Die Möglichkeit, Walter Benjamins Allegorie-Begriff in akademischen Untersuchungen mit der Prosa Jean Pauls in Verbindung zu bringen, wurde von Benjamin noch selbst abgewogen: in der Rezension einer frühen Abhandlung zu diesem Thema, die er für zu kurz gegriffen befand. Ein solches Vorhaben, das beste Chancen böte, dürfe sich nämlich nicht auf literaturwissenschaftliche und geistesgeschichtliche Perspektiven beschränken. Notwendig sei vielmehr, auch die Dimension der Alltagskultur einzubeziehen und Jean Pauls Hinabgreifen in Tiefen des Volkstums und der Tradition zu berücksichtigen. Diesem Hinweis Benjamins (...) folgt die vorliegende Untersuchung. Indem sie sich auf den Bereich der materiellen Kultur konzentriert, legt sie eine Geschichte der Theorie der Dingwelt offen. Jean Pauls ästhetische Überlegungen zur projektiven Belehnung der Dingwelt mit seelischen Regungen wurden von Aby Warburg aufgegriffen und für seine kulturwissenschaftliche Methode fruchtbar gemacht. Dabei erschliesst er unter anderem einen Traditionsstrang des Denkens von materieller Kultur im ästhetischen und kultur anthropologischen Kontext, der geprägt ist von aus der Antike herrührenden abergläubischen Vorstellungen über die Einflüsse der Planeten auf die menschliche Geistesverfassung wie etwa die Saturnfürchtigkeit. (shrink)

Cognitive Science, Volume 46, Issue 6, June 2022.

Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation. Participants (N = 44) completed two tasks. In the Evaluation task, participants rated how well sets of equations were solved. Some sets violated principles of arithmetic and others did not. Participants rated non‐violation (...) sets higher than violation sets for two different principles for subtraction with a negative number. In the Word Problem task, participants read word problems and set up equations that could be used to solve them. Participants who displayed greater knowledge of principles of arithmetic with a negative number were more likely to set up equations that involved negative numbers. Thus, participants' knowledge of arithmetic principles was related to their problem representations. (shrink)

We all do it -- Social lies -- Lying out of fear -- Lying to get ahead -- Lies that wow -- Lying to yourself -- The truth of the matter.

In this paper, we study the relationship among classical logic, intuitionistic logic, and quantum logic . These logics are related in an interesting way and are not far apart from each other, as is widely believed. The results in this paper show how they are related with each other through a dual intuitionistic logic . Our study is completely syntactical.

The interpretability of AI is just as important as its performance. In the LegalAI field, there have been efforts to enhance the interpretability of models, but a trade-off between interpretability and prediction accuracy remains inevitable. In this paper, we introduce a novel framework called LK-IB for compulsory measure prediction (CMP), one of the critical tasks in LegalAI. LK-IB leverages Legal Knowledge and combines an Interpretable model and a Black-box model to balance interpretability and prediction performance. Specifically, LK-IB involves three steps: (...) (1) inputting cases into the first module, where first-order logic (FOL) rules are used to make predictions and output them directly if possible; (2) sending cases to the second module if FOL rules are not applicable, where a case distributor categorizes them as either “simple” or “complex“; and (3) sending simple cases to an interpretable model with strong interpretability and complex cases to a black-box model with outstanding performance. Experimental results demonstrate that the LK-IB framework provides more interpretable and accurate predictions than other state-of-the-art models. Given that the majority of cases in LegalAI are simple, the idea of model combination has significant potential for practical applications. (shrink)

LK is much more difficult than NK, and to make matters worse, Gentzen's intention is still unclear when it comes to that system (LK). -/- This book, Vol.1 of the series titled What is LK?, tackles this issue, focusing on the sequent, the most enigmatic notion we find in LK. The dependence-relation we find in NK shall play a crucial role in that investigation. -/- The style is typically textbook-like, so readers can learn the system of LK, using this series (...) as a guidance, too. (shrink)

LK is much more difficult than NK, and to make matters worse, Gentzen's intention is still unclear when it comes to that system (LK). -/- The second and third volumes of the series titled What is LK? conduct the detailed survey of each inference-figure in a toe-to-toe way, as it were, which most mathematicians looked through. -/- The present volume, Vol.2, looks deeper into structural inference-figures, which is never an easy task.

Gentzen’s sequent calculi LK and LJ are landmark proof systems. They identify the structural rules of weakening and contraction as notable inference rules, and they allow for an elegant statement and proof of both cut elimination and consistency for classical and intuitionistic logics. Among the undesirable features of those sequent calculi is that their inferences rules are low-level and frequently permute over each other. As a result, large-scale structures within sequent calculus proofs are hard to identify. In this paper, we (...) present a different approach to designing a sequent calculus for classical logic. Starting with Gentzen’s LK proof system, we examine the proof search meaning of his inference rules and classify those rules as involving either don’t care nondeterminism or don’t know nondeterminism. Based on that classification, we design the focused proof system LKF in which inference rules belong to one of two phases of proof construction depending on which flavor of nondeterminism they involve. We then prove that the cut rule and the general form of the initial rule are admissible in LKF. Finally, by showing that the inference rules for LK are all admissible in LKF, we can give a relative completeness proof for LKF provability with respect to LK provability. We shall also apply these properties of the LKF proof system to establish other meta-theoretic properties of classical logic, including Herbrand’s theorem. (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)

Working within the sensing, intuition, feeling, thinking (SIFT) approach to biblical hermeneutics, the present study focuses attention on the distinctive voices of introverted intuition and extraverted intuition, by analysing the way in which two small groups, one comprising dominant introverted intuitive types and the other comprising dominant extraverted intuitive types, explored and reflected on the Lucan narrative of the Good Samaritan, a passage rich in material to stimulate the perceiving process. Two distinctive voices emerged from these two groups. CONTRIBUTION: Situated (...) within the reader perspective approach to biblical hermeneutics, the SIFT method is concerned with identifying the influence of the psychological type of the reader in shaping the interpretation of text. The foundations of the SIFT approach distinguish among the four functions of sensing, intuition, feeling, and thinking. The present study builds on this foundation by developing the nuance of the orientation in which the function is expressed, in this case focusing specifically on the comparison between introverted intuition and extraverted intuition. (shrink)

The article is on the exegesis of the parable of the Good Samaritan (Lk 10:25–35) and its relevance to the challenges that are being posed by COVID-19. Through the historical-critical approach, the article has concluded that the parable is relevant in troubleshooting the challenges that are caused by COVID-19, such as discrimination, stigma, hate and stereotypes. The article sees COVID-19 as teaching humanity the important lesson that no one can live in isolation, however powerful or economically strong they are. Therefore, (...) there is a need to take the opportunity of being a neighbour. Neighbourhood is understood as offering services to those in need and COVID-19 has presented a chance to the entire world to help someone with needs. A need-based world requires neighbours and this makes the parable relevant. Contribution: This article is a reflection of the challenges that are currently faced by people in response to the COVID-19 pandemic. It is within the scope of this theological journal that issues of identity, relationships, and theological reflection should be addressed, hence the article fits well within this scope. (shrink)

Nigeria is an example of developing countries characterised by mass poverty in the midst of plenty. Coincidentally, the Nigerian church is stupendously rich. Pastor Emmanuel, a former National Coordinator of the Redeemed Christian Church of God, Germany, notes that the annual revenue of the Nigeria church in 2014 is over ₦3 trillion while surprisingly, the national budget is ₦4.69tn for the year. Gigantic buildings, exotic cars and private jets are the hallmarks of the church’s wealth. Some pastors acquire jets ranging (...) from ₦2.3 to ₦6.4 billion with additional ₦8.4bn for maintenance and salaries annually. Surrounded by this ‘affluence’ are thousands of poor, unemployed and barely surviving church members. This calls for the need to examine what Lukan Jesus would have wanted the church to do with her wealth. This article examines Lukan parables on the rich and the poor using narratological method. Thus, the parables’ context, the characterisation and the plot is analysed, including lexical-syntactical relationships. Finally, the lessons derived is used via socio-scientific reading of the Nigerian situation to arrive at a theology of social action for the poor. Most parables are open-ended, a literary device that ensures the readers take a decision, therefore the message focuses on the church rather than individual Christians. Contribution: The article recommends that church-owned institutions should make education accessible to the poor, rise against socio-economic policies that will impoverish people while seeking economic independence of the poor. Finally, the church should also integrate the differently-abled into the church. (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)

This article seeks to reconstruct the phrase τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον in the light of an African predicament with the Ewe-Ghanaian context in focus. The article posits that the various interpretations of the phrase throughout the epochs of Christianity have arisen as a result of the ambiguity associated with ἐπιούσιος and the quest to make the Lord’s Prayer in general relevant to the life situation of the recipient communities. Although the Lord’s Prayer is still regarded as a prayer par (...) excellence in the Ewe-Ghanaian Christian community, its central theme in popular Ewe-Ghanaian spirituality has been demonological instead of eschatological. The demonological interpretation is premised on the primal Ewe belief that successful spiritual warfare against the evil forces believed to be militating against one’s destiny in life can restore one’s fortunes and lead to the blessing of material prosperity. Thus, the phrase τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον in popular Ewe-Ghanaian Christian spirituality is a call on God to ‘grant us the blessing of material prosperity, good health and longevity’. The demonological approach towards material prosperity, however, is discontinuous with the evangelisation approach, which was introduced into Ewe-Ghanaian spirituality through missionary activities in the mid-19th century. The missionaries identified the cardinal Ewe-Ghanaian predicament – poverty of the mind and spirit – and addressed them holistically through the message of the Gospel and the establishment of schools, hospitals, and agriculture to guarantee food security. This holistic approach to alleviating the poverty of the spirit and mind laid the foundation for the socio-economic development of their Ewe-Ghanaian Christian converts and the communities in which they practise their faith.Contribution: This article forms part of the researcher’s contribution to the academic knowledge on the Lord’s Prayer and inspires the use of Mother Tongue Biblical hermeneutics in the development of theological materials for the Ewe-Ghanaian Christian communities in Ghana, Togo, and Benin. (shrink)

This paper aims to develop the notion of ‘therapy of desire’ as a hermeneutic key for understanding Kierkegaard’s view of desire. First, I develop the notion of ‘therapy of desire’ as it has appeared in the secondary literature on Kierkegaard and Augustine, particularly in Lee C. Barrett. In my reading, I underscore how a ‘therapy of desire’ implies that the desire can be ‘healed’ and that the desirer has ‘agency’ over his/her desires. Second, I conduct a textual analysis of Kierkegaard’s (...) discourse on Lk 22:15, which deals with the desire for the Eucharist. In employing the notion of ‘therapy of desire’ as a hermeneutic key to interpret it, I characterize Kierkegaard’s view of desire as a lack of satisfaction and verify how the ideas of ‘agency’ and ‘healing’ appear in Kierkegaard’s text. Finally, I show how the characterization of desire as a constant lack of satisfaction that consists in a gift from God, that implies the possibility of undertaking a healing process and that underscores the agency of the desirer, differs from some Lutheran ideas, namely the relationship between grace and deeds and the understanding of original sin. (shrink)

Augustine’s interpretation of the parable of the rich man and Lazarus from Lk 16 shows how much the parables of Jesus are open to a variety of interpretations and applications depending upon which part of the parable is emphasised. In Augustine’s writings the second part of the parable only is commented upon (the exception being ep. 157) to illustrate points about the afterlife and the fate of the soul. However, in his homilies we find him engaging with both sections of (...) the parable (this life and the afterlife). We can note the dexterity with which Augustine handled diverse themes in the parable by selectively emphasising either the fate of the rich man in this life or the next or the fate of Lazarus in this life or the next. From these different perspectives Augustine could deal with questions of wealth and poverty either materially or spiritually. This research supports the notion that whatever Augustine had to say about almsgiving is to be understood within a soteriological context to urge his congregation to be rich in humility and poor in pride. (shrink)

Resolution and cut-free LK are the most popular propositional systems used for logical automated reasoning. The question whether or not resolution and cut-free LK have the same efficiency on the system of CNF formulas has been asked and studied since 1960 425–467). It was shown in Cook and Reckhow, J. Symbolic Logic 44 36–50 that tree resolution has super-polynomial speed-up over cut-free LK. Naturally, the current issue is whether or not resolution and cut-free LK expressed as directed acyclic graphs have (...) the same efficiency. In this paper, we introduce a new algorithm to eliminate atomic cuts and show that cut-free LK polynomially simulates resolution when the input formula is expressed as a k-CNF formula. As a corollary, we show that regular resolution does not polynomially simulate cut-free LK . We also show that cut-free LK polynomially simulates regular resolution. (shrink)