This paper analyzes the theory of area developed by Euclid in the Elements and its modern reinterpretation in Hilbert’s influential monograph Foundations of Geometry. Particular attention is bestowed upon the role that two specific principles play in these theories, namely the famous common notion 5 and the geometrical proposition known as De Zolt’s postulate. On the one hand, we argue that an adequate elucidation of how these two principles are conceptually related in the theories of Euclid and Hilbert is highly (...) relevant for a better understanding of the respective geometrical practices. On the other hand, we claim that these conceptual relations unveil interesting issues between the two main contemporary approaches to the study of area of plane rectilinear figures, i.e., the geometrical approach consisting in the geometrical theory of equivalence and the metrical approach based on the notion of measure of area. Finally, in an appendix logical relations among equivalence, comparison and addition of magnitudes are examined schematically in an abstract setting. (shrink)

This paper presents an analysis and discussion of the opinions of two generations of Asian parents with regard to their young children's education. A large number of parents were interviewed during 1970-1974 and a smaller number during 1995 to ascertain their views on a variety of topics relating to their children's early education. The findings are discussed in a qualitative way and reveal the increasing satisfaction of Asian parents with their children's education. A higher proportion of the mothers of the (...) 1990s help their children with homework, read them stories and are generally more participatory in their children's education compared with the 1970s group. The second generations are concerned with the lack of facilities for the teaching of mother tongues in schools. These and other findings are discussed within the changing lifestyles of second-generation Asians. (shrink)

The first part of this paper argued that the traditional application of the Cave to the Line was not intended by Plato, and led to a misunderstanding of both similes. The Cave, it was said, is attached to the simile of the Sun and the Line by the visible region outside the cave, which is a reintegration of the symbolism of sun, originals and images in the sunlight, and the new system of objects inside the cave is compared and contrasted (...) with the natural objects in the visible outside. As we know that the natural symbolism illustrates the Platonic education, our main task in this paper will be to find the meaning of the cave, untrammelled by the associations of the lower line. (shrink)

This new edition brings Farquharson's authoritative 1944 translation up to date and includes a helpful introduction and notes for the student and general reader. Rutherford includes a selection of letters from Marcus to his tutor Fronto--most of which date from his earlier years--that offer personal detail and help to fill out the somber portrait of the emperor that is found in the Meditations.

This paper is a survey of V.A. Smirnovs main results in modern logic.

Silence has gained a prominent role in the field of psychotherapy because of its potential to facilitate a plethora of therapeutically beneficial processes within patients’ inner dynamics. This study examined the phenomenon from a conversation analytical perspective in order to investigate how silence emerges as an interactional accomplishment and how it attains interactional meaning by the speakers’ adjacent turns. We restricted our attention to one particular sequential context in which a patient’s turn comes to a point of possible completion and (...) receives a continuer by the therapist upon which a substantial silence follows. The data collection consisted of 74 instances of such post-continuer silences. The analysis revealed that silence can retroactively become part of a topic closure sequence, can become shaped as an intra-topic silence, and can be explicitly characterized as an activity in itself that is relevant for the therapy in process. Only in this last case, the absence of talk is actually treated as disruptive to the ongoing talk. Although silence is often seen as a therapeutic instrument that can be implemented intentionally and purposefully, our analysis demonstrated how it is co-constructed by speakers and indexically obtains meaning by adjacent turns of talk. In the ensuing turns, silence indeed shows to facilitate access to the patient’s subjective experience at unconscious levels. (shrink)