Study is recently re-invoked as an alternative educational formation to disrupt the learning trap and trope. This paper calibrates study and learning as two hermeneutic principles and correlates them with seeing, hearing, and observing as three onto-epistemic modes that respectively underpin Greco-Christian, Rabbinic, and ancient Chinese exegetical traditions. Linking study and learning with the hermeneutic issues of language, text, meaning, and reality, my calibration unfolds in four steps. First, I introduce an epistemic aporia encountered in interpreting some Chinese educational “wind” texts, exposing our naturalized reasoning of learning along a representational enclosure. Second, turning to Susan Handelman’s writing, I trace this learning-as-representation enclosure as being conditioned upon the Greco-Christian exegetical mode of seeing, meanwhile correlating study back with the Rabbinic hearing hermeneutic. Third, I move on to explicate an onto-cosmological Yijing observing, proffering a study hermeneutic as a movement of observing, following, and attuning to wendao, literally put, “a crisscrossing pattern that (re-)turns with dao.” Finally, I re-observe and study the crisscrossing Chinese educational “wind” texts, evoking a Chinese “wind-teaching” sensibility so far rarely discerned through representational thinking and learning.
In this paper, I explore an intriguing view of definable numbers proposed by a Cambridge mathematician Ernest Hobson, and his solution to the paradoxes of definability. Reflecting on König’s paradox and Richard’s paradox, Hobson argues that an unacceptable consequence of the paradoxes of definability is that there are numbers that are inherently incapable of finite definition. Contrast to other interpreters, Hobson analyses the problem of the paradoxes of definability lies in a dichotomy between finitely definable numbers and not finitely definable numbers. To bypass this predicament, Hobson proposes a language dependent analysis of definable numbers, where the diagonal argument is employed as a means to generate more and more definable numbers. This paper examines Hobson’s work in its historical context, and articulates his argument in detail. It concludes with a remark on Hobson’s analysis of definability and Alan Turing’s analysis of computability. 相似文献
