The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the application of a term/function to any other term/function, including itself. The calculus can be seen as a formal theory with certain pre-established axioms and inference rules, which can be interpreted by models. Dana Scott proposed the first non-trivial model of the extensional lambda calculus, (...) known as $ D_{\infty }$, to represent the $\lambda $-terms as the typical functions of set theory, where it is not allowed to apply a function to itself. Here we propose a construction of an $\infty $-groupoid from any lambda model endowed with a topology. We apply this construction for the particular case $D_{\infty }$, and we see that the Scott topology does not provide enough information about the relationship between higher homotopies. This motivates a new line of research focused on the exploration of $\lambda $-models with the structure of a non-trivial $\infty $-groupoid to generalize the proofs of term conversion to higher-proofs in $\lambda $-calculus. (shrink)

This essay is written on the following premises and argues for them. “Enlightenment” is a word or signifier, and not a single or unifiable phenomenon which it consistently signifies. There is no single or unifiable phenomenon describable as “the Enlightenment,” but it is the definite article rather than the noun which is to be avoided. In studying the intellectual history of the late seventeenth century and the eighteenth, we encounter a variety of statements made, and assumptions proposed, to which the (...) term “Enlightenment” may usefully be applied, but the meanings of the term shift as we apply it. The things are connected, but not continuous; they cannot be reduced to a single narrative; and we find ourselves using the word “Enlightenment” in a family of ways and talking about a family of phenomena, resembling and related to one another in a variety of ways that permit of various generalizations about them. We are not, however, committed to a single root meaning of the word “Enlightenment,” and we do not need to reduce the phenomena of which we treat to a single process or entity to be termed “the” Enlightenment. It is a reification that we wish to avoid, but the structure of our language is such that this is difficult, and we will find ourselves talking of “the French” or “the Scottish,” “the Newtonian” or the “the Arminian” Enlightenments, and hoping that by employing qualifying adjectives we may constantly remind ourselves that the keyword “Enlightenment” is ours to use and should not master us. (shrink)

The texts collected in this volume, which was originally published in 1969, contain Herder's most original and stimulating ideas on politics, history and language. They had for the most part not been previously available in English. In his introduction, Professor Barnard analyses the basic premises of Herder's political thought against the background of the Enlightenment. He examines Herder's concepts of language, community and culture, his theory of historical interaction, and his approach to the problem of change and progress. Finally, he (...) provides a brief comparative analysis of traditionalist thought following the French Revolution, showing how substantive writers like Burke differed from Herder despite the close similarity of political vocabulary. (shrink)

The first English translation of Fichte’s second set of 1804 lectures on the Wissenschaftslehre.

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant Λ is discussed by using Inönü–Wigner contractions of the de Sitter groups and spaces. When Λ→∞, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c→∞ is further considered, the kinematical group in this case being a modified Galilei (...) group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology. (shrink)

A precise fomulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity but allowing for the presence of torsion. For the sake of brevity, a concise statement is proposed for the Principle: An ideal observer immersed in a gravitational field can choose a reference frame in which gravitation goes unnoticed. This statement is given a clear mathematical meaning through an accurate (...) discussion of its terms. It holds for ideal observers (time-like smooth non-intersecting curves), but not for real, spatially extended observers. Analogous results hold for gauge fields. The difference between gravitation and the other fundamental interactions comes from their distinct roles in the equation of force. (shrink)

Students’ educational engagement is both an important predictor of study success and a key preventive factor for dropout. Vocational tracks in secondary education show high dropout rates. There is strong evidence that the solution to educational disengagement lies in student‐centred, powerful learning environments. This study investigates characteristics of PLEs from the perspective of students in vocational secondary education. Students’ perspectives on a learning environment are crucial for their satisfaction and learning engagement. Therefore, we investigated whether the perceived learning environment meets (...) the requirements of PLEs, and to what extent it meets students’ preferences. Additionally, it was investigated whether students who perceive their learning environment as more powerful, are also more engaged for school. Survey data of 532 students showed that student perceptions of their current learning environment were largely discrepant from the characteristics of PLEs. Students strongly asked for more challenging learning pathways, in combination with adaptive learning support. Students who perceived the characteristics of PLEs as being present, reported higher satisfaction and stronger engagement than students who perceived their education to be a less powerful environment. There is a need to redesign curricula in vocational education in such a way that these more intensely implement characteristics of PLEs. (shrink)

Critical scholarly edition of J. G. Fichte's Closed Commercial State.

In recent work, Adlam (2022b), Chen & Goldstein (2022), and Meacham (2023) have defended accounts of laws that take laws to be primitive global constraints. A major advantage of these accounts is that they’re able to accommodate the many different kinds of laws that appear in physical theories. In this paper I’ll present these three accounts, highlight their distinguishing features, and note some key differences that might lead one to favor one of these accounts over the others. I’ll conclude by (...) briefly discussing a version of a “constraint” account that I think is especially attractive. (shrink)

Jeffrie G. Murphy's third collection of essays further pursues the topics of punishment and retribution that were explored in his two previous collections: Retribution, Justice and Therapy and Retribution Reconsidered. Murphy now explores these topics in the light of reflections on issues that are normally associated with religion: forgiveness, mercy, and repentance. He also explores the general issue of theory and practice and discusses a variety of topics in applied ethics - e.g., freedom of artistic expression, the morality of gambling, (...) and the value of forgiveness in psychological counseling. As always, his perspective may be described as Kantian; and, indeed, this collection contains the first extended piece of Kant scholarship that he has done in years: a long essay on Kant on theory and practice. (shrink)

Pocock, J. G. A. (John Greville Agard) 1924- "Quentin Skinner: The History of Politics and the Politics of History" Common Knowledge - Volume 10, Issue 3, Fall 2004, pp. 532-550.