In the philosophical debate on aging, it is common to raise the question of the theoretical definition of aging in terms of its possible characterization as a disease. Understanding aging as a disease seems to imply its medicalization, which has important practical consequences. In this paper, we analyze the question of whether aging is a disease by appealing to the concept of disease in the philosophy of medicine. As a result of this analysis, we argue that a pragmatist approach (...) to the conception of disease is the best alternative to highlight the relevance of the medicalization of aging. From this pragmatist perspective, it can be seen that the notion of aging is going through a conceptual change, and aging can today be understood as a not radically different process from any other condition that is usually considered a disease. (shrink)

This paper evaluates the proof-theoretic definition of ground developed by Poggiolesi in a range of recent publications and argues that her proposed definition fails. The paper then outlines an alternative approach where logical consequence relations and the logical operations are defined in terms of ground.

No entendimento de Habermas, "direito", na expressão "direitos humanos", é um conceito jurídico, donde direitos humanos, para ele, serem direitos jurídicos, normas legais declaradas em atos de fundações do Estado ou anunciadas em convenções do direito internacional e/ou constituições estatais. Ao conceber assim os direitos e tematizar os direitos humanos numa abordagem tríplice (focando-os entre moral, direito e política), ele fornece diferentes definições teóricas dos direitos humanos. O texto apresenta uma exposição sistemática dessas definições e focaliza os diferentes problemas que (...) motivaram Habermas a alterar e ampliar suas concepções de direitos humanos. In the understanding of Habermas, "right" in the phrase "human rights" is a legal concept, where human rights are legal rights, i.e., legal norms declared in acts of foundations of the State or announced conventions of international law and/or State constitutions. By conceiving of rights in this way and by treating human rights in a threefold approach (placing them between morals, law and politics), he presents different theoretical definitions of human rights. This paper presents a systematic exposition of these definitions, and focuses on the different problems that motivated Habermas to change and expand his conceptions of human rights. (shrink)

We interpret intuitionistic theories of (iterated) strictly positive inductive definitions (s.p.-ID i′ s) into Martin-Löf's type theory. The main purpose being to obtain lower bounds of the proof-theoretic strength of type theories furnished with means for transfinite induction (W-type, Aczel's set of iterative sets or recursion on (type) universes). Thes.p.-ID i′ s are essentially the wellknownID i -theories, studied in ordinal analysis of fragments of second order arithmetic, but the set variable in the operator form is restricted to occur (...) only strictly positively. The modelling is done by constructivizing continuity notions for set operators at higher number classes and proving that strictly positive set operators are continuous in this sense. The existence of least fixed points, or more accurately, least sets closed under the operator, then easily follows. (shrink)

The paper provides a proof theoretic characterization of the Russellian theory of definite descriptions (RDD) as characterized by Kalish, Montague and Mar (KMM). To this effect three sequent calculi are introduced: LKID0, LKID1 and LKID2. LKID0 is an auxiliary system which is easily shown to be equivalent to KMM. The main research is devoted to LKID1 and LKID2. The former is simpler in the sense of having smaller number of rules and, after small change, satisfies cut elimination but fails to (...) satisfy the subformula property. In LKID2 an additional analysis of different kinds of identities leads to proliferation of rules but yields the subformula property. This refined proof theoretic analysis leading to fully analytic calculus with constructive proof of cut elimination is the main contribution of the paper. (shrink)

I n order to appreciate properly what we are doing in this book it is necessary to realize that our approach to linguistic theorizing differs from the prevailing views. Our approach can be described by indicating what distinguishes it from the methodological ideas current in theoretical linguistics, which I consider seriously misguided. Linguists typically construe their task in these days as that of making exceptionless generalizations from particular examples. This explanatory strategy is wrong in several different ways. It presupposes (...) that we can have "intuitions" about particular examples, usually examples invented by the linguist himself or herself, reliable and sharp enough to serve as a basis of sharp generalizations. It also presupposes that we cannot have equally reliable direct access to general linguistic regularities. Both assumptions appear to me extremely dubious, and the first of them has in effect been challenged by linguists like Dwight Bol inger. There is also some evidence that the degree of unanimity among linguists is fairly low when it comes to less clear cases, even in connection with such relatively simple questions as grammaticality (acceptability). For this reason we have tried to rely more on quotations from contemporary fiction, newspapers and magazines than on linguists' and philosophers' ad hoc examples. I also find it strange that some of the same linguists as believe that we all possess innate ideas about general characteristics of humanly possible grammars assume that we can have access to them only via their particular consequences. (shrink)

The problem of the interpretation of theoretical terms is outlined, and some difficulties connected with the distinction between partial definitions and empirical postulates are discussed. A reconstruction is sketched which is intended to explicate the 'definitional' character of partial definitions. Finally, some implications for the methodology of theory construction are indicated.

This paper discusses attempts to define health within a public policy arena and practical and conceptual difficulties that arise. An Australian Aboriginal definition of health is examined. Although there are certain difficulties of translation, this definition is prominent in current Australian health policy and discourse about health. The definition can be seen as broadly holistic in comparison to other holistic definitions such as that of the World Health Organization. The nature of this holism and its grounding within the context (...) of Aboriginal Australia is discussed. In particular, its implications for the phenomenon of medicalization, which may be associated with a holistic notion of health, is critically explored, as is the link of notions of health to culture and the question of the possibility of a universal definition of health. The question of to what extent a definition of health is inspirational or operational is also raised. (shrink)

SummaryA simple and precise definition is offered of “term t of theory T being T‐theoretical” which can be applied to any formalized theory. The definition is in line with and emends traditional accounts of theoreticity. Its adequacy is demonstrated by application to three examples: exchange economics, classical mechanics and collision mechanics.

I provide a case-by-case definition of essential truths based on the notions of metaphysical necessity and ontological dependence. Relying on suggestions in the literature, I adopt a definition of the latter notion in terms of the notion of ground. The resulting account is adequate in the sense that it is not subject to Kit Fine’s famous counterexamples to the purely modal account of essence. In addition, it provides us with a novel conception of truths pertaining to the essence of objects, (...) which might help to dispel doubts on the legitimacy of the notion of essence itself. (shrink)

A general definition theory should serve as a foundation for the mathematical study of definitional structures. The central notion of such a theory is a precise explication of the intuitively given notion of a definitional structure. The purpose of this paper is to discuss the proof theory of partial inductive definitions as a foundation for this kind of a more general definition theory. Among the examples discussed is a suggestion for a more abstract definition of lambda-terms (derivations in natural (...) deduction) that could provide a basis for a more systematic definitional approach to general proof theory. (shrink)

Stakeholder theory is widely accepted but elementary aspects remain indeterminate as the term ‘stakeholder’ is an essentially contested concept, being variously describable, internally complex and open in character. Such contestability is highly problematic for theory development and empirical testing. The extent of essential contestability, previously unknown, is demonstrated in this paper through a bounded systematic review of 593 different stakeholder theory definitions. As an essentially contested concept, the solution does not lie in a universal stakeholder definition, but in debating (...) the boundaries of stakeholder identification. To this end, this paper presents the first major attempt at sorting, filtering and ordering stakeholder theory and stakeholder definitions to produce a comprehensive, multi-dimensional classification of stakeholder theory. The constructs of the classification model juxtapose existing stakeholder theories and contributions from across the multi-contextual applications of stakeholder theory, thereby providing an invaluable overview of what we know about stakeholder theory in one model. The classification model is then tested with positive results. The paper concludes with a comprehensive discussion of the implications of classification stakeholder theory definitions, which has for future research. (shrink)

Resumen: El estatuto teórico del concepto de la violencia escolar se ha resuelto parcialmente mediante el uso de definiciones. En el caso del campo científico chileno las definiciones de violencia escolar se formulan desde una episteme dualista, que establece la distinción entre lo escolar y lo no escolar, priorizan a un individuo abstracto, donde el espacio prima sobre el tiempo, las relaciones son causales y, en menor medida, de tipo covariación, constructiva de realidades y especular. El componente performativo es doble: (...) i) un modo de codificación y clasificaciones que estabilizan a un objeto que irrumpe en el campo científico y escolar; ii) producen una ausencia y exclusión de las relaciones y categorías posibles. No obstante, se observa que al interior de las propias definiciones se encuentran las semillas para un trabajo de transformación hacia epistemes no dualistas y complejas mediante las dimensiones de producción, reproducción y cruce de las violencias en la institución escolar según un enfoque tríadico. Esta reconstrucción se basa en un corpus de artículos indexados del campo de la educación sobre Chile entre los años 2001 a 2013.: The theoretical statute of the concept of school violence has been partly solved using definitions. In the case of the Chilean scientific field, the definitions of school violence are defined from a dualistic episteme that establishes the distinction between what is part of the school and what is not, that prioritizes an abstract subject, where space is more important than time, the relationships are of causal type and, to a lesser extent, of covariation type, that builds realities and that is speculative. The performative component has two aspects: i) a coding mode and classifications that stabilize an object that disrupts the scientific and school fields, and ii) produce a lack and exclusion of the relationships and potential categories. Nevertheless, it has been observed that there are some elements within the own definitions that could work for the transformation of dualistic and complex epistemes, through a dimension of production, reproduction, and the cross of different types of violence at school, following a triadic approach. This reconstruction is based on a corpus of articles from indexed journals about the Chilean educational field between 2001 and 2013. (shrink)

It is a rather remarkable fact that in most discussions of Aquinas’s ethics, Q. 21 of the De Veritate which deals with Aquinas’s notion of Good, is almost entirely overlooked. For example D. J. O’Connor’s book Aquinas and Natural Law refers only once to the De Veritate and that is not a reference to Q. 21. Even the massive work of Gilson, The Christian Philosophy of St. Thomas Aquinas, in the entire third section which deals with Aquinas’s moral theory has (...) only six references to the De Veritate and again none are to Q. 21. H. J. McCloskey in Meta-Ethics and Normative Ethics, provides what he considers two definitive repudiations of Aquinas’s theory but there is no mention or reference to the De Veritate. There may be a reason for this. Thomists like Gilson may not be attuned to or interested in answering the specific problems which contemporary ethical theorists address themselves to, while ethical theorists like O’Connor seem to depend upon traditional Thomistic accounts to locate the pertinent passages in Aquinas’s ethical writings, accounts which follow the order of one or other of the Summas. Be that as it may, some of the most illuminating sections of Aquinas dealing with ethical-theoretical issues are to be found in Question 21 of the De Veritate, for in this question is found a definition of the good as well as explanations of this definition. Consider the following passages where Aquinas lists what seem to be necessary conditions for calling something good. (shrink)

Central to much medical ethical analysis is the concept of the role of the physician. While this concept plays an important role in medical ethics, its function is largely tacit. The present paper attempts to bring the concept of a social role to prominence by focusing on an historically recent and rather richly contextured role, namely, that of consultation liaison psychiatry. Since my intention is primarily theoretical, I largely ignore the empirical studies which purport to develop the detailed functioning (...) of the role. My limited intent is to draw attention to the theoretical complexity of the consultation liaison role as an example of the general relevance of role concepts to medical ethics. For this reason, consultation liaison psychiatry will function as an illustration of fundamental concepts of medical ethics rather than as a subject of analysis in its own right. Similarly, the concept of the social role will be developed only as is necessary to explore the general relationship between the consultation liaison role and ethical analysis. Keywords: medical ethics, consultation liaison psychiatry, social role, autonomy, institution CiteULike Connotea Del.icio.us What's this? (shrink)

Definitions of terms that are central to a theoretical understanding of the Royal Government of Bhutan's policy of Gross National Happiness.

In his recent article, ``Self-Consciousness'’, George Bealer has set outa novel and interesting argument against functionalism in the philosophyof mind. I shall attempt to show, however, that Bealer's argument cannotbe sustained.In arguing for this conclusion, I shall be defending three main theses.The first is connected with the problem of defining theoreticalpredicates that occur in theories where the following two features arepresent: first, the theoretical predicate in question occurswithin both extensional and non-extensional contexts; secondly, thetheory in question asserts that the (...) relevant theoretical states enterinto causal relations. What I shall argue is that a Ramsey-styleapproach to the definition of such theoretical terms requires twodistinct quantifiers: one which ranges over concepts, and theother which ranges over properties in the world.My second thesis is a corollary: since the theories on whichBealer is focusing have both of the features just mentioned, and sincethe method that he employs to define theoretical terms in his argumentagainst functionalism does not involve both quantifiers that range overproperties and quantifiers that range over concepts, that method isunsound.My final thesis is that when a sound method is used, Bealer's argumentagainst functionalism no longer goes through.The structure of my discussion is as follows. I begin by setting out twoarguments – the one, a condensed version of Bealer's argument, andthe other, an argument that parallels Bealer's argument very closely.The parallel argument leads to a conclusion, however, that, rather thanbeing merely somewhat surprising, seems very implausible indeed. Forwhat the second argument establishes, if sound, is that there can betheoretical terms that apply to objects by virtue of their first-orderphysical properties, but whose meaning cannot be defined via aRamsey-style approach.Having set out the two parallel arguments, I then go on to focus uponthe second, to determine what is wrong with it. My diagnosis will bethat the problem with the argument arises from the fact that it involvesdefining a theoretical term that occurs both inside and outside ofopaque contexts, for the method employed fails to take into account thefact that the types of entities that are involved in the relevanttruthmakers are different when a sentence occurs within an extensionalcontext from those involved when a sentence occurs within anon-extensional context.I then go on to discuss how one should define a theoretical term thatoccurs within such theories, and I argue that in such a case one needstwo quantifiers, ranging over different types of entities – on theone hand, over properties and relations, and the other, over concepts. Ithen show that, when such an approach is followed, the argument inquestion collapses.I then turn to Bealer's argument against functionalism, and I show,first, that precisely the same method of defining theoretical terms canbe applied there, and, secondly, that, when this is done, it turns outthat that argument is also unsound.Next, I consider two responses that Bealer might make to my argument,and I argue that those responses would not succeed.Finally, I conclude by asking exactly where the problem lies in the caseof Bealer's argument. My answer will be that it is not simply the factthat one is dealing with a theoretical term that occurs in bothextensional and non-extensional contexts. It is rather the combinationof that feature together with the fact that the theory in questionasserts that the relevant type of theoretical state enters into causalrelations. For the first of these features means that the Ramseysentence for the theory must involve quantification over concepts, whilethe presence of the second feature means that the Ramsey sentence mustinvolve quantification over properties in the world, and so no attemptto offer a Ramsey-style account of the meaning of the relevanttheoretical term can succeed unless one employs both quantification overconcepts and quantification over properties. Bealer, however, in hisargument against functionalism, uses a method of defining theoreticalterms that does not involve both types of quantification, and it isprecisely because of this that his argument does not in the end succeed. (shrink)

Several recent commentators argue that Thomas Hobbes’s account of the nature of science is conventionalist. Engaging in scientific practice on a conventionalist account is more a matter of making sure one connects one term to another properly rather than checking one’s claims, e.g., by experiment. In this paper, I argue that the conventionalist interpretation of Hobbesian science accords neither with Hobbes’s theoretical account in De corpore and Leviathan nor with Hobbes’s scientific practice in De homine and elsewhere. Closely tied (...) to the conventionalist interpretation is the deductivist interpretation, on which it is claimed that Hobbes believed sciences such as optics are deduced from geometry. I argue that Hobbesian science places simplest conceptions as the foundation for geometry and the sciences in which we use geometry, which provides strong evidence against both the conventionalist and deductivist interpretations. (shrink)

. The term inversion principle goes back to Lorenzen who coined it in the early 1950s. It was later used by Prawitz and others to describe the symmetric relationship between introduction and elimination inferences in natural deduction, sometimes also called harmony. In dealing with the invertibility of rules of an arbitrary atomic production system, Lorenzen’s inversion principle has a much wider range than Prawitz’s adaptation to natural deduction. It is closely related to definitional reflection, which is a principle for reasoning (...) on the basis of rule-based atomic definitions, proposed by Hallnäs and Schroeder-Heister. After presenting definitional reflection and the inversion principle, it is shown that the inversion principle can be formally derived from definitional reflection, when the latter is viewed as a principle to establish admissibility. Furthermore, the relationship between definitional reflection and the inversion principle is investigated on the background of a universalization principle, called the ω- principle, which allows one to pass from the set of all defined substitution instances of a sequent to the sequent itself. (shrink)

Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use (...) the operational view of them as provided by uniform proof-search—the proof-theoretic foundation of logic programming (LP)—to establish the completeness of IPL for the B-eS. This perspective allows negation, a subtle issue in P-tS, to be understood in terms of the negation-as-failure protocol in LP. Specifically, while the denial of a proposition is traditionally understood as the assertion of its negation, in B-eS we may understand the denial of a proposition as the failure to find a proof of it. In this way, assertion and denial are both prime concepts in P-tS. (shrink)

This paper proposes substitutional definitions of logical truth and consequence in terms of relative interpretations that are extensionally equivalent to the model-theoretic definitions for any relational first-order language. Our philosophical motivation to consider substitutional definitions is based on the hope to simplify the meta-theory of logical consequence. We discuss to what extent our definitions can contribute to that.

This book proposes guidelines for constructing and evaluating definitions of terms, i.e. words or phrases of general application. The guidelines extend to adoption of nomenclature. The book is meant to be a practical guide for people who find themselves in their daily lives or their employment producing or evaluating definitions of terms. It can be consulted rather than being read through. The book’s theoretical framework is a distinction, due to Robert H. Ennis, of three dimensions of (...) class='Hi'>definitions: the act of the definer, the content of the definition, and its form. The act of a definer is what the definer does in defining a term; the book distinguishes, following Ennis, three basic acts of defining: reporting, stipulating, and advocating. The content of a definition is in one sense the information that the definition conveys and in another sense the words in its defining part. The form of a definition is the way it is expressed, for example as a definition by genus and differentia. (shrink)

This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descriptions recommended (...) here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’. (shrink)

In this paper we show how Dummett-Prawitz-style proof-theoretic semantics has to be modified in order to cope with paradoxical phenomena. It will turn out that one of its basic tenets has to be given up, namely the definition of the correctness of an inference as validity preservation. As a result, the notions of an argument being valid and of an argument being constituted by correct inference rules will no more coincide. The gap between the two notions is accounted for by (...) introducing the distinction between sense and denotation in the proof-theoretic-semantic setting. (shrink)

The age-old question “What is truth?” is not an unambiguous one. There are at least two different meanings. In one sense, it is a semantic question about the meaning of the word “truth” and/or a metaphysical question about the nature of the property of truth, that is, how truth can be defined in terms of other notions, if it is definable at all. In another sense, it is an epistemological question about the criterion or test of truth, that is, how (...) we can recognize or accept (empirical) propositions as true. Ayer, in Language, Truth and Logic (LTL) and some other articles, tried to convince us that when we attempt to elucidate a theory of truth, we are only engaging in the epistemological project of finding the criterion of truth. This anti-semantical and anti-metaphysical view is based on Ayer’s (radical) deflationism about truth. In this chapter, I will argue that since Ayer did not accept that the criterion of truth is intimately related to the concept of truth, he can be seen as a deflationist about the nature of truth and as an advocate of a certain (Schlickian) kind of correspondence conception about the criterion of truth. His position would not be tenable if he had maintained what some of his contemporaries accepted, namely that there is a close connection between the two truth-theoretical tasks: the definitional and the criterial one. (shrink)

The general theme of this article is the actual practice of how definitions are justified and formulated in mathematics. The theoretical insights of this article are based on a case study of topological definitions of chaos. After introducing this case study, I identify the three kinds of justification which are important for topological definitions of chaos: natural-world-justification, condition-justification and redundancy-justification. To my knowledge, the latter two have not been identified before. I argue that these three kinds (...) of justification are widespread in mathematics. After that, I first discuss the state of the art in the literature about the justification of definitions in the light of actual mathematical practice. I then go on to criticize Lakatos’s account of proof-generated definitions—the main account in the literature on this issue—as being limited and also misguided: as for topological definitions of chaos, in nearly all mathematical fields various kinds of justification are found and are also reasonable. (shrink)

The Buddhist technical term was first translated as ‘mindfulness’ by T.W. Rhys Davids in 1881. Since then various authors, including Rhys Davids, have attempted definitions of what precisely is meant by mindfulness. Initially these were based on readings and interpretations of ancient Buddhist texts. Beginning in the 1950s some definitions of mindfulness became more informed by the actual practice of meditation. In particular, Nyanaponika's definition appears to have had significant influence on the definition of mindfulness adopted by those (...) who developed MBSR and MBCT. Turning to the various aspects of mindfulness brought out in traditional Theravāda definitions, several of those highlighted are not initially apparent in the definitions current in the context of MBSR and MBCT. Moreover, the MBSR and MBCT notion of mindfulness as ‘non-judgmental’ needs careful consideration from a traditional Buddhist perspective. Nevertheless, the difference in emphasis apparent in the theoretical definitions of mindfulness may not be so significant in the actual clinical application of mindfulness techniques. (shrink)

In her commentary of Field (1999), Hammerl (1999) has drawn attention to several interesting points concerning the issue of contingency awareness in evaluative conditioning. First, she comments on several contentious issues arising from Field's review of the evaluative conditioning literature, second she critiques the data from his pilot study and finally she argues the case that EC is a distinct form of conditioning that can occur in the absence of contingency awareness. With reference to these criticisms, this reply attempts to (...) address Hammerl's comments by exploring the issues of how awareness is defined, how it is best measured, and whether it is reasonable to believe that EC uniformly occurs in the absence of contingency awareness. The article concludes that the available evidence supports Field's proposition that EC is, in fact, Pavlovian learning. (shrink)

In his paper "Are There Set Theoretic Possible Worlds?", Selmer Bringsjord argued that the set theoretic definition of possible worlds proffered by, among others, Robert Adams and Alvin Plantinga is incoherent. It is the purpose of this note to evaluate that argument. The upshot: these set theoretic accounts can be preserved, but only by abandoning the power set axiom.

In the fifth version of our response-paper [26] to Imamura’s criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy – otherwise they (...) would be inapplicable. We point out several errors and false statements by Imamura [21] with respect to the inf/sup of nonstandard subsets, also Imamura’s “rigorous definition of neutrosophic logic” is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the Transfer Principle from R to R* is questionable. After his criticism, several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such, I extended the NonStandard Analysis by adding the left monad closed to the right, right monad closed to the left, pierced binad (we introduced in 1998), and unpierced binad - all these in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of NonStandard Unit Interval and NonStandard Neutrosophic Logic, together with NonStandard Neutrosophic Operators are presented. (shrink)

When new theoretical terms are introduced into scientific discourse, prevailing accounts imply, analytic or semantic truths come along with them, by way of either definitions or reference-fixing descriptions. But there appear to be few or no analytic truths in scientific theory, which suggests that the prevailing accounts are mistaken. This paper looks to research on the psychology of natural kind concepts to suggest a new account of the introduction of theoretical terms that avoids both definition and reference-fixing (...) description. At the core of the account is a novel psychological process that I call introjection. (shrink)

I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equivalence; and "interpretational" equivalence, which is the idea that two theories are equivalent just in case they have the same interpretation. It also includes a discussion of several formal notions of equivalence that have been considered in the recent philosophical literature, including definitional (...) equivalence and categorical equivalence. The article concludes with a brief discussion of the relationship between equivalence and duality. (shrink)

As a prolegomenon to understanding the sense in which dualities are theoretical equivalences, we investigate the intuitive `equivalence' of hyper-regular Lagrangian and Hamiltonian classical mechanics. We show that the symplectification of these theories provides a sense in which they are isomorphic, and mutually and canonically definable through an analog of `common definitional extension'.

The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: (i) negative (...) introduction and elimination rules, and (ii) positive and negative introduction rules. The paper suggests a proof-theoretical definition of duality (not referring to truthtables), using which double harmony is defined. The paper proves that in a doubly-harmonious system, the coordination rule, typical to bilateral systems, is admissible. (shrink)

A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: we take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then mathematically formalised to produce a general measure of intelligence for arbitrary (...) machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines. (shrink)

This chapter criticizes the standard truth–theoretic model of implicit definition whereby we stipulate that a word is to have whatever meaning will make true a certain set of sentences containing it. The alternative model proposed here is that, in such cases, the word derives its meaning from our way of using it, from our regarding those sentences as true—and so it acquires that meaning even if they are not true. It is argued, on this basis, that there is no route (...) from meanings, so constituted, to our a priori knowledge in logic, arithmetic, or geometry. (shrink)

The paper presents an application of game-theoretical ideas to the semantics of natural language, especially the analysis of quantifiers and anaphora. The paper also introduces the idea of games of imperfect information and connects to partial logics.

One of the most significant discoveries of early twentieth century mathematical logic was a workable definition of ‘ordered pair’ totally within set theory. Norbert Wiener, and independently Casimir Kuratowski, are usually credited with this discovery. A definition of ‘ordered pair’ held the key to the precise formulation of the notions of ‘relation’ and ‘function’ — both of which are probably indispensable for an understanding of the foundations of mathematics. The set-theoretic definition of ‘ordered pair’ thus turned out to be a (...) key victory for logicism, providing one admits set theory is logic. The definition also was instrumental in achieving the appearance of ontological economy — since it seemed only sets were needed — although this feature was emphasized only later. (shrink)