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)

(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)

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 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)

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)

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. © 2004 Cognitive Science Society, Inc. All rights reserved.

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)

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)

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)

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 earlier publications Jaakko Hintikka has introduced the interrogative model of inquiry and studied some of its applications.1 At its simplest, the interrogative model takes the form of a game between a player known as the Inquirer and a source of information we call Nature. The inquirer is trying to derive a conclusion C from a given set of premises T by standard deductive means augmented by additional information gained from Nature. (We can think of C as a set of (...) formulas related disjunctively to each other.) The inquirer may obtain this additional information by means of questions put to Nature. The answers to these questions, when available, are then added to the premise set T. When a question is answerable but no true answer is available, Nature may respond with a false answer.The deductive steps employed are subject to certain limitations. For instance, if the derivation is being carried out in a Beth-style tableau system, we require that the deductive steps obey the subformula principle.2. (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)

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)

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)

Truth diagrams are introduced as a novel graphical representation for propositional logic. To demonstrate their epistemic efficacy a set of 28 concepts are proposed that any comprehensive representation for PL should encompass. TDs address all the criteria whereas seven other existing representations for PL only provide partial coverage. These existing representations are: the linear formula notation, truth tables, a PL specific interpretation of Venn Diagrams, Frege’s conceptual notation, diagrams from Wittgenstein’s Tractatus, Pierce’s alpha graphs and Gardner’s shuttle diagrams. The comparison (...) of the representations succeeds in distinguishing ideas that are fundamental to PL from features of common PL representations that are somewhat arbitrary. (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)

In the literature over the Ramsey-sentence approach to structural realism, there is often debate over whether structural realists can legitimately restrict the range of the second-order quantifiers, in order to avoid the Newman problem. In this paper, I argue that even if they are allowed to, it won’t help: even if the Ramsey sentence is interpreted using such restricted quantifiers, it is still an implausible candidate to capture a theory’s structural content. To do so, I use the following observation: if (...) a Ramsey sentence did encode a theory’s structural content, then two theories would be structurally equivalent just in case they have logically equivalent Ramsey sentences. I then argue that this criterion for structural equivalence is implausible, even where frame or Henkin semantics are used. (shrink)

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

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)

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”.

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)

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)

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)

§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)

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)

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)

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)

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)

The Price equation provides a comprehensive representation of evolutionary processes. Since its original formulation by George Price, it has been used to model a variety of phenomena in quantitative genetics and related fields. However, there is no consensus on the explanatory power of the equation. In this article we aim to clarify its place within modern evolutionary theory. To this end, we first state the basic concepts from which the Price equation can be derived as a theorem. From this axiomatization, (...) we conclude that the Price equation is not explanatory in itself. It merely provides a phenomenological description of evolutionary processes. We argue that its role is analogous to that of Galilean kinematics in classical mechanics. Both the Price equation and Galilean kinematics function as conceptual frameworks that define the basic features of the behavior of a class of systems. Practitioners are encouraged to theorize further on these frameworks to find the possible explanation of this behavior in various specific scenarios. Thus, despite its phenomenological character, the Price equation integrates different fields of evolutionary biology by providing a common formalization of their shared explanandum. (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)

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)

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)

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)

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.

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)

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)

An introduction to the model-theoretic approach in the philosophy of science is given and it is argued that this program is further enhanced by the introduction of partial structures. It is then shown that this leads to a natural and intuitive account of both "iconic" and mathematical models and of the role of the former in science itself.

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)

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.

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)

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.