Logicians have strongly preferred first-order natural deductive systems over Peirce's Beta Graphs even though both are equivalent to each other. One of the main reasons for this preference, I claim, is that inference rules for Beta Graphs are hard to understand, and, therefore, hard to apply for deductions. This paper reformulates the Beta rules to show more fine-grained symmetries built around visual features of the Beta system, which makes the rules more natural and easier to use (...) and understand. Noting that the rules of a natural deductive system are natural in a different sense, this case study shows that the naturalness and the intuitiveness of rules depends on the type of representation system to which they belong. In a diagrammatic system, when visual features are discovered and fully used, we have a more efficacious deductive system. I will also show that this project not only helps us to apply these rules more easily but to understand the validity of the system at a more intuitive level. (shrink)

The well‐known “Consequence Argument” for the incompatibility of freedom and determinism relies on a certain rule of inference; “Principle Beta”. Thomas Crisp and Ted Warfield have recently argued that all hitherto suggested counterexamples to Beta can be easily circumvented by proponents of the Consequence Argument. I present a new counterexample which, I argue, is free from the flaws Crisp and Warfield detect in earlier examples.

This paper investigates the analysis of the de re/de dicto distinction and related facts. I start with the assumption, supported by Cresswell 1990, that the evaluation of the truth of a proposition relative to a particular possible world/situation is mediated via the presence in the syntax of a silent pronoun with type-s denotation. In this system, the de re/de dicto distinction arises from a difference in which an operator binds a given situation pronoun. Percus 2000 shows that such a system (...) potentially overgenerates, in that a third type of reading is predicted to exist for sentences which actually have only two: de re and de dicto. Percus proposes constraints on the binding of situation pronouns, which correctly rule out these third readings. This paper shows, however, that extrinsic constraints on the binding of situation pronouns are not necessary to rule out the unwanted readings, as long as we develop a more precise theory of binding in the first place. I adapt the binding operator argued for by Büring 2004, originally developed only for overt pronouns, and show that when used as an operator for situation pronouns, the unwanted readings are not predicted to occur. (shrink)

Name der Zeitschrift: Byzantinische Zeitschrift Jahrgang: 107 Heft: 1 Seiten: 37-50.

Nelson’s stochastic quantum mechanics provides an ideal arena to test how the Born rule is established from an initial probability distribution that is not identical to the square modulus of the wavefunction. Here, we investigate numerically this problem for three relevant cases: a double-slit interference setup, a harmonic oscillator, and a quantum particle in a uniform gravitational field. For all cases, Nelson’s stochastic trajectories are initially localized at a definite position, thereby violating the Born rule. For the double (...) slit and harmonic oscillator, typical quantum phenomena, such as interferences, always occur well after the establishment of the Born rule. In contrast, for the case of quantum particles free-falling in the gravity field of the Earth, an interference pattern is observed before the completion of the quantum relaxation. This finding may pave the way to experiments able to discriminate standard quantum mechanics, where the Born rule is always satisfied, from Nelson’s theory, for which an early subquantum dynamics may be present before full quantum relaxation has occurred. Although the mechanism through which a quantum particle might violate the Born rule remains unknown to date, we speculate that this may occur during fundamental processes, such as beta decay or particle-antiparticle pair production. (shrink)

The present paper deals with a systemS of propositional calculus, conjunction, equivalence and falsum being its primitive terms.The only primitive rule inS is the rule of extensionality defined by the scheme: $\frac{{E\alpha \beta ,\Phi (\alpha )}}{{\Phi (\beta )}}$.

Jesus of Nazareth, like Socrates, left nothing behind written by himself. Yet, the records of his teaching indicate a rich interest in dialogic pedagogy, reflected in his use of the parable, primarily an oral genre, as a dialogic provocation. Working at the interface of pedagogy, theology and philosophy, this article explores the parable of the Good Samaritan from the perspective of dialogic pedagogy. It employs an analytical approach termed diacognition, developed from the notions of dialogue, position and cognition, to analyse (...) the moves within the parable and the teaching situation in which it is located. The article explores how Jesus engages the dialogue of and around the parable to position and reposition his interlocutor, provoking a re-cognition of what it means to love one’s neighbour. It concludes by reflecting on the implications of this analysis for the relation of meaning to knowing and doing. (shrink)

The information explosion and digital modes of learning often combine to inform the quest for the best ways of transforming information in digital form for pedagogical purposes. This quest has become more urgent and pervasive with the ‘turn’ to online learning in the context of COVID-19. This can result in linear, asynchronous, transmission-based modes of teaching and learning which commodify, package and deliver knowledge for individual ‘customers’. The primary concerns in such models are often technical and economic – technology as (...) a cost-effective ‘solution’ to educational challenges. In this paper I argue for the importance of dialogic learning space in teaching and learning by means of Information and Communication Technologies, whether in the form of fully online learning, blended learning or face-to-face encounters using ICT affordances. Although the 20th Century theorists Mikhail Bakhtin (1895–1975) and Hans-Georg Gadamer (1900–2002) produced their seminal works before the advent of ICTs, they were both concerned with the quality and authenticity of human engagement with texts and with other persons and contexts. Besides a shared interest in dialogue as an ontological feature of human life and being, they both used spatiotemporal concepts for understanding and interpreting texts. The article draws on Gadamer’s notions of dialogue and horizon, and Bakhtin’s notions of dialogue and chronotope, to conceptualize dialogic possibilities for online education. Its purpose is to provide a framework, grounded in Bakhtin’s and Gadamer’s ideas, for a dialogic approach to online teaching and learning in higher education. (shrink)

Dialogue is a seminal concept within the work of the Brazilian adult education theorist, Paulo Freire, and the Russian literary critic and philosopher, Mikhail Bakhtin. While there are commonalities in their understanding of dialogue, they differ in their treatment of dialectic. This paper addresses commonalities and dissonances within a Bakhtin-Freire dialogue on the notions of dialogue and dialectic. It then teases out some of the implications for education theory and practice in relation to two South African contexts of learning that (...) facilitate the access to education of disadvantaged groups, one in higher education and the other in early childhood education. (shrink)

This article examines the relationship between online dispute resolution (ODR) and trust. We discuss what trust is, why trust is important, and how trust develops. Our claim is that efforts to implement online dispute resolution on a site or service in a manner that promotes trust need to consider ODR as just one tool in a broader toolbox of trust-building tools and techniques. These techniques are amongst others marketing, education, trust seals, and transparency. By evaluating ODR in its proper context (...) as one component of a larger trust strategy, we can more accurately set expectations for its results and position our projects for success. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.