Modal structuralism promises an interpretation of set theory that avoids commitment to abstracta. This article investigates its underlying assumptions. In the first part, I start by highlighting some shortcomings of the standard axiomatisation of modal structuralism, and propose a new axiomatisation I call MSST (for Modal Structural Set Theory). The main theorem is that MSST interprets exactly Zermelo set theory plus the claim that every set is in some inaccessible rank of the cumulative hierarchy. In the second part (...) of the article, I look at the prospects for supplementing MSST with a modal structural reflection principle, as suggested in Hellman (2015). I show that Hellman’s principle is inconsistent (Theorem 5.32), and argue that modal structural reflection principles in general are either incompatible with modal structuralism or extremely weak. (shrink)

This paper has two goals. The first goal is to show that the structuralists’ claims about dependence are more significant to their view than is generally recognized. I argue that these dependence claims play an essential role in the most interesting and plausible characterization of this brand of structuralism. The second goal is to defend a compromise view concerning the dependence relations that obtain between mathematical objects. Two extreme views have tended to dominate the debate, namely the view that (...) all mathematical objects depend on the structures to which they belong and the view that none do. I present counterexamples to each of these extreme views. I defend instead a compromise view according to which the structuralists are right about many kinds of mathematical objects (roughly, the algebraic ones), whereas the anti-structuralists are right about others (in particular, the sets). I end with some remarks about how to understand the crucial notion of dependence, which despite being at the heart of the debate is rarely examined in any detail. (shrink)

Contents: Foreword. Wolfgang BALZER and C. ULISES MOULINES: Introduction. José A. DÍEZ CALZADA: Structuralist Analysis of Theories of Fundamental Measurement. Adolfo GARCÍA DE LA SIENRA and Pedro REYES: The Theory of Finite Games in Extensive Form. Hans Joachim BURSCHEID und Horst STRUVE: The Theory of Stochastic Fairness - its Historical Development, Formulation and Justification. Wolfgang BALZER and Richard MATTESSICH: Formalizing the Basis of Accounting. Werner DIEDERICH: A Reconstruction of Marxian Economics. Bert HAMMINGA and Wolfgang BALZER: The Basic Structure of Neoclassical (...) General Equilibrium Theory. Klaus MANHART: Balance Theories: Two Reconstructions and the Problem of Intended Applications. Rainer WESTERMANN: Festinger's Theory of Cognitive Dissonance: A Structuralist Theory-Net. Rainer REISENZEIN: Wundt's Three-Dimensional Theory of Emotion. Pablo LORENZANO: Classical Genetics and the Theory-Net of Genetics. Hinne HETTEMA and Theo A.F. KUIPERS: The Formalisation of the Periodic Table. C. ULISES MOULINES: The Basic Core of Simple Equilibrium Thermodynamics. Thomas BARTELBORTH: An Axiomatization of Classical Electrodynamics. Author's Index. Subject Index. (shrink)

One kind of structuralism holds that mathematics is about structures, conceived as a type of abstract entity. Another denies that it is about any distinctively mathematical entities at all—even abstract structures; rather it gives purely general information about what holds of any collection of entities conforming to the axioms of the theory. Of these, pure structuralism is most plausibly taken to enjoy significant advantages over platonism. But in what appears to be its most plausible—modalised—version, even restricted to elementary (...) arithmetic, it requires defence of a very strong possibility claim: that there could be a completed w-sequence of concrete objects. There are very serious epistemological difficulties in the way of providing the requisite defence. (shrink)

From a post-structuralist position, it is problematic and seemingly impossible to refer to God as the Trinity. This article describes possibilities for thinking about the Trinity (religion and God) within a post-structuralist context. As an example of such thinking, the 2015 culture-critique film, The Brand New Testament, will be analysed. It is a creative retelling of the Christian story and of the Trinity in a secular and post-metaphysical vein. This ‘Brand New Testament’ reveals God as ‘one’ – as the encompassing (...) love, hope and life which we may experience in this life. The life-giving characteristics of this ‘god’ are surprisingly close to the biblical understanding of the Trinity. In the ‘Brand New Testament’, however, the Trinity is portrayed radically differently than in the Christian tradition. The personae of father, son and spirit are deconstructed in the film, in that a daughter and a mother also form part of the godhead. This deconstruction of the Trinity, which should not be confused with blasphemy, opens up a possible post-structuralist imagining of God. It playfully reveals a powerless god who shares some fundamental characteristics with the Trinity – such as love, joy and life. It allows for the ‘oneness of god’ to include more, and less, than the ‘Holy Trinity’. (shrink)

Neofregeanism and structuralism are among the most promising recent approaches to the philosophy of mathematics. Yet both have serious costs. We develop a view, structuralist neologicism, which retains the central advantages of each while avoiding their more serious costs. The key to our approach is using arbitrary reference to explicate how mathematical terms, introduced by abstraction principles, refer. Focusing on numerical terms, this allows us to treat abstraction principles as implicit definitions determining all properties of the numbers, achieving a (...) key neofregean advantage, while preserving the key structuralist advantage, which objects play the number role does not matter. (shrink)

THE STRUCTURALISTIC ENDEAVOUR. THE WORLD AS MUSICAL SCORE The recent decades of this century have witnessed unusually rapid and far- reaching changes in the ...

Ontic structural realism is a thesis of fundamentality metaphysics: the thesis that structure, not objects, has fundamental status. Claimed as the metaphysic most befitting of modern physics, OSR first emerged as an entreaty to eliminate objects from the metaphysics of fundamental physics. Such elimination was urged by Steven French and James Ladyman on the grounds that only it could resolve the ‘underdetermination of metaphysics by physics’ that they claimed reduced any putative objectual commitment to a merely ‘ersatz’ form of realism. (...) Few, however, have joined French and Ladyman either in acknowledging that such underdetermination exists or in attributing to it such drastic consequences. However, an alternative view that physics does sanction objects, albeit merely as ontologically secondary entities, represents a different and seemingly less extreme route to the same conclusion regarding the fundamentality of structure. But since what it means to be ‘ontologically prior’ is itself a vexed philosophical question, a stance must be taken as to how we are to understand priority before its prospects may be evaluated. In an earlier paper, I outlined how Fine’s notion of ontological dependence might be utilized to defend the priority-based approach to structuralism. Since then, however, I have become convinced that that ontological dependence is not a relation of priority after all. As a result, the arguments outlined in that paper stand in need of reassessment. In this work, I consider the prospects for priority-based structuralism when expressed in the idiom of determination. My conclusion will be that it has yet to be vindicated by our best physical theories, owing to the failure of symmetry structures to determine the world’s inventory of fundamental kinds. Nevertheless, the same symmetry considerations point towards there being renewed prospects for eliminativism—an eliminativism, moreover, of more naturalistic appeal than that hitherto associated with OSR. 1Introduction 2Structuralist Strategies 3Defining Ontological Priority: Dependence or Determination? 4Structuralism in the Idiom of Determination 4.1Determining plurality 4.2Determining kind properties 5A Reinvigorated Eliminativism. (shrink)

According to structural realism, in mature science there is structural continuity along theoretical change. A major counterexample to this thesis is the transition from the Eightfold Way to the Standard Model in particle physics. Nevertheless, the notion of structure is significantly important in comprehending the theoretical picture of particle physics, where particles change and undergo transmutations, while the only thing which remains unchanged is the basic structure, i.e. the symmetry group which controls the transmutations. This kind of view agrees with (...) the paradigmatic case where the structure is an internal symmetry and the instantiations are the elementary particles. The metaphysical view which reflects this situation is a version of ontic structuralism. (shrink)

Structural realism has recently re-entered mainstream discussions in the philosophy of science. The central notion of structure, however, is contested by both advocates and critics. This paper briefly reviews currently prominent structuralist accounts en route to proposing a metaphysics of structure that is capable of supporting the epistemic aspirations of realists, and that is immune to the charge most commonly levelled against structuralism. This account provides an alternative to the existing epistemic and ontic forms of the position, incorporating elements (...) of both. Structures are here identified with relations between first order, causal properties: properties that confer specific dispositions for relations. This form of structuralism constitutes an explicit proposal for what seem implicit structuralist tendencies in sophisticated but more traditional characterizations of realism. An outline of the proposal's response to the anti-realist's pessimistic induction on the history of scientific theories is considered. (shrink)

The chapter takes structuralism to be the thesis that if F and G are alike causally, then F and G are the same property. It follows that our beliefs about the world can be true in various brain-in-a-vat scenarios, giving us refuge from skeptical arguments. The trouble is that structuralism doesn’t do justice to certain metaphysical aspects of property identity having to do with fundamentality, intrinsicality, and the unity of the world. A closely related point is that the (...) relation…lies-at-some-spatial-distance-from…obeys necessary truths that need not apply to other relations with the same causal profile. This observation is especially important if, as David Lewis argued, the only alternatives to skepticism are structuralism and an anti-Humean stance toward modality. Some pertinent views of David Chalmers’s are discussed, and parallels are drawn between the structuralist response to skepticism and functionalism in the philosophy of mind. (shrink)

This paper aims to set forth Carnapian structuralism, i.e., a syntactic view of the structuralist approach which is deeply inspired by Carnap’s dual level conception of scientific theories. At its core is the axiomatisation of a metatheoretical concept AE(T) which characterises those extensions of an intended application that are admissible in the sense of being models of the theory-element T and that satisfy all links, constraints and specialisations. The union of axiom systems of AE(T) (where T is an element (...) of the theory-net N) will allow us to present scientific theories in an axiomatic fashion so that deductive reasoning in science can be formalised. Thereupon defeasible and paraconsistent means of reasoning will be introduced. The logical study of scientific reasoning is the key motivation of Carnapian structuralism. A further motivation is to help overcome the syntactic-semantic split in the philosophy of science. (shrink)

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.

Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a non-trivial automorphism, distinct indiscernible positions within the structure cannot be shown to be non-identical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include 'irreflexive two-place relations'. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positions that have all the same properties as each other and exactly the (...) same relations to all objects (including themselves). I conclude that realistic structuralists must compromise and treat some structures eliminativistically. (shrink)

Historically, the empirical study of phenotypic diversification has fallen into two rough camps; (1) "structuralist approaches" focusing on developmental constraint, bias, and innovation (with evo-devo at the core); and (2) "adaptationist approaches" focusing on adaptation, and natural selection. Whilst debates, such as that surrounding the proposed "Extended" Evolutionary Synthesis, often juxtapose these two positions, this review focuses on the grey space in between. Specifically, here I present a novel analysis of structuralism which enables us to take a more nuanced (...) look at the motivations behind the structuralist and adaptationist positions. This makes clear how the two approaches can conflict, and points of potential commensurability. The review clarifies (a) the value of the evo-devo approach to phenotypic diversity, but also (b) how it properly relates to other predominant approaches to the same issues in evolutionary biology more broadly. (shrink)

The approach of structuralism came to philosophy from social science. It was also in social science where, in 1950–1970s, in the form of the French structuralism, the approach gained its widest recognition. Since then, however, the approach fell out of favour in social science. Recently, structuralism is gaining currency in the philosophy of mathematics. After ascertaining that the two structuralisms indeed share a common core, the question stands whether general structuralism could not find its way back (...) into social science. The nature of the major objections raised against French structuralism – concerning its alleged ahistoricism, methodological holism and universalism – are reconsidered. While admittedly grounded as far as French structuralism is concerned, these objections do not affect general structuralism as such. The fate of French structuralism thus does not seem to preclude the return of general structuralism into social science, rather, it provides some hints where the difficulties may lie. (shrink)

Cartesian arguments for global skepticism about the external world start from the premise that we cannot know that we are not in a Cartesian scenario such as an evil-demon scenario, and infer that because most of our empirical beliefs are false in such a scenario, these beliefs do not constitute knowledge. Veridicalist responses to global skepticism respond that arguments fail because in Cartesian scenarios, many or most of our empirical beliefs are true. Some veridicalist responses have been motivated using verificationism, (...) externalism, and coherentism. I argue that a more powerful veridicalist response to global skepticism can be motivated by structuralism, on which physical entities are understood as those that play a certain structural role. I develop the structuralist response and address objections. (shrink)

Since Benacerraf’s ‘What Numbers Could Not Be, ’ there has been a growing interest in mathematical structuralism. An influential form of mathematical structuralism, modal structuralism, uses logical possibility and second order logic to provide paraphrases of mathematical statements which don’t quantify over mathematical objects. These modal structuralist paraphrases are a useful tool for nominalists and realists alike. But their use of second order logic and quantification into the logical possibility operator raises concerns. In this paper, I show (...) that the work of both these elements can be done by a single natural generalization of the logical possibility operator. (shrink)

The structuralist approach represents the relation between a model and physical system as a relation between two mathematical structures. However, since a physical system is _prima facie_ _not_ a mathematical structure, the structuralist approach seemingly fails to represent the fact that science is about concrete, physical reality. In this paper, I take up this _problem of lost reality_ and suggest how it may be solved in a purely structuralist fashion. I start by briefly introducing both the structuralist approach and the (...) problem of lost reality and discussing the various (non-structuralist) solutions that have been proposed in the literature. Following this, I decompose the problem into the _ontological mismatch_ and _specification_ problems. In response to the former, I present a _metascientific dissolution argument_, according to which the difference in kind between mathematical structures and physical systems poses no deep obstacle to the structuralist approach, and consider some upshots of this argument for our views on representation. By way of conclusion, I argue that the metascientific dissolution argument paves the way for a solution to the specification problem as well. (shrink)

“In its less dramatic versions,” writes author Dan Palmer, “structuralism is just a method of studying language, society, and the works of artists and novelists. But in its most exuberant form, it is a philosophy, an overall worldview that provides an account of reality and knowledge.” Poststructuralism is a loosely knit intellectual movement, comprised mainly of ex-structuralists who either became dissatisfied with the theory or felt they could improve it. Structuralism and Poststructuralism For Beginners is an illustrated tour (...) through the mysterious landscape of these two theories. The book’s starting point is the linguistic theory of Ferdinand de Saussure. The book moves on to the anthropologist and literary critic Claude Levi-Strauss; the semiologist and literary critic Roland Barthes; the Marxist philosopher Louis Althusser; the psychoanalyst Jacques Lacan; the deconstructionist Jacques Derrida. The book concludes by examining the postmodern obsession with language and with the radical claim of the disappearance of the individual–obsessions that unite the work of all of these theorists. (shrink)

The program of “neurophenomenal structuralism” is presented as an agenda for a genuine structuralist neuroscience of consciousness that seeks to understand specific phenomenal experiences as strictly relational affairs. The paper covers a broad range of topics. It starts from considerations about neural change detection and relational coding that motivate a solution of the Newman problem of the brain in terms of spatiotemporal relations. Next, phenomenal quality spaces and their Q-structures are discussed. Neurophenomenal structuralism proclaims a homomorphic mapping of (...) the structures of self-organized neural maps in the brain onto Q-structures, and it will be demonstrated how this leads to a new and special version of structural representationalism about phenomenal content. A methodological implication of neurophenomenal structuralism is that it proposes measurement procedures that focus on the relationships between different stimuli (as, for instance, similarity ratings or representational geometry methods). Finally, it will be shown that neurophenomenal structuralism also has strong philosophical implications, as it leads to holism about phenomenal experiences and serves to reject inverted qualia scenarios. (shrink)

Structuralism took part in the efforts to revive intellectual development in the former Czecho-Slovakia in the 1960s as an efficient methodological instrument, a scientific meta-theory, as well as an inovation in the field of philosophical theory . Open discussions were focused on the questions such as the relation between methodology and philosophy, system and structure, system and development, problem of the connection of synchronicity and diachronicity, the role of the subject, etc. Czecho-Slovak school applied the dynamic aspect of the (...) structure as a dynamic whole. This school came up with its own concept of dialectical structuralism, specific and different from French conceptual-instrumental model of structuralism. (shrink)

According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of the elements in a (...) collection without counting them), or on the ability to approximate quantities (i.e., to assess anapproximatequantity of the elements in a collection without counting them), or both, fail to provide a conceptual basis for bootstrapping the concept of an exact natural number. In particular, I argue that none of the existing theories explains one of the key characteristics of the natural number structure: the equidistances between successive elements of the natural numbers progression. I suggest that this regularity could be based on another innate cognitive ability, namely sensitivity to the regularity of rhythm. In the final section, I propose a new position within the core cognition paradigm, inspired by structuralist positions in philosophy of mathematics. (shrink)

With developments in the 19th and early 20th centuries, structuralist ideas concerning the subject matter of mathematics have become commonplace. Yet fundamental questions concerning structures and relations themselves as well as the scope of structuralist analyses remain to be answered. The distinction between axioms as defining conditions and axioms as assertions is highlighted as is the problem of the indefinite extendability of any putatively all-embracing realm of structures. This chapter systematically compares four main versions: set-theoretic structuralism, a version taking (...) structures as sui generis universals, structuralism based on category theory, and a quasi-nominalist modal-structuralism. While none of the approaches is problem-free, it appears that some synthesis of the category-theoretic approach with modal-structuralism can meet the challenges set out, given the notion of “logical possibility.”. (shrink)

The aim of this paper is to characterize the various structuralist reduction concepts as structure-preserving maps in a succinct and unifying way. To begin with, some important intuitive adequacy conditions are discussed that a good (structuralist) reduction concept should satisfy. Having reconstructed these intuitive conditions in the structuralist framework, it turns out that they divide into two mutually incompatible sets of requirements. Accordingly there exist (at least) two essentially different types of structuralist reduction concepts: the first type stresses the existence (...) of a deductive or inferential link between the reducing and the reduced theory; the second type emphasizes the greater explanatory power the reducing theory should have in comparison with the reduced theory. The problem of the incompatibility of equally plausible reduction concepts is treated in the last section and a proposal is made for its solution consisting in the definition of a multiple synthetizing reduction relation. (shrink)

According to structuralism in philosophy of mathematics, arithmetic is about a single structure. First-order theories are satisfied by models that do not instantiate this structure. Proponents of structuralism have put forward various accounts of how we succeed in fixing one single structure as the intended interpretation of our arithmetical language. We shall look at a proposal that involves Tennenbaum's theorem, which says that any model with addition and multiplication as recursive operations is isomorphic to the standard model of (...) arithmetic. On this account, the intended models of arithmetic are the notation systems with recursive operations on them satisfying the Peano axioms. [A]m Anfang […] ist das Zeichen. (shrink)

The scientific transformation of the hermeneutic art has been the common goal for the various formalist-structuralist programs of interpretation that have dominated human studies in our century - such as New Criticism in literary analysis, the formalist programs in art history and musicology, the Gestalt and Freudian psychology, structuralism in linguistics and anthropology, etc. In this volume, these formalist-structuralist programs shall be called structural programs of interpretation in Europe and America.

This paper develops the first parts of a logical framework for the empirical sciences, by means of a redefinition of theory structuralism as originally developed by Joseph Sneed, Wolfgang Stegmüller, and others, in the context of a ‘rigid’ logic as based on a fixed (therefore rigid) ontology. The paper defends a formal conception of the empirical sciences that has an irreducible ontological basis and is unable, in general, to provide purely structural characterizations of the domain of a theory. The (...) extreme rationalist utopia of a characterization of the real world ‘up to isomorphism’, therefore, is rejected. (shrink)

Structuralism is a view about the subject matter of mathematics according to which what matters are structural relationships in abstraction from the intrinsic nature of the related objects. Mathematics is seen as the free exploration of structural possibilities, primarily through creative concept formation, postulation, and deduction. The items making up any particular system exemplifying the structure in question are of no importance; all that matters is that they satisfy certain general conditions—typically spelled out in axioms defining the structure or (...) structures of interest—characteristic of the branch of mathematics in question. Thus, in the basic case of arithmetic, the famous “axioms” of Richard Dedekind (taken over by Giuseppe Peano, as he acknowledged) were conditions in a definition of a “simply infinite system”, with an initial item, each item having a unique next one, no two with the same next one, and all items finitely many steps from the initial one. (The latter condition is guaranteed by the axiom of mathematical induction.) All such systems are structurally identical, and, in a sense to be made more precise, the shared structure is what mathematics investigates. (In other cases, multiple structures are allowed, as in abstract algebra with its many groups, rings, fields, and so forth.) This structuralist view of arithmetic thus contrasts with the absolutist view, associated with Gottlob Frege and Bertrand Russell, that natural numbers must in fact be certain definite objects, namely classes of equinumerous concepts or classes. (shrink)

If structuralism is a true view of mathematics on which the statements of mathematicians are taken ‘at face value’, then there are both structures on which classical second-order arithmetic is a correct report, and structures on which intuitionistic second-order arithmetic is correct. An argument due to Dedekind then proves that structures and structures are isomorphic. Consequently, first- and second-order statements true in structures must hold in , and conversely. Since instances of the general law of the excluded third fail (...) in structures but hold in , a contradiction ensues. (shrink)

The article draws a conceptual distinction the (French) structuralism of the 50’s–60’s and the post-structuralism of the 70’s, which are discussed as overlapping in their intellectual paths; their mutual dynamics is defined as a reaction of the intelligence to the pressure of depersonalized unified schemes within the logic of structuralism against free improvisation and loose interpretation instead of total explanations in the post-structuralism interpretation. The article establishes a conceptual identity of the paradoxical nature between post-structuralism (...) (and deconstructionism, which is homogeneous and identical thereto in a number of aspects), on the one hand, and constructionism with its specific process of language dismantling – social/ideological languages, social group dialects, on the other hand, which naturally leads the authors to the analysis of the paradoxicality principles, defined by post-structuralism (five principles of paradoxicality of Gilles Deleuze – paradox of regress, paradox of sterile reiteration, paradox of neutrality, paradox of absurd, paradox of Levi-Strauss); poststructuralists’ paralogisms are examined through paradoxical denotation; the late Roland Barthes’ phenomenon of paradoxicality, becoming a plot-forming principle of narration, is analyzed. Poststructuralism is conceptualized in the article as the first decisive step of post-modernism; the affinity of post-structuralist and postmodernist commitment to parody, game and irony is stated; the theory of language games in post-modern interpretation is explored; one of those games – a game of carnival – is explored within the diachronic retrospective; the affinity of parody and carnival tradition of post-structuralism and post-modernism to the romantic irony of the XIXth century and its inconsistency with the popular culture of laugh is established. The genesis of poststructuralism and post-modernism is connected with the ideological restart of the Western society before the “very end” of the Resistance ideas and the disappointment of the left European intellectuals in the “great legends” and illusions of Marxism. The blurred concepts of relativism are connected with the mutual disproportion of different layers of historical experience. (shrink)

One textbook may introduce the real numbers in Cantor’s way, and another in Dedekind’s, and the mathematical community as a whole will be completely indifferent to the choice between the two. This sort of phenomenon was famously called to the attention of philosophers by Paul Benacerraf. It will be argued that structuralism in philosophy of mathematics is a mistake, a generalization of Benacerraf’s observation in the wrong direction, resulting from philosophers’ preoccupation with ontology.

Structuralism provides useful resources for advancing our understanding of the intertheoretic reduction relation and its place in the history of science. This paper begins by surveying these resources and assessing their metascientific significance. Nevertheless, important challenges remain. I close by arguing that the reductionism implicit in current scientific practice in a paradigmatic reductionistic scientific field –“molecular and cellular cognition”– is better understood on an “intervene and track” model rather than as any kind of intertheoretic relation. I illustrate my alternative (...) model by describing briefly a recent reductionistic result from the field. It appears doubtful that any structuralist resources will illuminate this newly-recognized type of reduction-in-actual-scientific-practice. (shrink)

In spite of the ‘experimental turn’ now fashionable in the philosophy of science, the question of the structure and identity criteria of scientific theories continues to be a central issue for the philosophical analysis of empirical science. We need a precise metatheory of empirical theories to deal with this issue. Metatheoretical structuralism appears to offer the most adequate approach in this sense so far. First, some basic intuitions about what empirical theories are, and how they are structured, are laid (...) out. Then, the main notions used by metatheoretical structuralism to analyze theories are explained, and they are illustrated by applying them to an example of a simple physical theory. Finally, it is argued that the picture of the structure and identity of empirical theories coming out of structuralistic analysis adequately corresponds to the basic intuitions stated at the beginning. (shrink)

Øystein Linnebo and Richard Pettigrew have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They argue that their theory of abstract structures proves a consistent version of the structuralist thesis that positions in abstract structures only have structural properties. They do this by defining a subset of the properties of positions in structures, so-called fundamental properties, and argue that all fundamental properties of positions are structural. In this article, we argue that the structuralist thesis, (...) even when restricted to fundamental properties, does not follow from the theory of structures that Linnebo and Pettigrew have developed. To make their account work, we propose a formal framework in terms of Kripke models that makes structural abstraction precise. The formal framework allows us to articulate a revised definition of fundamental properties, understood as intensional properties. Based on this revised definition, we show that the restricted version of the structuralist thesis holds. 1Introduction 2The Structuralist Thesis 3LP-Structuralism 4Purity 5A Formal Framework for Structural Abstraction 6Fundamental Relations 7The Structuralist Thesis Vindicated 8Conclusion. (shrink)

The present paper aims at a synthesis of belief revision theory with the Sneed formalism known as the structuralist theory of science. This synthesis is brought about by a dynamisation of classical structuralism, with an abductive inference rule and base generated revisions in the style of Rott (2001). The formalism of prioritised default logic (PDL) serves as the medium of the synthesis. Why seek to integrate the Sneed formalism into belief revision theory? With the hybrid system of the present (...) investigation, a substantial simplification of the ranking information that is necessary to define revisions and contractions uniquely is achieved. This system is, furthermore, expressive enough to capture complex and non-trivial scientific examples. It is thus closely related to a novel research area within belief revision theory which addresses the dynamics of scientific knowledge. (shrink)

This paper explores the status of causation in structuralist metaphysics of physics. What role (if any) does causation play in understanding ‘structure’ in ontological structural realism? I address this question by examining, in a structuralist setting, arguments for and against the idea that fundamental physics deals, perhaps exclusively, with causal properties. I will argue (against Esfeld, Dorato and others) that a structuralist interpretation of fundamental physics should diverge from ‘causal structuralism’. Nevertheless, causation outside fundamental physics, and the basic motivation (...) for causal structuralism outside fundamental physics, can be captured with an appropriate conception of causation. (shrink)

The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the book considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical (...) possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives. (shrink)

A prominent version of mathematical structuralism holds that mathematical objects are at bottom nothing but "positions in structures," purely relational entities without any sort of nature independent of the structure to which they belong. Such an ontology is often presented as a response to Benacerraf's "multiple reductions" problem, or motivated on hermeneutic grounds, as a faithful representation of the discourse and practice of mathematics. In this paper I argue that there are serious difficulties with this kind of view: its (...) proponents rely on a distinction between "essential" and "nonessential" features of mathematical objects, and there's no good way to articulate this distinction which is compatible with basic structuralist commitments. But all is not lost. For I further argue that the insights motivating structuralism (or at least those worth preserving) can be preserved without formulating the view in ontologically committal terms. (shrink)

This essay is about how the notion of “structure” in ontic structuralism might be made precise. More specifically, my aim is to make precise the idea that the structure of the world is given by the relations inhering in the world, in such a way that the relations are ontologically prior to their relata. The central claim is the following: one can do so by giving due attention to the relationships that hold between those relations, by making use of (...) certain notions from algebraic logic. (shrink)

This paper explores the consequences of the two most prominent forms of contemporary structural realism for the notion of objecthood. Epistemic structuralists hold that we can know structural aspects of reality, but nothing about the natures of unobservable relata whose relations define structures. Ontic structuralists hold that we can know structural aspects of reality, and that there is nothing else to know—objects are useful heuristic posits, but are ultimately ontologically dispensable. I argue that structuralism does not succeed in ridding (...) a structuralist ontology of objects. (shrink)

This is the basis of the first part of the book.

Structuralism can be defined as an important concept of using “units” as elements of form and space-giving, where the whole form is made not only up of a “texture”, a certain flexible grid, or an algorithm of shape-giving, but it depends also on the relationships created and how people use it. The hypothesis of this study is that “Modular Construction” can also have an aesthetically pleasing outlook and that modular housing can definitely have increasing importance in the future. Modular (...) housing due to its cheap, and manufactural way of construction can be replicable in various locations. Structuralism and Modular Construction have been at the core of the Modernist movement. Although postmodernism marked the decline of modular construction adopting methods known for a more close sense of place, vernacular, and locality, which differs from the ubiquitous model of modernism, it is the universality of space and habitation seen since the times of Hippodamus Grid, Japanese Tattami systems, and rational universal space in housing known in Europe that make grid and modular design an excellent system in obtaining, rationality, functionality, flexibility, and energy efficiency, including quick construction and possibility for replication. In this regard, modular construction has a future, especially in times of crisis and economic instability. (shrink)