The standard propositional exposition of necessary and sufficient conditions, as available in introductory logic texts, leads to a contradiction. It should be abolished.

We emphasize the role of the choice of vocabulary in formalization of a mathematical area and remark that this is a particular preoccupation of logicians. We use this framework to discuss Kennedy’s notion of ‘formalism freeness’ in the context of various schools in model theory. Then we clarify some of the mathematical issues in recent discussions of purity in the proof of the Desargues proposition. We note that the conclusion of ‘spatial content’ from the Desargues proposition involves arguments which are (...) algebraic and even metamathematical. Hilbert showed that the Desargues proposition implies the coordinatizing ring is associative, which in turn implies the existence of a three-dimensional geometry in which the given plane can be embedded. With W. Howard we give a new proof, removing Hilbert’s ‘detour’ through algebra, of the ‘geometric’ embedding theorem. Finally, our investigation of purity leads to the conclusion that even the introduction of explicit definitions in a proof can violate purity. We argue that although both involve explicit definition, our proof of the embedding theorem is pure while Hilbert’s is not. Thus the determination of whether an argument is pure turns on the content of the particular proof. Moreover, formalizing the situation does not provide a tool for characterizing purity. (shrink)

The essentially comparative conception of value entails that the value of a state of affairs does not depend solely upon features intrinsic to the state of affairs, but also upon extrinsic features, such as the set of feasible alternatives. It has been argued that this conception of value gives us reason to abandon the transitivity of the better than relation. This paper shows that the support for intransitivity derived from this conception of value is very limited. On its most plausible (...) interpretations, it merely provides a necessary, but not sufficient, condition for intransitivity. It is further argued that the essentially comparative conception of value appears to support a disjunctive conclusion: there is incommensurability of value or betterness is not transitive. Of these two alternatives, incommensurability is preferable, because it is far less threatening to our other axiological commitments. (shrink)

Since the beginning of the 20th century, philosophers of science have asked, "what kind of thing is a scientific theory?" The logical positivists answered: a scientific theory is a mathematical theory, plus an empirical interpretation of that theory. Moreover, they assumed that a mathematical theory is specified by a set of axioms in a formal language. Later 20th century philosophers questioned this account, arguing instead that a scientific theory need not include a mathematical component; or that the mathematical component need (...) not be specified by a set of axioms in a formal language. We survey various accounts of scientific theories entertained in the 20th century -- removing some misconceptions, and clearing a path for future research. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...) Q is one whose existentialization, ∃ x Q, is logically true; otherwise, Q is existential-import-free or simply import-free.How abundant or widespread is existential import? How abundant or widespread are existential-import predicates in themselves or in comparison to import-free predicates? We show that existential-import predicates are quite abundant, and no less so than import-free predicates. Existential.. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (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)

Four current accounts of theory reduction are presented, first informally and then formally: (1) an account of direct theory reduction that is based on the contributions of Nagel, Woodger, and Quine, (2) an indirect reduction paradigm due to Kemeny and Oppenheim, (3) an "isomorphic model" schema traceable to Suppes, and (4) a theory of reduction that is based on the work of Popper, Feyerabend, and Kuhn. Reference is made, in an attempt to choose between these schemas, to the explanation of (...) physical optics by Maxwell's electromagnetic theory, and to the revisions of genetics necessitated by partial biochemical reductions of genetics. A more general reduction schema is proposed which: (1) yields as special cases the four reduction paradigms considered above, (2) seems to be in better accord with both the canons of logic and actual scientific practice, and (3) clarifies the problems of meaning variance and ontological reduction. (shrink)

In this article, we redefine classical notions of theory reduction in such a way that model-theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model-theoretic reconstruction of science in which theory succession or reduction is often better - or at a finer level of analysis - interpreted as the result of model succession or reduction. This analysis leads to 'defeasible reduction', defined as follows: The conjunction of the assumptions of a reducing theory (...) T with the definitions translating the vocabulary of a reduced theory T' to the vocabulary of T, defeasibly entails the assumptions of reduced T'. This relation of defeasible reduction offers, in the context of additional knowledge becoming available, articulation of a more flexible kind of reduction in theory development than in the classical case. Also, defeasible reduction is shown to solve the problems of entailment that classical homogeneous reduction encounters. Reduction in the defeasible sense is a practical device for studying the processes of science, since it is about highlighting different aspects of the same theory at different times of application, rather than about naive dreams concerning a metaphysical unity of science. (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)

1. A Historical Look at Unity 2. Field Guide to Modern Concepts of Reduction and Unity 3. Kitcher's Revisionist Account of Unification 4. Critics of Unity 5. Integration Instead of Unity 6. Reduction via Mechanisms 7. Case Studies in Reduction and Unification across the Disciplines.

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)

Most paradoxes of self-reference have a dual or ‘hypodox’. The Liar paradox (Lr = ‘Lr is false’) has the Truth-Teller (Tt = ‘Tt is true’). Russell’s paradox, which involves the set of sets that are not self-membered, has a dual involving the set of sets which are self-membered, etc. It is widely believed that these duals are not paradoxical or at least not as paradoxical as the paradoxes of which they are duals. In this paper, I argue that some paradox’s (...) duals or hypodoxes are as paradoxical as the paradoxes of which they are duals, and that they raise neglected and interestingly different problems. I first focus on Richard’s paradox (arguably the simplest case of a paradoxical dual), showing both that its dual is as paradoxical as Richard’s paradox itself, and that the classical, Richard-Poincaré solution to the latter does not generalize to the former in any obvious way. I then argue that my argument applies mutatis mutandis to other paradoxes of self-reference as well, the dual of the Liar (the Truth-Teller) proving paradoxical. (shrink)

There is nowadays consensus in the community of didactics of science regarding the need to include the philosophy of science in didactical research, science teacher education, curriculum design, and the practice of science education in all educational levels. Some authors have identified an ever-increasing use of the concept of ‘theoretical model’, stemming from the so-called semantic view of scientific theories. However, it can be recognised that, in didactics of science, there are over-simplified transpositions of the idea of model. In this (...) sense, contemporary philosophy of science is often blurred or distorted in the science education literature. In this paper, we address the discussion around some meta-theoretical concepts that are introduced into didactics of science due to their perceived educational value. We argue for the existence of a ‘semantic family’, and we characterise four different versions of semantic views existing within the family. In particular, we seek to contribute to establishing a model-based didactics of science mainly supported in this semantic family. (shrink)

We discuss three problems concerning the use of formal languages in theoretical physics: (i) the definability of time and spacetime in classical physical theories; (ii) how to cope with indistinguishable elementary particles in quantum mechanics without labeling them; and (iii) how to get a formal picture of quantum states jumping.

In this article, I discuss Alf Ross's claim that the concept of a legal right is best understood as a technical tool of presentation, which ties together a disjunction of operative facts and a conjunction of legal consequences, and that rights statements render the content of a number of legal norms in a convenient manner. I argue that while Ross's analysis is appealing, it is problematic in at least three respects. I also argue, however, that despite these difficulties Ross's analysis (...) deserves our continued attention, because the fundamental idea—that the concept of a legal right must be understood functionally—is sound. (shrink)

The paper takes off from the problem of finding a proper content for the relation of identity as it holds or fails to hold among ordinary things or substances. The necessary conditions of identity are familiar, the sufficient conditions less so. The search is for conditions at once better usable than the Leibnizian Identity of Indiscernibles (independently suspect) and strong enough to underwrite all the formal properties of the relation.It is contended that the key to this problem rests at the (...) level of metaphysics and epistemology alike with a sortalist position. Sortalism is the position which insists that, if the question is whether a and b are the same, it has to be asked what are they? Any sufficiently specific answer to that question will bring with it a principle of activity or functioning and a mode of behaviour characteristic of some particular kind of thing by reference to which questions of persistence or non-persistence through change can be adjudicated.These contentions are illustrated by reference to familiar examples such as the human zygote, the Ship of Theseus and Shoemaker's Brown-Brownson. The first example is hostage for a mass of unproblematical cases. The problems presented by the second and third sort of examples arise chiefly (it is claimed) from an incompleteness in our conceptions of the relevant sort—the what the thing in question is. That incompleteness need not prevent us from knowing perfectly well which thing we are referring to. In the concluding section, sortalism is defended against various accusations of anthropocentrism.The paper touches on the interpretation of Heraclitus, Leibniz's theory of clear indistinct ideas, the difficulties of David Lewis's ‘perdurantist’ or stroboscopic view of persistence, four-dimensionalism, and the relation of personal identity both to experiential memory and to the particular bodily physiognomy of a subject. At some points—as in connection with the so-called Only a and b rule—the paper corrects, supplements or extends certain theses or formulations proposed in the author's Sameness and Substance Renewed (2001). (shrink)

Formulations of Anselm’s ontological argument have been the subject of a number of recent studies. We examine these studies in light of Anselm’s text and (a) respond to criticisms that have surfaced in reaction to our earlier representations of the argument, (b) identify and defend a more refined representation of Anselm’s argument on the basis of new research, and (c) compare our representation of the argument, which analyzes that than which none greater can be conceived as a definite description, to (...) a representation that analyzes it as an arbitrary name. (shrink)

According to a widely held view, rationality demands that the preferences of a person be transitive. The transitivity assumption is an axiom in standard theories of rational choice. It is also prima facie very plausible. I argue here that transitivity is not a necessary condition of rationality; it is a constraint only in some cases. The argument presented here is based on the non-linearity of differential utility functions. This paper has four parts. First, I present an argument against the transitivity (...) assumption (I, II). Second, I discuss some objections; this will also bring out some features of the view defended here, like the essentially comparative nature of choice (III). Then, I discuss certain proposals that promise to avoid my conclusion (IV). Finally, I go into some implications concerning the nature of rational decision making (V). To accept some intransitivities as rational does not make our life easier; it can even lead to hard choices. However, it does not lead to skepticism about rational choice. (shrink)

The question “what is an interpretation?” is often intertwined with the perhaps even harder question “what is a scientific theory?”. Given this proximity, we try to clarify the first question to acquire some ground for the latter. The quarrel between the syntactic and semantic conceptions of scientific theories occupied a large part of the scenario of the philosophy of science in the 20th century. For many authors, one of the two currents needed to be victorious. We endorse that such debate, (...) at least in the terms commonly expressed, can be misleading. We argue that the traditional notion of “interpretation” within the syntax/semantic debate is not the same as that of the debate concerning the interpretation of quantum mechanics. As much as the term is the same, the term “interpretation” as employed in quantum mechanics has its meaning beyond (pure) logic. Our main focus here lies on the formal aspects of the solutions to the measurement problem. There are many versions of quantum theory, many of them incompatible with each other. In order to encompass a wider variety of approaches to quantum theory, we propose a different one with an emphasis on pure formalism. This perspective has the intent of elucidating the role of each so-called “interpretation” of quantum mechanics, as well as the precise origin of the need to interpret it. (shrink)

In the past century the received view of definition in mathematics has been the stipulative conception, according to which a definition merely stipulates the meaning of a term in other terms which are supposed to be already well known. The stipulative conception has been so absolutely dominant and accepted as unproblematic that the nature of definition has not been much discussed, yet it is inadequate. This paper examines its shortcomings and proposes an alternative, the heuristic conception.

In this essay, I first consider a popular view of models and modeling, the similarity view. Second, I contend that arguments for it fail and it suffers from what I call “Hughes’ worry.” Third, I offer a deflationary approach to models and modeling that avoids Hughes’ worry and shows how scientific representations are of apiece with other types of representations. Finally, I consider an objection that the similarity view can deal with approximations better than the deflationary view and show that (...) this is not so. (shrink)

Keywords: climate change, integrated assessment, knowledge integration, transdisciplinary research, vulnerability, vulnerability assessment. This thesis explores how transdisciplinary knowledge integration can be facilitated in the context of integrated assessments and vulnerability assessments of climate change. Even though knowledge integration is fundamental in such transdisciplinary assessments, the actual process of integrating knowledge is rarely addressed explicitly and methodically. Here, knowledge integration is conceptualised into the subsequent phases of the elaboration of a shared language and the design of a methodology. Three devices for (...) facilitating knowledge integration are put forward: 1. semantic ascent or the shift from speaking in a language to speaking in a meta-language about the former, 2. formalisation or the translation of statements made in ordinary or technical language into a formal language, and 3. knowledge integration methods, which are methods that provide a meta-language for speaking about the knowledge to be integrated and organise the process of integration. Four cases of knowledge integration are presented. First, the general problem of methodology design is addressed and a graphical framework for representing methodologies is presented. Second, the problem of developing a shared language for speaking about vulnerability to climate change is addressed. A formal mathematical framework of vulnerability and related concepts is presented. Third, a special case of methodology design, the integration of computer models in the context of modular integrated assessment modelling is addressed. A modular approach developed in the PIAM project is presented. Fourth, the integration of computer models, this time in the context of a global assessment of coastal vulnerability to sea-level rise, is addressed. A knowledge integration method, which was developed and applied in the DINAS-COAST project, is presented. These cases show that semantic ascent is a useful device in those cases in which it is difficult to directly elaborate a shared language at the beginning of the assessment. Formalisation can contribute to the elaboration of a shared language in those cases in which concepts overlap non trivially in their meanings. More emphasis should be placed on the development and application of iterative knowledge integration methods as iteration is crucial in order to benefit from the mutual learning during the course of the assessment. (shrink)

La parution de la monographic de Sneed,The Logical Structure of Mathematical Physics a suscité un renouveau d'intérêt en philosophie contemporaine des sciences. Cet ouvrage arrivait à un moment où l'épistémologie des sciences, telle que développée dans les milieux germaniques et anglo-saxons, accusait de graves insuffisances dans la reconstruction rationnelle du développement historique des théories physiques. Mis sur la défensive par les thèses et arguments historiques de Kuhn et de Feyerabend, ces milieux « orthodoxes » devaient reconnaitre l'état embryonnaire de ce (...) qui devait être uneépistémologie diachroniquedes sciences, une épistémologie du changement scientifique où les méthodes d'analyse formelle puissent être aussi mises á contribution. A cela s'ajoutait un certain malaise, une certaine stagnation de la problématique, plus synchronique, de l'approche traditionnelle issue du mouvement empiriste logique. Le probleme de la dichotomielangage théorique—langage observationnel, ainsi que son fidèle compagnon, le problème destermes théoriques, le statut épistémologique desrègies de correspondance, la dèfinition du concept d'analyticitéen science, autant de questions qui avaient été discutées et critiquées, à maintes reprises, pour aboutir à des résultats peu concluants aux yeux des philosophes, comme à ceux des physiciens préoccupés des fondements de leur discipline et à qui la teneur de cette discussion semblait souvent étrangère à la pratique scientifique. (shrink)

The positivistic Received View construed scientific theories syntactically as axiomatic calculi where theoretical terms were given a partial semantic interpretation via correspondence rules connecting them to observation statements. This paper assesses what, with hindsight, seem the most important defects in the Received View; surveys the main proposed successor analyses to the Received View--various Semantic Conception versions and the Structuralist Analysis; evaluates how well they avoid those defects; examines what new problems they face and where the most promising require further development (...) or leave unanswered questions; explores implications of recent work on models for understanding theories; and rebuts the few criticisms of the Semantic Conception that have surfaced. (shrink)

The area of investigation known as general systems theory or research features the study of systems as interesting in its own right or one fruitful approach to the study of science in general. This leads to an interesting and still open problem, namely, explicating the concept of a system that seems to unify the interests of researchers in this area. Contrary to received opinion, I argue that there is a unique and interesting concept of a system that underlies the expressed (...) interests of general systems researchers and that it can be given a satisfactory explication. The concept in question has systems as extralinguistic entities that we theorize about, namely, certain sorts of sets of re-related elements. Criteria for its explication are suggested; examples of systems, earlier analyses, and various objections are all considered in leading up to a partial formal explication of the concept and a statement of additional open problems. (shrink)

I begin by distinguishing two notions of model, the notion of a truth-making structure and the notion of a mathematical model (in one specific sense). I then argue that although the models of the semantic view have often been taken to be both truth-making structures and mathematical models, this is in part due to a failure to distinguish between two ways of truth-making; in fact, the talk of truth-making is best excised from the view altogether. The result is a version (...) of the semantic view which is better supported by the direct evidence offered for it, better equipped to achieve its avowed aims, and, I think, closer to the intentions of the original proponents of the view in many ways, despite some of their own declarations to the contrary. (shrink)

In formal theories of measurement meaningfulness is usually formulated in terms of numerical statements that are invariant under admissible transformations of the numerical representation. This is equivalent to qualitative relations that are invariant under automorphisms of the measurement structure. This concept of meaningfulness, appropriately generalized, is studied in spaces constructed from a number of conjoint and extensive structures some of which are suitably interrelated by distribution laws. Such spaces model the dimensional structures of classical physics. It is shown that this (...) qualitative concept corresponds exactly with the numerical concept of dimensionally invariant laws of physics. (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)

John Stuart Mill regards economics as an inexact and separate science which employs a deductive method. This paper analyzes and restates Mill's views and considers whether they help one to understand philosophical peculiarities of contemporary microeconomic theory. The author concludes that it is philosophically enlightening to interpret microeconomics as an inexact and separate science, but that Mill's notion of a deductive method has only a little to contribute.

The prevalence of optimality models in the literature of evolutionary biology is testimony to their popularity and importance. Evolutionary biologist R. C. Lewontin, whose criticisms of optimality models are considered here, reflects that "optimality arguments have become extremely popular in the last fifteen years, and at present represent the dominant mode of thought." Although optimality models have received little attention in the philosophical literature, these models are very interesting from a philosophical point of view. As will be argued, optimality models (...) are central to evolutionary thought, yet they are not readily accomodated by the traditional view of scientific theories. According to the traditional view, we would expect optimality models to employ general, empirical laws of nature, but they do not. Fortunately, the semantic view of scientific theories, a recent alternative to the traditional view, more readily accomodates optimality models. As we would expect on the semantic view, optimality models can be construed as specifications of ideal systems. These specifications may be used to describe empirical systems--that is, the specifications may have empirical instances. But the specifications are not empirical claims, much less general, empirical laws. Although philosophers have yet to discuss the general features and uses of optimality models, these topics have stimulated much recent discussion among evolutionary biologists. Their discussions raise a number of precautions concerning the proper use of optimality models. Moreover, many of their caveats can be interpreted as general reminders that 1) optimality models specify ideal systems whose empirical instantiations may be quite restricted, and that 2) optimality models should not be construed as general, empirical laws. As G. F. Oster and E. O. Wilson caution, "the prudent course is to regard optimality models as provisional guides to further empirical research and not necessarily as the key to deeper laws of nature." It seems, then, that the semantic view of theories is more sensitive to the nature and limitations of optimality models than is the more traditional view of theories. (shrink)

The leitmotif of Mario Bunge’s work was that the philosophy of science should be informed by a comprehensive scientific philosophy, and vice versa; with both firmly rooted in realism and materialism. Now Bunge left such a big oeuvre, comprising more than 70 books and hundreds of articles, that it is impossible to review it in its entirety. In addition to biographical remarks, this obituary will therefore restrict itself to some select issues of his philosophy: his scientific metaphysics, his philosophy of (...) physics, his concept of mechanismic explanation, his philosophy of social science and technology, and his approach to the demarcation problem. The final section will explore why Bunge, despite the extent and depth of his work, has not achieved a more prominent status in the philosophical community. (shrink)

This Ph.D. thesis provides a pilosophical account of the structure of the evolutionary synthesis of the 1930s and 40s. The first, more historical part analyses how classical genetics came to be integrated into evolutionary thinking, highlighting in particular the importance of chromosomal mapping of Drosophila strains collected in the wild by Dobzansky, but also the work of Goldschmidt, Sumners, Timofeeff-Ressovsky and others. The second, more philosophical part attempts to answer the question wherein the unity of the synthesis consisted. I argue (...) that it exemplifies a weak of form of explanatory unification. (shrink)

Thirty years after the conference that gave rise to The Structure of Scientific Theories, there is renewed interest in the nature of theories and models. However, certain crucial issues from thirty years ago are reprised in current discussions; specifically: whether the diversity of models in the science can be captured by some unitary account; and whether the temporal dimension of scientific practice can be represented by such an account. After reviewing recent developments we suggest that these issues can be accommodated (...) within the partial structures formulation of the semantic or model-theoretic approach. (shrink)

The conditions are examined under which one theory is said to be replaceable by another, while preserving those features of the original theory which made it serviceable for a given purpose. Among such replacements, special attention is given to ones which qualify as so-called reductions of a theory, and some theorems are proved concerning the notion of a reduction.

This article considers the following question: What is the relationship between supervenience and reduction? I investigate this formally: first, by introducing a recent argument by Christian List to the effect that one can have supervenience without reduction; then, by considering how the notion of Nagelian reduction can be related to the formal apparatus of definability and translation theory; then, by showing how, in the context of propositional theories, topological constraints on supervenience serve to enforce reducibility; and, finally, by showing how (...) constraints derived from the theory of ultraproducts can enforce reducibility in the context of first-order theories. (shrink)

In recent papers Hans Halvorson has offered a critique of the semantic view of theories, showing that theories may be the same although the corresponding sets of models are different and, conversely, that theories may be different although the corresponding sets of models are the same. This critique will be assessed, first, as it pertains to issues concerning scientific models in the empirical sciences and, second, independent of any concern with empirical science.

I invoke the conceptual machinery of contemporary possible-world semantics to provide an account of the metaphysical status of "bridge laws" in intertheoretic reductions. I argue that although bridge laws are not definitions, and although they do not necessarily reflect attribute-identities, they are supervenient. I.e., they are true in all possible worlds in which the reducing theory is true.

I reconstruct Aristotle’s analytical procedure in Prior Analytics I.45 and its metalogical implications. Aristotle’s analysis unfolds three groups of syllogisms: symmetrically analysable, asymmetrically analysable, and non-analysable syllogisms. From the first and the third group could be extracted 27 combinations of the two mutually non-derivable deductive rules. Aristotle’s reduced deductive system in APr. I.7 with the two moods in the first figure (traditionally called Barbara and Celarent) follows this pattern. I demonstrate that the deductive system with Barbara and Celarent is just (...) one of 27 possible complete deductive systems with the two mutually non-derivable syllogistic rules. On top of that, given the fact that there are two combinations of mutually non-derivable conversion rules, I conclude that Prior Analytics hides in itself 54 complete deductive systems with a minimal number of mutually non-derivable rules. Finally, it is commented what might be the role of analysis; to what extent Aristotle could be aware of possibilities presented here; why he still prefers only one deductive system to many others with the same deductive power. (shrink)

(1) This paper uses the following binary relations: > (is preferred to); ⩽ (is not preferred to); < (is less preferred than); ~ (is indifferent to). (2) Savage used primitive ⩾, postulated to be connected and transitive onA (the set of acts), to define the others: [x ~ y ⇔ (x ⩽ y and y ⩽ x)]; [y < x ⇔ notx ⩽ y]; [x > y ⇔ y < x]. Independently of the axioms, this definition implies that ⩽ and (...) > are complementary relations onA: [x < y ⇔ notx > y]. (3) Pratt, Raiffa and Schlaifer used primitive ⩽, postulated to be transitive onL (the set of lotteries), to define the others with a different expression for <: [x < y ⇔ (x ⩽ y and noty ⩽ x)]. Thus, ⩽ and > are not necessarily complementary onL; since ⩽ is not postulated to be connected onL, but connected ⩽ is necessary and sufficient for such complementarity. Since the restriction of ⩽ to the subsetA ofL is connected, ⩽ and > are complementary onA. (4) Fishburn used primitive < onA to define the others with different expression for ~ and ⩽: [x ~ y ⇔ (notx < y and noty < x)]; [x ⩽ y ⇔ (x < y orx ~ y)]. His version of Savage's theory then assumed that < is asymmetric and negatively transitive onA. Thus, ⩽ and > are complementary, since asymmetric < is necessary and sufficient for such complementarity. (5) This analysis provides a new proof that the same list of elementary properties of binary relations onA applies to all three theories: ⩽ is connected, transitive, weakly connected, reflexive, and negatively transitive; while both < and > are asymmetric, negatively transitive, antisymmetric, irreflexive, and transitive; but only ~ is symmetric. (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)

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)

Prouver des théorèmes est une pratique mathématique qui semble clairement améliorer notre compréhension mathématique. Ainsi, prouver et reprouver des théorèmes en mathématiques, vise à apporter une meilleure compréhension. Cependant, comme il est bien connu, les preuves mathématiques totalement formalisées sont habituellement inintelligibles et, à ce titre, ne contribuent pas à notre compréhension mathématique. Comment, alors, comprendre la relation entre prouver des théorèmes et améliorer notre compréhension mathématique. J'avance ici que nous avons d'abord besoin d'une notion différente de preuve (formelle), qui (...) ne tienne pas la forme pour opposée au contenu. La pratique de la preuve algébrique au xviiie siècle fournit un exemple de preuve à la fois pleinement rigoureuse et porteuse de contenu, et dans ce cas, il est possible de voir comment une preuve mathématique apporte une compréhension mathématique. Il s'agira alors de mobiliser les enseignements de cet exemple pour étudier le type de raisonnement déductif à partir de concepts, qui a constitué la norme dans la pratique mathématique depuis le xixe siècle. (shrink)

In his book, The Structure of Time, William H. Newton-Smith claims that we cannot decide whether the structure of time is continuous or merely dense. I discuss here the extent to which he is correct. I argue that he fails to provide strong enough arguments to defend his claim, but I then suggest how he might overcome this issue. I also argue that we must reconsider the consequences that he draws from his “undecidability result”.