The standard version of the story of Russell's theory of types gives legitimately precedence to the vicious circle principle, but it fails to appreciate the significance of the doctrine of incomplete symbols and of the ultimate universalist perspective of Russell's logic. It is what the Author tries to do. This enables him to resolve the apparent contradiction which exists in "Principles" between the ontological commitment of the theory itself with respect to individuals, propositions, and functions, and the (...) inventory of the world, according to which there are only individuals and elementary facts. (shrink)

SummaryP. Vardy asserts the thesis that the vicious circle principle has the same structure as Russell's paradox. But structure is not the thing itself. It is the thing objectivated from the wiewpoint of a mathematician. So this structure can be expressed in a mathematical formalism, e. g. the Λ‐calculus. Russell's paradox is understood as a result of the error of taking purely logical concepts, like negation, as lkiewise formalisable without change of meaning. The illusion of meaning in (...) the liar's proposition: Yl'am telling a lie can also be explained be the formalisable self‐referential structure of this proposition. Yet it remains an illusion because the logical intention cannot follow the structure.ResumeLe « Principe du cercle vicieux » a la même structure que le paradoxe de Russel: c'est une thèse de P. Várdy. Mais la structure n'est pas la chose même. Elle est la chose objectivée du point de vue du mathématicien et peut done être exprimée dans un formalisme mathématique, p. ex. le Λ‐calcul. L'erreur qui conduit au paradoxe de Russel, c'est de juger des concepts purement logique, p. ex. la négation, comme étant également exprimable dans un formalisme sans que leur sens ne change.L'illusion de sens que donne l'énoncé«je mens» dans le paradoxe du menteur peut aussi être expliquée par la structure formalisable d'autoréférence de cette proposition. Mais l'illusion persiste, parce que l'intention logique ne peut pas suivre la structure.ZusammenfassungRussells «Vicious circle principle» hat dieselbe Struktur wie die Russellsche Antinamie. So lautet die These P. Várdys. Aber die Struktur ist nicht die Sache selbst, sondern nur die vom mathematischen Standpunkte aus objektivierte Sache, die in einem Formalis‐onus ausgedrückt werden kann. Die Antinomie Russells wird Als Folge der irrigen Auffassung verstanden, rein logische Begriffe, wie z. B. die Negation, konnten formalisiert werden, ohne dass dabei ihr Sinn verwandelt würde. Die Sinnillusion des Satzes «Ich lüge» kann dann auch aus der selbstbezüglichen formalen Struktur des Satzes erklärt werden. Doch bleibt dies blosse Illusion, weil die logische Intention der Struktur nicht gerecht werden kann. (shrink)

Prompted by Poincaré, Russell put forward his celebrated vicious-circle principle (vcp) as the solution to the modern paradoxes. Ramsey, Gödel, and Quine, among others, have raised two salient objections against Russell's vcp. First, Gödel has claimed that Russell's various renderings of the vcp really express distinct principles and thus, distinct solutions to the paradoxes, a claim that gainsays one of Russell's positions on the nature of the solution to the paradoxes, namely, that such a solution be uniform. (...) Secondly, Ramsey, Gödel, and Quine have protested that the vcp's proscription against impredicative specification is incompatible with a realistic conception of the domain of quantification, a conception that Russell certainly held. I examine Russell's vcp and defend it against these objections. (shrink)

In a definition (∀ x )(( x є r )↔D[ x ]) of the set r, the definiens D[ x ] must not depend on the definiendum r . This implies that all quantifiers in D[ x ] are independent of r and of (∀ x ). This cannot be implemented in the traditional first-order logic, but can be expressed in IF logic. Violations of such independence requirements are what created the typical paradoxes of set theory. Poincaré’s Vicious (...) class='Hi'>Circle Principle was intended to bar such violations. Russell nevertheless misunderstood the principle; for him a set a can depend on another set b only if ( b є a ) or ( b ⊆ a ). Likewise, the truth of an ordinary first-order sentence with the Gödel number of r is undefinable in Tarki’s sense because the quantifiers of the definiens depend unavoidably on r. (shrink)

Here we give a semantical account of propositional quantification that is intended to formally represent Russell’s view that one cannot express a proposition about "all" propositions. According to the account the authors give, Russell’s view bears an interesting relation to the view that there are no sets which are members of themselves.

The classical paradox of the stone, namely, whether an omnipotent being can create a stone that the being itself cannot lift is traditionally circumvented by a response propounded by Thomas Aquinas, that even omnipotent beings cannot accomplish the logically impossible. However, in their paper “The New Paradox of the Stone,” Alfred R. Mele and M.P. Smith attempt to reinstate the paradox without falling foul of the Thomistic logical constraint. According to Mele and Smith, instead of interpreting the paradox as posing (...) a competition between a pair of omnipotent beings—represented by God at two different times—the paradox can be reformulated as posing a question about simultaneous competition between a pair of omnipotent beings. The purpose of this paper is, therefore, to probe the possibility of the simultaneous existence of two omnipotent beings in view of the theological arguments for the “unicity of the omnipotent.”. (shrink)

To investigate the phenomenon of patient–physician mistrust in China, a qualitative study involving 107 physicians, nurses and health officials in Guangdong Province, southern China, was conducted through semi-structured interviews and focus groups. In this paper we report the key findings of the empirical study and argue for the essential role of medical professionalism in rebuilding patient-physician trust. Health professionals are trapped in a vicious circle of mistrust. Mistrust leads to increased levels of fear and self-protection by doctors which (...) exacerbate difficulties in communication; in turn, this increases physician workloads, adding to a strong sense of injustice and victimization. These factors produce poorer healthcare outcomes and increasingly discontented and angry patients, escalate conflicts and disputes, and result in negative media coverage, all these ultimately contributing to even greater levels of mistrust. The vicious circle indicates not only the crisis of patient-physician relationship but the crisis of medicine as a profession and institution. Underlying the circle is the inherent conflict of interest in the healthcare system by which health professionals and hospitals have become profit-driven. This institutional conflict of interest seriously compromises the fundamental principle of medical professionalism—the primacy of patient welfare—as well as the traditional Chinese ideal of “medicine as the art of humanity”. Patient trust can be restored through rectifying this institutional conflict of interest and promoting medical professionalism via a series of recommended practical measures. (shrink)

[full article, abstract in English; abstract in Lithuanian] Modern revolution as the beginning of founding a new political order has to confront the vicious circle inhered in all beginnings: in so far as it is the beginning, where does its principle come from? Or, if there is no principle, how could the beginning establish one? Set in the context of modern political experience, the aporia is equal to the problem of how modern politics to be self-grounded (...) or how to reestablish political authority in modernity? By an exploration into the relevant writings of Hannah Arendt, the article tries to investigate the vicious circle of beginning and principle in the political realm, and to point out that Arendt has told a story about the mutual generating of beginning and principle, turning the so-called vicious circle into a hermeneutic circle, in which those implicit principles become explicit through the performance of founding actions. (shrink)

Legal and sociological theories of sovereignty disagree about the role of legal and social matters in grounding state power. This paper defends a constructivist view, according to which the constitution is a judgment of practical reason. The paper argues that a constitution sets out a comprehensive institutional architecture of social life in terms of principles and official roles that are necessary for any legitimate scheme of social cooperation to exist. It follows that legal and sociological theories of sovereignty capture only (...) part of the truth of sovereignty. Legal reasoning engages with political power, but it is not determined by it. There is no causal chain between power and validity, as suggested by the legal positivists. The relation between power and law is interpretive, not causal. It follows that the circularity of law and the constitution, namely the fact that the law makes the constitution and the constitution makes the law, is not a vicious circle. It is part of an ordinary process of deliberation. (shrink)

In the literature, predicativism is connected not only with the Vicious Circle Principle but also with the idea that certain totalities are inherently potential. To explain the connection between these two aspects of predicativism, we explore some approaches to predicativity within the modal framework for potentiality developed in Linnebo (2013) and Linnebo and Shapiro (2019). This puts predicativism into a more general framework and helps to sharpen some of its key theses.

Russell takes his paper ?On denoting? to have achieved the repudiation of the theory of denoting concepts and Frege?s theory of sense, and the invention of the notion of incomplete symbols.This means that Russell attempts to solve the set theoretic and semantic paradoxes without making use of a theory of sense.Instead, his strategy is to revise his logical ontology by arguing that certain symbols should be treated as incomplete.In constructing such arguments Russell, at various points, makes use of epistemological and (...) metaphysical considerations.These arguments do not form themselves into a systemic set of considerations to be used in appraising a logical system.Finally, the vicious circle principle is argued for on the basis of considerations, which are presumed evident, about the nature of propositional functions.The stringency of this principle is a basic problem for the system of Principia mathematica.However, even given the terms of the argument, ?On denoting? does not offer a complete repudiation of the notion of sense.This allows the possibility of retaining some of the insights of Principia mathematica whilst rejecting the stringency of the vicious circle principle.The basis of such a system is the theory of sense. (shrink)

This work is, in large part, a series of refutations; it is also the author's Ph.D. thesis. First to be refuted is Russell's vicious circle principle as a general remedy for the solution of the paradoxes. The author rejects the classification of paradoxes into syntactic and semantic, since in his view there are no purely syntactic paradoxes. The distinction in logic between the uninterpreted syntactical aspect of a system and the system when given a determinate interpretation is (...) held to be untenable. Tarski's distinction between object-language and meta-language and his concept of semantically closed language are considered irrelevant for the solution of the Liar paradox. The author claims that the usual versions of the Liar paradox have the same structure as the Barber paradox, viz., [S ↔ ~S]. The author solves the Liar paradox by pointing out that it does not have a proper reference. Cantor's diagonal argument for the indenumerability [[sic]] of the real numbers is labeled as unsatisfactory. Since the diagonal number is dependent upon the real numbers in the constructed list, the author claims that this makes the diagonal number to be of a different nature and status than the real numbers in the list; thus we have what the author calls the dependence fallacy. The author also refuses to accept Cantor's nested interval proof of the indenumerability [[sic]] of the real numbers. Within the proof, two infinite sequences are constructed, each of which converges to a limit. Because the proof does not give a "definite rule of convergence," the author is not satisfied that the infinite sequences converge. Also rejected is Cantor's theorem. Other paradoxes analyzed are the Berry, Richard, heterological, "Richardian", Russell, Cantor, and Burali-Forti paradoxes.--T. G. N. (shrink)

A paradox, according to Wittgenstein, is something surprising that is taken out of its context. Thus, one way of dealing with paradoxical sentences is to imagine the missing context of use. Wittgenstein formulates what I call the paradigm paradox: ‘one sentence can never describe the paradigm in another, unless it ceases to be a paradigm.’ There are several instances of this paradox scattered throughout Wittgenstein’s writings. I argue that this paradox is structurally equivalent to Russell’s paradox. The above quotation is (...) Wittgenstein’s version of the vicious circle principle which counteracts the paradox. The prohibition Wittgenstein describes is, however, limited to a certain language-game. Finally, I argue that there is a structural analogy between a noun being employed as a self-membered set and a paradigmatic sample being included in or excluded from the set it generates. Paradoxical sentences are not prohibited forever; they can indicate a change in our praxis with a given paradigm. (shrink)

A paradox, according to Wittgenstein, is something surprising that is taken out of its context. Thus, one way of dealing with paradoxical sentences is to imagine the missing context of use. Wittgenstein formulates what I call the paradigm paradox: ‘one sentence can never describe the paradigm in another, unless it ceases to be a paradigm.’ (PG, p.346) There are several instances of this paradox scattered throughout Wittgenstein’s writings. I argue that this paradox is structurally equivalent to Russell’s paradox. The above (...) quotation is Wittgenstein’s version of the vicious circle principle which counteracts the paradox. The prohibition Wittgenstein describes is, however, limited to a certain language-game. Finally, I argue that there is a structural analogy between a noun being employed as a self-membered set and a paradigmatic sample being included in or excluded from the set it generates. Paradoxical sentences are not prohibited forever; they can indicate a change in our praxis with a given paradigm. (shrink)

The paper defends the philosophical method of "regimentation" by example, especially in relation to the theory of mind. The starting point is the Place-Smart after-image argument: A green after-image will not be located outside the skull, but if we cracked open your skull, we won't find anything green in there either. (If we did, you'd have some disturbing medical news.) So the after-image seems not to be in physical space, suggesting that it is non-physical. In response, I argue that the (...) green blob is a fictional object, while assuming a weak sort of realism about fictional objects (where they exist as mind-dependent objects). This view can look like dualism, however, but I try to interpret it not as implying metaphysical dualism, but rather as reflecting a dualism of theory. Roughly, there can be a theory of mind-independent objects, and a theory of mind-dependent objects. Yet there are principled reasons why we cannot integrate the two into a consistent whole, for reasons related to Russell's vicious circle principle. Most of the paper motivates this by an analogy between the physicalist's theory of the world, and drawing a map with a complete representation of the map itself. Regimentation unearths the inconsistencies that arise, when trying to represent as part of a model the very representations used to define the model. (shrink)

1. For simplicity, let the domain of our first-level quantifiers, ‘∀ x’ and so on, be words, and in particular just those words which are adjectives. And let the adjective ‘heterological’ be abbreviated just to As is well known, one cannot legitimately stipulate that Why not? Well, the obvious answer is that if is supposed to be an adjective, then this alleged stipulation would imply the contradiction But contradictions cannot be true, and it is no use stipulating that they shall (...) be. Do we need to say anything more? Russell would apparently wish to add this: the stipulation is illegitimate because it attempts to define the word by a quantification over all words, and the word is itself taken to be one of the words quantified over. That is how this supposed definition would infringe his vicious-circle principle . 1 It is of course true that if our quantification is taken to range only over words of a certain kind, say first-order adjectives, and if the word is taken to be a word of a different kind, say a second-order adjective, then the contradiction is avoided. For the supposed stipulation then has no implications for whether is or is not true of any second-order words. Russell imagines the stipulation to be strengthened by adding that is to be true only of first-order words, and hence that it is not true of itself. But no contradiction now results from this. However, one must ask: did we need this explanation in terms of the VCP? It may seem helpful, because there is an initial temptation to say that the original stipulation could not be illegitimate. This is because it is thought of as introducing a new word, and explaining what it means, and one is apt to think that we …. (shrink)

Can a theory turn back, as it were, upon itselfand vouch for its own features? That is, canthe derived elements of a theory be the veryprimitive terms that provide thepresuppositions of the theory? This form of anall-embracing feature assumes a totality inwhich there occurs quantification over thattotality, quantification that is defined bythis very totality. I argue that the Machprinciple exhibits such a feature ofall-embracing nature. To clarify the argument,I distinguish between on the one handcompleteness and on the other wholeness andtotality, (...) as different all-embracing features:the former being epistemic while the latter –ontological.I propose an analogy between the Mach principleas a possible selection principle in generalrelativity, and the vicious-circle principle infoundations of mathematics. I finally concludewith a consequence of this analogyvis-à-vis completeness and totality,viz., both should be constrained if they wereto be valid concepts for a physical theory. (shrink)

The state of affairs of some things falling under a predicate is supposedly a single entity that collects these things as its constituents. But whether we think of a state of affairs as a fact, a proposition or a possibility, problems will arise if we adopt a plural logic. For plural logic says that any plurality include themselves, so whenever there are some things, the state of affairs of their plural self-inclusion should be a single thing that collects them all. (...) This leads to paradoxes analogous to those that afflict naïve set theory. Here I suggest that they are the very same paradoxes, because sets can be reduced to states of affairs. However, to obtain a consistent theoretical reduction we must restrict the usual axiom scheme of Comprehension for plural logic to ‘stratified’ formulas, to avoid viciously circular definitions. I prove that with this modification to the background plural logic, the theory of states of affairs is consistent; moreover, it yields the axioms of the familiar set theory NFU. (shrink)

This concise work is a study of the semantical aspects of various paradoxes arising in formal logic. The author constructs a second-order system T with an interpretation in order to provide apparatus for stating and dodging the antinomies. After presenting a number of paradoxes, the author discusses a semantic vicious-circle principle, and provides a clarification of the problems by its application. He then discusses semantic aspects of some classical meta-mathematical results of Gödel, Tarski, Kleene, and Turing on (...) unsolvable problems. Also treated is the topic of impredicative definition in mathematics, especially as it relates to the vicious-circle principle.—P. J. M. (shrink)

A Christian approach to scholarship, directed by the central biblical motive of creation, fall and redemption and guided by the theoretical idea that God subjected all of creation to His Law-Word, delimiting and determining the cohering diversity we experience within reality, in principle safe-guards those in the grip of this ultimate commitment and theoretical orientation from absolutizing or deifying anything within creation. In this article my over-all approach is focused on the one-sided legacy of mathematics, starting with Pythagorean arithmeticism (...) (“everything is number”), continuing with the geometrization of mathematics after the discovery of irrational numbers and once again, during the nineteenth century returning to an arithmeticistic position. The third option, never explored during the history of mathematics, guides our analysis: instead of reducing space to number or number to space it is argued that both the uniqueness of these two aspects and their mutual coherence ought to direct mathematics. The presence of different schools of thought is highlighted and then the argument proceeds by distinguishing numerical and spatial facts, while accounting for the strict correlation of operations on the law side of the numerical aspect and their correlated numerical subjects (numbers). Discussing the examples of 2 + 2 = 4 and the definition of a straight line as the shortest distance between two points provide the background for a brief sketch of the third alternative proposed (inter alia against the background of an assessment of infinity and continuity and the vicious circles present in contemporary mathematical arithmeticistic claims). (shrink)

Vicious Circles traces the history of development of public education and the near simultaneous advent of educational reform from its very beginning. Drawing on history, politics, law, sociology, and educational research, all aspects of public schooling are brought to light using a non-partisan analytical approach. Critically examining areas such as institutional racism, sexism, ableism, ethnocentrism, and xenophobia, as well as the corporatization and privatization of public schooling, Shyman extracts the fundamental problems that have ever plagued, and continue to plague, (...) successful education reform. (shrink)

Michael Durrant’s rejection is examined of Frege’s and Wittgenstein’s thesis that a name has meaning only in the context of a proposition (the Context Principle). Durrant argues that in two ways the Context Principle makes it impossible for a hearer to determine the meaning of a name, for such identification would involve both an infinite regress and a vicious circle of reasoning. I reply that a finite (rather than infinite) set of propositions could suffice; and that (...) making corrigible assumptions allows people to believe propositions and thus to understand names ahead of knowing what the propositions are about. Durrant’s arguments, then, are inconclusive. Since, however, names can be bestowed and their meanings learned in and through acts of nonpropositional naming, then, unless special senses of ‘name’ and‘proposition’ are intended, the Context Principle is false. (shrink)

On the work of Frank Ramsey, emphasizing topics most relevant to philosophy of science.

Este texto é uma análise da caracterização dos princípios morais elaborada por Richard Holton, no seu conhecido trabalho de 2002. Defende-se aqui a tese de que a idéia de Holton sobre a premissa “Isso é tudo” envolve um círculo vicioso. PALAVRAS-CHAVE – Metaética. Particularismo. Universalismo. ABSTRACT This is an analysis of the characterisation of moral principles presented by Richard Holton in his influential paper of 2002. It is argued here that Holton’s idea of a premise ‘That’s it’ involves a (...) class='Hi'>vicious circle. KEY WORDS – Metaethics. Particularism. Universalism. (shrink)

Contemporary education now appears to be dominated by the continual drive for improvement measured against the assessment of what students have learned. It is our contention that a foundational relation with assessment organises contemporary education. Here we draw on a 'way of thinking' that is deconstructive in its intent. Such thinking makes clear the vicious circularity of the argument for improvement, wherein assessment valorised in discourses of improvement provides not only a rationalisation for improvement via assessment, but also the (...) very means of achieving such possibilities via targets grounded in limited specifications of assessment. On reading Heidegger's 'question concerning technology' we sought to reconsider the vicious circle of improvement in relation to Being. We claim that the means-ends driven technology of assessment, rather than being at our disposal and under our control, only serves to reveals the Real to us in accordance with the restricting principle of reason. The principle of reason, we argue, grounds 'Enframing' that ranks and orders the very beings of education as objects to produce an objective 'world as picture', rather than opening the possibility of their identity as belongings with a movement of difference. So, 'improvement' becomes normative and binding for institutions and practices on grounds of the principle of assessment, and renders agents of education as functionaries of 'Enframing'. (shrink)

As Russell's paradox of "the set of all sets that do not contain themselves" indicated long ago, matters go seriously amiss if one operates an ontology of unrestricted totalization. Some sort of restriction must be placed on such items as "the set of all sets that have the feature F' or "the conjunction of all truths that have the feature G." But generally, logicians here introduce such formalized and complex devices as the theory of types or the doctrine of impredictivity. (...) The present paper argues for the informal and elementary idea that the items invoked in a proper identification have themselves already been identified. Even as an explanation is not satisfactory that proceeds in terms of items that themselves require prior explanation, so the same holds with identification. And heed of this elementary idea suffices to sideline those otherwise paradoxical perplexities. (shrink)

This paper analyzes the ethical-political dilemma in Kant’s work, sometimes expressed through the metaphor of the “crooked wood of humanity.” Kant separates external and internal freedom and the types of legislation each form of freedom requires (coercive and noncoercive). Yet, he also argues that corrupt political institutions adversely affect individual ethical development, and, reciprocally, corrupt inner dispositions of a populace adversely affect the establishment of just political institutions. I argue that a major way in which Kant addresses this vicious (...) circle is through ethical institutions, that is, noncoercive public resources for articulating and disseminating the principles of the moral law. I discuss the idea of an ethico-civil society or ethical community formulated in the Religion as an ideal model for ethical institutions mediating the ethical and the legal-political in a noncoercive, progressive manner. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:January 22, 2009 (8:41 pm) G:\WPData\TYPE2802\russell 28,2 048red.wpd russell: the Journal of Bertrand Russell Studies n.s. 28 (winter 2008–09): 127–42 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631; online 1913-8032 YABLO’S PARADOX AND RUSSELLIAN PROPOSITIONS Gregory Landini Philosophy / U. of Iowa Iowa City, ia 52242–1408, usa [email protected] Is self-reference necessary for the production of Liar paradoxes? Yablo has given an argument that self-reference is not necessary. He (...) hopes to show that the indexical apparatus of self-reference of the traditional Liar paradox can be avoided by appealing to a list, a consecutive sequence, of sentences correlated one-one withnaturalnumbers.Yabloopens his “Paradox without Self-Reference” (Analysis, 1993) with the assumption that there is a sequence such that: Snz: “(;k)(k > n.!. True Sk)” Each sentence on Yablo’s list is supposed to be correlated one-one with number n. Each sentence is supposed to say that for every natural number kz greater than n, the k-th sentence on the list is not true. By comparing Yablo’s construction to an analogous construction with early Russellian propositions, we show that Yablo has failed to generate a paradox. 1. vicious circularity in yablo’s paradox S elf-reference has been taken to be the source of paradoxes. Poincaré and Russell are commonly associated with this thesis. In an amusing passage, the mathematician Jourdain recalls something of the dialogue between them: Nearly all mathematicians agreed that the way to solve these paradoxes was simply not to mention them; but there was some divergence of opinion as to how they were to be unmentioned. It was clearly unsatisfactory merely not to mention them. Thus Poincaré was apparently of the opinion that the best way of avoiding such awkward subjects was to mention that they were not to be mentioned. But [as Russell put it] “one might as well, in talking to a man with January 22, 2009 (8:41 pm) G:\WPData\TYPE2802\russell 28,2 048red.wpd 128 gregory landini 1 Philip Jourdain, The Philosophy of Mr. B*rtr*nd R*ss*llz (London: Allen & Unwin, 1918), p. 77. Russell is quoted from “Mathematical Logic as Based on the Theory of Types” (1908), LK, p. 63. 2 “On ‘Insolubilia’ and Their Solution By Symbolic Logic”, in B. Russell, Essays in Analysis, ed. Douglas Lackey (London: Allen & Unwin, 1973), p. 196. 3 I believe that this is Russell’s view in 1906. See Gregory Landini, “Russell’s Separation of the Logical and Semantic Paradoxes”, Revue internationale de philosophie 58 (2004): 257–94 (issue titled “Russell en héritage / Le centenaire des Principes”, ed. Philippe de Rouilhan). a long nose, say: ‘When I speak of noses, I except such as are inordinately long’, which would not be a very successful eTort to avoid a painful topic.”1 Poincaré maintained that one should exclude the oTending cases and therebyavoid“viciouscircles”ofself-referencewhichgenerateparadoxes. Russell objected: We may illustrate this by what M. Poincaré says concerning Richard’s paradox. Having Wrst put E = “all numbers deWnable in a Wnite number of words” we arrive at a paradox, due, says M. Poincaré, to our having included a number only deWnable in a Wnite number of words by means of E. This vicious circle he proposes to avoid by deWning E as “all numbers deWnable in a Wnite number of words without mentioning Ey”. To the uninitiated, this deWnition looks more circular than ever.2 Russell held that some paradoxes such as those of classes require, in order to exclude oTending cases without mentioning them, a “reconstruction of logical Wrst principles”. Others, such as Richard’s, are to be dismissed because they involve confused and viciously circular notions of “deWnability ”.3 Is self-reference necessary for paradoxes? The question is not well crafted. There are quite diTerent notions ofz “self-reference” involved in paradoxes. The self-reference involved in the Liar “This sentence is false” is provided by an apparatus of indexicals. This apparatus is quite distinct from the self-reference involved in Russell’s early ontology of propositions (as mind- and language-independent states of aTairs). This is an ontological self... (shrink)

We study here equiformity, the standard identity criterion for sentences. This notion was put forward by Lesniewski, mentioned by Tarski and defined explicitly by Presburger. At the practical level this criterion seems workable but if the notion of sentence is taken as a fundamental basis for logic and mathematics, it seems that this principle cannot be maintained without vicious circle. It seems also that equiformity has some semantical features ; maybe this is not so clear for individual (...) signs but sentences are often considered as meaningful combinations of signs. If meaning has to play a role, we are thus maybe in no better position than when dealing with identity criterion for propositions. In formal logic, one speaks rather about well-formed formulas, but closed formulas are called sentences because they are meaningful in the sense that they can be true or false. Formulas look better like mathematical objects than material inscriptions and equiformity does not seem to apply to them. Various congruencies can be considered as identities between formulas and in particular "to have the same logical form". One can say that the objects of study of logic are rather logical forms than sentences conceived as material inscriptions. (shrink)

Recognized as a masterpiece of Nietzsche scholarship, NIETZSCHE AND THE VICIOUS CIRCLE is available here for the first time in English. Author Pierre Klossowski suggests that Nietzsche's ideas and beliefs did not stem from his personal pathology, but rather were applied in a pathological manner. Thereby Nietzsche's beliefs resonated dynamically and intellectually with his alternating lucidity and delirium.

I am a 40-year-old woman with lived experience of mental ill health and experience of the services and support available for patients. I accessed support from my teenage years until the present day...