There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...) is designed to study. (shrink)

We introduce a simple inference system based on two primitive relations between terms, namely, inclusion and exclusion relations. We present a normalization theorem, and then provide a characterization of the structure of normal proofs. Based on this, inferences in a syllogistic fragment of natural language are reconstructed within our system. We also show that our system can be embedded into a fragment of propositional minimal logic.

We propose a new information sharing system, named ``BisNet'', which automatically gathers information about the bookmarks stored in users' web browsers and helps the users exchange URIs of possibly interesting web pages with others who have similar interest with them. Being different from other typical agent services that gather and provide information according to pre-registered user profiles, BisNet is expected to share more relevant information because of its use of web browser bookmarks that are actively selected and ordered by many (...) humans. To enhance the relevance of information being shared, we developed a novel algorithm for directory evaluation. This algorithm only looks at the local referential structure between bookmark directories and URIs and calculates for each directory the ``order index'' that represents how well its content URIs are put in order with a focus on specific areas of interest. Then each directory receives new URIs from other related directories with large order indexes. The repetition of such URI exchanges makes the whole directory-URI networks dynamically form directory groups according to the commonness of the URIs they refer to. Our method is unique in that it pays no attention to the actual contents of web pages, and thus is much simpler and faster than other methods based on the result of content analysis. We carried out a field trial that involved 45 people who used a prototype version of BisNet clients. The result indicated that the relevance of shared URIs positively correlated with the ``order index'' of surrounding related directories, demonstrating the effectiveness of the method we proposed. (shrink)

Feinberg and Mallatt, in their presentation of neurobiological naturalism, have suggested that visual consciousness was acquired by early vertebrates and inherited by a wide range of descendants, and that its neural basis has shifted to nonhomologous nervous structures during evolution. However, their evolutionary scenario of visual consciousness relies on the assumption that visual consciousness is closely linked with survival, which is not commonly accepted in current consciousness research. We suggest an alternative idea that visual consciousness is linked to a specific (...) class of agency, consequently justifying their phylogenetic claim. We also examine the implication of their phylogenetic claim: visual consciousness is homologous across vertebrates, but its neural basis is not. This apparent incongruence illustrates a general phenomenon of homology, and that the resulting hierarchical view of visual consciousness and its neural basis can be straightforwardly accommodated by neurobiological naturalism. Throughout these discussions, we aim to address the potential theoretical issues in neurobiological naturalism and refine the picture illustrated by Feinberg and Mallatt regarding phylogenetic distribution and trajectories of visual consciousness. (shrink)

In sub-Sect. 3.3, the terms “one-person” and “-person” were incorrectly updated by mistake during the correction stage in the online published article.

Neuroscientific claims have a significant impact on traditional philosophy. This essay, focusing on the field of moral neuroscience, discusses how and why philosophy can contribute to neuroscientific progress. First, viewing the interactions between moral neuroscience and moral philosophy, it becomes clear that moral philosophy can and does contribute to moral neuroscience in two ways: as explanandum and as explanans. Next, it is shown that moral philosophy is well suited to contribute to moral neuroscience in both of these two ways in (...) the context of the problem of ecological validity. Philosophy can play the role of an agent for ecological validity, since traditional philosophy shapes and reflects part of our social reality. Finally, based on these arguments, I tentatively sketch how a Kantian account of moral incentive can play this role. (shrink)

What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible world, the laws (...) of logic fail. In this paper, I provide a definition of logically impossible worlds. I then show that there is nothing strange about admitting such worlds. (shrink)

La figure du chat fait son apparition dans la littérature japonaise au ixe siècle, mais son image évoluera de manière inattendue à l’époque médiévale. Des témoignages littéraires du xie et du xiie siècle, tels que les Notes de chevet de Sei Shônagon et Le Dit du Genji de Murasaki Shikibu, montraient clairement l’intérêt porté aux chats par les dames de cour. Pourtant, à partir du xiiie siècle, le félidé fera au contraire l’objet d’une forme de « diabolisation », et c’est (...) cette dimension plus inquiétante du chat que nous aimerions évoquer ici, à travers trois exemples tirés du Kokon chomon-jû, vaste recueil de contes et légendes. Cette œuvre méconnue en Europe est attribuée à Tachibana no Narisue et achevée en 1254. The figure of the cat made its appearance in Japanese literature in the 9th century, but its image evolved unexpectedly in medieval times. Literary evidence from the 11th and 12th centuries, such as the Bedside Notes by Sei Shônagon and The Tale of Genji by Murasaki Shikibu clearly showed the interest of court women in cats. However, from the 13th century, the feline became the object of a form of “demonization”, and it is this more disturbing dimension of the cat that we would like to describe here, through three examples taken from Kokon chomon-Jû, a vast collection of tales and legends. This work, unknown in Europe, has been attributed to Tachibana no Narisue and was completed in 1254. (shrink)

In 1A:7 of the Mengzi, Mengzi tries to convince King Xuan of Qi that he is a “true” king. As a reading of Mengzi’s reasoning involved in his attempt at persuasion, David Nivison advances an inferential view, according to which Mengzi’s persuasion involves inferences. In this paper, I consider the assumptions underlying the objections raised against Nivison’s inferential view. I argue that these objections assume a contemporary Western view about the nature of logic and inferences. I propose an alternative characterisation (...) of the relevant sense of inference that, I believe, is more sensitive to the classical Chinese philosophical context and argue that certain insights can be derived from reading Mengzi in light of this alternative characterization of inferences. (shrink)

Scientific progress in recent neurofeedback research may bring about a new type of moral neuroenhancement, namely, neurofeedback-based moral enhancement; however, this has yet to be examined thoroughly. This paper presents an ethical analysis of the possibility of neurofeedback-based moral enhancement and demonstrates that this type of moral enhancement sheds new light on the moral enhancement debate. First, I survey this debate and extract the typical structural flow of its arguments. Second, by applying structure to the case of neurofeedback-based moral enhancement, (...) I examine the ethical, legal, and social issues to show that this technique is unique and traditionalist, which makes it compatible with almost all our conservative notions, so that it, accordingly, can be seen as an ethically acceptable option. Third, by rejecting the premise in the moral enhancement debate that bio/neuro-enhancement has its unique ELSI that traditional methods would never create, I demonstrate that, by virtue of its traditional or conservative features, neurofeedback-based moral enhancement can be incorporated into the traditional moral education network. Finally, I conclude that, being a part of the traditional moral education network, neurofeedback-based moral enhancement can be a unique and ethically acceptable option of moral neuroenhancement. (shrink)

The moral status of human brain organoids (HBOs) has been debated in view of the future possibility that they may acquire phenomenal consciousness. This study empirically investigates the moral sensitivity in people’s intuitive judgments about actions toward conscious HBOs. The results showed that the presence/absence of pain experience in HBOs affected the judgment about the moral permissibility of actions such as creating and destroying the HBOs; however, the presence/absence of visual experience in HBOs also affected the judgment. These findings suggest (...) that people’s intuitive judgments about the moral status of HBOs are sensitive to the valence-independent value of phenomenal consciousness. We discuss how these observations can have normative implications; particularly, we argue that they put pressure on the theoretical view that the moral status of conscious HBOs is grounded solely in the valence-dependent value of consciousness. We also discuss how our findings can be informative even when such a theoretical view is finally justified or when the future possibility of conscious HBOs is implausible. (shrink)

Logic in Buddhist Philosophy concerns the systematic study of anumāna (often translated as inference) as developed by Dignāga (480-540 c.e.) and Dharmakīti (600-660 c.e.). Buddhist logicians think of inference as an instrument of knowledge (pramāṇa) and, thus, logic is considered to constitute part of epistemology in the Buddhist tradition. According to the prevalent 20th and early 21st century ‘Western’ conception of logic, however, logical study is the formal study of arguments. If we understand the nature of logic to be formal, (...) it is difficult to see what bearing logic has on knowledge. In this paper, by weaving together the main threads of thought that are salient in Dignāga’s and Dharmakīti’s texts, I shall re-conceive the nature of logic in the context of epistemology and demarcate the logical part of epistemology which can be recognised as logic. I shall demonstrate that we can recognise the logical significance of inference as understood by Buddhist logicians despite the fact that its logical significance lies within the context of knowledge. (shrink)

Priest holds anti-exceptionalism about logic. That is, he holds that logic, as a theory, does not have any exceptional status in relation to the theories of empirical sciences. Crucial to Priest’s anti-exceptionalism is the existence of ‘data’ that can force the revision of logical theory. He claims that classical logic is inadequate to the available data and, thus, needs to be revised. But what kind of data can overturn classical logic? Priest claims that the data is our intuitions about the (...) validity of inferences. In order to make sense of this claim, I will appeal to the Madhyamaka Buddhist philosopher Candrakīrti. I will then pose a problem for Priest’s anti-exceptionalism. Finally, I will suggest a way out of the problem for Priest. Whether or not he accepts my solution, I will let him decide. (shrink)

Lantiana, Boudesseulab, and Covac conducted two investigations to examine the moral acceptability of love drugs (Lantiana, Boudesseulab, and Covac 2024). In particular, their studies were designed...

Some skeptics question the very possibility of moral bioenhancement by arguing that if we lack a widely acceptable notion of morality, we will not be able to accept the use of a biotechnological technique as a tool for moral bioenhancement. I will examine this skepticism and argue that the assessment of moral bioenhancement does not require such a notion of morality. In particular, I will demonstrate that this skepticism can be neutralized in the case of recent neurofeedback techniques. This goal (...) will be accomplished in four steps. First, I will draw an outline of the skepticism against the possibility of moral bioenhancement and point out that a long-lasting dispute among moral philosophers nourishes this skepticism. Second, I will survey recent neurofeedback techniques and outline their three features: the variety of the target human faculties, such as emotion, cognition, and behavior; the flexibility or personalizability of the target brain state; and the nonclinical application of neurofeedback techniques. Third, I will argue that, by virtue of these three unique features, neurofeedback techniques can be a tool for moral bioenhancement without adopting any specific notion of morality. Fourth, I will examine the advantages and threats that neurofeedback-based moral enhancement may have. Finally, I will conclude that neurofeedback-based moral enhancement can become a new and promising tool for moral bioenhancement and requires further ethical investigations on its unique features. (shrink)

In his book review of Graham Priest's The Fifth Corner of Four, Mark Siderits, while criticising Priest's philology, suggests that Priest's work is 'of considerable interest' for two reasons. First, 'when two independent traditions use similar methods to work on similar issues, it is always possible that one may have hit on approaches that the other missed'. Second, 'the decentering that can be induced by looking at another tradition may trigger fresh insights, even if those insights are not ones that (...) were actually developed by the tradition marked 'other''. The main task of this paper is to unpack Siderits' thought. By analysing some of Priest's work, I will suggest a decentering that must have taken place in China when Buddhism was 'exported to China in Buddhist shipping containers'. For anyone familiar with the forms of Buddhist philosophy developed in India, various forms of Chinese Buddhism can often look strange. Some ideas that were debated and defended by Indian Buddhists do not appear anywhere in Chinese Buddhism and some assumptions have been quietly added to Buddhism by Chinese Buddhists. By showing that Priest's work brings out the 'innovation' that Chinese Buddhists gave to Buddhism, I will suggest that it is this decentering that Siderits suggests Priest makes use of. (shrink)

Possible worlds have revolutionised philosophy and some related fields. But, in recent years, tools based on possible worlds have been found to be limited in many respects. Impossible worlds have been introduced to overcome these limitations. This Element aims to raise and answer the neglected question of what is characteristically impossible about impossible worlds. The Element sheds new light on the nature of impossible worlds. It also aims to analyse the main features and utility of impossible worlds and examine how (...) impossible worlds can capture distinctions which are unavailable if we limit ourselves to possible world-based tools. (shrink)

Buddhist philosophers have developed a rich tradition of logic. Buddhist material on logic that forms the Buddhist tradition of logic, however, is hardly discussed or even known. This article presents some of that material in a manner that is accessible to contemporary logicians and philosophers of logic and sets agendas for global philosophy of logic.

In the 1958-1959 Collège de France course, Merleau-Ponty expounds a detailed commentary on the last paragraphs of the Einleitung from Hegel’s Phenomenology of Spirit. We examine in what sense this course has developed the notions that he was in the process of defining, notions such as “chiasm,” “reversibility,” “depth,” and “flesh.” What seems crucial in this course is to clearly define good ambiguity as opposed to bad ambiguity, that is, to the simple mixture of finitude and universality, of interiority and (...) exteriority. It is a question then of revealing, even within Hegelian thought, the operation, although unstable, of good ambiguity and of instituting it beyond the distinction between anthropology and logic without a return to naturalism. It should first be noted that consciousness is for Hegel violence against itself, it gives itself its measure, such that the distinction between measuring and measured is internal to it. By insisting on this “reversibility” of the measuring and the measured, Merleau-Ponty comes to emphasize that the self-relation of consciousness is simultaneously its opening onto a transcendent – an opening whereby it learns something. This leads him to define “the new ontological milieu” which is the depth of the life of consciousness. It is within this depth that the interrogative experience winds on itself. Secondly, if there truly must be a moment where the Hegelian Zweideutigkeit becomes good ambiguity, it will not suffice to explore preobjective depth; it would still be necessary to discern “the hinge” which is “solid, unwavering” and which “remains irremediably hidden.” It is this unwavering hinge that supports phenomena and that, in simultaneously decentering and recentering the fields of appearances, opens a place where one can follow the genesis of sense. Finally, we note that this discovery of the new ontological milieu can be considered as the recovery of the notion of institution that Merleau-Ponty had proposed in 1954-1955: on the one hand, the notion of chiasm invites us to reveal the hinge which at once decenters and recenters the fields of appearances. This hinge is free from the alternative of nature and culture, of subjective and objective spirit; it is the rootedness of our interrogative experience in brute being, which is not object but starts an indefinite search of self. But, on the other hand, the notion of institution, which is essentially descriptive and factual, makes us better feel the weight of the instituted that is also irremediably hidden. It makes us feel the inertia of the instituting event, as well as its fecundity and its cumulativity. (shrink)

The Genesis of the Social and the Carnal Donation of the Non-Presentable. The Range of the Notion of Institution in Merleau-PontyThis article examines the range of the notion of institution that Merleau-Ponty proposes in his course at the Collège de France (1954-55), by notably insisting on the importance of the question of the genesis of the social for the deepening of his thought. By broadening his investigative domains in two complementary directions (that is, lateral passivity and socio-historical institution), Merleau-Ponty aims (...) in this course to grasp in a better way the lateral relations of our Urstiftung (originary institution) and the instituting subject who obliquely goes beyond the institution towards its sense. That leads him to introduce the perceptual field as being essentially lacunary, because it marks a place where the consciousness is present at the divergence in relation to consciousness. It is certain that the Phenomenology of Perception addressed this question by considering the social as a place where “I am given to myself”. However, the psychological starting point of this work, as well as the originary temporal and unilateral character of radical reflection, prevented one from really grasping the institutional junction of the concrete event and the symbolic matrix. One was not able to thematize an auto-articulation which appears suddenly between radical reflection and the unreflective. This is why Lévi-Strauss’ structuralist thought, by considering the social as symbolism, allows for a better understanding of this institutional nexus. But this idea does not lead to the dogmatic positing of the reality and the autonomy of the social. Instead, it encourages us to practice “the perception of history,” which consists in guessing, in the very process of sociological idealization, the carnal and wild donation of the non-presentable. Far from returning to psychologism, this perception aims at actively achieving the movement internal to the symbolic, that is, its incarnation.La genesi del sociale e la donazione carnale del non-presentabile. La portata della nozione di istituzione in Merleau-PontyQuesto articolo esamina la portata della nozione d’istituzione che Merleau-Ponty propone nel suo corso al Collège de France del 1954-1955, insistendo in particolare sull’importanza della questione della genesi del sociale per l’approfondimento del suo pensiero.Estendendo i propri domini di ricerca in due direzioni complementari (la passività laterale e l’istituzione socio-storica), Merleau-Ponty si propone in questo corso di cogliere meglio i rapporti laterali della nostra Urstiftung (l’istituzione originaria) e del soggetto istituente che la supera obliquamente in direzione del suo senso. Ciò induce a presentare il campo percettivo come essenzialmente lacunoso, poiché manca di un luogo dove la coscienza possa assistere allo scarto rispetto a se stessa.È certo che la Fenomenologia della percezione affrontava questa questione considerando il sociale come un luogo dove “io sono donato a me stesso”. I presupposti psicologici di quest’opera, così come il carattere originariamente temporale e unilaterale della riflessione radicale, impedivano tuttavia di cogliere in maniera adeguata il legame istituzionale dell’evento concreto e della matrice simbolica, e di tematizzare un’autoarticolazione che sorgesse tra la riflessione radicale e l’irriflesso.È per questo motivo che il pensiero strutturalista di Lévi-Strauss, che considerava il sociale come simbolismo, permette di comprendere meglio questo nesso istituzionale. Quest’idea non conduce però a porre dogmaticamente la realtà e l’autonomia del sociale, essa incita piuttosto a praticare “la percezione della storia” che consiste nell’individuare, nel processo stesso dell’idealizzazione sociologica, la donazione carnale e selvaggia del non-presentabile. Lungi dal rappresentare un ritorno allo psicologismo, questa nozione di percezione mira a completare attivamente il movimento interno al simbolico, ovvero la sua incarnazione. (shrink)

One of the prime characteristics of the increasingly technological and interconnected world is the disappearance of analogue experience in all aspects of life. Due to technological invention, we are exposed to a variety of news and information, checking emails in private and business accounts for a significant amount of time each day. Our information-driven minds are constantly occupied by the desire to seek out more information. The ways we engage in music also have changed. We now download mp3 files and (...) listen to music on iPods. People are used to web-based, digitalized music listening.1 It is in this context that many people in the modern world are turning to indigenous forms of music that allow them to.. (shrink)

Sleep is a fundamental property conserved across species. The homeostatic induction of sleep indicates the presence of a mechanism that is progressively activated by the awake state and that induces sleep. Several lines of evidence support that such function, namely, sleep need, lies in the neuronal assemblies rather than specific brain regions and circuits. However, the molecular mechanism underlying the dynamics of sleep need is still unclear. This review aims to summarize recent studies mainly in rodents indicating that protein phosphorylation, (...) especially at the synapses, could be the molecular entity associated with sleep need. Genetic studies in rodents have identified a set of kinases that promote sleep. The activity of sleep-promoting kinases appears to be elevated during the awake phase and in sleep deprivation. Furthermore, the proteomic analysis demonstrated that the phosphorylation status of synaptic protein is controlled by the sleep-wake cycle. Therefore, a plausible scenario may be that the awake-dependent activation of kinases modifies the phosphorylation status of synaptic proteins to promote sleep. We also discuss the possible importance of multisite phosphorylation on macromolecular protein complexes to achieve the slow dynamics and physiological functions of sleep in mammals. (shrink)

This paper considers the computational complexity of the design of voting rules, which is formulated by simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.

Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms of regions as in (...) the standard approach, but in terms of topological relations between diagrammatic objects. We formalize the unification rule, which plays a central role in Euler diagrammatic reasoning, in a style of natural deduction. We prove the soundness and completeness theorems with respect to a formal set-theoretical semantics. We also investigate structure of diagrammatic proofs and prove a normal form theorem. (shrink)

Recent neuroscience studies have reported that neurofeedback training with the use of functional magnetic resonance imaging enables the regulation of an individual’s cognitive, emotion-related, and behavioral states through a real-time representation of her brain activities. Since this technique has been applied not only to clinical research to, for example, mitigate mental or psychiatric symptoms but also to non-clinical research to, for example, change the cognition or preferences of a so-called healthy participant, neurofeedback-based cognitive and/or moral enhancements may be realized in (...) the future. However, neurofeedback-based human enhancement is not the only issue that requires neuroethical consideration. I examine why and to what extent the dual application of neurofeedback technique will blur the lines between the mental, the social, and the moral, threatening some social norms, such as individual freedom and diversity. First, I consider the link between the mental and the social in psychiatry. Examining the definition of “mental disorder” provided by the American Psychiatric Association, I show that the mental is partly defined through social performance. Second, I make explicit the link between the social and the moral and argue that moral evaluation of an activity is gently but positively correlated with its social evaluation. Third, I demonstrate the links between the mental, the social, and the moral. In spite of a great deal of effort to distinguish these notions, the possibility of the dual application of this technique blurs the lines between them. Fourth, I examine whether such blurred lines signal sociocultural evolution or dystopia and argue that it can be understood as a beginning of the second advent of ethical virtue. I conclude that further cautious consideration of neuroethics is required because the establishment of this technique may have unique influences on our society. (shrink)

This paper points out an error of Parigot's proof of strong normalization of second order classical natural deduction by the CPS-translation, discusses erasing-continuation of the CPS-translation, and corrects that proof by using the notion of augmentations.

La figure diabolisée du chat dans la littérature japonaise évolue sans cesse au cours de l’époque médiévale, et nous prenons ici l’exemple d’un chat-monstre nommé nekomata. L’un des exemples littéraires les plus connus se trouve dans les Heures oisives, ouvrage écrit vers 1330 par Yoshida Kenkô. Il semble cependant que le terme nekomata soit apparu un siècle plus tôt, comme le montre l’entrée du 2 août 1233 dans le Journal de la lune brillante de Fujiwara no Teika, l’un des plus (...) grands poètes de son temps. Nous analyserons donc ce texte de première importance pour comprendre les origines de cette figure littéraire, puis tenterons de comprendre le sens de l’expression nekomata. The demonized figure of the cat in Japanese literature evolved constantly during medieval times, and here we take the example of a monster cat named nekomata. One of the best-known literary examples is found in Tsurezure-gusa, written around 1330 by Yoshida Kenkô. However, it seems that the term nekomata appeared a century earlier, as can be seen from the August 2, 1233 entry in Meigetsu-ki, the diary of Fujiwara no Teika, one of the greatest poets of his time. We will examine this important text for a better understanding of the history of the monster cat and reflect on the meaning of the term nekomata. (shrink)

In this paper, we describe a collaborative information retrieval method among personal repositorie and an implementation of the method on a personal agent framework. We propose a framework for personal agents that aims to enable the sharing and exchange of information resources that are distributed unevenly among individuals. The kernel of a personal agent framework is an RDF(resource description framework)-based information repository for storing, retrieving and manipulating privately collected information, such as documents the user read and/or wrote, email he/she exchanged, (...) web pages he/she browsed, etc. The repository also collects annotations to information resources that describe relationships among information resources and records of interaction between the user and information resources. Since the information resources in a personal repository and their structure are personalized, information retrieval from other users' is an important application of the personal agent. A vector space model with a personalized concept-base is employed as an information retrieval mechanism in a personal repository. Since a personalized concept-base is constructed from information resources in a personal repository, it reflects its user's knowledge and interests. On the other hand, it leads to another problem while querying other users' personal repositories; that is, simply transferring query requests does not provide desirable results. To solve this problem, we propose a query equalization scheme based on a relevance feedback method for collaborative information retrieval between personalized concept-bases. In this paper, we describe an implementation of the collaborative information retrieval method and its user interface on the personal agent framework. (shrink)

A logic is said to be paraconsistent if it does not allow everything to follow from contradictory premises. There are several approaches to paraconsistency. This paper is concerned with several philosophical positions on paraconsistency. In particular, it concerns three ‘schools’ of paraconsistency: Australian, Belgian and Brazilian. The Belgian and Brazilian schools have raised some objections to the dialetheism of the Australian school. I argue that the Australian school of paraconsistency need not be closed down on the basis of the Belgian (...) and Brazilian schools’ objections. In the appendix of the paper, I also argue that the Brazilian school’s view of logic is not coherent. (shrink)

This paper gives the strong reduction of the combinatory calculus SCL, which was introduced as a combinatory calculus corresponding to the untyped Lambda-mu calculus. It proves the confluence of the strong reduction. By the confluence, it also proves the conservativity of the extensional equality of SCL over the combinatory calculus CL, and the consistency of SCL.

This paper gives new confluence proofs for several lambda calculi with permutation-like reduction, including lambda calculi corresponding to intuitionistic and classical natural deduction with disjunction and permutative conversions, and a lambda calculus with explicit substitutions. For lambda calculi with permutative conversion, naïve parallel reduction technique does not work, and traditional notion of residuals is required as Ando pointed out. This paper shows that the difficulties can be avoided by extending the technique proposed by Dehornoy and van Oostrom, called the Z (...) theorem: existence of a mapping on terms with the Z property concludes the confluence. Since it is still hard to directly define a mapping with the Z property for the lambda calculi with permutative conversions, this paper extends the Z theorem to compositional functions, called compositional Z, and shows that we can adopt it to the calculi. (shrink)

How can Buddhists prove that non-existent things do not exist? With great difficulty. For the Buddhist, this is not a laughing matter as they are largely global error theorists and, thus, many things are non-existent. The difficulty gets compounded as the Buddhist and their opponent, the non-Buddhist of various kinds, both agree that one cannot prove a thesis whose subject is non-existent. In this paper, I will first present a difficulty that Buddhist philosophers have faced in proving that what they (...) take to be non-existent does not exist. I will then survey two main solutions that they have provided. Those 'solutions' may not solve the problem or solve the problem but creates other problems. I will not survey the Buddhist treatment of the problem of proving about non-existence in order to present a new solution that we have yet to see. Instead, I will articulate a problem about non-existence that is unique to Buddhist philosophers. I will do so in order to present an interesting puzzle about non-existence that has largely escaped attention in the 'Western' literature. (shrink)