This is a review of the book ‘Memory Evolutive Systems; Hierarchy, Emergence, Cognition’, by A. Ehresmann and J.P. Vanbremeersch. I welcome the use of category theory and the notion of colimit as a way of describing how complex hierarchical systems can be organised, and the notion of categories varying with time to give a notion of an evolving system. In this review I also point out the relation of the notion of colimit to ideas of communication; the necessity of communications (...) to be symbolic representations; and the use of an analogy with mathematics to spell out some of the necessities of such a mode of communication to be powerful, robust and efficient. (shrink)

We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin''s axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey''s omitting types theorem fails for L n, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. L n has been recently (...) (and quite extensively) studied as a many-dimensional modal logic. (shrink)

Let α be an arbitrary infinite ordinal, and. In [26] we studied—using algebraic logic—interpolation and amalgamation for an extension of first order logic, call it, with α many variables, using a modal operator of a unimodal logic that contributes to the semantics. Our algebraic apparatus was the class of modal cylindric algebras. Modal cylindric algebras, briefly, are cylindric algebras of dimension α, expanded with unary modalities inheriting their semantics from a unimodal logic such as, or. When modal (...) cylindric algebras based on are just cylindric algebras, that is to say,. This paper is a sequel to [26], where we study algebraically other properties of. We study completeness and omitting types (s) for s by proving several representability results for so‐called dimension complemented and locally finite. Furthermore, we study the notion of atom‐canonicity for, the variety of n‐dimensional modal cylindric algebras. Atom canonicity, a well known persistence property in modal logic, is studied in connection to for, which is restricted to the first n variables. We further continue our study of interpolation in [26] for algebraizable extensions of by studying using both algebraic logic and category theory. Our main results on are Theorems 3.7, 4.4 & 4.6, while our main results on amalgamation are Theorems 5.7, 5.10, 5.13 & 5.16. (shrink)

Recently two pairs of authors have aimed to vindicate the longstanding "orthodox" or conventional claim that a first-class constraint generates a gauge transformation in typical gauge theories such as electromagnetism, Yang-Mills and General Relativity, in response to the Lagrangian-equivalent reforming tradition, in particular Pitts, _Annals of Physics_ 2014. Both pairs emphasize the coherence of the extended Hamiltonian formalism against what they take to be core ideas in Pitts 2014, but both overlook Pitts 2014's sensitivity to ways that one (...) might rescue the claim in question, including an additive redefinition of the electrostatic potential. Hence the bulk of the paper is best interpreted as arguing that the longstanding claim about separate first-class constraints is _either false or trivial_---de-Ockhamization (using more when less suffices by splitting one quantity into the sum of two) being trivial. Unfortunately section 9 of Pitts 2014, a primarily verbal argument that plays no role in other works, is refuted. Pooley and Wallace's inverse Legendre transformation to de-Ockhamized electromagnetism with an additively redefined electrostatic potential, however, opens the door to a precisely analogous calculation introducing a photon mass, which shows that a _second-class primary_ constraint generates a 'gauge transformation' in the exactly same sense---a _reductio ad absurdum_ of the orthodox claim that a first-class constraint generates a gauge transformation _and a second-class constraint does not_. A _reductio_ using massive electromagnetism was presaged in Pitts 2014. Gauge freedom by de-Ockhamization does not require any constraints at all, first-class or second-class, because any dynamical variable in any Lagrangian can be de-Ockhamized into exhibiting trivial additive artificial gauge freedom by splitting one quantity into the sum of two. Physically interesting gauge freedom, however, is typically generated by a tuned sum of first-class constraints, not each first-class constraint alone. (shrink)

The reductive nature of Kincaid's undertaking comes into sharper focus when we compare his kind of critical inquiry with that, say, of [Sheldon] Sacks or [Ralph] Rader. Kincaid concludes where they begin. For Sacks, the identification of some type, such as satire, is what initiates the critical process. What then remains is to move beyond type, which exists at the highest level of generality, to form and finally to those detailed analyses which will account for the peculiar powers of unique (...) works. His types, as he says, are "only elementary distinctions," and he adds that "at some point in an adequate criticism of a single literary work, we will inevitably be discussing those variations which distinguish a particular literary work from all other literary works of its class, even if that class has been defined according to the most subtle and intricate combination of variables possible."1 Similarly for Rader, our intuitions about formal principles and intentions are but first steps in critical inquiry. "My theory, " he says, "attempts not to establish 'general laws' . . . but to render explicit the structural features of our tacit experiences of literature in a way that will allow us to bring all its implications to bear simultaneously upon our explanation of any particular literary work."2 Such procedures as these, which are designed to give us particular knowledge, are ruled out by Kincaid's program, the most specific formal principle of which is something quite general: the competition among narrative patterns. There is finally, then, very little knowledge to be shared, for our inquiries will always arrive at the same conclusion. Although readers, in his view, can intend one thing rather than another, writers cannot, and this assumption that agents are somehow set apart from the other members of the species means, I suspect, that Kincaid is right about one thing: his effort to mediate does indeed place him in a "no-man's land." · 1. Sheldon Sacks, Fiction and the Shape of Belief , pp. 25-26 n.· 2. Rader, "Explaining Our Literary Understanding," Critical Inquiry 1 : 905. Robert Denham, editor of Northrop Frye: An Enumerative Bibliography and the forthcoming Northrop Frye on Culture and Literature , is associate professor and chairman of the department of English at Emory and Henry College. In this essay Robert Denham replies to James R. Kincaid's "Coherent Readers, Incoherent Texts" Critical inquiry, Summer 1977. (shrink)

We describe a knowledge representation and inference formalism, based on an intensional propositional semantic network, in which variables are structures terms consisting of quantifier, type, and other information. This has three important consequences for natural language processing. First, this leads to an extended, more natural formalism whose use and representations are consistent with the use of variables in natural language in two ways: the structure of representations mirrors the structure of the language and allows re-use phenomena such (...) as pronouns and ellipsis. Second, the formalism allows the specification of description subsumption as a partial ordering on related concepts (variable nodes in a semantic network) that relates more general concepts to more specific instances of that concept, as is done in language. Finally, this structured variable representation simplifies the resolution of some representational difficulties with certain classes of natural language sentences, namely, donkey sentences and sentences involving branching quantifiers. The implementation of this formalism is called ANALOG (A NAtural LOGIC) and its utility for natural language processing tasks is illustrated. (shrink)

We construct a local \-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state \\rangle \) as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state \\rangle \) which is different from the prepared quantum state \\rangle \) and has an ontic status. The ontic state of a single particle consists (...) of two parts. First, a single particle ontic quantum state \|i\rangle \), where \\) is a 3-space wavepacket and \ is a spin eigenstate of the future measurement setting. Second, a particle position in 3-space \\), which evolves via a de Broglie–Bohm type guidance equation with the 3-space wavepacket \\) acting as a local pilot wave. The joint ontic quantum state \\rangle \) fixes the measurement outcomes deterministically whereas the prepared quantum state \\rangle \) determines the distribution of the \\rangle \)’s over an ensemble. Both \\rangle \) and \\rangle \) evolve via the Schrodinger equation. Our model exactly reproduces the Bell correlations for any pair of measurement settings. We also consider ‘non-equilibrium’ extensions of the model with an arbitrary distribution of hidden variables. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. We argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics. (shrink)

We show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables. In the case of generalized quantifiers, explicit attention to relations of dependence becomes indispensible for setting up proof systems. It is shown that this can be done by turning variables into structured objects, governed by (...) various types of structural rules. These structured variables are interpreted semantically by means of a dependence relation. This relation is an analogue of the accessibility relation in modal logic. We then isolate a class of axioms for generalized quantifiers which correspond to first-order conditions on the dependence relation. (shrink)

The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of "rank-homogeneous" trees. We consider these conditions as a possible definition of what it means for a class of structures to have "Ulm type". The result says that there can be no Turing computable embedding of a class not of Ulm type (...) into one of Ulm type. We apply this result to show that there is no Turing computable embedding of the class of graphs into the class of "rank-homogeneous" trees. The second main result says that there is a Turing computable embedding of the class of rank-homogeneous trees into the class of torsion-free Abelian groups. The third main result says that there is a "rank-preserving" Turing computable embedding of the class of rank-homogeneous trees into the class of Boolean algebras. Using this result, we show that there is a computable Boolean algebra of Scott rank ${\mathrm{\omega }}_{1}^{\mathrm{C}\mathrm{K}}$. (shrink)

This paper presents the first purely algebraic characterization of classes of partial algebras definable by a set of strong equations. This result was posible due to new tools such as invariant congruences, i.e. a generalization of the notion of a fully invariant congruence, and extension of algebras, specific for strong equations.

We give a novel application of algebraic logic to first order logic. A new, flexible construction is presented for representable but not completely representable atomic relation and cylindric algebras of dimension n (for finite n > 2) with the additional property that they are one-generated and the set of all n by n atomic matrices forms a cylindric basis. We use this construction to show that the classical Henkin-Orey omitting types theorem fails for the finite variable fragments of (...) first order logic as long as the number of variables available is > 2 and we have a binary relation symbol in our language. We also prove a stronger result to the effect that there is no finite upper bound for the extra variables needed in the witness formulas. This result further emphasizes the ongoing interplay between algebraic logic and first order logic. (shrink)

One of the success stories of formal semantics is explicating responsive moves like answers to questions. There is, however, a significant lacune concerning the characterization of _initiating utterances_, which are strongly tied to the conversational activity [language game (Wittgenstein), speech genre (Bakhtin)], or—our terminology—_conversational type_, one is engaged in. To date there has been no systematic proposal trying to account for the range of possible _language games_/_speech genres_/_conversational types_ and their global structure. In particular, concerning the range of subject matter (...) that can and needs to be discussed and by whom—ultimately a semantic analogue of Laplace’s demon. We suggest that the subject matter problem for conversational types is a central task for any semantic theory for conversation. This paper develops a theory of conversational types, which embedded in the theory of conversational interaction KoS, enables this problem to be tackled for a wide range of conversational types drawn from the British National Corpus classification of conversational domains. The theory we develop treats conversational types as first class, not metatheoretical entities, in contrast to explications of corresponding notions in game theoretic approaches. We demonstrate that this allows us to explicate the possibilities interlocutors have to refer to and seek clarification about the types of conversations they are engaged in. (shrink)

In his paper "Why a Class Can't Change Its Members," Richard Sharvy appears to establish the impossibility of the existence of a variable class—that is, a class that at one time has a member that is not a member of it at another time. I first indicate the importance of Sharvy's argument for our understanding of the concept of identity in the contexts of time and modality, and I summarize his argument. Sharvy says that a (...) class='Hi'>class C that has one (non-variable) group of members at t2 and another (nonvariable) group of members at t2 would be identical with both the class C1 that always has the first group as members and the class C2 that always has the second group as members. This is an impossibility, since in general, one thing cannot be identical with two.I then criticize Sharvy's argument by pointing out a weakness in the defense of the claim that C = C1 and C = C2. This weakness is due to an ambiguity in Sharvy's Principle of Extensionality. (shrink)

Cook (1995) criticizes the work of Jacobs and Kosslyn (1994) on spatial relations, shape representations, and receptive fields in neural network models on the grounds that first‐order correlations between input and output unit activities can explain the results. We reply briefly to Cook's arguments here (and in Kosslyn, Chabris, Marsolek, Jacobs & Koenig, 1995) and discuss how new simulations can confirm the importance of receptive field size as a crucial variable in the encoding of categorical and coordinate spatial relations (...) and the corresponding shape representations; such simulations would testify to the computational distinction between the different types of representations. (shrink)

In this paper, we first propose a simple formal language to specify types of agents in terms of necessary conditions for their announcements. Based on this language, types of agents are treated as ‘first-class citizens’ and studied extensively in various dynamic epistemic frameworks which are suitable for reasoning about knowledge and agent types via announcements and questions. To demonstrate our approach, we discuss various versions of Smullyan’s Knights and Knaves puzzles, including the Hardest Logic (...) Puzzle Ever (HLPE) proposed by Boolos (in Harv Rev Philos 6:62–65, 1996). In particular, we formalize HLPE and verify a classic solution to it. Moreover, we propose a spectrum of new puzzles based on HLPE by considering subjective (knowledge-based) agent types and relaxing the implicit epistemic assumptions in the original puzzle. The new puzzles are harder than the previously proposed ones in the literature, in the sense that they require deeper epistemic reasoning. Surprisingly, we also show that a version of HLPE in which the agents do not know the others’ types does not have a solution at all. Our formalism paves the way for studying these new puzzles using automatic model checking techniques. (shrink)

We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We exhibit a number of natural correspondences between the model-theoretic properties of classes and their constituent models and the topological properties of the associated spaces. Tameness of Galois types, in particular, emerges as a topological separation principle. © 2011 WILEY-VCH Verlag GmbH & (...) Co. KGaA, Weinheim. (shrink)

The author here constructs a system of simple type theory in which the type hierarchy does not extend merely to any finite height, but to an infinite height; this added part allows him to prove the existence of infinite sets within the theory, instead of taking it as an axiom in the usual simple type theory. The system has been presented in such sufficient generality so as to make it able to accommodate current scientific theories; the author has turned in (...) the direction of using type theory rather than set theory as the underlying logic of scientific theories. The system is formalized in Church's lambda-calculus notation; the semantics of the system are treated in great detail and appear to be the most complete study so far in print. The system is shown to contain at each type a "basic logic" somewhat similar to first-order logic; the author also shows that Peano's axioms for arithmetic appear as theorems when cast in suitable form. This book is one of a number of recent studies of type theory; together they represent a revival of interest in the subject, both as a foundation for mathematics and as an object of interest in itself. The book stems from Andrews' Princeton doctoral thesis.—P. J. M. (shrink)

ObjectiveTest anxiety (TA) is a construct that has scarcely been studied based on Lang’s three-dimensional model of anxiety. The objective of this article is to investigate the repercussion of sociodemographic and academic variables on different responses for each component of anxiety and for the type of test in adolescent students.MethodA total of 1181 students from 12 to 18 years old (M= 14.7 and SD = 1.8) participated, of whom 569 were boys (48.2%) and 612 girls (51.8%). A sociodemographic questionnaire (...) and theCuestionario de Ansiedad ante los examenes-Adaptado (CAEX-A)[Test Anxiety Questionnaire-Adapted] an adaptation for Spanish secondary school levels (ESO) and Bachillerato were administered.ResultsGirls scored higher on the cognitive and physiological components of TA than boys, the intensity of the physiological response increasing with age. Bachillerato level students reported more physiological anxiety than those of ESO level. Students with better marks in the previous year presented more anxiety in the cognitive component, while those who obtained the lower mark presented higher anxiety values in the behavioral component. Participants reported that the types of tests that cause them more anxiety were oral tests in front of the class, oral presentation in front of a panel, and mathematics tests.ConclusionAdolescents show a differential response of TA based on the physiological, cognitive and motor components, mediated by the variables of gender, age, grade, academic performance and type of exam. These results serve to design specific intervention programs to manage anxiety in situations of academic assessment. (shrink)

For an arbitrary similarity type of Boolean Algebras with Operators we define a class ofSahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities arecanonical, that is, their validity is preserved under (...) taking canonical embedding algebras. Taken together, these properties imply that results about a Sahlqvist variety V van be obtained by reasoning in the elementary class of canonical structures of algebras in V.We give an example of this strategy in the variety of Cylindric Algebras: we show that an important identity calledHenkin's equation is equivalent to a simpler identity that uses only one variable. We give a conceptually simple proof by showing that the first-order correspondents of these two equations are equivalent over the class of cylindric atom structures. (shrink)

We study the first-order theories of some natural and important classes of coloured trees, including the four classes of trees whose paths have the order type respectively of the natural numbers, the integers, the rationals, and the reals. We develop a technique for approximating a tree as a suitably coloured linear order. We then present the first-order theories of certain classes of coloured linear orders and use them, along with the approximating technique, to establish complete axiomatisations of the (...) four classes of trees mentioned above. (shrink)

Despite their centrality to the scientific enterprise, both the nature of scientific variables and their relation to inductive inference remain obscure. I suggest that scientific variables should be viewed as equivalence classes of sets of physical states mapped to representations (often real numbers) in a structure preserving fashion, and argue that most scientific variables introduced to expand the degrees of freedom in terms of which we describe the world can be seen as products of an algorithmic inductive (...) inference first identified by William W. Rozeboom. This inference algorithm depends upon a notion of natural kind previously left unexplicated. By appealing to dynamical kinds—equivalence classes of causal system characterized by the interventions which commute with their time evolution—to fill this gap, we attain a complete algorithm. I demonstrate the efficacy of this algorithm in a series of experiments involving the percolation of water through granular soils that result in the induction of three novel variables. Finally, I argue that variables obtained through this sort of inductive inference are guaranteed to satisfy a variety of norms that in turn suit them for use in further scientific inferences. (shrink)

The year 2012 has witnessed worldwide celebrations of Alan Turing’s 100th birthday. A great number of conferences and workshops were organized by logicians, computer scientists and researchers in AI, showing the continued flourishing of computer science, and the fruitful interfaces between logic and computer science. Logic is no longer just the concept that Frege had about one hundred years ago, let alone that of Aristotle twenty centuries before. One of the prominent features of contemporary logic is its interdisciplinary character, connecting (...) across mathematics, philosophy, modern computer science, and even the cognitive and social sciences. -/- China is no exception. This special issue explores interfaces of logic with AI and other disciplines, and it attempts to give a bird’s eye view of the developing landscape of logic and AI in China. Our contributors come from computer science, AI, philosophy and linguistics, united by their interest in using formal logical tools and notions to deal with substantial problems in their fields. We are aware that AI is a vast area, and that the limitations of space in a volume like this may provide a somewhat incomplete or biased view. Still we hope that the six papers selected here illustrate the concerns and curiosity driving Chinese researchers, on topics shared with our colleagues around the world. -/- One of the active research areas in AI is planning under uncertainty, with incomplete knowledge, where a well-established logical framework is the action language of Son and Baral (Son and Baral 2001). This language can express the notions of sensing actions and making conditional plans. However, its current semantics is not yet satisfactory, since according to the semantics an agent would not have knowledge of what happens after a plan is executed, which can be a serious problem in a safety-critical environment. In their paper Proof Systems for Planning under Cautious Semantics (Shen and Zhao 2013), Yuping Shen and Xishun Zhao address this problem and propose a cautious and weakly cautious semantics for the action language. This new semantics enables the agent to know exactly what happens after executing an action. Hoare style proof systems are then proposed and proved to be sound and complete. What is more, the proposed new system reduces the reasoning complexity of the action language. -/- In Preferential Semantics for Plausible Subsumption in Possibility Theory (Qi and Zhang 2013), Guilin Qi and Zhizheng Zhang investigate another important issue in AI: how to handle exceptions in a knowledge-based system. This has become a hot topic in recent years, especially in ontological design, where description logics are widely used. The question then arises whether we can get a nonmonotonic extension of description logic. To answer this, the authors first propose three preferential semantics for plausible subsumption in the framework of possibility theory (Dubois and Prade 1985) and study their properties and their relationships. Then they introduce preferential subsumptions to a description logic-based knowledge system, and define an entailment relation of plausible subsumption. Moreover, they study reductions of the new semantics to standard semantics for an expressive description logic. -/- Counterfactual reasoning has been explored extensively by philosophers, cf. Lewis (1973), Stalnaker (1968). But in the last two decades, causal models have been proposed for modeling counterfactual reasoning by researchers in AI. In A Lewisian Logic of Causal Counterfactuals (Zhang 2013), Jiji Zhang studies classes of causal models and provides formal characterizations. In particular, a new logic system is proposed and proved complete for the class of ‘Lewisian models’ satisfying all the principles of David Lewis’s logic of counterfactuals. Moreover, Zhang compares his new framework with those of Lewis and Stalnaker, and also establishes formal connections with more recent approaches by Galles and Pearl, and by Halpern. -/- Consistency is a fundamental notion in logic, but it also plays a key role in many techniques for solving constraint satisfaction problems (Mackworth 1977). In Variable-Centered Consistency in Model RB (Li et al. 2013), Liang Li, Tian Liu and Ke Xu start with a discussion of i-consistency in ‘Model RB’ and ‘Model RD’, two models of random constraint satisfaction problems with growing domain size, then compare it with the notion of t-consistency and strong t-consistency in well-known earlier work by Freuder. After that, the authors define a new kind of variable-centered consistency, and show an upper bound on a suitably chosen parameter in Model RB and Model RD, such that up to this bound, all typical instances of Model RB are variable-centered consistent. -/- Language understanding is a cognitive process that human beings carry out every day. Metaphor is a pervasive phenomenon in natural languages, and its cognitive role calls for interpretation. There is a growing body of literature on cognitive mechanisms underlying metaphor. The paper An Ontology-Based Approach to Metaphor Cognitive Computation (Huang et al. 2013) by Xiaoxi Huang, Huaxin Huang, Beishui Liao, and Cihua Xu proposes a theoretical framework for metaphor understanding based on recent results from cognitive science (Shutova 2010). They then introduce ontology as a knowledge representation method, and present a new ontological model to formalize metaphor-based knowledge. An algorithmic description is provided using a quantitative measure of integrated degree, and its effectiveness is demonstrated. -/- Puzzles and their solution mechanisms are a recurrent theme in many fields. Dynamic epistemic logic (van Ditmarsch et al. 2007); (van Benthem 2011) is a recent framework that can handle information dynamics in knowledge puzzles. In Reasoning About Agent Types and the Hardest Logic Puzzle Ever (Liu and Wang 2013), Fenrong Liu and Yanjing Wang propose a new dynamic-epistemic logic that can specify different types of agents and analyse agents’ knowledge, communication and reasoning. To demonstrate its power, Smullyan’s well-known Knights and Knaves puzzles are formalized, as well as the Hardest Logic Puzzle Ever (HLPE) of Boolos (Boolos 1996). Moreover, a spectrum of new puzzles is found involving knowledge-based agent types, and their solution complexity is shown to be harder than that for existing logic puzzles. It is also shown that a version of HLPE in which the agents do not know the others’ types does not have a solution at all. -/- Finally, we would like to thank the editor of Minds and Machines, Gregory Wheeler, for his efficient assistance and kind support. We also thank Ties Nijssen at Springer for his encouragement to start this project at the first place. And of course, our appreciation goes to our authors, as well as all the colleagues who have helped us review the papers in this collection. (shrink)

The essay introduces a non-Diodorean, non-Kantian temporal modal semantics based on part-whole, rather than class, theory. Formalizing Edmund Husserl’s theory of inner time consciousness, §3 uses his protention and retention concepts to define a relation of self-awareness on intentional events. §4 introduces a syntax and two-valued semantics for modal first-order predicate object-languages, defines semantic assignments for variables and predicates, and truth for formulae in terms of the axiomatic version of Edmund Husserl’s dependence ontology (viz. the Calculus [CU] (...) of Urelements) introduced by The Ontology of Intentionality I & II. It then uses the §3 results to define the modalities of truth, and §5 extends the semantics to identity claims. §6 defines and contrasts synthetic a priori truths to analytic a priori truths, and §7 compares Brentano School noetic semantic and Leibnizian possible-world semantic perspectives on modality. The essay argues that the modal logics it defines semantically are two-valued, first-order versions of the type of language which Husserl viewed as the language of any ontology of experience (i.e. of any science), and conceived as the logic of intentionality. (shrink)

In the first part ("Determination"), I consider different notions of determination, contrast and compare modal with non-modal accounts and then defend two a-modality theses concerning essence and supervenience. I argue, first, that essence is a a-modal notion, i.e. not usefully analysed in terms of metaphysical modality, and then, contra Kit Fine, that essential properties can be exemplified contingently. I argue, second, that supervenience is also an a-modal notion, and that it should be analysed in terms of constitution relations (...) between properties. In the second part ("A Theory of Truthmaking"), I first review the literature on ontological commitment, and argue that the notion of truthmaking is better suited to play its explanatory rôle. I then argue that we should take truthmaker theory seriously, and that we should provide actual truthmakers for all truths there are. In the last chapter of this part, I review Armstrong's truthmaker theories and argue that they are unsatisfactory. I generalise my criticism to an argument against truthmaker necessitarianism, the view that truthmakers necessarily make true the truths they are truthmakers of. In the third part ("Properties and their Kind(s)"), I discuss qualitative determination. I present and endorse the truthmaker argument for universals, and defend universalism against friends of tropes, states of affairs and facts. I then give a novel characterisation of the important class of intrinsic properties, building on Lewis' work. With a workable notion of intrinsicness at hand, I argue that relations are ontologically – but not "ideologically" – dispensable: qualitative determination in general is a matter of intrinsic structure. In the future, I plan to add two parts and to publish my thesis as a book: In the fourth part ("Exemplification"), I argue for the existence of an exemplification relation tying universals and particulars together. I derive theoretical benefits from this relation by providing adverbialist theories of modality and tense and identify exemplification with a type of parthood. In the fifth part ("Qua qua qua"), I investigate the curious and interesting ontological category of so-called "qua-objects" (Picasso-as-a-painter, for example) and argue that they exist, are not identical with transworld indidivuals or modal parts and that they provide (contingent) truthmakers for all true predications. (shrink)

We investigated the possible causes of perceptual switching in ambiguous figures. Ambiguous figures are a special class of visual stimuli that can give rise to at least two alternative interpretations. Because the figures themselves stay the same, these stimuli are particularly suitable to study the dynamic changes in our visual apparatus that enable us to see the world in different ways. Recent studies stress the importance of both low-level and high-level processes in switching. We show that these processes lead (...) to switching independently, and that, when they co-occur, they do not occur at exactly the same time.We take these results to indicate that perceptual switching is a radically multiply realizable process, in that various neurological states can instantiate it in a single individual from time to time. We reflect on the consequences of this conclusion for experiential realism, in particular the notion that embodiment misleads us in identifying psychological types. (shrink)

This essay examines Charles S. Pierce’s critique of nominalism against the background of the debate about natural kinds at the time of the first reception of Darwin's _Origin of Species_. In the history of the so-called dispute over universals in Western philosophy, the phenomenon of species constancy has always been of central importance (since Plato). Darwin's historicization of species was seen by some of Peirce's contemporaries, including Chauncey Wright, as support for Mill's nominalism. Peirce believed the opposite, that Darwin's (...) history of the origin of species supports realism about universals. This is so because for Darwin species arise independently of the human mind. Just as a history of science does not have to cast doubt on the reality of scientific disciplines, a history of species does not have to make their reality appear questionable. However, a concept of modifiable species is needed to understand this history. Peirce develops such a concept by understanding species, ahead of his time, as variable clusters. (shrink)

The concept of totalitarianism as an “ideal type” found its fullest realization in Nazi Germany and the Soviet Union.1 Following the Soviet collapse, scholars gained access to an enormous amount of information concerning the inner workings of the Soviet system and the intentions of the Soviet leadership. For the first time, comprehensive data concerning the functioning of the coercive apparatus, the scope of terror and deportations, and, perhaps most important, the true extent of the militarization of Soviet economy and (...) society is now available. These data allow a much better understanding of Soviet reality and of 20th century totalitarian…. (shrink)

In this paper we study a specific subclass of abstract elementary classes. We construct a notion of independence for these AEC’s and show that under simplicity the notion has all the usual properties of first order non-forking over complete types. Our approach generalizes the context of 0-stable homogeneous classes and excellent classes. Our set of assumptions follow from disjoint amalgamation, existence of a prime model over 0/, Löwenheim–Skolem number being ω, -tameness and a property we call finite character. (...) We also start the studies of these classes from the 0-stable case. Stability in 0 and -tameness can be replaced by categoricity above the Hanf number. Finite character is the main novelty of this paper. Almost all examples of AEC’s have this property and it allows us to use weak types, as we call them, in place of Galois types. (shrink)

The two-fold ontological character of linguistic objects revealed due to the distinction between “type” and “token” introduced by Ch. S. Peirce can be a base of the two-fold, both theoretical and axiomatic, approach to the language. Referring to some ideas included in A. A. Markov’s work [1954] (in Russian) on Theory of Algorithms and in some earlier papers of the author, the problem of formalization of the concrete and abstract words theories raised by J. Słupecki was solved. The construction of (...) the theories presented here has two levels. The axiomatic theory of label-tokens: material, physical linguistic objects, constitutes the first one. Label-types, according to the literature of the subject, are defined on the other level as equivalence classes of equiform label-tokens. Assuming the opposite point of view, one can accept that theory of label-types: abstract labels, formalized on the first level, in which it is possible to define the notion of label-token as well as the derivative notions on the second level, should become the basis of formalization of the theory of linguistic expressions and the theory of language in general. The axioms and definitions of both theories of labels: T k and T p representing the other approach to the ontology of language are included in the sequel of the abstract. The foundations of the theory of labels T k in which the primary assumption as to the label-types existence is superfluous have been referred on the basis of the author's monography "Teorie Języków Syntaktycznie Kategorialnych" ( "The Theories of Syntactically Categorial Languages"), PWN, Warszawa-Wrocław 1985. The basis of the theory of labels T p which takes into account the other position has to be presented here for the first time. Some extended ideas of the paper will also be presented in author's paper "Logiczne podstawy ontologii składni Języka" ("Logical foundations of language syntax ontology), Studia Filozoficzne 6-7 (271-272), (1988), pp. 263-284. (shrink)

We introduce Lascar strong types in excellent classes and prove that they coincide with the orbits of the group generated by automorphisms fixing a model. We define a new independence relation using Lascar strong types and show that it is well-behaved over models, as well as over finite sets. We then develop simplicity and show that, under simplicity, the independence relation satisfies all the properties of nonforking in a stable first order theory. Further, simplicity for an excellent (...) class, as well as the independence relation itself, is uniquely determined. Finally, we show that an excellent class is simple if and only if it has extensible U-rank . We deduce that any excellent class of finite U-rank is simple, and that any uncountably categorical excellent class has an expansion with countably many constants which is simple. (shrink)

Potts et seq. presents an analysis of gap-containing supplements where the gap is modelled as a variable over the semantic type of the constituent that the as-clause adjoins to. This much allows the meaning of the gap to be resolved purely compositionally, by defining as as a function that allows the anchor to bind the gap variable. This article presents a class of as-clauses where Potts’s analysis seems to break down, in that the gap cannot be modelled as a (...) variable over the semantic type of the anchor. I propose that these cases can be unified with those in Potts’s work, as well as a larger class of ellipsis phenomena, by assuming that, under certain conditions, surface gaps are composite entities, containing a bound variable and a free variable that are resolved independently of each other. The bound variable is bound by the anchor, and the free variable is resolved by anaphora to a salient discourse object. (shrink)

How do people reason about their opponent in turn-taking games? Often, people do not make the decisions that game theory would prescribe. We present a logic that can play a key role in understanding how people make their decisions, by delineating all plausible reasoning strategies in a systematic manner. This in turn makes it possible to construct a corresponding set of computational models in a cognitive architecture. These models can be run and fitted to the participants’ data in terms of (...) decisions, response times, and answers to questions. We validate these claims on the basis of an earlier game-theoretic experiment about the turn-taking game “Marble Drop with Surprising Opponent”, in which the opponent often starts with a seemingly irrational move. We explore two ways of segregating the participants into reasonable “player types”. The first way is based on latent class analysis, which divides the players into three classes according to their first decisions in the game: Random players, Learners, and Expected players, who make decisions consistent with forward induction. The second way is based on participants’ answers to a question about their opponent, classified according to levels of theory of mind: zero-order, first-order and second-order. It turns out that increasing levels of decisions and theory of mind both correspond to increasing success as measured by monetary awards and increasing decision times. Next, we use the logical language to express different kinds of strategies that people apply when reasoning about their opponent and making decisions in turn-taking games, as well as the ‘reasoning types’ reflected in their behavior. Then, we translate the logical formulas into computational cognitive models in the PRIMs architecture. Finally, we run two of the resulting models, corresponding to the strategy of only being interested in one’s own payoff and to the myopic strategy, in which one can only look ahead to a limited number of nodes. It turns out that the participant data fit to the own-payoff strategy, not the myopic one. The article closes the circle from experiments via logic and cognitive modelling back to predictions about new experiments. (shrink)

That diagrams are analog, i.e., homomorphic, representations of some kind, and sentential representations are not, is a generally held intuition. In this paper, we develop a formal framework in which the claim can be stated and examined, and certain puzzles resolved. We start by asking how physical things can represent information in some target domain. We lay a basis for investigating possible homomorphisms by modeling both the physical medium and the target domain as sets of variables, each with a (...) constraint structure. When a homomorphism exists, the causality of the physical medium can provide a “free ride,” automatically determining the information that is needed to solve a problem. The modeling technique enables us to show how in sentential representations the structure of the 2-D space is used non-homomorphically to define tokens, and to provide a minimal homomorphism with respect to the ordering of the arguments for n-ary functions, predicates, and operators, but otherwise there is no homomorphism with the target domain. Our treatment also characterizes diagrams as a type of a more general class of physical representations in which physical causality plays a role in providing the information needed to solve a problem. (shrink)

The problematic features of Quine's set theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intensions) that their nominalizations denote as (...) singular terms. We argue against Quine's view that predicate quantifiers can be given a referential interpretation only if the entities predicates stand for on such an interpretation are the same as the classes (assuming extensionality) that nominalized predicates denote as singular terms. Quine's alternative of giving predicate quantifiers only a substitutional interpretation is compared with a constructive version of conceptual realism, which with a logic of nominalized predicates is compared with Quine's description of conceptualism as a ramified theory of classes. We argue against Quine's implicit assumption that conceptualism cannot account for impredicative concept-formation and compare holistic conceptual realism with Quine's class Platonism. (shrink)

It’s generally assumed that a compositional semantic theory will have to recognise a semantic category of expressions which serve simply to pick out some one object: e-type expressions. Kripke’s views about names, Kaplan’s about indexicals and demonstratives, the standard Tarskian semantics for bound variables, Heim and Kratzer’s Strawsonian view about definites, even an analysis of indefinites, assume as much. In this thesis, I argue that recent advances in the semantics of names and of quotation, and in metaphysics, give good (...) reason to doubt there is such a category. I do so in two parts. In the first part, comprising about two thirds of the thesis, I combine two recent views, one from semantics and one from metaphysics. From semantics, I take over predicativism about names, the view, as one might have guessed, that names are predicates. From metaphysics, I take over the doctrine that there are temporal parts. Putting them together, I hold that the semantic contribution of the name ’Joan’, in a sentence like ’Joan is a barrister’, is a predicate, and in particular a predicate the extension of which is Joan’s temporal parts. Names are not, as is commonly thought, e-type expressions. In the second part, building on the first, I further undermine the existence of a semantically important category of e-type expressions by arguing that a construction which might be thought to mandate such a category, namely de re attitude ascriptions, in fact, when properly analysed, does not do so. I argue this by considering the nature of transparent occurrences of expressions in opaque contexts in general, and in particular by considering the phenomenon of mixed quotation. I present a new theory of it, and show how it can be parlayed into a new Fregean theory of de re attitude ascriptions. The thesis overall, then, will provide strong evidence against the semantic importance of e-type expressions either in language, or in thought. (shrink)

Treating the existential quantification ∃ν i as a diamond $\diamond_i$ and the identity ν i = ν j as a constant δ ij , we study restricted versions of first order logic as if they were modal formalisms. This approach is closely related to algebraic logic, as the Kripke frames of our system have the type of the atom structures of cylindric algebras; the full cylindric set algebras are the complex algebras of the intended multidimensional frames called cubes. The (...) main contribution of the paper is a characterization of these cube frames for the finite-dimensional case and, as a consequence of the special form of this characterization, a completeness theorem for this class. These results lead to finite, though unorthodox, derivation systems for several related formalisms, e.g. for the valid n-variable first order formulas, for type-free valid formulas and for the equational theory of representable cylindric algebras. The result for type-free valid formulas indicates a positive solution to Problem 4.16 of Henkin, Monk and Tarski [16]. (shrink)

Various questions arise in semantic analysis concerning the nature of types. These questions include whether we need types in a semantic theory, and if so, whether some version of simple type theory (STT, Church 1940) is adequate or whether a richer more flexible theory is required to capture our semantic intuitions. Propositions and propositional attitudes can be represented in an essentially untyped first-order language, provided a sufficiently rich language of terms is adopted. In the absence of rigid (...) typing, care needs to be taken to avoid the paradoxes, for example by constraining what kinds of expressions are to be interpreted as propositions (Turner 1992). But the notion of type is ontologically appealing. In some respects, STT seems overly restrictive for natural language semantics. For this reason it is appropriate to consider a system of types that is more flexible than STT, such as a Curry-style typing (Curry & Feys 1958). Care then has to be taken to avoid the logical paradoxes. Here we show how such an account, based on the Property Theory with Curry Types (PTCT, Fox & Lappin 2005), can be formalised within Typed Predicate Logic (TPL, Turner 2009). This presentation provides a clear distinction between the classes of types that are being used to (i) avoid paradoxes (ii) allow predicative polymorphic types. TPL itself provides a means of expressing PTCT in a uniform language. (shrink)

This paper investigates the analysis of the de re/de dicto distinction and related facts. I start with the assumption, supported by Cresswell 1990, that the evaluation of the truth of a proposition relative to a particular possible world/situation is mediated via the presence in the syntax of a silent pronoun with type-s denotation. In this system, the de re/de dicto distinction arises from a difference in which an operator binds a given situation pronoun. Percus 2000 shows that such a system (...) potentially overgenerates, in that a third type of reading is predicted to exist for sentences which actually have only two: de re and de dicto. Percus proposes constraints on the binding of situation pronouns, which correctly rule out these third readings. This paper shows, however, that extrinsic constraints on the binding of situation pronouns are not necessary to rule out the unwanted readings, as long as we develop a more precise theory of binding in the first place. I adapt the binding operator argued for by Büring 2004, originally developed only for overt pronouns, and show that when used as an operator for situation pronouns, the unwanted readings are not predicted to occur. (shrink)

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to (...) applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

A first order representation (f.o.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and prove some general statements. Following this we compare some well-known (...) classes of spaces and first order representations. A principal result is that if X and Y are two Tichonov spaces whose posets of zero-sets are elementarily equivalent then their respective rings of bounded continuous real-valued functions satisfy the same positive-universal sentences. The proof of this uses the technique of constructing ultraproducts as direct limits of products in a category theoretic setting. (shrink)

This paper provides an analysis of the notational difference between Beta Existential Graphs, the graphical notation for quantificational logic invented by Charles S. Peirce at the end of the 19th century, and the ordinary notation of first-order logic. Peirce thought his graphs to be “more diagrammatic” than equivalently expressive languages for quantificational logic. The reason of this, he claimed, is that less room is afforded in Existential Graphs than in equivalently expressive languages for different ways of representing the same (...) fact. The reason of this, in turn, is that Existential Graphs are a non-linear, occurrence-referential notation. As a non-linear notation, each graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic that are obtained by permuting those elements that in the graphs lie in the same area. As an occurrence-referential notation, each Beta graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic in which the identity of reference of two or more variables is asserted. In brief, Peirce’s graphs are more diagrammatic than the linear, type-referential notation of first-order logic because the function that translates the latter to the graphs does not define isomorphism between the two notations. (shrink)

Fix 2 < n < ω. Let CA n denote the class of cylindric algebras of dimension n, and let RCA n denote the variety of representable CA n ’s. Let L n denote first-order logic restricted to the first n variables. Roughly, CA n, an instance of Boolean algebras with operators, is the algebraic counterpart of the syntax of L n, namely, its proof theory, while RCA n algebraically and geometrically represents the Tarskian semantics of (...) L n. Unlike Boolean algebras having a Stone representation theorem, RCA n ⊊ CA n. Using combinatorial game theory, we show that the existence of certain finite relation algebras RA, which are algebras whose domain consists of binary relations, implies that the celebrated Henkin omitting types theorem fails in a very strong sense for L n. Using special cases of such finite RA ’s, we recover the classical nonfinite axiomatizability results of Monk, Maddux, and Biro on RCA n and we re-prove Hirsch and Hodkinson’s result that the class of completely representable CA n ’s is not first-order definable. We show that if T is an L n countable theory that admits elimination of quantifiers, λ is a cardinal < 2 ℵ 0, and F = 〈 Γ i : i < λ 〉 is a family of complete nonprincipal types, then F can be omitted in an ordinary countable model of T. (shrink)

The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse 2 ). The new proof also shows the known results that the universal theory of Pse 2 is decidable and that every finite Pse 2 can be represented on (...) a finite base. Since the class Cs 2 of cylindric set algebras of dimension 2 forms a reduct of Pse 2 , these results extend to Cs 2 as well. (shrink)

This article first surveys a significant set of issues that are intertwined in asking whether social classes are real. It distinguishes two different notions of class: class as organized social entities and class as types of individuals based on individual characteristics. There is good evidence for some classes as social entities—ruling classes and underclasses in some societies—but other classes in contemporary society are sometimes best thought of in terms of types, not social entities. Implications (...) are drawn for pluralist accounts of social classification and the individualism-holism dispute. (shrink)

The orthodox view of proper names, Millianism, provides a very simple and elegant explanation of the semantic contribution of referential uses of names–names that occur as bare singulars and as the argument of a predicate. However, one problem for Millianism is that it cannot explain the semantic contribution of predicative uses of names. In recent years, an alternative view, so-called the-predicativism, has become increasingly popular. According to the-predicativists, names are uniformly count nouns. This straightforwardly explains why names can be used (...) predicatively, but is prima facie less congenial to an analysis of referential uses. To address this issue, the-predicativists argue that referential names are in fact complex determiner phrases consisting of a covert definite determiner and a count noun—and so, a referential name is a definite description. In this paper, I will argue that despite the appearance of increased theoretical complexity, the view that names are ambiguous between predicative and referential types is in fact superior to the unitary the-predicativist view. However, I will also argue that to see why this ambiguity view is better, we need to give up the standard Millian analysis. Consequently, I will first propose an alternative analysis of referential names that retains the virtues of Millianism, but provides an important explanatory connection to the predicative uses. Once this analysis of names is adopted, the explanation for why names are systematically ambiguous between referential and predicative types is both simple and elegant. Second, I will argue that the-predicativism has the appearance of being simpler than an ambiguity view, but is in fact unable to account for certain key properties of referential names without making ad hoc stipulations. (shrink)

Instantiation Theory presents a new, general unification algorithm that is of immediate use in building theorem provers and logic programming systems. Instantiation theory is the study of instantiation in an abstract context that is applicable to most commonly studied logical formalisms. The volume begins with a survey of general approaches to the study of instantiation, as found in tree systems, order-sorted algebras, algebraic theories, composita, and instantiation systems. A classification of instantiation systems is given, based on properties of substitutions, degree (...) of type strictness, and well-foundedness of terms. Equational theories and the use of typed variables are studied in terms of quotient homomorphisms and embeddings, respectively. Every instantiation system is a quotient system of a subsystem of first-order term instantiation. The general unification algorithm is developed as an application of the basic theory. Its soundness is rigorously proved, and its completeness and efficiency are verfied for certain classes of instantiation systems. Appropriate applications of the algorithm include unification of first-order terms, order-sorted terms, and first-order formulas modulo alpha-conversion, as well as equational unification using simple congruences. (shrink)

The classification of collusion behaviors of government-invested project tenderers is one of the important methods to describe the characteristics and laws of collusion behaviors and strengthen the governance of collusion. Firstly, the variables that affect the type of collusion behavior are selected and cluster analysis is carried out on the cases of collusion in government investment project bidding. Then use the social network to mine the types and characteristics of the collusion behavior of the tenderee. Finally, a BP (...) neural network automatic identification model is established to quickly discriminate the types of collusion, which can effectively overcome the subjectivity of traditional methods. As a result, three typical types of collusion of tenderees can be obtained: intervention type, opportunity type, and cooperation type. The study found that the three types of collusion behavior have their own characteristics and laws, and the relationship between the variables that affect the type of collusion behavior is complex and affects each other. (shrink)

Church’s type theory, aka simple type theory, is a formal logical language which includes classical first-order and propositional logic, but is more expressive in a practical sense. It is used, with some modifications and enhancements, in most modern applications of type theory. It is particularly well suited to the formalization of mathematics and other disciplines and to specifying and verifying hardware and software. It also plays an important role in the study of the formal semantics of natural language. When (...) utilizing it as a meta-logic to semantically embed expressive non-classical logics further topical applications are enabled in artificial intelligence and philosophy. A great wealth of technical knowledge can be expressed very naturally in it. With possible enhancements, Church’s type theory constitutes an excellent formal language for representing the knowledge in automated information systems, sophisticated automated reasoning systems, systems for verifying the correctness of mathematical proofs, and a range of projects involving logic and artificial intelligence. Some examples and further references are given in Sections 1.2.2 and 5 below. Type theories are also called higher-order logics, since they allow quantification not only over individual variables, but also over function, predicate, and even higher order variables. Type theories characteristically assign types to entities, distinguishing, for example, between numbers, sets of numbers, functions from numbers to sets of numbers, and sets of such functions. As illustrated in Section 1.2.2 below, these distinctions allow one to discuss the conceptually rich world of sets and functions without encountering the paradoxes of naive set theory. Church’s type theory is a formulation of type theory that was introduced by Alonzo Church in Church 1940. In certain respects, it is simpler and more general than the type theory introduced by Bertrand Russell in Russell 1908 and Whitehead & Russell 1927a. Since properties and relations can be regarded as functions from entities to truth values, the concept of a function is taken as primitive in Church’s type theory, and the λ-notation which Church introduced in Church 1932 and Church 1941 is incorporated into the formal language. Moreover, quantifiers and description operators are introduced in a way so that additional binding mechanisms can be avoided, λ-notation is reused instead. λ-notation is thus the only binding mechanism employed in Church’s type theory. (shrink)

This paper is devoted to the problem of existence of saturated models for first-order many-valued logics. We consider a general notion of type as pairs of sets of formulas in one free variable that express properties that an element of a model should, respectively, satisfy and falsify. By means of an elementary chains construction, we prove that each model can be elementarily extended to a $\kappa $-saturated model, i.e. a model where as many types as possible are realized. (...) In order to prove this theorem we obtain, as by-products, some results on tableaux (understood as pairs of sets of formulas) and their consistency and satisfiability and a generalization of the Tarski–Vaught theorem on unions of elementary chains. Finally, we provide a structural characterization of $\kappa $-saturation in terms of the completion of a diagram representing a certain configuration of models and mappings. (shrink)

Turkey has passed the import substitution economic model to a new model of the economy called open out since 1980. Along with the neoliberal policies implemented, the process of integration with the global economy has begun. The incomes of the religious people who cannot be excluded from the effects of this articulation also increased and their consumption behaviors has changed. On the other hand, some transport elements, especially the media, have enabled consumption codes to reach different segments. The new values (...) emerged in this process also caused transformations in individual consumption trends. In this study, the "Scale of Consumption Dynamics" (SCD) was developed in order to identify the trends of consumption of devotees and to find out how they changed. Quantitative research approach was adopted in the study and the datas were collected by face-to-face survey technique. The individuals included in our sample were selected by quota sampling. In this study, an expression pool was created as a result of literature review, expert opinion consultation, brainstorming with academicians and observations. The validity and reliability analysis of the scale was made using different statistics through the SPSS program. As a result of these steps, the dimensions of the scale consisting of 16 items and 3 dimensions are called "showy consumption", "wasteful consumption" and "religious priority consumption". Summary: The first studies on consumption history and sociology belong to Marx, Weber, Veblen and Simmel. In these studies consumption is examined as a part of production process and consumption forms were investigated as a social class aspect. Consumption phenomenon was later studied under critical approach (Frankfurt School) with Adorno, Max Horkheimer, Herbert Marcuse and Erich Fromm’s theories. Theorists at Frankfurt School study how social structure steers individuals to consumption. After the 1970’s, the meaning of consumption phenomenon has changed. There are studies by Jean Baudrillard, Mike Featherstone, George Ritzer, and Zygmunt Bauman on changing phenomenon of consumption. It is widely believed that modern consumption phenomenon was originated in the USA after the World War II. After the war Keynesian economic policies and Fordist consumption forms later influenced other Western nations. After 1950’s and 1960’s mass consumption was initiated in the USA and except very poor sections of the nations, other social classes, it started to spread out in Europe, the USA, and other countries. In 1970’s and 1980’s, it has merged with individuals’ identity definitions. After 1980’s in Turkey a new economic policy instead of import substitution was adopted. In application along with neo liberal policies, Turkey started to integrate to the rest of the World. Religious people as well influenced these changes and their incomes have increased along with their consumption habits. In addition to media, some other forms of communication channels have carried new consumption habits to other sections of the society. With the increased effects of mass communication media, new social sections have emerged and their cultural characteristics have become the norms of the whole society. A new values created in this process also transformed the consumption habits. In this article, in order to assess consumption habits of religious people as it is now and to understand which direction these habits evolve, Consumption Dynamics Scale (CDS) has been developed. Scales are widely used when a researcher tries to identify and measure respondents’ feelings and ideas on a subject matter. There are different scales used in social sciences such as Thurstone, Likert, Guttman, and Bogardus that are among the most widely used ones. A Likert Type scale has been used in this study. In the first phase of the study and pilot study 5 point Likert scale and in the second phase of the study 10 point Likert scales was used to collect the data. We could not come across with any study in the literature on investigating consumption characteristics Dynamics of individuals with a formal religious education. In the study, quantitative research method has been adopted and the research data has been collected with face to face administration of the survey instrument. The scale development phase lasted about 6 months from August, 2016. Based on 3% error rate, we determined to sufficient sample size as 516, yet we reached 600 individuals and end up with 563 usable responses. Sample has been determined with quota sampling methodology. We formed a pool of statements based on literature review, expert opinion, brain storming with academicians. 49 questions have been selected from the question pool where 93 questions were found, then they are merged, some questions are changed or totally eliminated and final 30 questioned questionnaires made ready for pilot study. Two pilot studies have been carried out. In the first pilot study, 47 people are reached and 30 questions with Likert scales have been administered. In the second phase of the study, 10 point Likert scales with 57 questions has been given to 54 individuals. After pilot studies, data was analyzed with SPSS 20 version and 32 questioned final survey instrument has been formed. In order to check sufficiency of data set for Factor Analysis Kaisser-Meyer-Olkin (KMO) test and the relationships among variables Bartlett test were used. Sample composed of 563 responses revealed significant results (3358,808, p=0,000) and KMO test revealed (KMO=0,812) value. After expletory factor analysis, factor loading less than 0,40 were deleted from the scale. Hence the final structure is composed of 29 questions with 8 different factors. The reliability of scales were calculated with Cronbach Alfa analysis separately for each dimension. After reliability analysis, items with 0,60 and less reliability score were taken out from the scales. Finally 16 items were made up 3 dimensions namely “ostentatious consumption”, “wasteful consumption”, and “religious priority consumption”. The items in Factor 1 are related with luxury, fashion and statue, in Factor 2 desire to make more shopping, purchase without need, advertisement and showcase, and factor 3 religious sensitive reference focus and religion first purchasing are decided as appropriate names. Based on the analysis, measurement was decided valid and sound. Therefore, this study is believed to contribute significantly to the existing literature. (shrink)