We examine corruption across three Central and Eastern Europe countries through a social psychology framework which integrates social identity theory, social cognitive theory and moral disengagement mechanisms. We illustrate how various social identities influence individual and collective action in terms of ethical behavior and corruption, thereby creating, maintaining and perpetuating petty, grand and systemic public/private corruption through triadic co-determination via cognition, behavior and the environment. Despite growing research on corruption normalization, less is known about the cognitive and behavioral mechanisms in (...) ethical decision making, the cognitive workings of how individuals reconcile unethical behavior and the social psychological processes behind corruption in society and organizations. Expert interviews reveal internally conflicted multi-layered social identities perpetuating corruption, some embedded in nationalistic history and others tied to the European Union, which supports the divergent paths of CEE countries since the fall of communism. Some moral disengagement mechanisms are common across all three countries, while others are linked to specific circumstances. Social identity mechanisms feed into moral disengagement, which individuals draw upon to reconcile the conflict between unethical behavior and moral codes. Patterns of moral disengagement aggregate to the country level and explain normalization of corruption in CEE society and organizations. (shrink)

Descartes's philosophy has had a considerable influence on the modern conception of the mind, but many think that this influence has been largely negative. The main project of The Subject's Point of View is to argue that discarding certain elements of the Cartesian conception would be much more difficult than critics seem to allow, since it is tied to our understanding of basic notions, including the criteria for what makes someone a person, or one of us. The crucial feature of (...) the Cartesian view defended here is not dualism--which is not adopted--but internalism. Internalism is opposed to the widely accepted externalist thesis, which states that some mental features constitutively depend on certain features of our physical and social environment. In contrast, this book defends the minority internalist view, which holds that the mind is autonomous, and though it is obviously affected by the environment, this influence is merely contingent and does not delimit what is thinkable in principle. Defenders of the externalist view often present their theory as the most thoroughgoing criticism of the Cartesian conception of the mind; Katalin Farkas offers a defence of an uncompromising internalist Cartesian conception. (shrink)

In a recent reply to Takacs and Bourrat’s article (Biol Philos 37:12, 2022), Autzen and Okasha (Biol Philos 37:37, 2022) question our characterization of the relationship between the geometric mean and arithmetic mean measures of fitness. We here take issue with the claim that our characterization falls prey to the mistakes they highlight. Briefly revisiting what Takacs and Bourrat (Biol Philos 37:12, 2022) accomplished reveals that the key issue of difference concerns cases of deterministic but nonconstant growth. Restricting (...) focus to such cases shows that there is in fact no reason for disagreement. (shrink)

During the last two decades, several different anti-physicalist arguments based on an epistemic or conceptual gap between the phenomenal and the physical have been proposed. The most promising physicalist line of defense in the face of these arguments – the Phenomenal Concept Strategy – is based on the idea that these epistemic and conceptual gaps can be explained by appeal to the nature of phenomenal concepts rather than the nature of non-physical phenomenal properties. Phenomenal concepts, on this proposal, involve unique (...) cognitive mechanisms, but none that could not be fully physically implemented. David Chalmers has recently presented a Master Argument to show that the Phenomenal Concept Strategy – not just this or that version of it, but any version of it – fails. Chalmers argues that the phenomenal concepts posited by such theories are either not physicalistically explicable, or they cannot explain our epistemic situation with regard to qualia. I argue that it is his Master Argument that fails. My claim is his argument does not provide any new reasons to reject the Phenomenal Concept Strategy. I also argue that, although the Phenomenal Concept Strategy is successful in showing that the physicalist is not rationally compelled to give up physicalism in the light of the anti-physicalist arguments, the anti-physicalist is not rationally compelled to give up the anti-physicalist argument in the light of the Phenomenal Concept Strategy either. (shrink)

On the dust jacket of The Subject's Point of View there is a detail from Vilhelm Hammershoi's Interior with Sitting Woman. It is hard to think of a painter who better captures the inner in his work. From the monochrome colour, to the back that faces us, to the door swung open to reveal yet another doorway, we are led to interiority – to the inner. This is a perfect image for a book whose author wants to persuade us to (...) return to the interior – a Cartesian interior.The Cartesian interior has come in for quite a drubbing in philosophy for some considerable time. In the mid-to-late 1970s, a style of argument emerged, designed to challenge this conception of mind and establish in its place an externalist conception of language and of mind. One version of the argument was due to Hilary Putnam and emerged in the context of considerations concerning linguistic meaning; another was due to Tyler Burge and emerged first in the context of considerations concerning the individual in relation to his/her social environment. In his earliest paper, on this topic, Burge wrote of ‘the elderly Cartesian tradition’ where ‘the spotlight is on what exists or transpires “in” the individual – his secret cognition, his innate cognitive structures, his private perceptions and introspections, his grasping of ideas, concepts or forms’. Farkas wants to defend this ‘elderly tradition’, but she does add to it some interesting twists. First and foremost, she places to one side ideas of privacy, of incorrigibility and infallibility. She also wishes to place the issue of dualism to one side. What Farkas concentrates on is privileged access and argues that this is …. (shrink)

This paper was chosen by The Philosopher’s Annual as one of the ten best articles appearing in print in 2000. Reprinted in Volume XXIII of The Philosopher’s Annual. In his very influential book David Chalmers argues that if physicalism is true then every positive truth is a priori entailed by the full physical description – this is called “the a priori entailment thesis – but ascriptions of phenomenal consciousness are not so entailed and he concludes that Physicalism is false. As (...) he puts it, “zombies” are metaphysically possible. I attempt to show that this argument is refuted by considering an analogous argument in the mouth of a zombie. The conclusion of this argument is false so one of the premises is false. I argue at length that this shows that the original conceivability argument also has a false premise and so is invalid. (shrink)

Experience indicates that the questioning and democratic nature of the community of enquiry can be demanding and unsettling for teachers, present.

Still the Heart of Darkness analyzes Richard Preston's best-selling account of an Ebola virus outbreak in Reston, Virginia in 1989. Through a textual examination of The Hot Zone, this essay demonstrates how Preston grounds his narrative about the threat of rare emerging viruses from the third world in terms of the colonialist discourse about Africa as the white man's grave, most notably Joseph Conrad's Heart of Darkness. By foregrounding previous outbreaks in Africa, Preston simultaneously darkens its landscape and inscribes the (...) Ebola filovirus as an external biological threat to Americans in a post-Cold War world with porous borders. (shrink)

This book honors J. Michael Dunn, who was a preeminent relevance logician. Dunn's career spanned over 50 years and his research results had an impact on philosophy, mathematics and informatics. Dunn often used algebraic techniques in his research into logics such as relevance, orthomodular and substructural logics. He invented the logic R-mingle and the sequent calculus LR+; he proved crucial theorems about 2-valued first-order logic and non-classical higher-order logics - among many other results. The papers in this volume touch upon (...) topics that Dunn was concerned with. Some authors were students or colleagues of Dunn; some other authors had not met Dunn in person, but share his research interests. None of the articles published here have appeared in print before; indeed, most of the papers were written specifically for this collection. The diversity of the themes of the articles reflects the scope of Dunn's own research in logic. It will also ensure that anybody with an interest in logic - whether a student, a logician or a scholar in another field - will find reading this book a worthwhile endeavor. The editor, Katalin Bimbó was the 14th Ph.D. student of J. Michael Dunn at Indiana University in Bloomington, IN, U.S.A.; currently, she is a professor of philosophy at the University of Alberta in Canada. (shrink)

In recent years, several philosophers have defended the idea of phenomenal intentionality : the intrinsic directedness of certain conscious mental events which is inseparable from these events’ phenomenal character. On this conception, phenomenology is usually conceived as narrow, that is, as supervening on the internal states of subjects, and hence phenomenal intentionality is a form of narrow intentionality. However, defenders of this idea usually maintain that there is another kind of, externalistic intentionality, which depends on factors external to the subject. (...) We may ask whether this concession to content externalism is obligatory. In this paper, I shall argue that it isn’t. I shall suggest that if one is convinced that narrow phenomenal intentionality is legitimate, there is nothing stopping one from claiming that all intentionality is narrow. (shrink)

It is an integral part of the phenomenology of mature perceptual experience that it seems to present to us an experience-independent world. I shall call this feature 'perceptual intentionality'. In this paper, I argue that perceptual intentionality is constructed by the structure of more basic sensory features, features that are not intentional themselves. This theory can explain why the same sensory feature can figure both in presentational and non-presentational experiences. There is a fundamental difference between the intentionality of sensory experiences (...) and the intentionality of thoughts: unlike the former, the latter is not constructed. (shrink)

Hallucinations occur in a wide range of organic and psychological disorders, as well as in a small percentage of the normal population According to usual definitions in psychology and psychiatry, hallucinations are sensory experiences which present things that are not there, but are nonetheless accompanied by a powerful sense of reality. As Richard Bentall puts it, “the illusion of reality ... is the sine qua non of all hallucinatory experiences” (Bentall 1990: 82). The aim of this paper is to find (...) out what lends an experience ‘a sense of reality’: what features are required for an experience to feel ‘real’, in the relevant sense? I will investigate the claim that phenomenological features are largely responsible for a sense of reality, and will find this claim wanting. My suggestion is that a sense of reality is created and sustained by the larger nexus of the subject's beliefs. (shrink)

"At places distant from where you are, but also uncomfortably close," writes David Takacs, "a holocaust is under way. People are slashing, hacking, bulldozing, burning, poisoning, and otherwise destroying huge swaths of life on Earth at a furious pace." And a cadre of ecologists and conservation biologists has responded, vigorously promoting a new definition of nature: biodiversity --advocating it in Congress and on the Tonight Show; whispering it into the ears of foreign leaders redefining the boundaries of science and (...) politics, ethics and religion, nature and our ideas of nature. These scientists have infused the environmental movement with new focus and direction, but by engaging in such activities, they jeopardize the societal trust that allows them to be public spokespersons for nature in the first place. The Idea of Biodiversity analyzes what biodiversity represents to the biologists who operate in broader society on its behalf, drawing on in-depth interviews with the scientists most active today in the mission to preserve biodiversity, including Peter Raven, Thomas Lovejoy, Jane Lubchenco, and Paul Ehrlich. Takacs explores how and why these biologists shaped the concept of biodiversity and promoted it to society at large--examining their definitions of biodiversity their opinions about spirituality and its role in scientific work the notion of biodiversity as something of intrinsic value and their views on biophilia, E. O. Wilson's idea that humans are genetically predisposed to love nature. Takacs also looks at the work of twentieth-century forerunners of today's conservation biologists--Aldo Leopold, Charles S. Elton, Rachel Carson, David Ehrenfeld--and points out their contributions to the current debates. He takes readers to Costa Rica, where a group of scientists is using biodiversity to remake nature and society. And in an extended section, he profiles the thoughts and work of E. O. Wilson. "When I'm asked, 'should we save this species orthat species, or this place or that place?' the answer is always 'Yes!' with an exclamation point. Because it's obvious. And if you ask me to justify it, then I switch into a more cognitive consciousness and can start giving you reasons, economic reasons, aesthetic reasons. They're all dualistic, in a sense. But the feeling that underlies it is that 'yes!' And that 'yes!' comes out of the affirmation of being part of it all, being part of this whole evolutionary process. And agreeing with Arne Naess that each species, each entity, should be allowed to continue its evolution and to live out its destiny... just do its thing, as we say. Why not? And the 'why not?' is there's too many people."--Michael E. Soule, from an interview in The Idea of Biodiversity "An important contribution, a first distanced examination of a critical, modern topic by a scholarly, honest broker."--E. O. Wilson, Harvard University. (shrink)

In this paper I begin to develop an account of the acquaintance that each of us has with our own conscious states and processes. The account is a speculative proposal about human mental architecture and specifically about the nature of the concepts via which we think in first personish ways about our qualia. In a certain sense my account is neutral between physicalist and dualist accounts of consciousness. As will be clear, a dualist could adopt the account I will offer (...) while maintaining that qualia themselves are non-physical properties. In this case the non-physical nature of qualia may play no role in accounting for the features of acquaintance. But although the account could be used by a dualist, its existence provides support for physicalism. (shrink)

Papineau in his book provides a detailed defense of physicalism via what has recently been dubbed the “phenomenal concept strategy”. I share his enthusiasm for this approach. But I disagree with his account of how a physicalist should respond to the conceivability arguments. Also I argue that his appeal to teleosemantics in explaining mental quotation is more like a promissory note than an actual theory.

The central and paradigmatic cases of knowledge discussed in philosophy involve the possession of truth. Is there in addition a distinct type of practical knowledge, which does not aim at the truth? This question is often approached through asking whether states attributed by “know-how” locutions are distinct from states attributed by “know-that”. This paper argues that the question of practical knowledge can be raised not only about some cases of “know-how” attributions, but also about some cases of so-called “know-wh” attributions; (...) and that certain features of this practical knowledge-wh put pressure on the standard analysis of know-wh. (shrink)

Topics in Cognitive Science, Volume 13, Issue 1, Page 187-205, January 2021.

According to the Extended Mind thesis, the mind extends beyond the skull or the skin: mental processes can constitutively include external devices, like a computer or a notebook. The Extended Mind thesis has drawn both support and criticism. However, most discussions—including those by its original defenders, Andy Clark and David Chalmers—fail to distinguish between two very different interpretations of this thesis. The first version claims that the physical basis of mental features can be located spatially outside the body. Once we (...) accept that the mind depends on physical events to some extent, this thesis, though not obvious, is compatible with a large variety of views on the mind. The second version applies to standing states only, and has to do with how we conceive the nature of such states. This second version is much more interesting, because it points to a potential tension in our conception of minds or selves. However, without properly distinguishing between the two theses, the significance of the second is obscured by the comparative triviality of the first. (shrink)

Proponents of non-conceptual content have recruited it for various philosophical jobs. Some epistemologists have suggested that it may play the role of “the given” that Sellars is supposed to have exorcised from philosophy. Some philosophers of mind (e.g., Dretske) have suggested that it plays an important role in the project of naturalizing semantics as a kind of halfway between merely information bearing and possessing conceptual content. Here I will focus on a recent proposal by Jerry Fodor. In a recent paper (...) he characterizes non-conceptual content in a particular way and argues that it is plausible that it plays an explanatory role in accounting for certain auditory and visual phenomena. So he thinks that there is reason to believe that there is non-conceptual content. On the other hand, Fodor thinks that non-conceptual content has a limited role. It occurs only in the very early stages of perceptual processing prior to conscious awareness. My paper is examines Fodor’s characterization of non-conceptual content and his claims for its explanatory importance. I also discuss if Fodor has made a case for limiting non-conceptual content to non-conscious, sub-personal mental states. (shrink)

Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. _Generalized Galois Logics_ develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.

The content of the externalist thesis about the mind depends crucially on how we define the distinction between the internal and the external. According to the usual understanding, the boundary between the internal and the external is the skull or the skin of the subject. In this paper I argue that the usual understanding is inadequate, and that only the new understanding of the external/internal distinction I suggest helps us to understand the issue of the compatibility of externalism and privileged (...) access. (shrink)

On a Cartesian conception of the mind, I could be a solitary being and still have the same mental states as I currently have. This paper asks how the lives of other people fit into this conception. I investigate the second-person perspective—thinking of others as ‘you’ while engaging in reciprocal communicative interactions with them—and argue that it is neither epistemically nor metaphysically distinctive. I also argue that the Cartesian picture explains why other people are special: because they matter not just (...) for the effect that they have on us. (shrink)

The purpose of our study was to measure the relationship between performance on various attentional tasks and hypnotic susceptibility. Healthy volunteers participated in a study, where they had to perform several tasks measuring various attention components in a waking state: sustained attention, selective or focused attention, divided attention and executive attention in task switching. Hypnotic susceptibility was measured in a separate setting by the Waterloo-Stanford Groups Scale of Hypnotic Susceptibility, Form C .We found no significant correlation between any of the (...) attentional measures and hypnotic susceptibility. Highly hypnotizables did not prove to be superior to or worse than the other individuals in any of the tests.These results do not support the neuropsychophysiological model of hypnosis, as they show no consistent relationship between hypnotic susceptibility and waking attentional performance. (shrink)

Most discussions in epistemology assume that believing that p is a necessary condition for knowing that p. In this paper, I will present some considerations that put this view into doubt. The candidate cases for knowledge without belief are the kind of cases that are usually used to argue for the so-called ‘extended mind’ thesis.

Fitness is a central but notoriously vexing concept in evolutionary biology. The propensity interpretation of fitness is often regarded as the least problematic account for fitness. It ties an individual's fitness to a probabilistic capacity to produce offspring. Fitness has a clear causal role in evolutionary dynamics under this account. Nevertheless, the propensity interpretation faces its share of problems. We discuss three of these. We first show that a single scalar value is an incomplete summary of a propensity. Second, we (...) argue that the widespread method of “abstracting away” environmental idiosyncrasies by averaging over reproductive output in different environments is not a valid approach when environmental changes are irreversible. Third, we point out that expanding the range of applicability for fitness measures by averaging over more environments or longer time scales (so as to ensure environmental reversibility) reduces one's ability to distinguish selectively relevant differences among individuals because of mutation and eco‐evolutionary feedbacks. This series of problems leads us to conclude that a general value of fitness that is both explanatory and predictive cannot be attained. We advocate for the use of propensity‐compatible methods, such as adaptive dynamics, which can accommodate these difficulties. (shrink)

Know -wh ascriptions are ubiquitous in many languages. One standard analysis of know -wh is this: someone knows-wh just in case she knows that p, where p is an answer to the question included in the wh-clause. Additional conditions have also been proposed, but virtually all analyses assume that propositional knowledge of an answer is at least a necessary condition for knowledge-wh. This paper challenges this assumption, by arguing that there are cases where we have knowledge-wh without knowledge- that of (...) an answer, for example in the cases familiar from arguments for the Extended Mind hypothesis. (shrink)

Four-valued semantics proved useful in many contexts from relevance logics to reasoning about computers. We extend this approach further. A sequent calculus is defined with logical connectives conjunction and disjunction that do not distribute over each other. We give a sound and complete semantics for this system and formulate the same logic as a tableaux system. Intensional conjunction and its residuals can be added to the sequent calculus straightforwardly. We extend a simplified version of the earlier semantics for this system (...) and prove soundness and completeness. Then, with some modifications to this semantics, we arrive at a mathematically elegant yet powerful semantics that we call generalized Kripke semantics. (shrink)

Jennifer Hornsby’s Simple Mindedness consists of twelve essays organized into sections focusing on three issues: the ontology of persons and mental events, how actions fit into a world of natural law, and the nature of intentional explanations. Most of the essays have been previously published but many of these are revised and include addenda. The collection is unified by its defending a position in the philosophy of mind Hornsby calls “naive naturalism.” She advertises naive naturalism as neither physicalist nor Cartesian. (...) Hornsby claims that the mind-body problem as currently discussed, that is, the question of how the mind fits into nature, arises because contemporary analytic philosophers have an overly scientistic view of nature restricting their concept of nature to whatever can be the proper subject matter of science. In her view, if naive naturalism were adopted, the mind-body problem, as it is currently discussed, would disappear. Hornsby is thus a member of that venerable tradition of English philosophers who see the mind-body problem as arising through an excessive fascination with science. (shrink)

Abstract: This paper introduces and analyses the doctrine of externalism about semantic content; discusses the Twin Earth argument for externalism and the assumptions behind it, and examines the question of whether externalism about content is compatible with a privileged knowledge of meanings and mental contents.

Sequent calculi constitute an interesting and important category of proof systems. They are much less known than axiomatic systems or natural deduction systems are, and they are much less known than they should be. Sequent calculi were designed as a theoretical framework for investigations of logical consequence, and they live up to the expectations completely as an abundant source of meta-logical results. The goal of this book is to provide a fairly comprehensive view of sequent calculi -- including a wide (...) range of variations. The focus is on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, through linear and modal logics. A particular version of sequent calculi, the so-called consecution calculi, have seen important new developments in the last decade or so. The invention of new consecution calculi for various relevance logics allowed the last major open problem in the area of relevance logic to be solved positively: pure ticket entailment is decidable. An exposition of this result is included in chapter 9 together with further new decidability results (for less famous systems). A series of other results that were obtained by J. M. Dunn and me, or by me in the last decade or so, are also presented in various places in the book. Some of these results are slightly improved in their current presentation. Obviously, many calculi and several important theorems are not new. They are included here to ensure the completeness of the picture; their original formulations may be found in the referenced publications. This book contains very little about semantics, in general, and about the semantics of non-classical logic in particular. (shrink)

This article is about the special, subjective concepts we apply to experience, called “phenomenal concepts”. They are of special interest in a number of ways. First, they refer to phenomenal experiences, and the qualitative character of those experiences whose metaphysical status is hotly debated. Conscious experience strike many philosophers as philosophically problematic and difficult to accommodate within a physicalistic metaphysics. Second, PCs are widely thought to be special and unique among concepts. The sense that there is something special about PCs (...) is very closely tied up with features of the epistemic access they afford to qualia. When we deploy phenomenal concepts introspectively to some phenomenally conscious experience as it occurs, we are said to be acquainted with our own conscious experiences. Accounts of PCs either have to explain the acquaintance relation, or acquaintance with our phenomenal experiences has to be denied. PCs have received much attention in recent philosophy of mind mainly because they figure in arguments for dualism and in physicalist responses to these arguments. The main topic of this article is to explore different accounts of phenomenal concepts and their role in recent debates over the metaphysical status of phenomenal consciousness. (shrink)

This paper deals with the origin, history and various appearances of the problem of coincidences (matches, rencontres) in the theory of probability.

Existentialism and existentialist thinkers enjoyed sustained interest in Hungary under communist rule. From the late 1940s to the late 1980s, this branch of “bourgeois philosophy” never ceased to generate renewed attention. However, this reception was not subsumed into the ideological orthodoxy, nor was it simply destined to fuel Marxist–Leninist criticism. Whereas Georg Lukács’s polemics with existentialism in the 1940s set the agenda to embrace a highly critical reception, it was precisely Sartre’s influence in the 1960s that had opened the door (...) for a more open-minded Marxist reading of existentialist thinkers in Hungary. This paper seeks to reconstruct the intellectual motifs and contexts that underlie this uncommon development. In focusing predominantly on the period of the 1960–1980s, I am particularly interested in exploring Lukács’s role in the changing attitude towards existentialism in Hungary; the controversies between various Marxist approaches dealing with existentialist thinkers and the ways which the influence of Sartre, de Beauvoir, and Camus in literary circles influenced the tenor of their philosophical reception. Through this exploration, I will seek to provide a deep insight into one of the richest intellectual landscapes of the philosophical culture in state socialist Hungary. (shrink)

It is commonly assumed that besides knowledge of facts or truths, there is also knowledge of things–for example, we say that we know people or know places. We could call this "objectual knowledge". In this paper, I raise doubts about the idea that there is a sui generis objectual knowledge that is distinct from knowledge of truths.

The evolution of complex life forms, such as multicellular organisms, is the result of a number of evolutionary transitions in individuality (ETIs). Several attempts have been made to explain their origins, many of which have been internalist (i.e., based largely on internal properties of these life form's ancestors). Here, we show how an externalist perspective, via the ecological scaffolding model in which properties of complex life forms arise from an external scaffold, can shed new light on the question of ETIs. (...) Ultimately, we anticipate progress in the field will occur by recognizing the importance of both the internalist and externalist modes of explanation for ETIs. We illustrate this by considering an extension of the ecological scaffolding model by niche construction in which particles modify the environment which later becomes the scaffold giving rise to collective-level individuality. (shrink)

Two consecution calculi are introduced: one for the implicational fragment of the logic of entailment with truth and another one for the disjunction free logic of nondistributive relevant implication. The proof technique—attributable to Gentzen—that uses a double induction on the degree and on the rank of the cut formula is shown to be insufficient to prove admissible various forms of cut and mix in these calculi. The elimination theorem is proven, however, by augmenting the earlier double inductive proof with additional (...) inductions. We also give a new purely inductive proof of the cut theorem for the original single cut rule in Gentzen’s sequent calculus $ LK $ without any use of mix. (shrink)

Two consecution calculi are introduced: one for the implicational fragment of the logic of entailment with truth and another one for the disjunction free logic of nondistributive relevant implication. The proof technique—attributable to Gentzen—that uses a double induction on the degree and on the rank of the cut formula is shown to be insufficient to prove admissible various forms of cut and mix in these calculi. The elimination theorem is proven, however, by augmenting the earlier double inductive proof with additional (...) inductions. We also give a new purely inductive proof of the cut theorem for the original single cut rule in Gentzen’s sequent calculus $ LK $ without any use of mix. (shrink)