model mappings and theory mappings. Between the classes of models and theories, i.e., the set of sentences verified by a model, it obtains a connection that is well-known within algebra as Galois correspondence. Many basic semantical properties can be derived from this observation. A sentence A is a semantical consequence of T if every model of T is also a model of A. A model mapping is adequate for a consequence operation if its semantical inference operation is identical with the consequence operation. We study how properties of an adequate model mapping reflect the properties of the consequence operation and vice versa. In particular, we show how every concept of the theory of consequence operations can be formulated semantically. (shrink)

The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing (...) of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular. (shrink)

“Small” large cardinal notions in the language of ZFC are those large cardinal notions that are consistent with V = L. Besides their original formulation in classical set theory, we have a variety of analogue notions in systems of admissible set theory, admissible recursion theory, constructive set theory, constructive type theory, explicit mathematics and recursive ordinal notations (as used in proof theory). On the face of it, it is surprising that such distinctively set-theoretical notions (...) have analogues in such disaparate and relatively constructive contexts. There must be an underlying reason why that is possible (and, incidentally, why “large” large cardinal notions have not led to comparable analogues). My long term aim is to develop a common language in which such notions can be expressed and can be interpreted both in their original classical form and in their analogue form in each of these special constructive and semi-constructive cases. This is a program in progress. What is done here, to begin with, is to show how that can be done to a considerable extent in the settings of classical and admissible set theory (and thence, admissible recursion theory). The approach taken here is to expand the language of set theory to allow us to talk about (possibly partial) operations applicable both to sets and to operations and to formulate the large cardinal notions in question in terms of operational closure conditions; at the same time only minimal existence axioms are posited for sets. The resulting system, called Operational Set Theory, is a partial adaptation to the set-theoretical framework of the explicit mathematics framework Feferman (1975). The.. (shrink)

E-commerce poverty alleviation has become a new wisdom in China’s rural poverty alleviation, but there are a few empirical researches on e-commerce poverty alleviation based on farmer cooperatives. Taking four typical poverty counties in Zhejiang Province as an example, based on the actor network theory, this paper defines the participants and their obligatory passage point from the e-commerce poverty alleviation actor network, combs the roles and interest demands of various stakeholders, and constructs the EPAAN model based on farmer cooperatives (...) according to the translation process. We found that the EPAAN is a heterogeneous network by constantly updating, which consists of human actors with cooperatives as the main body and non-human actors. Moreover, our study illustrates that the formation and operation mechanism of cooperative e-commerce poverty alleviation network alliance under the background of targeted poverty alleviation can be well analyzed with the help of actor network theory. This study contributes to provide a feasible Chinese plan for the cause of poverty eradication all over the world, and provides a great reference value for global poverty governance. (shrink)

We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible (...) universe. (shrink)

We interpret the (formal) postulates of measurement in quantum theory in terms of measurement procedures that can be done in the laboratory (at least in principle).

We discuss a generalization of the standard notion of probability space and show that the emerging framework, to be called operational probability theory, can be considered as underlying quantal theories. The proposed framework makes special reference to the convex structure of states and to a family of observables which is wider than the familiar set of random variables: it appears as an alternative to the known algebraic approach to quantum probability.

Dr Seuren's study deals with the problem of presenting an adequate model of grammatical description. The model he proposes conforms in its main outlines to the transformational generative grammar established by Chomsky, but differs in important respects. These mainly affect that part of Chomsky's syntactic component known as the 'base', which generates basic or 'deep' structures. In the model of the base proposed here two main constituents are distinguished for every deep structure representation of a sentence, vis-a-vis the operators and (...) the nucleus. The deep structure of a sentence is thus seen to be very similar to the logical structure of a proposition. The arguments given in support of this analysis are based on mainly on considerations of simplicity and semantic adequacy. (shrink)

We present an extension of constructive Zermelo{Fraenkel set theory [2]. Constructive sets are endowed with an applicative structure, which allows us to express several set theoretic constructs uniformly and explicitly. From the proof theoretic point of view, the addition is shown to be conservative. In particular, we single out a theory of constructive sets with operations which has the same strength as Peano arithmetic.

We study the extension of Feferman’s operational set theory provided by adding operational versions of unbounded existential quantification and power set and determine its proof-theoretic strength in terms of a suitable theory of sets and classes.

In this paper it is shown that the intuitionistic fixed point theory equation image for α times iterated fixed points of strictly positive operator forms is conservative for negative arithmetic and equation image sentences over the theory equation image for α times iterated arithmetic comprehension without set parameters. This generalizes results previously due to Buchholz [5] and Arai [2].

We have seen that the operational imperative is a prescriptive thesis about formulations of theories which imposes restrictions on the sorts of theories science may employ. We assessed the operational imperative by investigating a number of relationships holding between theory formulations, theories, physical systems, and phenomena, and then applying our findings to the operational imperative. These applications showed that the operational definitions required by the operational imperative were not definitions at all, being rather statements of putative empirical regularities holding (...) between particulars which in effect are formulations of empirically true or false theories. From this fact it followed that the supposed epistemic pay-offs of following the operational imperative fail to accrue: Operational definitions do not enable one to go deductively from knowledge of observables to knowledge of unobservables, and operational definitions do not provide a means for testing theories about unobservable phenomena. As such the operational imperative should be rejected in both its weak and strong versions. However, we did discover a grain of truth in the observational imperative — namely that theories with non-observable parameters are testable only if these parameters have observable manifestations. But that grain of truth does not lead to the operational imperative as typically advanced unless one embraces certain epistemological theories about observation which recent work on observation makes highly doubtful. (shrink)

Despite its long tradition in social psychology, we consider that Cognitive Dissonance Theory presents serious flaws concerning its methodology which question the relevance of the theory, limit breakthroughs, and hinder the evaluation of its core hypotheses. In our opinion, these issues are mainly due to operational and methodological weaknesses that have not been sufficiently addressed since the beginnings of the theory. We start by reviewing the ambiguities concerning the definition and conceptualization of the term cognitive dissonance. We (...) then review the ways it has been operationalized and we present the shortcomings of the actual paradigms. To acquire a better understanding of the theory, we advocate a stronger focus on the nature and consequences of the cognitive dissonance state itself. Next, we emphasize the actual lack of standardization, both in the ways to induce cognitive dissonance and to assess it, which impairs the comparability of the results. Last, in addition to reviewing these limits, we suggest new ways to improve the methodology and we conclude on the importance for the field of psychology to take advantage of these important challenges to go forwards. (shrink)

We study a theory PTO of polynomial time computability on the type of binary strings, as embedded in full lambda calculus with total application and extensionality. We prove that the closed terms of type W → W are exactly the polynomial time operations. This answers a conjecture of Strahm [13].

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

The general theory of variable binding term operators is an interesting recent development in logic. It opens up a rich class of semantic and model-theoretic problems. In this paper we survey the recent literature on the topic, and offer some remarks on its significances and on its connections with other branches of mathematical logic.