Definitions of Infinity: An Attempt to Gain Conceptual Clarity with Mathematical and Theological Ramifications

無限性之定義：一種獲取概念的清晰性以及數學和神學的結果之嘗試

威瑟爾(Leonard P. Wessell)

《漢語基督教學術論評》 12期 (2011/12) Pp. 67-103

https://doi.org/10.30106/SCSAIJBTP.201112.0003

摘要

至少從亞里斯多德的時代起便開始區分潛無限和實無限。在康托的著作面世之前，實無限通常被限制成一種最適宜用來討論上帝的本體論範疇。無限通常在數學討論中缺席。隨著康托著作的問世，學界因著它作為整體的無限性而開始留意一系列潛無限的自然數。這樣的一種考量使得實無限得以被數學理論化。中世紀哲學家相反地只允許對無限唯一的實在範例，突然就有一種過多的，實際上來說是無限的數的無限性。在以下的討論中，我的意圖是獲取概念的清晰性，以致於能夠使潛在沒有終點的系列全體化，換言之，轉變成被設想為無限的數或是被設想成作為無限的上帝的實無限。這個結果的獲致，乃是透過對於潛無限和實無限的定義，以作為一篇序言，展開在數學和神學中實無限的邏輯完善性的一個判斷的形成。以下的這個方法導致對於先前無限性概念之數學和神學使用的批判，並且發現實無限一旦應用到數學領域乃是概念的矛盾修飾，一旦應用到神學領域便問題叢生。

關鍵字

潛無限 ； 實無限 ； 否定神學 ； 肯定神學 ； 刪除法

並列摘要

At least since the time of Aristotle a distinction has been made between potential and actual infinity. Before the work of Georg Cantor, actual infinity was generally limited to being an ontological category most appropriate for a discussion of divinity. Infinity was generally absent from mathematical considerations. With Cantor the attempt was made to conceive of a series of natural numbers, potentially infinite because of its endlessness, as a totality or whole. Such a consideration renders actual infinity accessible to mathematical theorizing. Whereas medieval philosophers allowed for only one actual exemplification of infinity, suddenly there was a plethora, indeed, an infinity of infinite numbers. My intention in the following discussion is to achieve conceptual clarity so as to be able to render a rational judgment concerning the totalization of a series potentially without end, i.e., its transformation into actual infinity conceived of as an infinite number or as God qua infinity. This is achieved by producing definitions of potential and actual infinity as a preface to the formulation of a judgment on the logical integrity of actual infinities in mathematics and theology. This method follows leads to a fundamental critique of previous conceptualizations of infinity for mathematical and theological use and finds actual infinity to be a conceptual oxymoron when applied to mathematics and problematic when applied to theology.

並列關鍵字

potential infinity ； actual infinity ； negative theology ； positive theology ； Exclusionary method

參考文獻

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