A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons (“If a polygon is divided into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon”). We formulate an abstract version of this postulate and derive it from some (...) selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5 (“The whole is greater than the part”), and analyze its logical relation to the former proposition. These results prove to be relevant for the clarification of some key conceptual aspects of Hilbert’s proof of De Zolt’s postulate, in his classicalFoundations of Geometry(1899). Furthermore, our abstract treatment of this central proposition provides interesting insights for the development of a well-behaved theory ofcompatiblemagnitudes. (shrink)
Although the author's critical view of functionalism has a considerable intuitive pull, his argument based on the color room scenario does not work. Functionalism and other relational views of the mind are capable of providing coherent accounts of conscious experience that meet the challenge set up by the “color room argument.” A simple example of such an account is presented.
The study aims to help characterize the sort of structures about which people can acquire unconscious knowledge. It is already well established that people can implicitly learn n-grams and also repetition patterns. We explore the acquisition of unconscious structural knowledge of symmetry. Chinese Tang poetry uses a specific sort of mirror symmetry, an inversion rule with respect to the tones of characters in successive lines of verse. We show, using artificial poetry to control both n-gram structure and repetition patterns, that (...) people can implicitly learn to discriminate inversions from non-inversions, presenting a challenge to existing models of implicit learning. (shrink)
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)
A theory of magnitudes involves criteria for their comparison, equivalence and addition. We examine these aspects from an abstract viewpoint, stressing independence and definability. These considerations are triggered by the so-called De Zolt’s principle in the theory of equivalence of plane polygons.
Vryheid is naas regverdiging een van die belangrikste temas van die Reformatoriese teologie. Luther se geskrif 'Oor die vryheid van 'n Christenmens' is een van sy hoofgeskrifte. In hierdie geskrif beskryf hy die vryheid van die innerlike en die uiterlike mens. Die innerlike mens is vry en niemand se onderdaan nie. Die uiterlike mens is weer elke ander mens se onderdaan en dienskneg. Die Christen dien sy medemens deur die liefde. Luther se verstaan van naasteliefde word vanuit ander geskrifte toegelig. (...) Johannes Calvyn se verstaan van vryheid volgens sy 'Institusie' van 1559 word ook bespreek. Daar word op die groot ooreenstemming tussen Luther en Calvyn gewys. Die verskille tussen die twee Reformatore is minimaal. Calvyn het egter wel groter aandag aan die adiafora-vraagstuk gegee. Daar word ook deurgaans na Philipp Melanchthon se invloed op Calvyn gewys. Die relevansie van die vryheidsvraagstuk lê nie in die instrumentalisering van die Christelike vryheid nie, maar in die hernude bestudering van die klassieke tekste met die bedoeling om die belangrike reformatoriese motiewe te herontdek. Hierdie motiewe is relevant - ook in ons samelewing. (shrink)
Öz Çalışmanın konusu irfanî geleneğin on beşinci yüzyıldaki önemli temsilcilerinden ve aynı zamanda İbnü’l-Arabî’nin takipçilerinden biri olan İbn Türke’nin varlık mertebelerine dair görüşleridir. Konu, İbn Türke’nin varlık ve varlığın mertebeleri ile ilgili düşüncelerinden hareketle hazırlanmıştır. Birincil kaynakların esas alındığı bu çalışmada, İbn Türke ve Ekberî geleneğin önemli temsilcilerinin eserlerine müracaat edilmiştir. Çalışmanın amacı, felsefe ve kelâmın yanı sıra tasavvuf felsefesinin en önemli konularından biri olan varlık düşüncesi ve varlık mertebelerini İbn Türke’nin görüşleri çerçevesinde ele alarak âlemdeki varoluşun hakikatinin ne olduğu, (...) insanoğlunun özünün nereden geldiği gibi temel sorulara cevap olabilecek özgün bir çalışma ortaya koymaktır. Bu çalışmayla; varlığın bir ve tek hakikat olduğu, Hak’tan feyz ederek görünür âlemde ortaya çıkan her şeyin O’nun isim ve sıfatlarının tecellisi olduğu, her ne kadar Hak’tan ayrıymış gibi görünse de aslında Hakk’a doğru sonsuz bir dönüş içerisinde olduğu, dolayısıyla tek varlıktan kaynaklı çok sayıda varlığın esasen yokluğa mahkûm olduğu ve asıl varlığın Allah olduğu sonucuna varılmıştır. (shrink)
