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)

John King-Farlow's ‘The Positive McTaggart on Time’ brings out extremely important likenesses between ‘abstract’ metaphysicians and ‘concrete’ philosophers of science. These striking similarities illustrate a perennial human quest for Something More Basic than Time, a quest which characterizes not only mystics who rejoice in contradictions but hard-headed philosophers who submit to the rigours of logic. King-Farlow is largely concerned with the McTaggart of 1908 and his motivation for writing ‘The Unreality of Time’. I should like to explore further the surprising (...) bond between the Search for Something Deeper in the later McTaggart of The Nature of Existence and the writings on Time of Hans Reichenbach and Adolf Grünbaum. Reflection on this similarity should enable us better to evaluate the view that our vulgar, if practically useful, assertions about Time's Arrow must be reinterpreted by the wise in terms of chastened logical constructions out of statements about Something Deeper—logical constructions which are alleged, if chaste enough, to be eliminable. (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)

The paper discusses problems which arise in attempts to axiomatize parts of religion or religious belief systems. Besides those problems already investigated by Bochenski, like that of the propositional content or the meaning of religious discourse there are several further ones. This paper deals with the question whether full Classical Logic is suitable, whether one universe of discourse is sufficient, how to use definitions and analogous concepts and whether justifications satisfy credibility criteria.

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.

The "problem of counterfactuals," as proposed by Goodman and Chisholm, cannot be solved. However, a similar program, pioneered by Hiż and Mrs. Milmed, but largely neglected, can be completed and promises a satisfactory analysis of subjunctive conditionals.

The so-called Ramsey–Carnap approach, or Ramseyfication, has gone out of fashion in the philosophy of science. Advocates have tried to argue for a revival by writing methodological and metatheoretical studies of Ramseyfication. For this paper I have chosen a different approach; I will apply Ramseyfication to infrared spectroscopy—a method used in analytical chemistry—in order to logically analyse the relation between measurements and mathematical structures. My aim in doing so is to contribute to the debate about the _Application Problem of Mathematics_, (...) thereby making a case for Ramseyfication as a method of study for scientific theories. (shrink)

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X‐and‐Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners' interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems.

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)

To consider metaphysical claims a priori and devoid of empirical content, is a rather commonplace received opinion. This paper attempts an exploration of a contemporary philosophical heresy: it is possible to test metaphysical claims if they play an indispensable role in producing empirical success, i.e. novel predictions. To do so one, firstly, needs to express the metaphysical claims employed in the logico-mathematical language of a scientific theory, i.e. to explicate them. Secondly, one should have an understanding of what it is (...) to test and to verify or to falsify a metaphysical claim. Finally, one also need to consider the philosophical practice of testing a metaphysical claim. These three aspects are introduced in this paper and they are illustrated by means of the metaphysical concept of common cause and the principle of the common cause. (shrink)

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 task of axiomatizing physical theories has attracted, in recent years, some interest among both empirical scientists and logicians. However, the axiomatizations produced by either one of these two groups seldom appear satisfactory to the members of the other. It is the purpose of this paper to develop an approach that will satisfy the criteria of both, hence permit us to construct axiomatizations that will meet simultaneously the standards and needs of logicians and of empirical scientists.

Theories in the usual sense, as characterized by a language and a set of theorems in that language ("statement view"), are related to theories in the structuralist sense, in turn characterized by a set of potential models and a subset thereof as models ("non-statement view", J. Sneed, W. Stegmüller). It is shown that reductions of theories in the structuralist sense (that is, functions on structures) give rise to so-called "representations" of theories in the statement sense and vice versa, where representations (...) are understood as functions that map sentences of one theory into another theory. It is argued that commensurability between theories should be based on functions on open formulas and open terms so that reducibility does not necessarily imply commensurability. This is in accordance with a central claim by Stegmüller on the compatibility of reducibility and incommensurability that has recently been challenged by D. Pearce. (shrink)

Caenorhabditis elegans (C. elegans) is a tiny worm that has become the focus of a large number of worldwide research projects examining its genetics, development, neuroscience, and behavior. Recently several groups of investigators have begun to tie together the behavior of the organism and the underlying genes, neural circuits, and molecular processes implemented in those circuits. Behavior is quintessentially organismal--it is the organism as a whole that moves and mates--but the explanations are devised at the molecular and neurocircuit levels, and (...) tested in populations using protocols that span many levels of aggregation. Following a brief review of the main relevant features of C. elegans, I describe some of these circuits, and then discuss two contrasting approaches in behavioral genetics and neural network analysis of the worm. Finally, I outline the rudiments of a "field and focus" explanation model using the two contrasting approaches. (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)

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.

Patrick Suppes'' set-theoretical approach to the analysis of theories, and Joseph D. Sneed''s metatheory are briefly outlined. The notions of observation, illusion and hallucination are reconstructed according to these approaches. It is argued that the terms perception and truth are theoretical with respect to observation but nontheoretical with respect to illusion and hallucination. Hallucination is construed as a special kind of illusion.

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)

We propose a model of cognition grounded in ancient Greek philosophy which encompasses Aristotle’s categories. Taking for First Principles the brute facts of the mental actions of separation, aggregation and ordering, we derive Aristotle’s categories as follows. First, Separation lets us see single entities, giving the simple concept of an individual. Next, Aggregation lets us see instances of some kind, giving the basic concept of a particular. Then, Ordering lets us see both wholes-with-parts as well as parts-of-some-whole, giving the subtle (...) concept of a relational or Gestalt. The basic and the subtle concept give us the major and minor categories. The categories constitute a top-level ontology and describe universal usage so that any other category necessarily describes particular or domain usage. (shrink)

The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic \({\mathbf{NC}}_{\mathbf{3}}\). As a result, for each binary extension of \({\mathbf{NC}}_{\mathbf{3}}\), we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining _n_-sequent proof systems for any _n_-valent logic (...) with deterministic or non-deterministic matrices is not applicable to \({\mathbf{NC}}_{\mathbf{3}}\) and its binary extensions. (shrink)

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)

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)

It is argued that Hempel's original rejection of the prediction criterion of confirmation in [8] (on the grounds that it leads to a circular definition of confirmation) was ill-conceived, and that his own approach exhibits undesirable consequences to the degree that it deviates from this criterion. A version of the prediction criterion is formulated which, in addition to being-non circular, escapes the criticisms advanced against Hempel's satisfaction criterion, offers certain clear advantages over alternative approaches, and may serve as the basis (...) for a theory of qualitative confirmation. The definition of confirmation developed here violates two of Hempel's three criteria of adequacy, and in showing why it should do so some light is shed on various issues in the debate concerning the acceptability of these criteria. (shrink)

In a recent article, Barrett & Halvorson define a notion of equivalence for first-order theories, which they call “Morita equivalence.” To argue that Morita equivalence is a reasonable measure of “theoretical equivalence,” they make use of the claim that Morita extensions “say no more” than the theories they are extending. The goal of this article is to challenge this central claim by raising objections to their argument for it and by showing why there is good reason to think that the (...) claim itself is false. In light of these criticisms, this article develops a natural way for the advocate of Morita equivalence to respond. I prove that this response makes her criterion a special case of bi-interpretability, an already well-established barometer of theoretical equivalence. I conclude by providing reasons why the advocate of Morita equivalence should opt for a notion of theoretical equivalence that is defined in terms of interpretability rather than Morita extensions. (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)

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)

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)

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 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)

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)

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)

Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics, which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supply a classical concept of truth and to fully (...) support the rules and metarules of classical logic, and it is applied to vague terms as well as to theoretical or open-ended terms from mathematics and science. The theory also demonstrates how diachronic or synchronic interpretational continuity across languages is compatible with semantic indeterminacy. (shrink)

This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: ZFCAσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathsf {ZFCA}_{\sigma }$$\end{document} with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.

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)

In this paper we start from the assumption that in a metaphor, or an analogy, some terms belonging to one domain (source domain) are used to refer to objects other than their conventional referents belonging to a possibly different domain (target domain). We describe a formalism, which is based on the First Order Predicate Calculus, for representing the knowledge structure associated with a domain and then develop a theory of Constrained Semantic Transference [CST] which allows the terms and the structural (...) relationships of the source domain to be transferred coherently across to the target domain. We show how metaphors and analogies can be characterized in CST in such a way that many of their cognitive properties con be explained.We then propose a theory of Approximate Semantic Transference [AST] which is a computational version of CST and is derived from it by replacing the coherency requirement with approximate coherency. We show how AST can be used as a basis for designing models of cognitive processes involved in comprehending metaphors and analogies. (shrink)

A sentence mentioning an object can be regarded as saying any one of several things about that object, without there by being ambiguous. Some of the repercussions of this commonplace observation are recorded, and some critical discussion is provided of views which would appear to go against it.

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.

In his 1933 monograph on the concept of truth, Alfred Tarski claimed that his definition of truth satisfied “the usual conditions of methodological correctness”, which in a 1935 article he identified as consistency and back-translatability. Following the rules of defining for an axiomatized theory was supposed to ensure satisfaction of the two conditions. But Tarski neither explained the two conditions nor supplied rules of defining for any axiomatized theory. We can make explicit what Tarski understood by consistency and back-translatability, with (...) the help of (1) an account by Ajdukiewicz (1936) of the criteria underlying the practice of articulating rules of defining for axiomatized theories and (2) a critique by Frege (1903) of definitions that conjure an object into existence as that which satisfies a specified condition without first proving that exactly one object does so. I show that satisfaction of the conditions of consistency and back-translatability as thus explained is guaranteed by the rules of defining articulated by Leśniewski (1931) for an axiomatized system of propositional logic. I then construct analogous rules of defining for the theory within which Tarski developed his definition of truth. Tarski’s 32 definitions in this theory occasionally violate these rules, but the violations are easily repaired. I argue that the Leśniewski-Ajdukiewicz theory of formal correctness of definitions within which Tarski worked is superior in some respects to the widely accepted analogous theory articulated by Suppes (1957). (shrink)

§1. The mission of axiomatic set theory. What is set theory needed for in the foundations of mathematics? Why cannot we transact whatever foundational business we have to transact in terms of our ordinary logic without resorting to set theory? There are many possible answers, but most of them are likely to be variations of the same theme. The core area of ordinary logic is by a fairly common consent the received first-order logic. Why cannot it take care of itself? (...) What is it that it cannot do? A large part of every answer is probably that first-order logic cannot handle its own model theory and other metatheory. For instance, a first-order language does not allow the codification of the most important semantical concept, viz. the notion of truth, for that language in that language itself, as shown already in Tarski. In view of such negative results it is generally thought that one of the most important missions of set theory is to provide the wherewithal for a model theory of logic. For instance Gregory H. Moore asserts in his encyclopedia article “Logic and set theory” thatSet theory influenced logic, both through its semantics, by expanding the possible models of various theories and by the formal definition of a model; and through its syntax, by allowing for logical languages in which formulas can be infinite in length or in which the number of symbols is uncountable. (shrink)