In semiclassical mechanics one finds explanations of quantum phenomena that appeal to classical structures. These explanations are prima facie problematic insofar as the classical structures they appeal to do not exist. Here I defend the view that fictional structures can be genuinely explanatory by introducing a model-based account of scientific explanation. Applying this framework to the semiclassical phenomenon of wavefunction scarring, I argue that not only can the fictional classical trajectories explain certain aspects of this quantum phenomenon, (...) but also that an explanation that does not make reference to these classical structures is, in a certain sense, deficient. (shrink)

The aim of this work is to revisit the proposal made by Dag Westerståhl a decade ago when he provided a modern reading of the traditional square of opposition and of related structures. We propose a formalization of this modern view and contrast it with the classical one. We discuss what may be a modern hexagon of opposition and a modern cube, and show their interest in particular for relating quantitative expressions.

We show how to encode, by classical structures, both the objects and the morphisms of the category of complete metric spaces and uniformly continuous maps. The result is a category of, what we call, cognate metric spaces and cognate maps. We show this category relativizes to all models of set theory. We extend this encoding to an encoding of complete metric structures by classical structures. This provide us with a general technique for translating results about infinitary logic on (...) classical structures to the setting of infinitary continuous logic on continuous structures. Our encoding will also allow us to talk about not only the relations between complete metric structures, but also the potential relations between complete metric structures, i.e. those which are satisfied in some larger model of set theory. For example we will show that given any two complete metric structures we can determine if they are potentially isomorphic by looking at any admissible set which contains them both. (shrink)

Department of Computer Science Philosophy Program, Research School of Social Sciences University of Skövde, S-54128, SWEDEN Australian National University, Canberra ACT 0200.

We present a novel approach to represent ecological systems using reaction networks, and show how a particular framework called chemical organization theory sheds new light on the longstanding complexity–stability debate. Namely, COT provides a novel conceptual landscape plenty of analytic tools to explore the interplay between structure and stability of ecological systems. Given a large set of species and their interactions, COT identifies, in a computationally feasible way, each and every sub-collection of species that is closed and self-maintaining. These (...) sub-collections, called organizations, correspond to the groups of species that can survive together in the long-term. Thus, the set of organizations contains all the stable regimes that can possibly happen in the dynamics of the ecological system. From here, we propose to conceive the notion of stability from the properties of the organizations, and thus apply the vast knowledge on the stability of reaction networks to the complexity–stability debate. As an example of the potential of COT to introduce new mathematical tools, we show that the set of organizations can be equipped with suitable joint and meet operators, and that for certain ecological systems the organizational structure is a non-boolean lattice, providing in this way an unexpected connection between logico-algebraic structures, popular in the foundations of quantum theory, and ecology. (shrink)

We present a novel approach to represent ecological systems using reaction networks, and show how a particular framework called chemical organization theory sheds new light on the longstanding complexity–stability debate. Namely, COT provides a novel conceptual landscape plenty of analytic tools to explore the interplay between structure and stability of ecological systems. Given a large set of species and their interactions, COT identifies, in a computationally feasible way, each and every sub-collection of species that is closed and self-maintaining. These (...) sub-collections, called organizations, correspond to the groups of species that can survive together in the long-term. Thus, the set of organizations contains all the stable regimes that can possibly happen in the dynamics of the ecological system. From here, we propose to conceive the notion of stability from the properties of the organizations, and thus apply the vast knowledge on the stability of reaction networks to the complexity–stability debate. As an example of the potential of COT to introduce new mathematical tools, we show that the set of organizations can be equipped with suitable joint and meet operators, and that for certain ecological systems the organizational structure is a non-boolean lattice, providing in this way an unexpected connection between logico-algebraic structures, popular in the foundations of quantum theory, and ecology. (shrink)

I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. These and (...) other considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning. (shrink)

The standard view is that the Lagrangian and Hamiltonian formulations of classical mechanics are theoretically equivalent. Jill North, however, argues that they are not. In particular, she argues that the state-space of Hamiltonian mechanics has less structure than the state-space of Lagrangian mechanics. I will isolate two arguments that North puts forward for this conclusion and argue that neither yet succeeds. 1 Introduction2 Hamiltonian State-space Has less Structure than Lagrangian State-space2.1 Lagrangian state-space is metrical2.2 Hamiltonian state-space is (...) symplectic2.3 Metric > symplectic3 Hamiltonian State-space Does Not Have Less Structure than Lagrangian State-space3.1 Lagrangian state-space has less than metric structure3.1.1 A potential worry3.1.2 General Lagrangians3.2 Hamiltonian state-space has more than symplectic structure3.2.1 A dual structure on the Hamiltonian state-space3.2.2 Simple Hamiltonians3.3 Comparing Lagrangian and Hamiltonian structures3.3.1 Counting mathematical structure3.3.2 Symplectic and metric structure are incomparable4 An Alternative Argument for LS4.1 The argument for P3*4.2 Symplectic manifold vs. tangent bundle structure4.3 Trying to patch up the argument for P3*5 Interpreting Mathematical Structure5.1 State-space realism5.2 Model isomorphism and theoretical equivalence6 Conclusion. (shrink)

The philosophy of science has lost its self-confidence, witness the lack of advanced textbooks in contrast to the abundance of elementary textbooks. Structures in Science is an advanced textbook that explicates, updates, accommodates, and integrates the best insights of logical-empiricism and its main critics. This `neo-classical approach' aims at providing heuristic patterns for research. The book introduces four ideal types of research programs and reanimates the distinction between observational laws and proper theories. It explicates various patterns of explanation by (...) subsumption and specification as well as structures in reductive and other types of interlevel research. Its analysis of theory evaluation leads to new characterizations of confirmation, empirical progress, and pseudoscience. Partial analogies between progress in nomological research and progress in explicative and design research emerge. Finally, special chapters are devoted to design research programs, computational philosophy of science, the structuralist approach to theories, and research ethics. (shrink)

I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students in philosophy; the presentation avoids mathematical formalism as much as possible.

One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...) the premises. The complementarity and interrelation of premise-conclusion arguments and premise-conclusion-mediation arguments resonate throughout the rest of the paper which articulates the conceptual structure found in logic from Aristotle to Tarski. This 1972 paper can be seen as anticipating Corcoran’s signature work: the more widely read 1989 paper, Argumentations and Logic, Argumentation 3, 17–43. MR91b:03006. The 1972 paper was translated into Portuguese. The 1989 paper was translated into Spanish, Portuguese, and Persian. (shrink)

This volume brings together a group of logic-minded philosophers and philosophically oriented logicians to address a diversity of topics on the structural analysis of non-classical logics. It mainly focuses on the construction of different types of models for various non-classical logics of current interest, including modal logics, epistemic logics, dynamic logics, and observational predicate logic. The book presents a wide range of applications of two well-known approaches in current research: structural modeling of certain philosophical issues in the framework (...) of non-classic logics, such as admissible models for modal logic, structural models for modal epistemology and for counterfactuals, and epistemological models for common knowledge and for public announcements; conceptual analysis of logical properties of, and formal semantics for, non-classical logics, such as sub-formula property, truthmaking, epistemic modality, behavioral strategies, speech acts and assertions. The structural analysis provided in this volume will appeal not only to graduate students and experts in non-classic logics, but also to readers from a wide range of disciplines, including computer science, cognitive science, linguistics, game theory and theory of action, to mention a few. (shrink)

The philosophy of science has lost its self-confidence. Structures in Science (2001) is an advanced textbook that explicates, updates and integrates the best insights of logical empiricism and its main critics. This "neo-classical approach" aims at providing heuristic patterns for research.The book introduces four ideal types of research programs (descriptive, explanatory, design and explicative) and reanimates the distinction between observational laws and proper theories without assuming a theory-free language. It explicates various patterns of explanation by subsumption and specification as (...) well as structures in reductive and other types of interlevel research. Its threefold analysis of theory evaluation leads to new characterizations of confirmation, empirical progress, and truth approximation. What emerges are partial analogies between progress in nomological research, presented in detail in From Instrumentalism to Constructive Realism (2000) and progress in explicative and design research. Finally, special chapters are devoted to design research programs, computational philosophy of science, the structuralist approach to theories, and research ethics.The present synopsis of Structures in Science highlights the main topics, the final emphasis being on design research and research ethics. (shrink)

We present a reconstruction of so-called classical, formal or Mendelian genetics using a notation which we believe is more legible than that of earlier accounts, and lends itself easily to computer implementation, for instance in PROLOG. By drawing from, and emending, earlier work of Balzer and Dawe (1986,1997), the present account presents the three most important lines of development of classical genetics: the so-called Mendel's laws, linkage genetics and gene mapping, in the form of a theory-net. This shows (...) that the set theoretic representation format used in the structuralist approach to the philosophy of science also applies to the domain of genetic theories. There construction is intended to lend more clarity to theme thodological, philosophical and didactical discussions of the foundations of genetics, and on the other hand to defend a formally, logically minded view of theories which seems to have become contested through the work of Feyerabend, Kuhn and Kitcher. (shrink)

The connection between quantum mechanics and classical statistical mechanics has motivated in the past the representation of the Schrödinger quantum-wave equation in terms of “projections” onto the quantum configuration space of suitable phase-space asymptotic kinetic models. This feature has suggested the search of a possible exact super-dimensional classical dynamical system, denoted as Schrödinger CDS, which uniquely determines the time-evolution of the underlying quantum state describing a set of N like and mutually interacting quantum particles. In this paper the (...) realization of the same CDS in terms of a coupled set of Hamiltonian systems is established. These are respectively associated with a quantum-hydrodynamic CDS advancing in time the quantum fluid velocity and a further one the RD-CDS, describing the relative dynamics with respect to the quantum fluid. (shrink)

The present article aims to expose some aspects of the specific features of classical Chinese analogisms. First, it exposes the supposition that this type of analogism did not focus exclusively on forms without considering their content, that is, that it was linguistically and semantically determined. Second, it also aims to show that classical Chinese analogies are based on structural relations between the objects in question, which constitute the similarity of two types of things that share certain attributes. This (...) article additionally sheds light on the question of how and why the structure underlying these relations represents a semantic and axiological referential framework that functions as the... (shrink)

This is an essay review of Jill North’s book Physics, Structure, and Reality. It focuses on two of the main topics of the book. The first is North’s idea that we can use coordinates as a window into the structure that a theory posits; the second is North’s argument for the inequivalence of Lagrangian and Newtonian mechanics.

It is exhibited that mature scientific economical theory is a set of propositions that describe the relationship between theoretical objects of two types - basic objects and derivative ones. The set of basic objects makes up the aggregate of initial idealizations (the Fundamental Theoretical Scheme or FTS) with no direct reference to experimental data. The derivative theoretical objects are formed from the basic ones according to certain rules. The sets of derivative objects form partial theoretical schemes or PTS. Any mature (...) economics scientific theory grows due to transitions, in order to describe each new experimental situation, from FTS to PTS. Each PTS construction from the FTS represents a problem that cannot be reduced to a strict algorithm. (shrink)

Gentzen’s classical sequent calculus has explicit structural rules for contraction and weakening. They can be absorbed by replacing the axiom P,¬P by Γ,P,¬P for any context Γ, and replacing the original disjunction rule with Γ,A,B implies Γ,AB.This paper presents a classical sequent calculus which is also free of contraction and weakening, but more symmetrically: both contraction and weakening are absorbed into conjunction, leaving the axiom rule intact. It uses a blended conjunction rule, combining the standard context-sharing and context-splitting (...) rules: Γ,Δ,A and Γ,Σ,B implies Γ,Δ,Σ,AB. We refer to this system as minimal sequent calculus.We prove a minimality theorem for the propositional fragment : any propositional sequent calculus S is complete if and only if S contains. Thus one can view as a minimal complete core of Gentzen’s. (shrink)

Thomas S. Kuhn’s The Structure of Scientific Revolutions was a watershed event when it was published in 1962, upending the previous understanding of science as a slow, logical accumulation of facts and introducing, with the concept of the “paradigm shift,” social and psychological considerations into the heart of the scientific process. More than fifty years after its publication, Kuhn’s work continues to influence thinkers in a wide range of fields, including scientists, historians, and sociologists. It is clear that The (...) Structure of Scientific Revolutions itself marks no less of a paradigm shift than those it describes. In Kuhn’s “Structure of Scientific Revolutions” at Fifty, leading social scientists and philosophers explore the origins of Kuhn’s masterwork and its legacy fifty years on. These essays exhume important historical context for Kuhn’s work, critically analyzing its foundations in twentieth-century science, politics, and Kuhn’s own intellectual biography: his experiences as a physics graduate student, his close relationship with psychologists before and after the publication of Structure, and the Cold War framework of terms such as “world view” and “paradigm.”. (shrink)

After almost 30 years of publications, Journal of Business Ethics (JBE) has achieved the position of main marketplace for business ethics discussion and knowledge generation. Given the large amount of knowledge produced, an assessment of the state of the art could benefit both the constructive development of the discipline and the further growth of the journal itself. As the evolution of a discipline is set to be reflected in the evolution of its leading journal, we attempt to characterize changes in (...) the intellectual structure of business ethics through a bibliometric analysis of articles published in JBE . Specifically, we conduct a knowledge-stock analysis to assess the evolution, major trends, and current state of the journal. Additionally, we use citation and co-citation analysis to provide an accurate description of the content and the advancement of research in business ethics. Through the results of our analysis, we are able to: (1) pinpoint the characteristics of the growing stock of knowledge published by JBE over the years; (2) identify the most influential works on business ethics research; and (3) detect the formation and evolution of schools of thought in business ethics. (shrink)

In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.

At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would generate a non-distributive lattice of propositions, and from quantum superpositions, which would entail new rules for quantum disjunctions. While the quantum logic program is not as popular as it once was, a crucial question remains unsettled: what is the relationship between the logical (...) structures of classical and quantum mechanics? In this essay we answer this question by showing that the original arguments promoting quantum logic contain serious flaws, and that quantum theory does satisfy the classical distributivity law once the full meaning of quantum propositions is properly taken into account. Moreover, we show that quantum mechanics can generate a distributive lattice of propositions, which, unlike the one of quantum logic, includes statements about expectation values which are of undoubtable physical interest. Lastly, we show that the lattice of statistical propositions in classical mechanics follows the same structure, yielding an analogue non-commutative sublattice of classical propositions. This fact entails that the purported difference between classical and quantum logic stems from a misconstructed parallel between the two theories. (shrink)

In the history of Newtonian Mechanics physicists and astronomers did not rely on so-called inertial frames, indeed they were not able to identify such frames. So the usual neo-Newtonian formalism of Newtonian Mechanics contains some superfluous components. In the present paper I will formulate a formal system for classical particle mechanics in Leibnizian space-time, where a relation, a counterpart of the second law of motion, between force on bodies and derivative of their momentum will be defined relative to every, (...) inertial or not, reference frame. And I will present a view that in the research process under Newtonian mechanics the accumulation of those models of the relation that satisfied some realistic conditions determined an additional structure of non-rotating frames to Leibnizian space-time. (shrink)

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell’s equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum (...) into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics. (shrink)

I examine a property of theories called "background-independence" that Einsteinian gravitation is thought to exemplify. This concept has figured in the work of Rovelli (2001, 2004), Smolin (2006), Giulini (2007), and Belot (2011), among others. I propose and evaluate a few candidates for background-independence, and I show that there is something chimaerical about the concept. I argue, however, that there is a proposal that clarifies the feature of Einsteinian gravitation that motivates the concept.

The political legacy of classical German philosophy can contribute in a crucial way to the most recent developments of contemporary political thought, thereby also making sense of the contradictions underlying the social practices and institutional values of our societies. What justifies this perspective is, in the first place, the complexity of contemporaneity, which holds within itself a doubleness that can be understood in the light of the conceptual tools of classical German philosophy. On the one hand, contemporary societies (...) seem to be facing relentless crises in the modern idea of democracy, the political subject of the nation-state, and capitalist economic structures. On the other hand, there is an ever-increasing demand for rights and new forms of recognition, not to mention the emergence of grassroots movements that strive for greater political participation and generate new collective subjectivities. By radically questioning traditional philosophical categories, Kant, Fichte and Hegel provide a new and insightful understanding of the crucial challenges of modernity. They outline a conception of practical rationality and its multiple manifestations that is irreplaceable for philosophically understanding our contemporary world. (shrink)

In this paper, I use the cases of intuitionistic arithmetic with Church’s thesis, intuitionistic analysis, and smooth infinitesimal analysis to argue for a sort of pluralism or relativism about logic. The thesis is that logic is relative to a structure. There are classical structures, intuitionistic structures, and (possibly) paraconsistent structures. Each such structure is a legitimate branch of mathematics, and there does not seem to be an interesting logic that is common to all of them. One main (...) theme of my ante rem structuralism is that any coherent axiomatization describes a structure, or a class of structures. If one weakens the logic, then more axiomatizations become coherent. (shrink)

This book undertakes a critical analysis of the moral, legal, political, and social thought of ancient India - as reflected in the Vedas, Upanishads, Puranas, Dharmasastras, Buddhist, Jaina and Agamic literature - from a tradition-rooted yet liberal/modern point of view.

The symplectic structures (brackets, Hamilton's equations, and Lagrange's equations) for the Dirac electron and its classical model have exactly the same form. We give explicitly the Poisson brackets in the dynamical variables (x μ,p μ,v μ,S μv). The only difference is in the normalization of the Dirac velocities γμγμ=4 which has significant consequences.

We give a precise and modern mathematical characterization of the Newtonian spacetime structure (ℕ). Our formulation clarifies the concepts of absolute space, Newton's relative spaces, and absolute time. The concept of reference frames (which are “timelike” vector fields on ℕ) plays a fundamental role in our approach, and the classification of all possible reference frames on ℕ is investigated in detail. We succeed in identifying a Lorentzian structure on ℕ and we study the classical electrodynamics of Maxwell (...) and Lorentz relative to this structure, obtaining the important result that there exists only one intrinsic generalization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed intrinsic generalizations of the Lorentz force law appearing in the literature. We present also a formulation of Newtonian gravitational theory as a curve spacetime theory and discuss its meaning. (shrink)