Online research in philosophy

Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic ...

CONTINUOUS MODEL THEORY CHAPTER I TOPOLOGICAL PRELIMINARIES. Notation Throughout the monograph our mathematical notation does not differ drastically from ...

The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture known as the Mouse Set Conjecture (MSC). One particular (...) motivation for resolving MSC is that it provides grounds for solving the inner model problem which dates back to 1960s. There have been some new partial results on MSC and the methods used to prove the new instances suggest a general program for solving the full conjecture. It is then our goal to communicate the ideas of this program to the community at large. (shrink)

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical (...) structures, namely, Priest's Collapsing Lemma and Dunn's Theorem in 3-Valued Logic. (shrink)

This book contains the material for a first course in pure model theory with applications to differentially closed fields.

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)

We introduce a new framework for classifying logics on finite structures and studying their expressive power. This framework is based on the concept of almost everywhere equivalence of logics, that is to say, two logics having the same expressive power on a class of asymptotic measure 1. More precisely, if L, L ′ are two logics and μ is an asymptotic measure on finite structures, then $\scr{L}\equiv _{\text{a.e.}}\scr{L}^{\prime}(\mu)$ means that there is a class C of finite structures with μ (C)=1 (...) and such that L and L ′ define the same queries on C. We carry out a systematic investigation of $\equiv _{\text{a.e.}}$ with respect to the uniform measure and analyze the $\equiv _{\text{a.e.}}$ -equivalence classes of several logics that have been studied extensively in finite model theory. Moreover, we explore connections with descriptive complexity theory and examine the status of certain classical results of model theory in the context of this new framework. (shrink)

This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, (...) second-order, fixed-point, and infinitary logics to gain insight into phenomena in complexity theory and combinatorics. The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful way to analyze the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and treewidth, arise naturally in the application of finite model theory to database theory and AI. Students of logic and computer science will find here the tools necessary to embark on research into finite model theory, and all readers will experience the excitement of a vibrant area of the application of logic to computer science. (shrink)

Provability, Computability and Reflection.

Provability, Computability and Reflection.

A number of results have been obtained concerning Borel structures starting with Silver and Friedman followed by Harrington, Shelah, Marker, and Louveau. Friedman also initiated the model theory of Borel (in fact totally Borel) structures. By this we mean the study of the class of Borel models of a given first-order theory. The subject was further investigated by Steinhorn. The present work is meant to go further in this direction. It is based on the assumption that the (...) study of the class of, say, countable models of a theory reduces to analyzing a single $\omega_1$-saturated model. The question then arises as to when such a model can be totally Borel. We present here a partial answer to this problem when the theory under investigation is superstable. (shrink)

The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability (...) class='Hi'>theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course. (shrink)

In this paper, the (possible) role of model theory forstructuralism and structuralist definitions of ``reduction'' arediscussed. Whereas it is somewhat undecisive with respect tothe first point – discussing some pro's and con's ofthe model theoretic approach when compared with a syntacticand a structuralist one – it emphasizes that severalstructuralist definitions of ``reducibility'' do not providegenerally acceptable explications of ``reducibility''. This claimrests on some mathematical results proved in this paper.

What exactly do we do when we try to make sense of other people e.g. by ascribing mental states like beliefs and desires to them? After a short criticism of Theory-Theory, Interaction Theory and the Narrative Theory of understanding others as well as an extended criticism of the Simulation Theory in Goldman's recent version (2006), we suggest an alternative approach: the Person Model Theory . Person models are the basis for our ability to (...) register and evaluate persons having mental as well as physical properties. We argue that there are two kinds of person models, nonconceptual person schemata and conceptual person images , and both types of models can be developed for individuals as well as for groups. (shrink)

As Wilfrid Hodges has observed, there is no mention of the notion truth-in-a-model in Tarski's article 'The Concept of Truth in Formalized Languages'; nor does truth make many appearances in his papers on model theory from the early 1950s. In later papers from the same decade, however, this reticence is cast aside. Why should Tarski, who defined truth for formalized languages and pretty much founded model theory, have been so reluctant to speak of truth in (...) a model? What might explain the change in his practice? The answers, I believe, lie in Tarski's views on truth simpliciter. (shrink)

The object of this paper is to show how one is able to construct a paraconsistent theory of models that reflects much of the classical one. In other words the aim is to demonstrate that there is a very smooth and natural transition from the model theory of classical logic to that of certain categories of paraconsistent logic. To this end we take an extension of da Costa''sC 1 = (obtained by adding the axiom A A) and (...) prove for it results which correspond to many major classical model theories, taken from Shoenfield [5]. In particular we prove counterparts of the theorems of o-Tarski and Chang-o-Suszko, Craig-Robinson and the Beth definability theorem. (shrink)

This paper replies to Politzer’s ( 2007 ) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.

Some theorists approach the Gordian knot of consciousness by proclaiming its inherent tangle and mystery. Others draw out the sword of reduction and cut the knot to pieces. Philosopher Thomas Metzinger, in his important new book, Being No One: The Self-Model Theory of Subjectivity,1 instead attempts to disentangle the knot one careful strand at a time. The result is an extensive and complex work containing almost 700 pages of philosophical analysis, phenomenological reflection, and scientific data. The text offers (...) a sweeping and comprehensive tour through the entire landscape of consciousness studies, and it lays out Metzinger's rich and stimulating theory of the subjective mind. Metzinger's skilled integration of philosophy and neuroscience provides a valuable framework for interdisciplinary research on consciousness. Metzinger's overall goal in Being No One is to defend a representational theory of subjectivity, one that reduces subjective mental processes to representational mental processes. Subjective experiences take place whe n there is a conscious perspective, an active first-person point of view. It occurs in. (shrink)

Tarskian model theory is almost universally understood as a formal counterpart of the preformal notion of semantics, of the “linkage between words and things”. The wide-spread opinion is that to account for the semantics of natural language is to furnish its settheoretic interpretation in a suitable model structure; as exemplified by Montague 1974.

The present paper offers some remarks on the significance of first order model theory for our understanding of theories, and more generally, for our understanding of the “structuralist” accounts of the nature of theoretical knowledge that we associate with Russell, Ramsey and Carnap. What is unique about the presentation is the prominence it assigns to Craig’s Interpolation Lemma, some of its corollaries, and the manner of their demonstration. They form the underlying logical basis of the analysis.

Frege?s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such as arithmetic and set theory. As such, it was seen to fail by Gödel?s incompleteness theorem of 1931. It is argued, however, that this is to impose a later interpretation on the word ?complete? it is clear from Dedekind?s writings that at least as good as interpretation of completeness is categoricity. Whereas few interesting first-order mathematical theories are categorical (...) or complete, there are logical extensions of these theories into second-order and by the addition of generalized quantifiers which are categorical. Frege?s project really found success through Gödel?s completeness theorem of 1930 and the subsequent development of first- and higher-order model theory. (shrink)

Take a formula of first-order logic which is a logical consequence of some other formulae according to model theory, and in all those formulae replace schematic letters with English expressions. Is the argument resulting from the replacement valid in the sense that the premisses could not have been true without the conclusion also being true? Can we reason from the model-theoretic concept of logical consequence to the modal concept of validity? Yes, if the model theory (...) is the standard one for sentential logic; no, if it is the standard one for the predicate calculus; and yes, if it is a certain model theory for free logic. These conclusions rely inter alia on some assumptions about possible worlds, which are mapped into the models of model theory. Plural quantification is used in the last section, while part of the reasoning is relegated to an appendix that includes a proof of completeness for a version of free logic. (shrink)

This paper attempts to confine the preconceptions that prevented Frege from appreciating Hilbert?s Grundlagen der Geometrie to two: (i) Frege?s reliance on what, following Wilfrid Hodges, I call a Frege?Peano language, and (ii) Frege?s view that the sense of an expression wholly determines its reference.I argue that these two preconceptions prevented Frege from achieving the conceptual structure of model theory, whereas Hilbert, at least in his practice, was quite close to the model?theoretic point of view.Moreover, the issues (...) that divided Frege and Hilbert did not revolve around whether one or the other allowed metalogical notions.Frege, e.g., succeeded in formulating the notion of logical consequence, at least to the extent that Bolzano did; the point is rather that even though Frege had certain semantic concepts, he did not articulate them model?theoretically, whereas, in some limited sense, Hilbert did. (shrink)

We propose a first order modal logic, theQS4E-logic, obtained by adding to the well-known first order modal logicQS4 arigidity axiom schemas:A → □A, whereA denotes a basic formula. In this logic, thepossibility entails the possibility of extending a given classical first order model. This allows us to express some important concepts of classical model theory, such as existential completeness and the state of being infinitely generic, that are not expressibile in classical first order logic. Since they can (...) be expressed in -logic, we are also induced to compare the expressive powers ofQS4E and . Some questions concerning the power of rigidity axiom are also examined. (shrink)

The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics (...) is small. (shrink)

We establish constructive refinements of several well-known theorems in elementary model theory. The additive group of the real numbers may be embedded elementarily into the additive group of pairs of real numbers, constructively as well as classically.

In this paper we set out the basic model theory of differential fields of characteristic 0, which have finitely many commuting derivations. We give axioms for the theory of differentially closed differential fields with m derivations and show that this theory is ω-stable, model complete, and quantifier-eliminable, and that it admits elimination of imaginaries. We give a characterization of forking and compute the rank of this theory to be ω m + 1.

We explore some topics in the model theory of sheaves of modules. First we describe the formal language that we use. Then we present some examples of sheaves obtained from quivers. These, and other examples, will serve as illustrations and as counterexamples. Then we investigate the notion of strong minimality from model theory to see what it means in this context. We also look briefly at the relation between global, local and pointwise versions of properties related (...) to acyclicity. (shrink)

Researchers currently working on relational reasoning typically argue that mental model theory (MMT) is a better account than the inference rule approach (IRA). They predict and observe that determinate (or one-model) problems are easier than indeterminate (or two-model) problems, whereas according to them, IRA should lead to the opposite prediction. However, the predictions attributed to IRA are based on a mistaken argument. The IRA is generally presented in such a way that inference rules only deal with (...) determinate relations and not with indeterminate ones. However, (a) there is no reason to presuppose that a rule-based procedure could not deal with indeterminate relations, and (b) applying a rule-based procedure to indeterminate relations should result in greater difficulty. Hence, none of the recent articles devoted to relational reasoning currently presents a conclusive case for discarding IRA by using the well-known determinate vs indeterminate problems comparison. (shrink)

We study the model theory of fields k carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian group and prove (...) that the definable real valuation rings of k are in correspondence with the definable convex subgroups of the value group of a certain real valuation of k. (shrink)

Abstract Theories of induction in psychology and artificial intelligence assume that the process leads from observation and knowledge to the formulation of linguistic conjectures. This paper proposes instead that the process yields mental models of phenomena. It uses this hypothesis to distinguish between deduction, induction, and creative forms of thought. It shows how models could underlie inductions about specific matters. In the domain of linguistic conjectures, there are many possible inductive generalizations of a conjecture. In the domain of models, however, (...) generalization calls for only a single operation: the addition of information to a model. If the information to be added is inconsistent with the model, then it eliminates the model as false: this operation suffices for all generalizations in a Boolean domain. Otherwise, the information that is added may have effects equivalent (a) to the replacement of an existential quantifier by a universal quantifier, or (b) to the promotion of an existential quantifier from inside to outside the scope of a universal quantifier. The latter operation is novel, and does not seem to have been used in any linguistic theory of induction. Finally, the paper describes a set of constraints on human induction, and outlines the evidence in favor of a model theory of induction. (shrink)

The Martin-Steel coarse inner model theory is employed in obtaining new results in descriptive set theory. $\underset{\sim}{\Pi}$ determinacy implies that for every thin Σ 1 2 equivalence relation there is a Δ 1 3 real, N, over which every equivalence class is generic--and hence there is a good Δ 1 2 (N ♯ ) wellordering of the equivalence classes. Analogous results are obtained for Π 1 2 and Δ 1 2 quasilinear orderings and $\underset{\sim}{\Pi}^1_2$ determinacy is shown (...) to imply that every Π 1 2 prewellorder has rank less than $\underset{\sim}{\delta}^1_2$. (shrink)

Levelt et al. attempt to “model their theory” with WEAVER++. Modeling theories requires a model theory. The time is ripe for a methodology for building, testing, and evaluating computational models. We propose a tentative, five-step framework for tackling this problem, within which we discuss the potential strengths and weaknesses of Levelt et al.'s modeling approach.

Human behavior cannot be understood by using only models of explanation utilized in the natural sciences. Multiple models of explanation, which are not consistent with, or reducible to each other, are required and are in fact used in psychology to explain human actions. This situation, called "Multiexplanation," could cause a problem of developing a justified correspondence between psychological phenomena and multiple models of explanation. Unless this problem is solved, the explanatory capability of a psychological theory seems inconsistent and ad (...) hoc. A solution suggesting "correspondence guidelines" between phenomena and available models of explanation and "organization guidelines" for constructing a coherent psychological theory is offered. It contributes to the development of a "multiexplanation-model theory" (or a "multimodel theory" for brevity) which employs different models of explanation needed for proposing accounts of psychological phenomena. (shrink)

En el presente artículo, se examinan y discuten dos argumentos con consecuencias reduccionistas debidos a Jaegwon Kim y a Theodore Sider respectivamente. De acuerdo con el argumento de Kim, la superveniencia fuerte implicaría la coexistencia necesaria de propiedades (es decir, tal y como normalmente se interpreta, la reducción). De acuerdo con el de Sider, ocurriría lo mismo con la superveniencia global. Uno y otro hacen un uso esencial de sendas nociones de propiedad maximal, las cuales son discutidas aquí a la (...) luz de una interpretación natural e interesante de la teoría de las propiedades implícita en sus argumentos. Bajo esta nueva interpretación, en términos modelo-teóricos (véase apartado 4), obtenemos diversas posibilidades de relaciones formales entre las tesis de superveniencia y la reducción, según la lógica utilizada. Al menos bajo una interpretación interesante, los argumentos de Kim y Sider no son correctos, quedando demos-trado así que dichos argumentos no son válidos en general. We discuss and analyze two reductive arguments due to Jaegwon Kim and Theodore Sider respectively. According to the first one, strong supervenience would imply necessary coextension of properties (i.e., reduction). According to the second, this would be also the case of global supervenience. Kim and Sider make essential use of their respective notions of maximal properties, which we analyze here in the light of a natural and interesting interpretation of the underlying theory of properties. Under this interpretation, in terms of model theory (see § 4), we obtain different possibilities of formal relations between the superveniencie theses and reduction, depending on the logic we use. Under at least one interesting interpretation, the arguments of Kim and Sider are not correct and we become the conclusion that these arguments are not valid in general. (shrink)

We initiate the study of model theory in the absence of the Axiom of Choice, using the Axiom of Determinateness as a powerful substitute. We first show that, in this context, L ω 1 ω is no more powerful than first-order logic. The emphasis then turns to upward Lowenhein-Skolem theorems; ℵ 1 is the Hanf number of first-order logic, of L ω 1 ω , and of a strong fragment of L ω 1 ω . The main technical (...) innovation is the development of iterated ultrapowers using infinite supports; this requires an application of infinite-exponent partition relations. All our theorems can be proven from hypotheses weaker than AD. (shrink)

En el presente artículo, se examinan y discuten dos argumentos con consecuencias reduccionistas debidos a Jaegwon Kim y a Theodore Sider respectivamente. De acuerdo con el argumento de Kim, la superveniencia fuerte implicaría la coexistencia necesaria de propiedades (es decir, tal y como normalmente se interpreta, la reducción). De acuerdo con el de Sider, ocurriría lo mismo con la superveniencia global. Uno y otro hacen un uso esencial de sendas nociones de propiedad maximal, las cuales son discutidas aquí a la (...) luz de una interpretación natural e interesante de la teoría de las propiedades implícita en sus argumentos. Bajo esta nueva interpretación, en términos modelo-teóricos (véase apartado 4), obtenemos diversas posibilidades de relaciones formales entre las tesis de superveniencia y la reducción, según la lógica utilizada. Al menos bajo una interpretación interesante, los argumentos de Kim y Sider no son correctos, quedando demos-trado así que dichos argumentos no son válidos en general. We discuss and analyze two reductive arguments due to Jaegwon Kim and Theodore Sider respectively. According to the first one, strong supervenience would imply necessary coextension of properties (i.e., reduction). According to the second, this would be also the case of global supervenience. Kim and Sider make essential use of their respective notions of maximal properties, which we analyze here in the light of a natural and interesting interpretation of the underlying theory of properties. Under this interpretation, in terms of model theory (see § 4), we obtain different possibilities of formal relations between the superveniencie theses and reduction, depending on the logic we use. Under at least one interesting interpretation, the arguments of Kim and Sider are not correct and we become the conclusion that these arguments are not valid in general. (shrink)

The mental model theory predicts variations in the percentage of errors in meta-propositional reasoning tasks but does not specify the nature of these errors (Johnson-Laird & Byrne, 1990). In the present study, we drew predictions concerning the nature of errors in a meta-propositional reasoning task by importing and elaborating the distinction between implicit and explicit models previously applied by the mental model theory to the domain of propositional reasoning (Johnson-Laird, Byrne, & Schaeken, 1992). An experiment (...) was conducted in which participants were asked to solve problems concerning the truth or falsity of propositional assertions. The task was to determine the truth-status (liar or truth-teller) of two persons making a propositional assertion about their own truth-status and/or the truth-status of the other person. The results were consistent with the hypothesis that people may reason in ways that differ in the extent to which initially implicit models are made explicit. As such, the results corroborate a basic principle of the mental model theory: the errors that reasoners make are consistent with at least one of the mental models they construct during the process of reasoning. (shrink)

In this paper, I discuss the discovery of the DNA structure by Francis Crick and James Watson, which has provoked a large historical literature but has yet not found entry into philosophical debates. I want to redress this imbalance. In contrast to the available historical literature, a strong emphasis will be placed upon analysing the roles played by theory, model, and evidence and the relationship between them. In particular, I am going to discuss not only Crick and Watson's (...) well-known model and Franklin's x-ray diffraction pictures (the evidence) but also the less well known theory of helical diffraction, which was absolutely crucial to Crick and Watson's discovery. The insights into this groundbreaking historical episode will have consequences for the ‘new’ received view of scientific models and their function and relationship to theory and world. The received view, dominated by works by Cartwright and Morgan and Morrison ([1999]), rather than trying to put forth a ‘theory of models’, is interested in questions to do with (i) the function of models in scientific practice and (ii) the construction of models. In regard to (i), the received view locates the model (as an idealized, simplified version of the real system under investigation) between theory and the world and sees the model as allowing the application of the former to the latter. As to (ii) Cartwright has argued for a phenomenologically driven view and Morgan and Morrison ([1999]) for the ‘autonomy’ of models in the construction process: models are determined neither by theory nor by the world. The present case study of the discovery of the DNA structure strongly challenges both (i) and (ii). In contrast to claim (i) of the received view, it was not Crick and Watson's model but rather the helical diffraction theory which served a mediating purpose between the model and the x-ray diffraction pictures. In particular, Cartwright's take on (ii) is refuted by a comparison of Franklin's bottom-up approach with Crick and Watson's top-down approach in constructing the model. The former led to difficulties, which only a strong confidence in the structure incorporated in the model could circumvent. How to Get to the Structure 1.1 X-ray diffraction and its synthesis 1.2 Model building and Pauling's panache 1.3 The structure of proteins 1.3.1 A failed inference to the best explanation 1.3.2 The misleading 5.1 Å spot in proteins and how to get rid of it 1.3.3 Derived predictions from Pauling's alpha-helix of protein molecules The CCV Theory of Helical X-Ray Diffraction 2.1 The role of the CCV theory in the discovery of the DNA structure Killing the Helix 3.1 Appreciating all evidence—in vain Conclusion Epilogue: Chargaff's Ratios CiteULike Connotea Del.icio.us What's this? (shrink)

This paper develops a semantical model – theoretic account of (logical) content complementing the syntactically specified account of content developed in A New Theory of Content I, JPL 23: 596–620, 1994. Proofs of Completeness are given for both propositional and quantificational languages (without identity). Means for handling a quantificational language with identity are also explored. Finally, this new notion of content is compared, in respect of both logical properties and philosophical applications, to alternative partitions of the standard consequence (...) class relation proposed by Stelzner, Schurz and Wiengartner. (shrink)

Model theorists have been studying analytic functions since the late 1970s. Highlights include the seminal work of Denef and van den Dries on the theory of the p-adics with restricted analytic functions, Wilkie's proof of o-minimality of the theory of the reals with the exponential function, and the formulation of Zilber's conjecture for the complex exponential. My goal in this talk is to survey these main developments and to reflect on today's open problems, in particular for theories (...) of valued fields. (shrink)

I show that words with indefinite implicit complements occasion a dilemma for their model theory. There has been only two previous attempts to address this problem, one by Fodor and Fodor (1980) and one by Dowty (1981). Each requires that any word tolerating an implicit complement be treated as ambiguous between two different lexical entries and that a meaning postulate or lexical rule be given to constrain suitably the meanings of the various entries for the word. I show (...) that the positing of such an ambiguity runs counter to the facts and propose an alternative solution which does not appeal to ambiguity, meaning postulates or lexical rules. Indeed, I show that the dilemma posed by indefinite implicit complements is posed by all implicit complements and that a general solution to the problem of implicit complements follows from an independently motivated, single treatment of five other problems, that of subcategorization, that of phrasal projections of words, that of defining a model theoretic structure for phrase structure grammars, that of complement polyvalence and that of complement polyadicity. (shrink)

Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (non-degenerate) 3-valued counterpart of . Classical sentences that are true in are non-false in . Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic (the (...) proof for number theory was obtained earlier by R. K. Meyer and suggested the present abstract development). (shrink)

We study the relations between abelian groups B and C that every universal (resp. universal-existential) sentence true in B is also true in C, and give algebraic criteria for these relations to hold. As a consequence we characterize the inductive complete theories of abelian groups and prove that they are exactly the model-complete theories.

Johnson-Laird & Byrne (1991; 1993) present a theory of human deductive reasoning based on the notion of mental models. Unfortunately, the theory is incomplete. The present commentary argues that pragmatic considerations, particularly of the type discussed in Sperber and Wilson (1995), can complement the theory.

In [01], we gave algebraic characterizations of elementary equivalence for finitely generated finite-by-abelian groups, i.e. finitely generated FC-groups. We also provided several examples of finitely generated finite-by-abelian groups which are elementarily equivalent without being isomorphic. In this paper, we shall use our previous results to describe precisely the models of the theories of finitely generated finite-by-abelian groups and the elementary embeddings between these models.

The process of abstraction and concretisation is a label used for an explicative theory of scientific model-construction. In scientific theorising this process enters at various levels. We could identify two principal levels of abstraction that are useful to our understanding of theory-application. The first level is that of selecting a small number of variables and parameters abstracted from the universe of discourse and used to characterise the general laws of a theory. In classical mechanics, for example, (...) we select position and momentum and establish a relation amongst the two variables, which we call Newton’s 2nd law. The specification of the unspecified elements of scientific laws, e.g. the force function in Newton’s 2nd law, is what would establish the link between the assertions of the theory and physical systems. In order to unravel how and with what conceptual resources scientific models are constructed, how they function and how they relate to theory, we need a view of theory-application that can accommodate our constructions of representation models. For this we need to expand our understanding of the process of abstraction to also explicate the process of specifying force functions etc. This is the second principal level at which abstraction enters in our theorising and in which I focus. In this paper, I attempt to elaborate a general analysis of the process of abstraction and concretisation involved in scientific- model construction, and argue why it provides an explication of the construction of models of the nuclear structure. (shrink)

We define a mathematical formalism based on the concept of an ‘‘open dynamical system” and show how it can be used to model embodied cognition. This formalism extends classical dynamical systems theory by distinguishing a ‘‘total system’’ (which models an agent in an environment) and an ‘‘agent system’’ (which models an agent by itself), and it includes tools for analyzing the collections of overlapping paths that occur in an embedded agent's state space. To illustrate the way this formalism (...) can be applied, several neural network models are embedded in a simple model environment. Such phenomena as masking, perceptual ambiguity, and priming are then observed. We also use this formalism to reinterpret examples from the embodiment literature, arguing that it provides for a more thorough analysis of the relevant phenomena. (shrink)

George Lakoff (in his book Women, Fire, and Dangerous Things(1987) and the paper "Cognitive semantics" (1988)) champions some radical foundational views. Strikingly, Lakoff opposes realism as a metaphysical position, favoring instead some supposedly mild form of idealism such as that recently espoused by Hilary Putnam, going under the name "internal realism." For what he takes to be connected reasons, Lakoff also rejects truth conditional model-theoretic semantics for natural language. This paper examines an argument, given by Lakoff, against realism and (...) MTS. We claim that Lakoff's argument has very little, if any, impact for linguistic semantics. (shrink)

This is a review of From Discourse to Logic: Introduction to Model-theoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory, by Hans Kamp and Uwe Reyle, published by Kluwer Academic Publishers in 1993.

Robert Merton's essays on theories of the middle range and his essays on functional explanation and the structural approach are among the most influential in the history of sociology. But their import is a puzzle. He explicitly allied himself with some of the most extreme scientistic formalists and contributed to and endorsed the Columbia model of theory construction. But Merton never responded to criticisms by Ernest Nagel of his arguments or acknowledged the rivalry between Lazarsfeld and Herbert Simon, (...) rarely cited the philosophical and methodological literature, and responded to critics with ambiguous concessions, leaving the Mertonian legacy profoundly ambiguous. Key Words: Robert Merton • Paul Lazarsfeld • theory construction • middle range theory • causal modeling • Émile Durkheim. (shrink)

Schaffner’s model of theory reduction has played an important role in philosophy of science and philosophy of biology. Here, the model is found to be problematic because of an internal tension. Indeed, standard antireductionist external criticisms concerning reduction functions and laws in biology do not provide a full picture of the limits of Schaffner’s model. However, despite the internal tension, his model usefully highlights the importance of regulative ideals associated with the search for derivational, and (...) embedding, deductive relations among mathematical structures in theoretical biology. A reconstructed Schaffnerian model could therefore shed light on mathematical theory development in the biological sciences and on the epistemology of mathematical practices more generally. *Received November 2006; revised March 2009. †To contact the author, please write to: Philosophy Department, University of California, Santa Cruz, 1156 High St., Santa Cruz, CA 95064; e‐mail: rgw@ucsc.edu. (shrink)

We can look at this model theoretically as follows. By the linearly ordered predicate calculus, we simply mean ordinary predicate calculus with equality and a special binary relation symbol <. It is required that in all interpretations, < be a linear ordering on the domain. Thus we have the usual completeness theorem provided we add the axioms that assert that < is a linear ordering.

George Lakoff (in his book Women, Fire, and Dangerous Things (1987) and the paper "Cognitive semantics" (1988)) champions some radical foundational views. Strikingly, Lakoff opposes realism as a metaphysical position, favoring instead some supposedly mild form of idealism such as that recently espoused by Hilary Putnam, going under the name internal realism." For what he takes to be connected reasons, Lakoff also rejects truth conditional model-theoretic semantics for natural language.

Abstract ?Theory of Mind? (ToM) is widely held to be ubiquitous in our navigation of the social world. Recently this standard view has been contested by phenomenologists and enactivists. Proponents of the ubiquity of ToM, however, accept and effectively neutralize the intuitions behind their arguments by arguing that ToM is mostly sub-personal. This paper proposes a similar move on behalf of the phenomenologists and enactivists: it offers a novel explanation of the intuition that ToM is ubiquitous that is compatible (...) with the rejection of this ubiquity. According to this explanation, we use ToM-talk primarily to model and thereby reconstruct non-mentalizing social-cognitive processes in order to explain our assessment of the behaviour of others. The intuition that ToM is ubiquitous is the result of mistaking the model for the real thing. This explanation is argued to be more complete than the ?ToM-ist? explanation of the intuition that ToM is not ubiquitous. (shrink)

Weak Quantum Theory (WQT) and the Model of Pragmatic Information (MPI) are two psychophysical concepts developed on the basis of quantum physics. The present study contributes to their empirical examination. The issue of the study is whether WQT and MPI can not only explain ‘psi’-phenomena theoretically but also prove to be consistent with the empirical phenomenology of extrasensory perception (ESP). From the main statements of both models, 33 deductions for psychic readings are derived. Psychic readings are defined as (...) settings, in which psychics support or counsel clients by using information not mediated through the five senses. A qualitative approach is chosen to explore how the psychics experience extrasensory perceptions. Eight psychics are interviewed with a half-structured method. The reports are examined regarding deductive and inductive aspects, using a multi-level structured content analysis. The vast majority of deductions is clearly confirmed by the reports. Even though the study has to be seen as an explorative attempt with many aspects to be specified, WQT and MPI prove to be coherent and helpful concepts to explain ESP in psychic readings. (shrink)

This study examines the use of a modified form of the theory of planned behavior in understanding the decisions of undergraduate students in engineering and humanities to engage in cheating. We surveyed 527 randomly selected students from three academic institutions. Results supported the use of the model in predicting ethical decision-making regarding cheating. In particular, the model demonstrated how certain variables (gender, discipline, high school cheating, education level, international student status, participation in Greek organizations or other clubs) (...) and moral constructs related to intention to cheat, attitudes toward cheating, perceptions of norms with respect to cheating, and ultimately cheating behaviors. Further the relative importance of the theory of planned behavior constructs was consistent regardless of context, whereas the contributions of variables included in the study that were outside the theory varied by context. Of particular note were findings suggesting that the extent of cheating in high school was a strong predictor of cheating in college and that engineering students reported cheating more frequently than students in the humanities, even when controlling for the number of opportunities to do so. (shrink)

A generalization of Ehrenfest''s urn model is suggested. This will allow usto treat a wide class of stochastic processes describing the changes ofmicroscopic objects. These processes are homogeneous Markov chains. Thegeneralization proposed is presented as an abstract conditional (relative)probability theory. The probability axioms of such a theory and some simpleadditional conditions, yield both transition probabilities and equilibriumdistributions. The resulting theory interpreted in terms of particles andsingle-particle states, leads to the usual formulae of quantum and classicalstatistical mechanics; (...) in terms of chromosomes and allelic types, it allowsthe deduction of many genetical models including the Ewens sampling formula;in terms of agents'' strategies, it gives a justification of the ``herdbehaviour'''' typical of a population of heterogeneous economic agents. (shrink)

Hunt and Vitell''s General Theory (1992) is used in a cross-cultural comparison of U.S. and Taiwanese business practitioners. Results indicate that Taiwanese practitioners exhibit lower perceptions of an ethical issue in a scenario based on bribery, as well as milder deontological evaluations and ethical judgments relative to their U.S. counterparts. In addition, Taiwan respondents showed higher likelihood of making the payment. Several of the paths between variables in the theory are confirmed in both U.S. and Taiwan samples, with (...) summary data suggesting the Hunt and Vitell theory performs well in both U.S. and Taiwan. Some unanticipated linkages within the model were uncovered in the samples. Results and implications are discussed. (shrink)

The research on which the present paper makes a point in aimed at designing a cognitive model of Albert Einstein's discovery that is based on fundamental Einstein's publications and placed, ideally, at a meso-level, between macro-historical and micro-cognitive reconstructions (e.g. protocol analysis). As in a cognitive-historical analysis, we will trace some discovery heuristics in the construction of representations, that are on a continuum with those we employ in ordinary problem solving. Firstly, some theory-specific, reflexive heuristics—named orientative heuristics—are traced: (...) inner perfection, explain-or-assume, explanatory correspondence, and covariance/invariance. Then, other well-known abstractive heuristics as analogical and imagistic reasoning, thought experiment, limiting case analysis (e.g. Nersessian 1992) are shown occurring in Einstein's key-publications. A sketch of a socio-cognitive model for his discovery is then presented following two suggestions: (a) an idea of Van Fraassen about discovery phases, and (b) the Humean distinction between beliefs and ideas. (shrink)

We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: "MP", Affirmation of the Consequent "AC") and denial problems (Denial of the Antecedent "DA", and Modus Tollens "MT"). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are reliable effects of (...) a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

Although it is conceded (as argued by many)that distinct knowledge domains do presentparticular problems of coming to know, in thispaper it is argued that it is possible (anduseful) to construct a domain independent modelof the processes of coming to know, one inwhich observers share understandings and do soin agreed ways. The model in question is partof the conversation theory (CT) of Gordon Pask. CT, as a theory of theory construction andcommunication, has particular relevance forfoundational issues (...) in science and scienceeducation. CT explicitly propounds a ``radicalconstructivist'' (RC) epistemology. A briefaccount is given of the main tenets of RC andCT's place in that tradition and the traditionsof cybernetics. The paper presents a briefnon-technical account of the main concepts ofCT including elaborations by Laurillard andHarri-Augstein and Thomas. As part of CT, Pask also elaborated a methodology – knowledgeand task analysis – for analysing the structureof different knowledge domains; thismethodology is sketched in outline. (shrink)

Adjoin, to a countable standard model M of Zermelo-Fraenkel set theory (ZF), a countable set A of independent Cohen generic reals. If one attempts to construct the model generated over M by these reals (not necessarily containing A as an element) as the intersection of all standard models that include M ∪ A, the resulting model fails to satisfy the power set axiom, although it does satisfy all the other ZF axioms. Thus, there is no smallest (...) ZF model including M ∪ A, but there are minimal such models. These are classified by their sets of reals, and there is one minimal model whose set of reals is the smallest possible. We give several characterizations of this model, we determine which weak axioms of choice it satisfies, and we show that some better known models are forcing extensions of it. (shrink)

Methodology of scientific research programs (MSRP), model-building and actor-network-theory (ANT) are woven together to provide a layered study of the Leontief paradox. Neil De Marchi's Lakatosian account examined the paradox within an Ohlin-Samuelson research program. A model-building approach rather highlights the ability of Leontief's input-output model to mediate between international trade theory and the world by facilitating an empirical application of the Heckscher-Ohlin Theorem. The epistemological implications of this model-building approach provide an alternative explanation (...) of why Samuelson and other prominent economists ignored the paradox. By focusing on the network in which input-output analysis evolved, Bruno Latour's ANT further explains the response of international trade theorists. (shrink)

This paper argues that historical research is an important tool for modeling problem-solving in scientific invention and discovery. Two important cases in the history of modern physics—the invention of the transistor by John Bardeen and Walter Brattain and the development of the theory of superconductivity by Bardeen, Leon Cooper, and J. Robert Schrieffer—reveal factors essential to include in such a model. The focus is on problem-solving practices: problem decomposition, analogy, bridging principles, team-work, empirical tinkering, and library research. A (...) complete framework must encompass the full range of factors, including contingent individual traits and environmental circumstances. (shrink)

In this commentary, we question (1) how embodied Thelen et al.'s model is relative to their aims, and (2) how embodied the behavior of children is in particular response systems, relative to how much dynamic systems theory emphasizes this idea. We close with corrections to mischaracterizations of an alternative, neural network perspective on infant behavior.

A subset A $\subseteq$ M of a totally ordered structure M is said to be convex, if for any a, b $\in A: [a . A complete theory of first order is weakly o-minimal (M. Dickmann [D]) if any model M is totally ordered by some $\emptyset$ -definable formula and any subset of M which is definable with parameters from M is a finite union of convex sets. We prove here that for any model M of a (...) weakly o-minimal theory T, any expansion M + of M by a family of unary predicates has a weakly o-minimal theory iff the set of all realizations of each predicate is a union of a finite number of convex sets (Theorem 63), that solves the Problem of Cherlin-Macpherson-Marker-Steinhorn [MMS] for the class of weakly o-minimal theories. (shrink)

Public sphere is an important idea of Habermas in the early research, which guided his latter research, especially in political philosophy field. According to Habermas’ research on public sphere, this paper researches public sphere’s significance in solving the legalization crisis of capitalism and remedying the democratic theory of bourgeoisie. Public sphere idea set up a new model of the democratic theory, deliberative democracy, which is better than democracy of both liberalism and republicanism, and become the most important (...) theme of Habermas in theory and practice. (shrink)

In Rahul Banerjee and Bikas K. Chakrabarti (eds.), Progress in Brain Research, 168: 215-246. Amsterdam: Elsevier. Electronic offprint available upon request.

In [9] we introduced a new framework for asymptotic probabilities, in which a $\sigma-additive$ measure is defined on the sample space of all sequences $A = $ of finite models, where the universe of An is {1, 2, .., n}. In this framework we investigated the strong 0-1 law for sentences, which states that each sentence either holds in An eventually almost surely or fails in An eventually almost surely. In this paper we define the strong convergence law for formulas, (...) which carries over the ideas of the strong 0-1 law to formulas with free variables, and roughly states that for each formula φ(x), the fraction of tuples a in An, which satisfy the formula φ(x), almost surely has a limit as n tends to infinity. We show that the infinitary logic with finitely many variables has the strong convergence law for formulas for the uniform measure, and further characterize the measures on random graphs for which the strong convergence law holds. (shrink)

We introduce a new framework for asymptotic probabilities of sentences, in which we have a σ-additive measure on the sample space of all sequences A = {A n } of finite models, where the universe of A n is {1,2... n}, and use this framework to strengthen 0-1 laws for logics.

The aims of this paper are: (1) to present tense-logical versions of such classical notions as saturated and special models; (2) to establish several fundamental existence theorems about these notions; (3) to apply these powerful techniques to tense complexity.In this paper we are concerned exclusively with quantifiedK 1 (for linear time) with constant domain. Our present research owes much to Bowen [2], Fine [5] and Gabbay [6].

We discuss the problem of defining the collection of first-order elementary classes in terms of the natural topological space of countable models.

" In Being No One, Metzinger, a German philosopher, draws strongly on neuroscientific research to present a representationalist and functional analysis of...

In the opening chapter of ‘the Shorter Hodges’, we get a lot of fixing of terminology and notation, and some fairly natural definitions of ideas like that of isomorphism between structures. There are no really tricky ideas which need further exploration, nor any nasty proofs that could do with more elaboration. So I don’t pretend to have anything very thrilling by way of introductory comments. But let me make some more general philosophical comments.

A structure is a triple A = (A, {Ri: i ∈ I}, {ej: j ∈ J}), where A, the domain or universe of A, is a nonempty set, {Ri: i ∈ I} is an indexed family of relations on A and {ej: j ∈ J}) is an indexed set of elements —the designated elements of A. For each i ∈ I there is then a natural number λ(i) —the degree of Ri —such that Ri is a λ(i)-place relation on A, (...) i.e., Ri ⊆ Aλ(i). This λ may be regarded as a function from I to the set ω of natural numbers; the pair (λ, J) is called the type of A. Structures of the same type are said to be similar. Note that since an n-place operation f: An → A can be regarded as an (n+1)-place relation on A, algebraic structures containing operations such as groups, rings, vector spaces, etc. may be construed as structures in the above sense. (shrink)

A logical system is studied whose well-formed representations consist of diagrams rather than formulas. The system, due to Shin [2, 3], is shown to be complete by an argument concerning maximally consistent sets of diagrams. The argument is complicated by the lack of a straight forward counterpart of atomic formulas for diagrams, and by the lack of a counterpart of negation for most diagrams.