Husserl's mathematical philosophy of science can be considered an anticipation of the contemporary postpositivistic semantic approach, which regards mathematics and not logic as the appropriate tool for the exact philosophical reconstruction of scientific theories. According to Husserl, an essential part of a theory's reconstruction is the mathematical description of its domain, that is, the world (or the part of the world) the theory intends to talk about. Contrary to the traditional micrological approach favored by the members of the Vienna Circle, (...) Husserl, inspired by modern geometry and set theory, aims at a macrological analysis of scientific theories that takes into account the global structures of theories as structured wholes. This is set in the complementary theories of manifolds and theory forms considered by Husserl himself as the culmination of his formal theory of science. (shrink)

Approaches to the interpretation of physical theories provide accounts of how physical meaning accrues to the mathematical structure of a theory. According to many standard approaches to interpretation, meaning relations are captured by maps from the mathematical structure of the theory to statements expressing its empirical content. In this article I argue that while such accounts adequately address meaning relations when exact models are available or perturbation theory converges, they do not fare as well for models that give rise to (...) divergent perturbative expansions. Since truncations of divergent perturbative expansions often play a critical role in establishing the empirical adequacy of a theory, this is a serious deficiency. I show how to augment state-space semantics, a view developed by Beth and van Fraassen, to capture perturbatively evaluated observables even in cases where perturbation theory is divergent. This new semantics establishes a sense in which the calculations that underwrite the empirical adequacy of a theory are both meaningful and true, but requires departure from the assumption that physical meaning is captured entirely by the exact models of a theory. (shrink)

In place of earlier instrumentalist and phenomenalist interpretations of science both Quine and Sellars have developed highly influential realist positions centering around the doctrine that accepting a theory as explanatory and irreducible rationally entails accepting the entities posited by the theory. A growing reaction against this realism is partially based on perceived inadequacies in the doctrines of Quine and Sellars, but even more on reconstructions of scientific explanations which do not involve such ontic commitments. Three types of anti-realistic positions are (...) considered and criticized. Hesse's neo-Duhemian position couples a statistical theory of inference to a downgrading of purely theoretical statements. Sneed uses the method of axiomatrization through set-theoretic predicates to supply a reconstruction of Kuhn's account of scientific development. Here Ramsey-reduction sentences serve to eliminate purely theoretical terms. The longest section deals with van Fraassen's semantic model based on a state-space representation of scientific theories and the use of this model in interpreting quantum mechanics. It is argued that the model is valuable, but that the anti-realist interpretation accorded it is not justified and entails serious inconsistencies. (shrink)

I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are important according to the Received View. Finally, I argue against the claim that the Received View is intended to (...) make the concept of a theory more precise. Rather, it is meant as a generalizable framework for explicating specific theories. (shrink)

I provide an explicit formulation of empirical adequacy, the central concept of constructive empiricism, and point out a number of problems. Based on one of the inspirations for empirical adequacy, I generalize the notion of a theory to avoid implausible presumptions about the relation of theoretical concepts and observations, and generalize empirical adequacy with the help of approximation sets to allow for lack of knowledge, approximations, and successive gain of knowledge and precision. As a test case, I provide an application (...) of these generalizations to a simple interference phenomenon. (shrink)

I show that the central notion of Constructive Empiricism, empirical adequacy, can be expressed syntactically and specifically in the Received View of the logical empiricists. The formalization shows that the Received View is superior to Constructive Empiricism in the treatment of theories involving constants or functions from observable to unobservable objects. It also suggests a formalization of ‘full empirical informativeness’ in Constructive Empiricism.

Different conceptions of scientific theories, such as the state spaces approach of Bas van Fraassen, the phase spaces approach of Frederick Suppe, the set-theoretical approach of Patrick Suppes, and the structuralist view of Joseph Sneed et al. are usually put together into one big family. In addition, the definite article is normally used, and thus we speak of the semantic conception of theories and of its different approaches . However, in The Semantic Conception of Theories and Scientific Realism , starting (...) from certain remarks already made in “Theory Structure” , Current Research in Philosophy of Science, East Lansing: Philosophy of Science Association, 1979, pp. 317–338), Frederick Suppe excludes the structuralist view as well as other “European” versions from the semantic conception of theories. In this paper I will critically examine the reasons put forward by Suppe for this decision and, later, I will provide a general characterization of the semantic family and of the structuralist view of theories in such a way as to justify the inclusion of the structuralist view as a member of this family. (shrink)

When natural selection theory was presented, much active philosophical debate, in which Darwin himself participated, centered on its hypothetical nature, its explanatory power, and Darwin's methodology. Upon first examination, Darwin's support of his theory seems to consist of a set of claims pertaining to various aspects of explanatory success. I analyze the support of his method and theory given in the Origin of Species and private correspondence, and conclude that an interpretation focusing on the explanatory strengths of natural selection theory (...) accurately reflects neither Darwin's own self-consciously held views, nor the nature of his support. Darwin's methodological and philosophical arguments were at once consistently empiricist and more sophisticated than such interpretations credit to him. (shrink)

The conflation of two fundamentally distinct issues has generated serious confusion in the philosophical and biological literature concerning the units of selection. The questions of how a unit of selection is defined, theoretically, is rarely distinguished from the question of how to determine the empirical accuracy of claims--either specific or general--concerning which unit(s) are undergoing selection processes. In this paper, I begin by refining a definition of the unit of selection, first presented by William Wimsatt, that is grounded in the (...) structure of natural selection models. I then explore the implications of this definition for empirical evaluation of group selection models. I examine an objection to Wimsatt’s definition raised by Elliott Sober, and I conclude by indicating how the proposed refined definition can clarify which sorts of empirical evidence could be brought to bear on group selection controversies. (shrink)

In this paper I distinguish various ways in which empirical claims about evolutionary and ecological models can be supported by data. I describe three basic factors bearing on confirmation of empirical claims: fit of the model to data; independent testing of various aspects of the model, and variety of evident. A brief description of the kinds of confirmation is followed by examples of each kind, drawn from a range of evolutionary and ecological theories. I conclude that the greater complexity and (...) precision of my approach, as compared to, for instance, a Popperian approach, can facilitate detailed analysis and comparison of empirical claims. (shrink)

A precise formulation of the structure of modern evolutionary theory has proved elusive. In this paper, I introduce and develop a formal approach to the structure of population genetics, evolutionary theory's most developed sub-theory. Under the semantic approach, used as a framework in this paper, presenting a theory consists in presenting a related family of models. I offer general guidelines and examples for the classification of population genetics models; the defining features of the models are taken to be their state (...) spaces, parameters, and laws. The suggestions regarding the various aspects of the characterization of population genetics models provide an outline for further detailed research. (shrink)

The paper, as Part I of a two-part series, argues for a hybrid formulation of the semantic view of scientific theories. For stage-setting, it first reviews the elements of the model theory in mathematical logic (on whose foundation the semantic view rests), the syntactic and the semantic view, and the different notions of models used in the practice of science. The paper then argues for an integration of the notions into the semantic view, and thereby offers a hybrid semantic view, (...) which at once secures the view's logical foundations and enhances its applicability. The dilemma of either losing touch with the practice of science or yielding up the benefits of the model theory is thus avoided. (shrink)

This paper utilizes Scott domains (continuous lattices) to provide a mathematical model for the use of idealized and approximately true data in the testing of scientific theories. Key episodes from the history of science can be understood in terms of this model as attempts to demonstrate that theories are monotonic, that is, yield better predictions when fed better or more realistic data. However, as we show, monotonicity and truth of theories are independent notions. A formal description is given of the (...) pragmatic virtues of theories which are monotonic. We also introduce the stronger concept of continuity and show how it relates to the finite nature of scientific computations. Finally, we show that the space of theories also has the structure of a Scott domain. This result provides an analysis of how one theory can be said to approximate another. (shrink)

It’s uncontroversial that notions of idealization and approximation are central to understanding computer simulations and their rationale. So, for example, one common form of computer simulation is to abandon a realistic approach that is computationally non-tractable for a more idealized but computationally tractable approach. Many simulations of systems of interacting members can be understood this way. In such simulations, realistic descriptions of individual members are replaced with less realistic descriptions which have the virtue of making interactions computationally tractable. Such simulations (...) can be supplemented with empirically determined correction factors which render the output produced by means of the idealizations more in accord, one hopes, with what the more realistic approach would have produced had it been computationally tractable. Another way to utilize computers is to replace an idealized but analytically tractable account of some phenomenon with a less idealized account which has no closed form or analytical solutions but where the computer can be used generate approximations to the desired solutions. (shrink)

Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to be so used, (...) the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models. (shrink)

In the present paper Cohen's and Lee's theory of social conformity and Festinger's theory of cognitive dissonance are first reconstructed according to a revised form of the so-called “structuralist theory-conception” developed by Sneed and Stegmüller with their collaborators. Then the two theories are conceptually correlated in the sense of a technical notion of conceptual correlation which can be shown to be an essential generalization of the theory-relations handled by the structuralist. It will turn out that there is no unique way (...) to connect these theories with each other. However, it is shown that two ontologically and conceptually different theories can be correlated. This in turn gives in principle an opportunity to compare critically these two theories given that the constructed conceptual correlation is sufficiently sound and that the theories are empirically testable to a sufficient extent. (shrink)

Multiply realizable properties are those whose realizers are physically diverse. It is often argued that theories which contain them are ipso facto irreducible. These arguments assume that physical explanations are restricted to the most specific descriptions possible of physical entities. This assumption is descriptively false, and philosophically unmotivated. I argue that it is a holdover from the late positivist axiomatic view of theories. A semantic view of theories, by contrast, correctly allows scientific explanations to be couched in the most perspicuous, (...) powerful language available. On a semantic view, traditional notions of multiple realizability are thus very hard to motivate. At best, one must abandon either the idea that multiple realizability is an interesting scientific notion, or else admit that multiply realizable properties do not automatically block scientific reductions. (shrink)

Virtually all philosophers of science have construed fundamental theories as descriptions of entities, properties, and/or structures. Call this the “descriptive-ontological” view. I argue that this view is incorrect, at least insofar as physical theories are concerned. I propose a novel construal of theories that I call the “prescriptive-dynamical” view. The central tenet of this view, roughly put, is that the _essential_ content of fundamental physical theories is a _prescription for interfacing with natural systems and translating local data into compact theoretical (...) language_. The descriptive-ontological aspects of theories, if any, are taken as _inessential_ content on this view: they do not contribute to the predictive success of the theory. Rather than describing _what is there_, the essence of a physical theory is to tell us _what to do_ when interfacing with a physical system. (shrink)

This paper explores varieties of scientific structuralism. Central to our investigation is the notion of `shared structure'. We begin with a description of mathematical structuralism and use this to point out analogies and disanalogies with scientific structuralism. Our particular focus is the semantic structuralist's attempt to use the notion of shared structure to account for the theory-world connection, this use being crucially important to both the contemporary structural empiricist and realist. We show why minimal scientific structuralism is, at the very (...) least, a powerful methodological standpoint. Our investigation also makes explicit what more must be added to this minimal structuralist position in order to address the theory-world connection, namely, an account of representation. (shrink)

A logically complete interpretation of quantum mechanics is given in terms of a theory of quantum processes.

In the epistemological tradition, there are two main interpretations of the semantic relation that an empirical theory may bear to the real world. According to realism, the theory-world relationship should be conceived as truth; according to instrumentalism, instead, it should be limited to empirical adequacy. Then, depending on how empirical theories are conceived, either syntactically as a class of sentences, or semantically as a class of models, the concepts of truth and empirical adequacy assume different and specific forms. In this (...) paper, we review two main conceptions of truth (one sentence-based and one model-based) and two of empirical adequacy (one sentence-based and one model-based), we point out their respective difficulties, and we give a first formulation of a new general view of the theory-world relationship, which we call Methodological Constructive Realism (MCR). We then show how the content of MCR can be further specified and expressed in a definite and precise form. The bulk of the paper shows in detail how it is possible to accomplish this goal for the special case of deterministic dynamical phenomena and their correlated deterministic models. This special version of MCR is formulated as an axiomatic extension of set theory, whose specific axioms constitute a formal ontology that provides an adequate framework for analyzing the two semantic relations of truth and empirical correctness, as well as their connections. (shrink)

Unter dem Begriff der „Verwissenschaftlichung der Methodologie der Wissenschaft“ verstehen wir den Einfluß wissenschaftlicher Erkenntnis auf die eine oder andere Art und Weise auf die Methodologie der Wissenschaft, insbesondere den Gebrauch von wissenschaftlichen Ideen und Methoden für die Formulierung und Lösung von methodologischen Problemen der Wissenschaft und Problemen der Methodologie selbst. Es werden vier Haupttendenzen im Prozeß der Verwissenschaftlichung der Methodologie vorgestellt: (a) der Übergang vom „statement view“ zum mathematischen Holismus; (b) die Verwissenschaftlichung auf system-theoretischer Basis; (c) der Einzug soziologischer (...) Methoden in die methodologische Analyse der Wissenschaft und (d) die methodologischen Anwendungen von Forschungsresultaten im Bereich der Künstlichen Intelligenz. Darüberhinaus werden einige besondere Formen der Implementierung wissenschaftlicher Konstruktionen in der Methodologie ins Auge gefaßt. (shrink)

Even those generally skeptical of propensity interpretations of probability must now grant the following two points. First, the above single-case propensity interpretation meets recognized formal conditions for being a genuine interpretation of probability. Second, this interpretation is not logically reducible to a hypothetical relative frequency interpretation, nor is it only vacuously different from such an interpretation.The main objection to this propensity interpretation must be not that it is too vague or vacuous, but that it is metaphysically too extravagant. It asserts (...) not only that there are physical possibilities in nature, but further that nature itself contains innate tendencies toward these possibilities, tendencies which have the logical structure of probabilities. Thus the basic dispute between advocates of an actualist relative frequency interpretation and a single-case propensity interpretation is not a matter of epistemology, but metaphysics. The frequency theorist wishes to maintain that claims about physical probabilities are nothing more than claims about relative frequencies that will occur in the actual history of the world, be it infinite or no. It is a substantial, though hardly conclusive, argument for the propensity view that the mathematical structures commonly employed in studies of stochastic processes and statistical inference are richer than can be accommodated by a relative frequency interpretation. Whether it is possible to bridge this gap without going beyond an actualist metaphysics remains to be seen.38. (shrink)

The semantic, or model-theoretic, approach to theories has recently come under criticism on two fronts: (i) it is claimed that it cannot account for the wide diversity of models employed in scientific practice—a claim which has led some to propose a “deflationary” account of models; (ii) it is further contended that the sense of “model” used by the approach differs from that given in model theory. Our aim in the present work is to articulate a possible response to these claims, (...) drawing on recent developments within the semantic approach itself. Thus, the first is answered by utilizing the notion of a “partial structure”, first introduced in this context by da Costa and French in 1990. The second claim is undermined by consideration of van Fraassen's understanding of “model” which corresponds well with that evinced by modem mathematicians. This latter discussion, in particular, has an impact on the continuing debate regarding the relative merits of the semantic and syntactic views and the developments presented here can be taken to provide further support to the former. (shrink)

Michael Weisberg’s account of scientific models concentrates on the ways in which models are similar to their targets. He intends not merely to explain what similarity consists in, but also to capture similarity judgments made by scientists. In order to scrutinize whether his account fulfills this goal, I outline one common way in which scientists judge whether a model is similar enough to its target, namely maximum likelihood estimation method. Then I consider whether Weisberg’s account could capture the judgments involved (...) in this practice. I argue that his account fails for three reasons. First, his account is simply too abstract to capture what is going on in MLE. Second, it implies an atomistic conception of similarity, while MLE operates in a holistic manner. Third, Weisberg’s atomistic conception of similarity can be traced back to a problematic set-theoretic approach to the structure of models. Finally, I tentatively suggest how these problems might be solved by a holistic approach in which models and targets are compared in a non-set-theoretic fashion. (shrink)

This essay develops an inferential account of model explanation, based on Mauricio Suárez’s inferential conception of scientific representation and Alisa Bokulich’s counterfactual account of model explanation. It is suggested that the fact that a scientific model can explain is essentially linked to how a modeler uses an established model to make various inferences about the target system on the basis of results derived from the model. The inference practice is understood as a two-step activity, with the first step involving making (...) counterfactual statements about the model itself and the second step involving making hypothetical statements transferring over claims derived from the model onto the target. To illustrate how this two-step activity proceeds, an agent-based simulation model is discussed. (shrink)

Paul Thompson, John Beatty, and Elisabeth Lloyd argue that attempts to resolve certain conceptual issues within evolutionary biology have failed because of a general adherence to the received view of scientific theories. They maintain that such issues can be clarified and resolved when one adopts a semantic approach to theories. In this paper, I argue that such conceptual issues are just as problematic on a semantic approach. Such issues arise from the complexity involved in providing formal accounts of theoretical laws (...) and scientific explanations. That complexity is due to empirical and pragmatic considerations, not one's adherence to a particular formal approach to theories. This analysis raises a broader question. How can any formal account properly represent the complex nature of empirical phenomena? (shrink)

This paper examines E. W. Beth's work in the philosophy of physics, both from a historical and a systematic point of view. Beth saw the philosophy of physics first of all as an opportunity to illustrate and promulgate a new and modern general approach to the philosophy of nature and to philosophy tout court: an approach characterized negatively by its rejection of all traditional metaphysics and positively by its firm orientation towards science. Beth was successful in defending this new ideology, (...) and became its leading Dutch representative in the first two decades after the second world war. Beth also contributed importantly to the method of the philosophy of physics in a narrower sense, by proposing and promoting the semantic approach in the formal analysis of physical theories. Finally, he worked on several specific foundational questions; but he was probably too much of a logician to leave his mark in this area. (shrink)

This thesis considers the following problem: What methods should the epistemology of science use to gain insight into the structure and behaviour of scientific knowledge and method in actual scientific practice? After arguing that the elucidation of epistemological and methodological phenomena in science requires a method that is rooted in formal methods, I consider two alternative methods for epistemology of science. One approach is the classical approaches of the syntactic and semantic views of theories. I show that typical approaches of (...) this sort are inadequate and inaccurate in their representation of scientific knowledge by showing how they fail to account for and misrepresent important epistemological structure and behaviour in science. The other method for epistemology of science I consider is modeled on the methods used to construct valid models of natural phenomena in applied mathematics. This new epistemological method is itself a modeling method that is developed through the detailed consideration of two main examples of theory application in science: double pendulum systems and the modeling of near-Earth objects to compute probability of future Earth impact. I show that not only does this new method accurately represent actual methods used to apply theories in applied mathematics, it also reveals interesting structural and behavioural patterns in the application process and gives insight into what underlies the stability of methods of application. I therefore conclude that for epistemology of science to develop fully as a scientific discipline it must use methods from applied mathematics, not only methods from pure mathematics and metamathematics as traditional formal epistemology of science has done. (shrink)

This dissertation investigates the origin, intellectual development and use of a semantic variant of the idea of logical space found implicitly in Kant and explicitly in early Wittgenstein and van Fraassen. It elucidates the idea of logical space as the idea of images or pictures representative of reality organized into a logico-mathematical structure circumscribing a form of all possible worlds. Its main claim is that application of these images or pictures to reality is through a certain conception of self. The (...) first chapter presents a novel interpretation of Kant’s semantic theory of schemata in the Critique of Pure Reason, showing that a structure of the imagination induced by the transcendental self informs an implicit idea of logical space. The second chapter offers an intellectual history of the idea through developments in the organization of images introduced by Helmholtz and Hertz. The third chapter reveals early Wittgenstein’s idea of logical space to be his notion of the self, demonstrating how this serves to unify propositions of the Tractatus Logico-Philosophicus concerning solipsism, realism, ethics, aesthetics and mysticism with those pertaining to the picture theory of meaning. The fourth chapter provides a historical overview of the development of van Fraassen’s empiricism in relation to his adaptation of logical space, and evaluates his recent proposal in Scientific Representation: Paradoxes of Perspective that the problem of coordination in the semantic view of theories is dissolved through self-location in logical space. After identifying a number of problems this proposal creates for his empiricism, a brief suggestion is made about how van Fraassen might improve upon his conception of logical space, and how an empiricist view of scientific representation might be understood as a result. (shrink)

⦿ In my dissertation I introduce, motivate and take the first steps in the implementation of, the project of naturalising modal metaphysics: the transformation of the field into a chapter of the philosophy of science rather than speculative, autonomous metaphysics. -/- ⦿ In the introduction, I explain the concept of naturalisation that I apply throughout the dissertation, which I argue to be an improvement on Ladyman and Ross' proposal for naturalised metaphysics. I also object to Williamson's proposal that modal metaphysics (...) --- or some view in the area --- is already a quasi-scientific discipline. -/- ⦿ Recently, some philosophers have argued that the notion of metaphysical modality is as ill defined as to be of little theoretical utility. In the second chapter I intend to contribute to such skepticism. First, I observe that each of the proposed marks of the concept, except for factivity, is highly controversial; thus, its logical structure is deeply obscure. With the failure of the "first principles" approach, I examine the paradigmatic intended applications of the concept, and argue that each makes it a device for a very specific and controversial project: a device, therefore, for which a naturalist will find no use for. I conclude that there is no well-defined or theoretically useful notion of objective necessity other than logical or physical necessity, and I suggest that naturalising modal metaphysics can provide more stable methodological foundations. -/- ⦿ In the third chapter I answer a possible objection against the in-principle viability of the project: that the concept of metaphysical modality cannot be understood through the philosophical analysis of any scientific theory, since metaphysical necessity "transcends'' natural necessity, and science only deals with the latter. I argue that the most important arguments for this transcendence thesis fail or face problems that, as of today, remain unsolved. -/- ⦿ Call the idea that science doesn't need modality, "demodalism''. Demodalism is a first step in a naturalistic argument for modal antirealism. In the fourth chapter I examine six versions of demodalism to explain why a family of formalisms, that I call "spaces of possibility'', are (i) used in a quasi-ubiquitous way in mathematised sciences (I provide examples from theoretical computer science to microeconomics), (ii) scientifically interpreted in modal terms, and (iii) used for at least six important tasks: (1) defining laws and theories; (2) defining important concepts from different sciences (I give several examples); (3) making essential classifications; (4) providing different types of explanations; (5) providing the connection between theory and statistics, and (6) understanding the transition between a theory and its successor (as is the case with quantisation). -/- ⦿ In fifth chapter I propose and defend a naturalised modal ontology. This is a realism about modal structure: my realism about constraints. The modal structure of a system are the relationships between its possible states and between its possible states and those of other systems. It is given by the plurality of restrictions to which said system is subject. A constraint is a factor that explains the impossibility of a class of states; I explain this concept further. First, I defend my point of view by rejecting some of its main rivals: constructive empiricism, Humean conventionalism, and wave function realism, as they fail to make sense of quantum chaos. This is because the field requires the notion of objective modal structure, and the mentioned views have trouble explaining the modal facts of quantum dynamics. Then, I argue that constraint realism supersedes these views in the context of Bohm's standard theory and mechanics, and underpins the study of quantum chaos. Finally, I consider and reject two possible problems for my point of view. -/- ⦿ A central concern of modal metaphysicians has been to understand the logical system that best characterises necessity. In the sixth chapter I intend to recover the logical project applied to my naturalistic modal metaphysics. Scientists and philosophers of science accept different degrees of physical necessity, ranging from purely mathematically necessary facts that restrict physical behaviour, to kinetic principles, to particular dynamical constraints. I argue that this motivates a multimodal approach to modal logic, and that the time dependence of dynamics motivates a logic of historical necessity. I propose multimodal propositional (classical) logics for Bohmian mechanics and the Everettian theory of many divergent worlds, and I close with a criticism of Williamson's approach to the logic of state spaces of dynamic systems. (shrink)

The philosophical debate about quantum logic between the late 1960s and the early 1980s was generated mainly by Putnam's claims that quantum mechanics empirically motivates introducing a new form of logic, that such an empirically founded quantum logic is the `true' logic, and that adopting quantum logic would resolve all the paradoxes of quantum mechanics. Most of that debate focussed on the latter claim, reaching the conclusion that it was mistaken. This chapter will attempt to clarify the possible misunderstandings surrounding (...) the more radical claims about the revision of logic, assessing them in particular both in the context of more general quantum-like theories (in the framework of von Neumann algebras), and against the background of the current state of play in the philosophy and interpretation of quantum mechanics. Characteristically, the conclusions that might be drawn depend crucially on which of the currently proposed solutions to the measurement problem is adopted. (shrink)

El presente trabajo pretende explicitar que los operadores modales, como construcciones lógicas, insertos en las interpretaciones modales (MI) de la mecánica cuántica son usados de manera informal sin una semántica modal adecuada. Primero se estudiarán en detalle los motivos por los que ninguna lógica cuántica puede ofrecer una base apropiada para formalizar estos operadores en contextos mecánico-cuánticos. A continuación, se presentará el enfoque de las historias cuánticas como una nueva lógica cuántica (NQL) intrínsecamente booleana como posible herramienta para formalizar operadores (...) modales en el contexto de las MI. Tras comentar brevemente las principales MI, se propondrá abordar un estudio de las modalidades presentes en ellas desde esta NQL prestando siempre especial atención al problema de la medida como hilo conductor. Finalmente, se pretende señalar cuáles han de ser los primeros pasos necesarios para ofrecer una exposición lógicamente consistente de las modalidades en contextos cuánticos relevantes con NQL como herramienta, así como señalar las ventajas que esta perspectiva podría llegar a ofrecer. (shrink)

Philosophy can shed light on mathematical modeling and the juxtaposition of modeling and empirical data. This paper explores three philosophical traditions of the structure of scientific theory—Syntactic, Semantic, and Pragmatic—to show that each illuminates mathematical modeling. The Pragmatic View identifies four critical functions of mathematical modeling: (1) unification of both models and data, (2) model fitting to data, (3) mechanism identification accounting for observation, and (4) prediction of future observations. Such facets are explored using a recent exchange between two groups (...) of mathematical modelers in plant biology. Scientific debate can arise from different modeling philosophies. (shrink)

The received view on the development of the correspondence rules in Carnap’s philosophy of science is that at first, Carnap assumed the explicit definability of all theoretical terms in observational terms and later weakened this assumption. In the end, he conjectured that all observational terms can be explicitly defined in in theoretical terms, but not vice versa. I argue that from the very beginning, Carnap implicitly held this last view, albeit at times in contradiction to his professed position. To establish (...) this point I argue that, first, Carnap’s ‘Über die Aufgabe der Physik’ is a contribution to the philosophy of science of logical empiricism, contrary to Thomas Mormann and in agreement with Herbert Feigl. Second, Michael Friedman misunderstands the ‘Aufgabe’ with his claim that it describes a method for arriving at explicit definitions for theoretical terms. Another received view on Carnap’s philosophy of science is that it assumed a formalization of physical theories that was too detached from actual physics and thus justly disavowed in favor of the semantic view as, for example, developed by van Fraassen. But the ‘Aufgabe’ and related works including the Aufbau show that from the very beginning to his last works, Carnap suggested formalizing physical theories as restrictions in mathematical spaces, as in the state-space conception of scientific theories favored by van Fraassen. (shrink)

The main thrust of the argument of this thesis is to show the possibility of articulating a method of construction or of synthesis--as against the most common method of analysis or division--which has always been (so we shall argue) a necessary component of scientific theorization. This method will be shown to be based on a fundamental synthetic logical relation of thought, that we shall call inversion--to be understood as a species of logical opposition, and as one of the basic monadic (...) logical operators. Thus the major objective of this thesis is to This thesis can be viewed as a response to Larry Laudan's challenge, which is based on the claim that ``the case has yet to be made that the rules governing the techniques whereby theories are invented (if any such rules there be) are the sorts of things that philosophers should claim any interest in or competence at.'' The challenge itself would be to show that the logic of discovery (if at all formulatable) performs the epistemological role of the justification of scientific theories. We propose to meet this challenge head on: a) by suggesting precisely how such a logic would be formulated; b) by demonstrating its epistemological relevance (in the context of justification) and c) by showing that a) and b) can be carried out without sacrificing the fallibilist view of scientific knowledge. OBJECTIVES: We have set three successive objectives: one general, one specific, and one sub-specific, each one related to the other in that very order. (A) The general objective is to indicate the clear possibility of renovating the traditional analytico-synthetic epistemology. By realizing this objective, we attempt to widen the scope of scientific reason or rationality, which for some time now has perniciously been dominated by pure analytic reason alone. In order to achieve this end we need to show specifically that there exists the possibility of articulating a synthetic (constructive) logic/reason, which has been considered by most mainstream thinkers either as not articulatable, or simply non-existent. (B) The second (specific) task is to respond to the challenge of Larry Laudan by demonstrating the possibility of an epistemologically significant generativism. In this context we will argue that this generativism, which is our suggested alternative, and the simplified structuralist and semantic view of scientific theories, mutually reinforce each other to form a single coherent foundation for the renovated analytico-synthetic methodological framework. (C) The third (sub-specific) objective, accordingly, is to show the possibility of articulating a synthetic logic that could guide us in understanding the process of theorization. This is realized by proposing the foundations for developing a logic of inversion, which represents the pattern of synthetic reason in the process of constructing scientific definitions. (shrink)

The aim of the present paper is to contribute to the discussion on the constitutive a priori in science by linking it with the discussion on scientific laws and theories, in such a way to show how the different senses of the notion of constitutive a priori are not incompatible to each other and that they can be precised in a unified, though differentiated, manner.

This dissertation consists of three parts. Part I is a defense of an artificial language methodology in philosophy and a historical and systematic defense of the logical empiricists' application of an artificial language methodology to scientific theories. These defenses provide a justification for the presumptions of a host of criteria of empirical significance, which I analyze, compare, and develop in part II. On the basis of this analysis, in part III I use a variety of criteria to evaluate the scientific (...) status of intelligent design, and further discuss confirmation, reduction, and concept formation. (shrink)