The aim of this article is to discuss the objection of vicious circularity concerning the relation between the Phenomenology of Spiritand the Science of Logic. My argument is articulated in three stages: in the first place, I will provide a historical reconstruction of the debate and I will try to neutralize the objection of vicious circularity; in the second place, I will examine the latest positions of the Hegel-Forschungabout the issue of a possibly reciprocal presupposition between the PhG (...) and the SL; in the third place, I will analyze the meaning of a virtuous circularity, by showing its inner relation to a dynamic conception of systematicity. (shrink)

In this paper a complete proper subclass of Hilbert-style S4 proofs, named non-circular, will be determined. This study originates from an investigation into the formal connection between S4, as Logic of Provability and Logic of Knowledge, and Artemov's innovative Logic of Proofs, LP, which later developed into Logic of Justification. The main result concerning the formal connection is the realization theorem , which states that S4 theorems are precisely the formulas which can be converted to LP theorems with proper justificational (...) objects substituting for modal knowledge operators. We extend this result by showing that on the proof level, non-circular proofs are exactly the class of S4 proofs which can be realized to LP proofs. In turn, this study provides an alternative algorithm to achieve the realization theorem, and a novel logical system, called S4ΔS4Δ, is introduced, which, under an adequate interpretation, is worth studying for its own sake. (shrink)

The Liar paradox arises when we consider a sentence that says of itself that it is not true. If such self-referential sentences exist? and examples like?This sentence is not true? certainly suggest this?, then our logic and standard notion of truth allow to infer a contradiction: The Liar sentence is true and not true. What has gone wrong? Must we revise our notion of truth and our logic? Or can we dispel the common conviction that there are such self-referential sentences? (...) The present study explores the second path.0After comparing the Liar reasoning in formal and informal logic and showing that there are no Gödelian Liar sentences, the study moves on from the semantics of self-reference to the metaphysics of expressions and proposes a novel solution to the Liar paradox: Meaningful expressions are distinct from their syntactic bases and exist only relative to contexts. Detailed semantico-metaphysical arguments show that in this dynamic setting, an object can be referred to only after it has started to exist. Hence the circular reference needed in the Liar paradox cannot occur, after all. As this solution is contextualist, it evades the expressibility problems of other proposals. (shrink)

I propose in this text that Husserl’s response to his contemporaries, critics and immediate predecessors in Logical Investigations consists in the development of circular strategy. Husserl does not challenge psychologsim, empiricism or neo-Kantianism by immediately assuming a position of epistemological primacy over these philosophies. To the contrary, Husserl philosophically challenges these positions by enacting a circularity that already underlies them. Husserl’s critical distance from these theories implies a methodological proximity which enables him to advance his phenomenological project with (...) constant backward reference to the theories he challenges. Husserl’s circular philosophy transforms the themes it investigates and the theories it criticizes, transforming itself in that process. (shrink)

The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity of second and higher-order logic. However, the epistemological significance of such investigations has not received much attention in the contemporary foundational debate.We discuss Girard’s normalization proof for second order type theory or System F and compare it with two faulty consistency arguments: the one given by Frege for the logical system of the (...) Grundgesetze and the one given by Martin-Löf for the intuitionistic type theory with a type of all types.The comparison suggests that the question of the circularity of second order logic cannot be reduced to Russell’s and Poincaré’s 1906 “vicious circle” diagnosis. Rather, it reveals a bunch of mathematical and logical ideas hidden behind the hazardous idea of impredicative quantification, constituting a vast domain for foundational research. (shrink)

Using as a framework the logical treatment of causality in the Buddhist Madhyamika, a theory of the psychology of event coherence and causal connectedness is developed, and suggestive experimental evidence is offered. The basic claim is that events are perceived as coherent and causally bound to the extent that the outcome is seen to be already contained in the ground of the event in some form and the connecting link between them is seen as the appropriate means for changing (...) the outcome-in-the-ground to the outcome-as-perceived. There are four types of such connections: the identity of the object in the ground and outcome is seen as the same ; a property is seen to be transferred from ground to outcome ; for animate beings, a cognitive representation and a state of the world are seen to match - either the representation-as-outcome coming to match the world-as-ground or the world-as-outcome coming to match the representation-as-ground ; the `essence' of a category is seen to manifest itself . The standard critique of such coherence explanations is that they are tautological. We demonstrate that `nontautological' scientific accounts become convincing coherent explanations only to he extent that the outcome is re-introduced into the ground. Explanations which are noncausal altogether, such as probability or chance, are shown to be psychologically unstable. This critique suggests some new perspectives on causal thinking both in the cognitive sciences and the folk theories of daily life. (shrink)

HEGEL says that "when enquiry is made as to the kind of predicate belonging to [a] subject, the act of judgement necessarily implies an underlying concept [Begriff]; but this concept is expressed only by the predicate." According to this, some concept of the subject must precede predication. This circularity can be formulated as follows: If the statement is the "factory" in which concepts are produced, how is it that the concepts precede the statement and are not merely produced within (...) it in their function as subjects? And, on the other hand, if the subject is not, prior to predication, a concept--if it has by itself no meaning--how can a predicate be matched to it? There would, in fact, be nothing to match. We are caught in a circular thesis that requires for its elucidation a fresh analysis of the relationship between concept and statement. (shrink)

This article is concerned with some of the criteria which Hegel believes apply to a scientific treatment of logic. I briefly address criteria which I take Hegel to inherit from German rationalism before focusing on two fairly idiosyncratic criteria: the requirement that a science of logic exhibit a circular structure and that it begin with the concept of pure being. I offer an explanation of these criteria which understands them as motivated by anti-sceptical concerns, before arguing that Hegel’s mature treatment (...) of the latter criterion is problematically ambiguous. (shrink)

Research on epistemic circularity has focused more on the problem of whether circular arguments are able to justify their conclusions rather than on the nature of circularity itself, and has kept a sharp delimitation from other types of circularities (logical, linguistic, and of definition). In this paper, I aim to move the focus toward the general concept of circularity, which I relate to the concept of ‘epistemic worry’. Through a brief overview on the known types of (...) circularities, I show that circularity has multiple natures (not only that associated with its type), and the linguistic aspect is essential in qualifying a construct as circular, which in turn raises the problem of genuineness of a circularity. Within an extensional approach, I suggest generalizing the meaning of the key epistemological terms referred to in the classical definition of epistemic circularity to also cover additional associated concepts specific to other theoretical disciplines beyond epistemology. The proposed concepts and ideas are reflected in a structural unificatory account of circularity in terms of epistemic determination, which raises a challenge to the relational accounts of determination in regard to the transitivity of the determination relation. (shrink)

Epistemic circularity is a problem of arguments purporting to establish the reliability of our different sources of belief‐acquisition. For example:(TRA)At t1, S formed the perceptual belief that p, and p.At t2, S formed the perceptual belief that q, and q.At t3, …Therefore, sense perception is reliable source of beliefs.The problem is that any arguer putting forth this argument is ompelled to rely on the thing to be proven in establishing the second conjuncts of each premise. But relying on the (...) thing to be proven is begging the question; therefore, the argument is fallacious. This has been argued to have serious skeptical implications: if there is no other way to establish the conclusion, we have no way of showing the reliability of, e.g., sense perception. Different authors have tried to resist this result. Frederick F. Schmitt (2004) argues that sense perception skepticism only follows from epistemic circularity if certain questionable assumptions are granted. He also argues that epistemic circularity is a specific type of circularity that is not vicious in the way logically circular arguments are. I argue thatSchmitt’s dismissal of the discussed assumptions is questionable and that the argument (TRA) is viciously circular under very minimal assumptions about inferential justification. Therefore, Schmitt fails to dissolve the problematic nature of (TRA). (shrink)

Certain lines of reasoning common in evolutionary taxonomy have been termed viciously circular. They are quite obviously not logically circular. They do give the superficial appearance of epistemological circularity. This appearance arises from the method of successive approximation used by evolutionary taxonomists. It is argued that this method is not epistemologically circular, even when the only evidence that the taxonomist has to go on is the phenetic similarity of contemporary forms. The important criticism of evolutionary taxonomy is rather that (...) in the absence of fossil evidence phyletic reconstructions are not warranted. It is argued that this charge stems initially from a misunderstanding of the kind of certainty possible in empirical science. When this criticism is couched in appropriate terms, it may be seen to have some force. Many phyletic inferences are not as warranted as one might wish. However, there is a great deal of difference between arguing that a line of reasoning is unwarranted and arguing that it is viciously circular. (shrink)

I propose in this text that Husserl’s response to his contemporaries, critics and immediate predecessors in Logical Investigations consists in the development of circular strategy. Husserl does not challenge psychologsim, empiricism or neo-Kantianism by immediately assuming a position of epistemological primacy over these philosophies. To the contrary, Husserl philosophically challenges these positions by enacting a circularity that already underlies them. Husserl’s critical distance from these theories implies a methodological proximity which enables him to advance his phenomenological project with (...) constant backward reference to the theories he challenges. Husserl’s circular philosophy transforms the themes it investigates and the theories it criticizes, transforming itself in that process. (shrink)

In this paper we investigate two purely syntactical notions ofcircularity, which we call ``self-application'''' and ``self-inclusion.'''' Alanguage containing self-application allows linguistic items to beapplied to themselves. In a language allowing for self-inclusion thereare expressions which include themselves as a proper part. We introduceaxiomatic systems of syntax which include identity criteria andexistence axioms for such expressions. The consistency of these axiomsystems will be shown by providing a variety of different models –these models being our circular languages. Finally we will show what (...) apossible semantics for these circular languages could look like. (shrink)

"The book is divided into 8-10 chapters that are each only 2 or 3 pages long... this feels like a nice feature of the book, since you can dip in and just read a short bite before moving on. The author clearly has some interesting ideas and at times I found his writing to be quite engaging." MAA Review "I did enjoy reading (and re-reading) this book very much. Reading it deserves a warm recommendation not only for mathematicians but for (...) anybody... this book makes you think about how and what you think you are thinking." European Mathematical Society "Circularity" is the story of a Janus-faced conceptual structure, that on the one hand led to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that eventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinking. Another aspect of circularity, its ability to entertain, leads to a surprising insight on the time old question "What is humor." The book presents the ubiquity of circularity in many fields, and its power to confuse and to instruct. (shrink)

I develop a syntactic concept of circularity, which I call propositional circularity. With respect to a given use of an argument advanced as a statement of inference for the benefit of a reasoner R, if the direct and indirect premises R would have to accept in order to accept the conclusion includes the conclusion, then the collection of premises is propositionally circular. The argument fails to display a type of inference that R can perform. Appealing to propositional (...) class='Hi'>circularity, I articulate a sufficient condition for a use of an argument to beg the question, highlighting why question-begging is a defect. (shrink)

Expanding on a discussion by Hansson, this paper treats of Goodman's and Lewis' accounts of counterfactual conditionals, comparing the senses in which these theories may be accused of circularity. While I do maintain that in this respect Lewis has an edge over Goodman, the paper's aim is not so much to reach a firm conclusion as to disentangle some previously conflated aspects of the issue. It is also suggested that the importance of avoiding circularity may vary depending on (...) the philosophical purpose of one's analysis. (shrink)

David Miller claims that every valid deductive argument begs the question. Other philosophers and logicians have made similar claims. I show that the claim is false. Its appeal depends on the existence of logical terminology, particularly concerning what a proposition 'contains' or its 'logical content,' that is best understood as metaphoric and that, given its aptness to mislead, would be better eschewed. I show how the terminology appears to derive from early modern theories of the nature of mind, (...) ideas and reasoning that have since been rejected. (shrink)

In Posterior Analytics 1.3, Aristotle advances three arguments against circular proof. The third argument relies on his discussion of circular proof in Prior Analytics 2.5. This is problematic because the two chapters seem to deal with two rather disparate conceptions of circular proof. In Posterior Analytics 1.3, Aristotle gives a purely propositional account of circular proof, whereas in Prior Analytics 2.5 he gives a more complex, syllogistic account. My aim is to show that these problems can be solved, and that (...) Aristotle’s third argument in 1.3 is successful. I argue that both chapters are concerned with the same conception of circular proof, namely the propositional one. Contrary to what is often thought, the syllogistic conception provides an adequate analysis of the internal deductive structure of the propositional one. Aristotle achieves this by employing a kind of multiple-conclusion logic. (shrink)

One of the gravest charges that has been brought against Hume’s essay “Of the Standard of Taste” is that of circularity. Hume is accused of defining good art in terms of “true judges,” and of defining true judges in terms of their ability to judge good art. First, I argue that Hume avoids circularity since he offers a way of identifying good art that is logically independent of the verdict of true judges. Second, I argue that this clarifies (...) an enduring puzzle in the scholarship on Hume’s essay: why he appears to offer not one but two standards of taste. Hume’s standard does not consist of general rules; however, Hume needs general rules to establish that some individuals’ tastes are more “delicate” than others’. (shrink)

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth functions, and in particular (...) the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail. (shrink)

Logical abductivism is the epistemic view about logic according to which logical theories are justified by abduction (or Inference to the Best Explanation), that is on how well they explain the relevant evidence, so that the correct logical theory turns out to be the one that explains it best. Arguably, this view should be equally applied to both deductive and non-deductive logics, abduction included. But while there seems to be nothing wrong in principle in using abduction to (...) determine the correct logical theories of deduction and induction, things might be more complicated regarding logical theories of abduction. We may wonder whether allowing for an abductive justification of a theory of abduction is an epistemically legitimate move, since here circularity casts its shadow and makes the situation darker. This is the issue to which this work is devoted. I will defend that, to be effective, an abductive justification for a theory of abduction calls for a justification of abduction in advance, which we do not yet have. (shrink)

This book offers a new theory of begging the question as an informal fallacy, within a pragmatic framework of reasoned dialogue as a normative theory of critical argumentation. The fallacy of begging the question is analyzed as a systematic tactic to evade fulfillment of a legitimate burden of proof by the proponent of an argument. The technique uses a circular structure of argument to block the further progress of dialogue and, in particular, the capability of the respondent to ask legitimate (...) critical questions in reply to the argument. Walton analyzes the concept of burden of proof in argument, and provides chapters on the use of argument diagramming as a technique of argument reconstruction. This powerful method of argument analysis developed therein is then applied to more than 100 case studies of circular argumentation where the charge of begging the question is or has been thought to be an appropriate criticism. Throughout this work, Walton throws light on the relationship between the problem of circular reasoning and broader issues in the critical analysis of argumentation. Ground-breaking use is made of the pragmatic theory of argument as interactive dialogue. Rules for several kinds of dialogue framework provide standards of good reasoning to validate or to refute the criticism that a particular argument begs the question. This book is directed to students and professionals in the fields of speech communication, philosophy, linguistics, logic, dispute mediation, and education. (shrink)

In this paper, I explore the strategy of circularity employed by Kant and Husserl in their treatment of categoriality. I focus on the relation between transcendental and metaphysical deductions in Kant’s Critique of Pure Reason, and on the problem of “epistemic foundationalism” and categoriality in Husserl’s Sixth Logical Investigation. I propose that the strategy of circularity is manifested through the peculiar self-enclosure of the categories of transcendental deduction vis-à-vis metaphysical deduction (Kant) and categorial intuition vis-à-vis sensuous intuition (...) (Husserl). Although it is usually regarded as a deficient and damaging occurrence in argumentation, circularity appears to be a crucial component in the analysis of both thinkers. The analytical realms recognized by both these thinkers, are acknowledged as continually dependent upon the self-evidential “contingency” of the realms they are supposed to hierarchically overarch. The strict separation between the transcendental and phenomenological realms and their addressees appears to be founded on mutual circularity, where the relation between investigator and investigated extends beyond their separation and reconciliation. Both Kant and Husserl, through the circular relationship with empiricism-rationalism and psychologism radically re-articulated the logic-ontology and founding-founded polarities. (shrink)

A key theme throughout Maimon’s works is a circularity he diagnoses at the heart of Kant’s response to Hume. The objective validity of Kant’s category of causality ultimately rests, Maimon argues, upon the logical status of the hypothetical judgement – on its inclusion among the forms of pure general logic. In turn, however, the inclusion of the hypothetical within pure general logic itself rests upon the objective validity of causal judgements. This article examines Maimon’s diagnosis and traces it (...) back to a debate that has its origins in Wolff’s German Logic, concerning the relationship between categorical and hypothetical judgements. (shrink)

We raise an issue of circularity in the argument for the completeness of first-order logic. An analysis of the problem sheds light on the development of mathematics, and suggests other possible directions for foundational research.

This book analyzes the principle of circularity within logical and philosophical works of leading representatives of the continental tradition: Hegel, Marx, Husserl, and Heidegger. The review pays attention to circularity in everyday life elucidating Marx’s–Mamardashivili’s “converted form” as well as Hegel’s logical movement from less true to really true based on the speculative presupposition. It is also exposed how the constant self-disclosure of Being as aletheia is Dasein’s circular structure of a dynamic teleological transcending towards being-in-the-world (...) and being-with-others. Expressing the theme of intentionality is Husserl’s intersubjectivity as a way of relating better to the world, always moved by a telos. (shrink)

Descartes is traditionally accused of reasoning circularly in the _Meditations. Yet, it seems clear that there is no formal or logical circularity in his reasoning. There is another kind of circularity that William Alston calls epistemic circularity, and Descartes's reasoning seems to be circular in this sense. The question is whether this makes his reasoning viciously circular. It is argued that it does if we assume that his aim was to resolve the ancient Pyrrhonian problematic. Because (...) of epistemic circularity, the problematic cannot be resolved by his project. (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)

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)

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)

According to the view that Peacocke elaborates in _A Study of Concepts_ (1992), a concept can be individuated by providing the conditions a thinker must satisfy in or- der to possess that concept. Hence possessions conditions for concepts should be specifiable in a way that respects a non-circularity constraint. In a more recent paper.

We continue exploring analogues of o-minimality and weak o-minimality for circularly ordered sets. The main result is a description of ℵ0-categorical 1-transitive non-primitive weakly circularly minimal structures of convexity rank 1 up to binarity.

This paper examines Hegel’s chief paradigm for interpreting his dialectical method, which is that of circularity. The position that Hegel’s Logic (whether Greater or Lesser) begins without presuppositions loses validity upon clarification of this model of reasoning. Philosophy must begin necessarily with presuppositions, according to Hegel, and can only be justified adequately by explaining those presuppositions while also reflecting upon its own immanent method of explanation. Philosophy must therefore be self-reflexive, immanent, and systematic (or holistic). Such a view of (...) philosophy defends the goal of theoretical closure and excludes the assumption of a value-neutral standard of rationality. (shrink)

I argue that the analytic method has been circularly used to analyze the concept of “philosophy,” and that the result of this analysis has also been used to criticize African ethnophilosophy as nonphilosophical. I critically examine the criticism that ethnophilosophy implies cognitive relativism and the criticism that it implies authoritarianism. I defend ethnophilosophy against these criticisms, arguing that they are rooted in logical positivism, the view that philosophy essentially involves the use of the methods of science and logical (...) analysis. I argue that such analysis and criticisms, given their pedigree, do not provide an adequate or accurate picture of the nature of philosophy. (shrink)

We show that there are universes of sets which contain descending ϵ-sequences of length α for every ordinal α, though they do not contain any ϵ-cycle. It is also shown that there is no set universe containing a descending ϵ-sequence of length On. MSC: 03E30; 03E65.

Logic, in one of the many sense of that term, is a theory about what follows from what and why. Arguably, the correct theory has to be determined by abduction. Over recent years, so called logical anti-exceptionalists have investigated this matter. Current discussions have been restricted to deductive logic. However, there are also, of course, various forms of non-deductive reasoning. Indeed, abduction itself is one of these. What is to be said about the way of choosing the best theory (...) of non-deductive inferences? It would seem clear that an anti-exceptionalist should hold that essentially the same method of choice should apply to non-deductive logic. A number of issues need to be faced in the process, not the least of which is the circularity involved in an abductive justification for a theory of abduction. This paper discusses matters. (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)

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.

An argument whose conclusion C is essential evidence for one of its premises can provide its target audience with justification for believing C. This is possible because we can enhance our justification for believing a proposition C by integrating it into an explanatory network of beliefs for which C itself provides essential evidence. I argue for this in light of relevant features of doxastic circularity, epistemic circularity, and explanatory inferences. Finally, I confirm my argument with an example and (...) respond to objections. (shrink)

Kierkegaard notwithstanding, Hegel's notion of the "good" and "bad" infinity was not unprecedented. On the contrary, this attempt to invest a "logical" category with ethical significances goes back to the very roots of the Western metaphysical tradition. In the Pythagorean doctrine of limit and the unlimited, limit was the arche of the good; the unlimited of evil. In the Pythagorean concept of number as an ens, limit and the unlimited attained ontological status. And since number constituted the determinate character (...) of all things, the Pythagorean peras and apeiron was a logos doctrine, the rational principle of the universe. Thereby Pythagoreanism marked a great advance over the Ionian materialisms. (shrink)

I examine Paul Boghossian's recent attempt to argue for scepticism about logical rules. I argue that certain rule- and proof-theoretic considerations can avert such scepticism. Boghossian's 'Tonk Argument' seeks to justify the rule of tonk-introduction by using the rule itself. The argument is subjected here to more detailed proof-theoretic scrutiny than Boghossian undertook. Its sole axiom, the so-called Meaning Postulate for tonk, is shown to be false or devoid of content. It is also shown that the rules of Disquotation (...) and of Semantic Ascent cannot be derived for sentences with tonk dominant. These considerations deprive Boghossian's scepticism of its support. (shrink)

In this chapter, we will first argue that current practices in CBE are framed within the market or economic logic and miss the normative dimension of the call for circularity. The transition to the CBE requires a fundamental reflection on the role of economic actors in the social and ecological environment with significant consequences for their business practices. Second, we will argue that the transition to the CBE requires the acknowledgement of the normative and social dimensions of this transition (...) at the meso and macro levels, and the establishment of an environmental and social logic on the micro level of business practices. Third, we will argue that the concept of responsible innovation (RI) can help to articulate the normative and social dimensions of the transition to the CBE, and enables the operationalisation of the environmental and social logic at the micro level. In this respect, RI can be understood as a driver for the transition to the CBE. (shrink)

I examine Paul Boghossian's recent attempt to argue for scepticism about logical rules. I argue that certain rule- and proof-theoretic considerations can avert such scepticism. Boghossian's 'Tonk Argument' seeks to justify the rule of tonk-introduction by using the rule itself. The argument is subjected here to more detailed proof-theoretic scrutiny than Boghossian undertook. Its sole axiom, the so-called Meaning Postulate for tonk, is shown to be false or devoid of content. It is also shown that the rules of Disquotation (...) and of Semantic Ascent cannot be derived for sentences with tonk dominant. These considerations deprive Boghossian's scepticism of its support. (shrink)