On the dialectical foundations of mathematics

This paper tracks the systematic dialectical determination of mathematical concepts in Hegel's Encyclopädie der philosophischen Wissenschaften (1830, 1817) and investigates the insights that can be gained from such a perspective on the mathematical. To begin with, the determination of Numbers and arithmetical operations from Being shows that the One and the successor function have a qualitative base and need not be presupposed. It is also shown that even for infinite Intensive Magnitudes (cardinals) there exists an Extensive Magnitude through which they gain meaning. This makes the 'bad' in Hegel's 'bad infinity' a trifle problematic. Finally, if 'Dasein' is interpreted as the whole of perception in the present, Place can be viewed as the spatial Now, Motion as the passage from Place to Now and Matter as the actual (as opposed to observed) Presence of the natural realm

SET THEORY AND GEOMETRY IN HEGEL

This paper tracks the systematic dialectical determination of mathematical concepts in Hegel’s Encyclopädie der philosophischen Wissenschaften (1830, 1817) and investigates the insights that can be gained from such a perspective on the mathematical. To begin with, the determination of Numbers and arithmetical operations from Being shows that the One and the successor function have a qualitative base and need not be presupposed. It is also shown that even for infinite Intensive Magnitudes (cardinals) there exists an Extensive Magnitude through which they gain meaning. This makes the ‘bad’ in Hegel’s ‘bad infinity’ a trifle problematic. Finally, if ‘Dasein’ is interpreted as the whole of perception in the present, Place can be viewed as the spatial Now, Motion as the passage from Place to Now and Matter as the actual (as opposed to observed) Presence of the natural realm

The dynamic effect of context on interval timing in children and adults

Human reproductions of time intervals are often biased towards previously perceived durations, resulting in a central tendency effect. The aim of the current study was to compare this effect of temporal context on time reproductions within children and adults. Children aged from 5 to 7 years, as well as adults, performed a ready-set-go reproduction task with a short and a long duration distribution. A central tendency effect was observed both in children and adults, with no age-difference in the effect of global context on temporal performance. However, the analysis of the effect of local context (trial-by-trial) indicated that younger children relied more on the duration (objective duration) presented in the most recent trial than adults. In addition, statistical analyses of the influence on temporal performance of recently reproduced durations by subjects (subjective duration) revealed that temporal reproductions in adults were influenced by performance drifts, i.e., their evaluation of their temporal error, while children simply relied on the value of reproduced durations on the recent trials. We argue that the central tendency effect was larger in young children due to their noisier internal representation of durations: A noisy system led participants to base their estimation on experienced duration rather than on the evaluation of their judgment

UVSSA and USP7, a new couple in transcription-coupled DNA repair

Transcription-coupled nucleotide excision repair (TC-NER) specifically removes transcription-blocking lesions from our genome. Defects in this pathway are associated with two human disorders: Cockayne syndrome (CS) and UV-sensitive syndrome (UVSS). Despite a similar cellular defect in the UV DNA damage response, patients with these syndromes exhibit strikingly distinct symptoms; CS patients display severe developmental, neurological, and premature aging features, whereas the phenotype of UVSS patients is mostly restricted to UV hypersensitivity. The exact molecular mechanism behind these clinical differences is still unknown; however, they might be explained by additional functions of CS proteins beyond TC-NER. A short overview of the current hypotheses addressing possible molecular mechanisms and the proteins involved are presented in this review. In addition, we will focus on two new players involved in TC-NER which were recently identified: UV-stimulated scaffold protein A (UVSSA) and ubiquitin-specific protease 7 (USP7). UVSSA has been found to be the causative gene for UVSS and, together with USP7, is implicated in regulating TC-NER activity. We will discuss the function of UVSSA and USP7 and how the discovery of these proteins contributes to a better understanding of the molecular mechanisms underlying the clinical differences between UVSS and the more severe CS

On the dialectical foundations of mathematics

This paper tracks the systematic dialectical determination of mathematical concepts in Hegel’s Encyclopädie der philosophischen Wissenschaften (1830,1817) and investigates the insights that can be gained from such a perspective on the mathematical. To begin with, the determination of Numbers and arithmetical operations from Being shows that the One and the successor function have a qualitative base and need not be presupposed. It is also shown that even for infinite Intensive Magnitudes (cardinals) there exists an Extensive Magnitude through which they gain meaning. This makes the ‘bad’ in Hegel’s ‘bad infinity’ a trifle problematic. Finally, if ‘Dasein’ is interpreted as the whole of perception in the present, Place can be viewed as the spatial Now, Motion as the passage from Place to Now and Matter as the actual (as opposed to observed) Presence of the natural realm