英：algebra;法：algebre
代数学是把问题的解决还原为符号式操作的一门数学 (MATHEMATICS)分支。拉康在其 1955 年的著作中便开始使用一些代数学符号 (见：[[Schema L L图式]]), 以试图把精神分析加以形式化。在此种形式化目的的背后，存在着三个主要的原因：
(1)形式化是让精神分析取得科学性地位所必需的（见[[Science 科学]])。正如克劳德·列维-斯特劳斯运用了一些准数学的公式，以试图把人类学奠定在更具科学性的基础之上，拉康也尝试对精神分析做同样的事情。
(2)形式化可以给精神分析理论提供某种内核，从而使之甚至能够被完整地传递给那些从未体验过精神分析治疗的人们。因而，各种公式就变成了精神分析家训练当中的一个基本面向，它们作为一种传递精神分析知识的媒介同训练性分析并驾齐驱。
(3)根据代数学符号对精神分析理论加以形式化，是一种防止直觉化理解的手段，此种直觉化的理解被拉康看作阻碍通往象征界的一种想象性引诱。这些代数学符号应当以各种不同的方式来运用、操作并解读，而不是以一种直觉化的方式来理解 (见：E, 313).
拉康著作的大多数英文译本也都翻译了出现在其著作中的这些代数学符号。例如，阿兰·谢里丹就在其《著作集》的选译本中把符号 A (表示 Aure)译作 O (表示 Oher)。然而，诚如谢里丹自己所指出的那样，拉康却反对这样一种做法 (Sheridan, I 977:xi)。在这本辞典中，为了配合拉康自己的偏好，这些代数学符号均以它们在法语原文中的形式被保留
拉康所使用的代数学符号主要出现在各种 [[matheme 数元，数学型]], [[Schema L L图式]] 以及[[graph of desire 欲望图解]]当中，它们连同其最常见的意义一起被罗列在下面。然而，重要的是要记得，这些符号在拉康著作的不同地方并非总是指涉相同的概念，而是随着其著作的发展以不同的方式来使用的。有关此种意义上的转变，最重要的例子就是对于符号的使用，在 1950 年代与 1960 年代，这个符号是以两种根本不同的方式来使用的。然而，即便是其他那些在意义上相对稳定的符号，偶尔也都是以非常不同的方式来使用的：例如 s 几乎总是指代所指，然而在一则算法中却被用来表示假设知道的主体 (见：Lacan, 1967)。因此，在参考下面的等义列表时，读者应需特别谨慎
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这些排版印刷上的细节与区分性标志在拉康的代数学中是极其重要的。大写与小写符号之间的差异，斜体与非斜体符号之间的差异，橄号、负号以及下标的使用等，所有这些细则在代数学系统中皆具有其各自的作用。例如，大写字母往往指涉象征秩序，而小写字母则通常指涉想象界。杠的使用也同样重要，甚至在同一公式中亦会有所变化。
(algebre) Algebra is a branch of MATHEMATICSwhich reduces the solution ofproblems to manipulations of symbolic expressions. Lacanbegins to use algebraicsymbols in his work in 1955 (see SCHEMA L), in an attempt toformalisepsychoanalysis. Three main reasons lie behind this attempt at formalisation:
- Formalisation is necessary for psychoanalysis to acquire scientificstatus (seeSCIENCE). Just as Claude Levi-Strauss uses quasi-mathematical formulae in an attemptto set anthropology on a more scientific footing, Lacan attempts to do the sameforpsychoanalysis.
- Formalisation can provide a core of psychoanalytic theory which can be transmittedintegrally even to those who have never experienced psychoanalytic treatment. Thefommulae thus become an essential aspect of the training of psychoanalysts which taketheir place alongside the training analysis as a medium for the transmissionofpsychoanalytic knowledge.
- Formalisation of psychoanalytic theory in terms of algebraic symbols is a means ofpreventing intuitive understanding, which Lacan regards as an imaginary lure whichhinders access to the symbolic. Rather than being understood in an intuitive way, thealgebraic symbols are to be used, manipulated and read in various different ways (see E, 313)
Most English translations of Lacan also translate the algebraic symbols which appearin his work. For example, Alan Sheridan, in his translation of Ecrits, renders the symbolA (for Autre) as O (for Other). However, Lacan was opposed to such a practice, as Sheridan himself points out (Sheridan, 1977:xi). In this dictionary, in line with Lacan'sown preference, the algebraic symbols are left as they are in the original French texts.
The algebraic symbols used by Lacan, which appear principally in the MATHEMES, SCHEMA L and the GRAPH OF DESIRE, are listed below, together with their mostcommon meaning. However, it is important to remember that the symbols do not alwaysrefer to the same concept throughout Lacan's work, but are used in different ways as hiswork develops. The most important example of such a shift in meaning is the use of thesymbol a, which is used in radically different ways in the 1950 s and in the 1960 s. However, even other symbols which are relatively stable in meaning are occasionallyused in very different ways; for example, s nearly always designates the signified, but isused in one algorithm to denote the subject supposed to know (see Lacan, 1967). Therefore some caution should be exercised when referring to the following list ofequivalences.
The typographical details and diacritics are extremely important in Lacanian algebra.Thedifference between upper-and lower-case symbols,the difference between italicised andnon-italicised symbols,the use of the apostrophe,the minus sign,and subscripts;all thesedetails play their part in the algebraic system.For example the upper-case letters usuallyrefer to the symbolic order,whereas the lower-case letters usually refer to the imaginaryThe use of the bar is also important,and varies even within the same formula.