This paper discusses some of the ways in which circular definitions and circular explanations entail or fail to entail infinite regresses. And since not all infinite regresses are vicious, a few criteria of viciousness are examined in order to determine when the entailment of a regress refutes a circular definition or a circular explanation.

I defend the view that circular definitions can be useful and illuminating by focusing on the fitting-attitudes analysis of value. This definition states that an item has value if and only if it is a fitting target of attitudes. Good items are the fitting targets of positive attitudes, and bad items are the fitting targets of negative ones. I shall argue that a circular version of this definition, defended by Rabinowicz and Rønnow-Rasmussen (2006), is preferable to its (...) non-circular counterpart and upholds reasonable standards of acceptability. The standards I will be discussing come from Humberstone (1997), who claims that definitions cannot be informative as long as they are inferentially circular. (shrink)

This is a collection of eighteen solicited papers on the topics of the title: circularity, definition, and truth. The papers are loosely connected in subject matter, but present a great variety of issues, theories, and approaches. Amongst the many subjects discussed are: the revision theory of truth and applications of revision rules, partiality and fixed point constructions, substitutional quantification, fuzzy logic, negation, belief revision, context dependence, hierarchies, Tarski on truth, deflationism, correspondence theories of truth, and normative aspects of truth. The (...) Liar paradox figures prominently in this collection, but is not alone. Other familiar paradoxes are also discussed, including paradoxes of definability, the Sorites paradox, and the Surprise Exam paradox. So-called paradoxes of rationality, such as the Prisoner’s Dilemma, receive attention as well. (shrink)

We present an extension of the basic revision theory of circular definitions with a unary operator, □. We present a Fitch-style proof system that is sound and complete with respect to the extended semantics. The logic of the box gives rise to a simple modal logic, and we relate provability in the extended proof system to this modal logic via a completeness theorem, using interpretations over circular definitions, analogous to Solovay’s completeness theorem forGLusing arithmetical interpretations. We (...) adapt our proof to a special class of circular definitions as well as to the first-order case. (shrink)

Gupta's and Belnap's Revision Theory of Truth defends the legitimacy of circular definitions. Circularity, however, forces us to reconsider our conception of meaning. A readjustment of some standard theses about meaning is here proposed, by relying on a novel version of the sense-reference distinction.

The classical theory of definitions bans so-called circular definitions, namely, definitions of a unary predicate P, based on stipulations of the form $$Px =_{\mathsf {Df}} \phi,$$where ϕ is a formula of a fixed first-order language and the definiendumP occurs into the definiensϕ. In their seminal book The Revision Theory of Truth, Gupta and Belnap claim that “General theories of definitions are possible within which circular definitions [...] make logical and semantic sense” [p. IX]. (...) In order to sustain their claim, they develop in this book one general theory of definitions based on revision sequences, namely, ordinal-length iterations of the operator which is induced by the definition of the predicate. Gupta-Belnap’s approach to circular definitions has been criticised, among others, by D. Martin and V. McGee. Their criticisms point to the logical complexity of revision sequences, to their relations with ordinary mathematical practice, and to their merits relative to alternative approaches. I will present an alternative general theory of definitions, based on a combination of supervaluation and ω-length revision, which aims to address some criticisms raised against revision sequences, while preserving the philosophical and mathematical core of revision. (shrink)

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.

Circular denitions have primarily been studied in revision theory in the classical scheme. I present systems of circular denitions in the Strong Kleene and supervaluation schemes and provide complete proof systems for them. One class of denitions, the intrinsic denitions, naturally arises in both schemes. I survey some of the features of this class of denitions.

This original and enticing book provides a fresh, unifying perspective on many old and new logico-philosophical conundrums. Its basic thesis is that many concepts central in ordinary and philosophical discourse are inherently circular and thus cannot be fully understood as long as one remains within the confines of a standard theory of definitions. As an alternative, the authors develop a revision theory of definitions, which allows definitions to be circular without this giving rise to contradiction (...) (but, at worst, to “vacuous” uses of definienda). The theory is applied with varying levels of detail to a circular analysis of concepts as diverse as truth, predication, necessity, physical object, etc. The focus is on truth, and hope is expressed that a deeper understanding of the Liar and related paradoxes has been provided: “We have tried to show that once the circularity of truth is recognized, a great deal of its behavior begins to make sense. In particular, from this viewpoint, the existence of the paradoxes seems as natural as the existence of the eclipses” (p. 142). We think that this hope is fully justified, although some problems remain that future research in this field should take into account. (shrink)

Analyses, in the simplest form assertions that aim to capture an intimate link between two concepts, are viewed since Russell's theory of definite descriptions as analyzing descriptions. Analysis therefore has to obey the laws governing definitions including some form of a Substitutivity Principle (SP). Once (SP) is accepted the road to the paradox of analysis is open. Popular reactions to the paradox involve the fundamental assumption (SV) that sentences differing only in containing an analysandum resp. an analysans express the (...) same proposition, because analysandum and analysans are the same entity. Following suggestions of Gupta and Belnap it is argued that (SV) should be rejected. (shrink)

Analyses, in the simplest form assertions that aim to capture an intimate link between two concepts, are viewed since Russell's theory of definite descriptions as analyzing descriptions. Analysis therefore has to obey the laws governing definitions including some form of a Substitutivity Principle (SP). Once (SP) is accepted the road to the paradox of analysis is open. Popular reactions to the paradox involve the fundamental assumption (SV) that sentences differing only in containing an analysandum resp. an analysans express the (...) same proposition, because analysandum and analysans are the same entity. Following suggestions of Gupta and Belnap it is argued that (SV) should be rejected. (shrink)

I aim to show how and why some definitions can be benignly circular. According to Lloyd Humberstone, a definition that is analytically circular need not be inferentially circular and so might serve to illuminate the application-conditions for a concept. I begin by tidying up some problems with Humberstone's account. I then show that circular definitions of a kind commonly thought to be benign have inferentially circular truth-conditions and so are malign by Humberstone's test. (...) But his test is too demanding. The inferences we actually use to establish the applicability of, e.g., colour concepts are designed to establish warranted assertability and not truth. Understood thus, dispositional analyses are not inferentially circular. (shrink)

Several scholars have argued that Wittgenstein held the view that the notion of number is presupposed by the notion of one-one correlation, and that therefore Hume's principle is not a sound basis for a definition of number. I offer a new interpretation of the relevant fragments on philosophy of mathematics from Wittgenstein's Nachlass, showing that if different uses of ‘presupposition’ are understood in terms of de re and de dicto knowledge, Wittgenstein's argument against the Frege-Russell definition of number turns out (...) to be valid on its own terms, even though it depends on two epistemological principles logicist philosophers of mathematics may find too ‘constructivist’. (shrink)

There have long been calls from industry for guidance in implementing strategies for sustainable development. The Circular Economy represents the most recent attempt to conceptualize the integration of economic activity and environmental wellbeing in a sustainable way. This set of ideas has been adopted by China as the basis of their economic development, escalating the concept in minds of western policymakers and NGOs. This paper traces the conceptualisations and origins of the Circular Economy, tracing its meanings, and exploring (...) its antecedents in economics and ecology, and discusses how the Circular Economy has been operationalized in business and policy. The paper finds that while the Circular Economy places emphasis on the redesign of processes and cycling of materials, which may contribute to more sustainable business models, it also encapsulates tensions and limitations. These include an absence of the social dimension inherent in sustainable development that limits its ethical dimensions, and some unintended consequences. This leads us to propose a revised definition of the Circular Economy as “an economic model wherein planning, resourcing, procurement, production and reprocessing are designed and managed, as both process and output, to maximize ecosystem functioning and human well-being”. (shrink)

This dissertation is a study of some recent theories of truth. The theories fall into three groups: The Revision Theories, the context-sensitive theories, and the "Chrysippian theories". ;The "Chrysippian theories" are based on the intuition that pathologicalities arising from the concept of truth can be recognized and acknowledged with the concept of truth itself. Thus, from the pathologicality of the Liar, for example, we can conclude that the Liar is not true. This leads to immediate difficulties since the Liar claims (...) just that--that it is not true--and it would thus seem to be true. The Chrysippian theories are designed to avoid these difficulties while preserving the motivating intuition. Haim Gaifman's Pointer Semantics, and Brian Skyrms' Intensional Fixed-Point Theory of Truth are examples of such theories. They are exposited and criticized. ;The context-sensitive theories dealt with are Tyler Burge's Indexical Theory of Truth and the theory of Jon Barwise and John Etchemendy. These theories claim that an ambiguity due to a contextual parameter is the reason for the difficulties we encounter. Burge offers a theory of Tarskian levels coupled with a pragmatic theory that explains the assignment of levels to occurrences of 'true'. Barwise and Etchemendy make explicit a situational parameter in their account of propositions. They consider the ambiguity with respect to the situation a propositions is about a main source of the paradoxes. ;Finally, the Revision Theories of Truth of Anil Gupta and Nuel Belnap and two variations of this theory are considered. One is due to Aladdin Yaqub, the other, the "fully-varied theory", is due to Gupta and Belnap but remains largely unexplored. Revision theories are put forward as the most promising account of the difficulties. They are based on a definitional reading of all Tarski biconditionals. The circularity implied by such a reading is handled by Gupta's and Belnap's general theory of definitions. ;Yaqub's objections raised against the standard theory are examined, and his proposed solution is shown to be inadequate. The fully-varied Revision Theory is shown to provide a better solution. (shrink)

Sometimes pernicious circularities appear in definitions of fundamental concepts of argumentation theory. For instance, in pragma-dialectical theory, the concept of a fallacy and that of a critical discussion aiming at resolving a difference of opinion mutually presuppose one another. A similar relationship obtains, in argumentation theory at large, between the concept of argumentation and that of rationality. Again, the concept of an argumentative dialogue presupposes a concept of statement. Yet, statementhood is sometimes claimed to be determined by a locution’s (...) function in dialogue. Similarly, for the concepts of proof and argument. Are these circularities really objectionable? Are they resolvable? If they are not, how can we live with them? It will be argued that some of these problems can be neglected some of the time, but not all of them all of the time. Though there may be no royal road towards resolution, several strategies can be applied. But sometimes patience is what is needed. (shrink)

In this paper, we strengthen Hardy’s [1995] and Ketland’s [2005] arguments on the issues surrounding the self-referential nature of Yablo’s paradox [1993]. We first begin by observing that Priest’s [1997] construction of the binary satisfaction relation in revealing a fixed point relies on impredicative definitions. We then show that Yablo’s paradox is ‘ω-circular’, based on ω-inconsistent theories, by arguing that the paradox is not self-referential in the classical sense but rather admits circularity at the least transfinite countable ordinal. (...) Hence, we both strengthen arguments for the ω-inconsistency of Yablo’s paradox and present a compromise solution of the problem emerged from Yablo’s and Priest’s conflicting theses. (shrink)

Contemporary philosophical accounts of the applicability of mathematics in physical sciences and the empirical world are based on formalized relations between the mathematical structures and the physical systems they are supposed to represent within the models. Such relations were constructed both to ensure an adequate representation and to allow a justification of the validity of the mathematical models as means of scientific inference. This article puts in evidence the various circularities (logical, epistemic, and of definition) that are present in these (...) formal constructions and discusses them as an argument for the alternative semantic and propositional-structure accounts of the applicability of mathematics. (shrink)

In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that such (...) formalization shows that Yablo’s Paradox involves implicit circularity. In the same direction, Beall (2001) has introduced epistemic factors in this discussion. Even more, Priest has also argued that the introduction of infinitary reasoning would be of little help. Finally, one could reject definitions of circularity in term of fixed-point adopting non-well-founded set theory. Then, one could hold that the Yablo paradox and the Liar paradox share the same non-well-founded structure. So, if the latter is circular, the first is too. In all such cases, I survey Cook’s approach (2006, forthcoming) on those arguments for the charge of circularity. In the end, I present my position and summarize the discussion involved in this volume. En este artículo, describo y examino los principales resultados vinculados a la formalización de la paradoja de Yablo en la aritmética. Aunque es natural suponer que hay una representación correcta de la paradoja en la aritmética de primer orden, hay algunos resultados técnicos que hacen surgir dudas acerca de esta posibilidad. Más aún, presento algunos argumentos que han cuestionado que la construcción de Yablo no sea circular. Así, Priest (1997) ha argumentado que la formalización de la paradoja de Yablo en la aritmética de primer orden muestra que la misma involucra implícitamente circularidad. En la misma dirección, Beall (2001) ha introducido factores epistémicos en esta discusión. Más aún, Priest ha también argumentado que la introducción de razonamiento infinitario como complemento de la formalización en la aritmética sería de poca ayuda. Finalmente, se podría rechazar todo intento de dar definiciones de circularidad en términos de puntos fijos adoptando teoría de conjuntos infundados. Entonces, se podría sostener que la paradoja de Yablo y la del mentiroso comparten la misma estructura infundada. Por eso, si la última es circular, también lo es la primera. En todos los casos, presento el enfoque de Roy Cook (2006, en prensa) sobre estos argumentos que atribuyen circularidad a la construcción de Yablo. En el final, presento mi posición y un breve resumen de la discusión involucrada en este volumen. (shrink)

In my response to the paper by Jagers op Akkerhuis, I object against giving definitions of life, since they bias anything that follows. As we don’t know how life originated, authors characterise life using criteria derived from present-day properties, thus emphasising widely different ones, which gives bias to their further analysis. This makes their results dependent on their initial suppositions, which introduces circularity in their reasoning.

The International System of Units tries to find or construct something that does not change with time and place, since such constancy is the best possible ground for definitions of fundamental measurement units. This problem of constancy has received scant attention within the philosophy of science, but is the topic of the paper. The paper first highlights inevitable kinds of circularities, semantic and epistemic, that belongs to the search for constancy, and then discusses contingent dependencies between unit definitions. (...) The New SI proposal is criticized for not paying due attention to the fact that it defines units for one kind of quantity by means of a constancy that belongs to another. This inattention flaws the kilogram definition. The New SI definitions of the mole and the second neglect the distinction between discrete and continuous quantities; which make the definitions refer to constancies that are not invariants of nature. (shrink)

The comments focus on a presumed circular reasoning in the operator hierarchy and the necessity of understanding life’s origin for defining life. Below it is shown that its layered structure prevents the operator hierarchy from circular definitions. It is argued that the origin of life is an insufficient basis for a definition of life that includes multicellular and neural network organisms.

According to the standard definition of time travel due to David Lewis, an object time travels if and only if the separation in time between departure and arrival does not equal the duration of its journey. After arguing that the standard definition of time travel is inadequate by discussing a world with circular time, I suggest a new definition of time travel that does not fail in situations involving circular time.

Since summer 2019 there is a new document that defines what in science should be regarded as being one second, one meter, and one kilogram, respectively. It is the ninth edition of the SI Brochure. Compared with older editions, a new definitional approach has been used. The seven base units are now defined by being directly related to a so-called defining constant. The paper discusses the second, the meter, and the kilogram. One odd salient, but nonetheless not discussed, feature of (...) the formulations of the definitions is that, from a purely linguistic point of view, they are circular. That is, symbols for what is to be defined appear also in the defining expressions. However, underneath the circularities there are, appearances notwithstanding, substantially non-circular definitions. The aim of the paper is to uncover these never before presented definitional structures. It is made by means of the two notions absolutely discrete quantities and metrical coordinative definitions. When the true definitional structures become visible, two important substantial metrological facts can be seen. First, the new definition of the kilogram is very much in need of further discussion. Second, contrary to what the Brochure hints at, there is no need to try to exchange the atomic parameter used in the definition of the second. (shrink)

THE PROJECT OF THIS PAPER IS TO GIVE AN EXPLICIT DEFINITION OF 'PRIMA FACIE' DUTY EMPLOYING THE NOTION OF DUTY (SIMPLICITER) AS THE ONLY MORAL NOTION. THIS DEFINITION AVOIDS THE CIRCULARITY OF SOME DEFINITIONS WHILE ALSO BEING SUFFICIENTLY GENERAL SO AS NOT TO DEPEND ON THE ADOPTION OF ANY PARTICULAR MORAL VIEWPOINT. THIS PAPER ATTACKS THE VIEW THAT A MORAL PHILOSOPHER (OR AN ANTHROPOLOGIST DESCRIBING A MORAL CODE) CAN ALWAYS IN PRINCIPLE AVOID EMPLOYING THE NOTION OF A 'PRIMA FACIE' (...) DUTY SIMPLY BY GIVING A CAREFUL STATEMENT OF EACH RULE MAKING EXPLICIT ITS EXCEPTIONS. (shrink)

In the history of philosophy, especially its recent history, a number of definitions of necessity have been ventured. Most people, however, find these definitions either circular or subject to counterexamples. I will show that, given a broadly Fregean conception of properties, necessity does indeed have a noncircular counterexample-free definition.

In lieu of an abstract, here is a brief excerpt of the content:Against DefinitionEric Matthews (bio)Keywordsdefinition, mental illness, ideologyVarelius rightly says, in the very first sentence of his article, that 'The nature of mental disorder is a controversial issue.' But I do not think he recognizes just how deeply controversial it is. He hopes to be able to find a way of resolving the controversy by his chosen method, based on a consideration of 'the goals that we have in classifying (...) certain persons as mentally disordered.' However, not only does the adoption of that method presuppose that the controversy is resoluble, it is also somewhat circular. For, to be able to set out the goals that we have in classifying some people as mentally disordered, we already have to know which persons we so classify, and so what is meant by calling them 'mentally disordered.' There are several appeals to alleged 'intuitions' and one to a 'paradigm case' in Varelius's article; but, if we had such intuitions, they would be all we needed to define the concept of mental disorder, and there would be no need for the further reference to our goals in demarcating this class of human conditions.I want to argue that any alleged 'intuitions' we might have in regard to mental disorder are philosophically useless, and that the controversy about the nature of mental disorder is intrinsically irresoluble. Any claimed intuition can always be met by a rival intuition that is irreconcilable with the first. It is this, indeed, that makes the dispute about mental disorder essentially philosophical, rather than scientific, in character. Philosophical positions have to be based on, and defended by, rational argument, but there necessarily comes a point in any philosophical dispute at which no rational argument can settle the matter one way or the other. Varelius derives his methodology of considering goals of demarcation from some work done using this method on the concept of science. But people have different goals for demarcating 'science' from 'non-science' or 'pseudo-science.' The demarcation is not made, as Varelius suggests, on the basis of such criteria as testability of hypotheses or clarity of concepts; or rather, the application of these criteria themselves is determined by the goals of demarcation.The debate about what is to count as a 'science' is irresoluble in part because what we classify as such has evaluative and practical consequences. To be a 'science,' in our culture, is to be a valued activity, to have a status to be aspired to. This makes arguments about what it is to be scientific what I would like to call 'ideological' in character. Similar considerations apply to the dispute about the nature of mental disorder. Human societies have always distinguished madness from reason, disturbed or disordered behavior, thoughts, and emotions from those that are not disordered. But the purpose of making the distinction, and thus the character of the distinction made, has varied from society to society and from one historical period to another. The historian Roy Porter, in his short work Madness: A Brief History (2002) describes some of the different images of madness which have prevailed at different times in Western culture—as a divine punishment for hubris, as [End Page 53] a source of poetic inspiration, as the inevitable result of moral excess, as diabolical possession, and so on. The modern idea of mental disorder as mental illness is only one possible way of classifying together certain sorts of deviations from normality.Varelius's method of arriving at a definition of mental illness involves 'considering the goals that we have in classifying certain persons as mentally disordered.' But we can ask who are the 'we' in question, and whether 'we' have only one set of goals in classifying people in this way. The history referred to in the preceding paragraph suggests that 'we' means those members of society who do not regard themselves as disordered—the 'normal' people whose behavior can be readily understood by other normal people. Classifying someone as mentally disordered is distinguishing them as 'not one of us,' and this can serve various purposes, for instance, treating them as objects of entertainment in a human zoo, as in Bedlam; or treating them as moral... (shrink)

I argue that a general logic of definitions must tolerate ω‐inconsistency. I present a semantical scheme, S, under which some definitions imply ω‐inconsistent sets of sentences. I draw attention to attractive features of this scheme, and I argue that S yields the minimal general logic of definitions. I conclude that any acceptable general logic should permit definitions that generate ω‐inconsistency. This conclusion gains support from the application of S to the theory of truth.

Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of arithmetical induction. This (...) proves, without any use of arithmetical induction, that Frege's definition is extensionally correct and so answers the circularity objections. (shrink)

We propose that, for the purpose of studying theoretical properties of the knowledge of an agent with Artificial General Intelligence (that is, the knowledge of an AGI), a pragmatic way to define such an agent’s knowledge (restricted to the language of Epistemic Arithmetic, or EA) is as follows. We declare an AGI to know an EA-statement φ if and only if that AGI would include φ in the resulting enumeration if that AGI were commanded: “Enumerate all the EA-sentences which you (...) know.” This definition is non-circular because an AGI, being capable of practical English communication, is capable of understanding the everyday English word “know” independently of how any philosopher formally defines knowledge; we elaborate further on the non-circularity of this circular-looking definition. This elegantly solves the problem that different AGIs may have different internal knowledge definitions and yet we want to study knowledge of AGIs in general, without having to study different AGIs separately just because they have separate internal knowledge definitions. Finally, we suggest how this definition of AGI knowledge can be used as a bridge which could allow the AGI research community to import certain abstract results about mechanical knowing agents from mathematical logic. (shrink)

Une théorie physique s'appuie généralement sur un modèle physique. Un modèle habituel est formé par des corps en mouvements rectilignes uniformes. Il est tout aussi légitime de considérer un autre modèle formé par des corps en mouvements circulaires uniformes. Les conclusions concernant la simultanéité, l'écoulement du temps, obtenues à partir du premier modèle, ne semblent pas pouvoir être étendues au second.A physical theory is generally based on a physical model. One ordinary model consists of bodies in uniform rectilinear motion. It (...) is just as legitimate to consider another model consisting ofbodi.es in uniform circular motion. It seems that the conclusions on simultaneity obtained from the uniform rectilinear model cannot be extended to the uniform circular model. (shrink)

We start by noting that the set-theoretic and semantic paradoxes are framed in terms of a definition or series of definitions. In the process of deriving paradoxes, these definitions are logically represented by a logical equivalence. We will firstly examine the role and usage of definitions in the derivation of paradoxes, both set-theoretic and semantic. We will see that this examination is important in determining how the paradoxes were created in the first place and indeed how they (...) are to be solved in a uniform way. There are three features that are special about these definitions used in the derivation of most of the above paradoxes. The first is the use of self-reference between the definiens and the definiendum, the second is the generality of the definiendum, and the third is the under-determination and over-determination of concepts that usually occur as a result of these definitions. We will examine the impact of these three features on the logical representation of definitions and show how this representation then leads to a uniform paradox solution using an appropriate logic that is both paraconsistent and paracomplete. However, it is the paracompleteness, exhibited through the rejection of the Law of Excluded Middle, together with the rejection of contraction principles, that enables the solution of the paradoxes to go through. We characterize definitions as involving syntactic identity and/or meaning identity. We point out that some paradoxes do not have explicit self-reference or circularity and some may not utilize the generality of the definiendum, but the general characterizations of definitions that we give will still apply. We also look beyond all this to paradoxes that rely on illicit definitions between objects that are essentially different to start with. (shrink)

Russell’s type theory has been the standard property theory for years, relying on rigid type distinctions at the grammatical level to circumvent the paradoxes of predication. In recent years it has been convincingly argued by Bealer, Cochiarella, Turner and others that many linguistic and ontological data are best accounted for by using a type-free property theory. In the spirit of exploring alternatives and “to have as many opportunities as possible for theory comparison”, this paper presents another type-free property theory, to (...) be called P*, intended for applications in Montague-style natural language semantics and formal ontology. The theory is philosophically grounded on Gupta’s and Belnap’s revision theory of definitions and its basic idea is viewing predication (exemplification) as a ‘circular concept’ that can be captured by circular definitions. The paper has the following fourteen sections: (1) Introduction; (2) Formal type-free property theory; (3) Applying RTD [revision theory of definitions] to exemplification; (4) The system P*; (5) Some features of P*; (6) A comparison with Turner’s system; (7) Entailment and P*; (8) P* and natural language semantics; (9) Noun phrases; (10) The need for type-freedom in semantics; (11) Arithmetic in P*; (12) Arithmetic in PN*; (13) Complexity of P*; (14) Conclusion, and acknowledgments. (shrink)

This commentary argues that the question of metalanguage is a key issue in emotion research. Izard (2010) ignores this issue (and all the earlier literature relating to it, including the debate in Emotion Review, 2009, 1[1]), and thus falls into the old traps of circularity, obscurity, and ethnocentrism. This commentary rejects Izard’s claim that “emotion” defies definition, and it offers a viable definition of “emotion” formulated in simple and universal human concepts, using the English version of the universal conceptual lingua (...) franca called Natural Semantic Metalanguage (NSM). Once again, this commentary draws attention to the centrality of the question of language in emotion research. (shrink)

A Nyaya definition the major purpose of which is efficient use of words and avoiding ambiguities and errors, is the statement of a unique feature that belongs to each definiendum and nothing else so that there is none of the three faults of overcoverage, undercoverage and failure to belong to any definiendum. There should be no circularity that is of three kinds, self-dependence (where the definiendum appears in the definiens); mutual dependence (where the definiendum and the definiens are used in (...) the definition of each other) and defining in a circle. A definition should also be economical: there are mainly three kinds of economy; economy in constitution (that avoids including anything superfluous or unnecessary to distinguish the definiendum from everything else), economy in relation (the directly related is preferable to the indirectly related) and economy in cognition (something cognitively prior is preferable to something posterior). While more than one definition is possible that need not state the essence, the test of economy is in place to avoid redundancy and provide criteria of preference among defining features that are unique and non-circular. (shrink)

Much of the scholarship on Kant’s theory of concept formation has focused on the question of whether his theory suffers from circularity, i. e., whether it presupposes the very concepts whose origin it should explain. In this article, I defend Kant against a well-known objection raised by Hannah Ginsborg. Ginsborg, I argue, overlooks the relatively narrow aim of Kant’s theory of concept formation. Kant explicitly frames it as an account of a concept’s inherent generality, or form. However, Ginsborg’s objection is (...) not about a concept’s form; it concerns the concept’s content. Moreover, Kant addresses the issue that she raises in his theory of definitions, which explains how a concept’s content can be revised and perfected. Kant considered all empirical concepts to be incomplete and imprecise. For this reason, he denied that they can be properly defined. Kant also did not regard the content of empirical concepts as fixed or permanent. Indeed, he expected that we would continually expand and revise their content on the basis of experience. I argue that these facts, along with the narrow scope of Kant’s theory of concept formation, effectively defuse Ginsborg’s objection. (shrink)