禮書侯制尺度鄭玄注辨析

禮家論侯制，漢時已有異義，鄭玄遍注《三禮》，會通彼此，構擬出獨特的三侯之制。侯制尺度，禮書或有定數，或有明確的比例，或有兩者俱無而可遞推而知者。鄭玄以互注互證之法會通《周禮》及《儀禮》，通過跨文本的整合，並以經文關目為紐帶，應用"推致之法"計算出侯制尺度。自孔穎達、賈公彥以降，禮家大多沿用鄭説，少有如劉敞、郝敬、梁景福、林昌彝等人就其尺度提出異議的。今人墨子涵 (Dianel Patrick Morgan) 運用數學原理，重新計算鄭玄侯制尺度，結果顯示 : 鄭玄在侯的幾何構造上失算，所言侯的幾何構造的計算 (calculation of target geometries)，按照自然法則來説是不可能的 (physically impossible)。鄭玄致誤的主因在於從二維 (two dimensions) 視角，以三侯相疊不離運算,而不是從三維 (three dimensions) 視角，以三侯同道相離來運算。精讀細究，墨子涵計算出的數字還有不盡精確之處，亦未有將堂高計算在內。鄭玄所言侯制，不免脱離實際，無關實用。但其演算結果，一概依據經文，將來源不同、參互錯綜之文融合為一，串連作解。鄭玄精通算術，其説侯之用心，不在乎數字切合實際與否，而旨在詮釋經文，藉以重構周代侯制，蓋無復興古制之意存乎其間。
<eng>Debate among classical scholars regarding the hou (侯, archery target) system had already begun to diverge during the Han dynasty. In his comprehensive commentaries on the Three Books of Rites (三禮, Sanli), Zheng Xuan (127-200) sought to reconcile these differences and established a distinctive tripartite hou system. The measurements of the hou found in the ritual classics are variously presented as fixed values, explicit ratios, or, in some cases, left unstated but inferable through logical reasoning. Zheng Xuan adopted a method of cross-textual corroboration, drawing upon the Rites of Zhou (周禮, Zhouli) and the Book of Ritual and Etiquette (儀禮, Yili), and employed key textual references as connecting threads. Through this “method of deductive derivation” (推致之法), he calculated the dimensions of the hou. From the time of Kong Yingda (孔穎達, 574-648) and Jia Gongyan (賈公彥, life dates unknown), most scholars of ritual studies have followed Zheng Xuan’s interpretations, with notable exceptions such as Liu Chang (劉敞, 1019-1068), Hao Jing (郝敬, 1558-1639), Fan Jingfu (范景福, life dates unknown), and Lin Changyi (林昌彝, 1803-1876), who questioned the accuracy of the measurements. More recently, Daniel Patrick Morgan has applied mathematical principles to recalculate Zheng Xuan’s hou system, concluding that Zheng’s geometric construction of the target was mathematically flawed—his calculations led to a structure that is, according to the laws of nature, “physically impossible.” Morgan argues that Zheng Xuan’s error arose from his two-dimensional approach, treating the three hou as overlapping rather than as three-dimensional structures arranged along a single axis. Closer scrutiny reveals that Morgan’s own calculations are not without minor errors, such as the omission of the elevation of the ceremonial platform (tang gao, 堂高). Whilst Zheng Xuan’s hou system may lack practical viability, his derivations were rigorously grounded in classical texts, synthesising disparate and often contradictory passages into a coherent framework. An accomplished mathematician, Zheng Xuan’s purpose was not to achieve numerical realism, but rather to interpret the hou system as a means of reconstructing the archery targets of the Zhou dynasty as described in the classics—with no intention of reviving ancient institutions.