The use of the three labels (logicism, formalism, intuitionism) to denote the three foundational schools of the early twentieth century are now part of literature. Yet, neither their number nor their adoption has been stable over the twentieth century. They were not introduced by the founding fathers of each school: namely, neither Frege nor Russell spoke of ‘logicism’; and even Hilbert did not use the word ‘formalism’ to introduce his foundational programs. At a certain point, only Brouwer used the label ‘intuitionism’ in his scientific production to personify his philosophy of mathematics and he used the label ‘formalism’ for Hilbert’s foundational viewpoint. Starting with Brouwer, the origin of the use of the three labels to represent a foundational meaning, will be analysed in this paper. Thereafter, the role that Brouwer’s pupil Arend Heyting had in the production and use of foundational labels will be considered. On the basis of the comparison of the attitudes of these two scholars I will finally advance the thesis that not only the creation but also the use of labels, far from being a mere gesture of academic reference to literature, can be a sign of the cultural operation each scholar wanted to do.

中文翻译：

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塑造敌人：LEJ Brouwer 和 A. Heyting 的基础标签

使用三个标签（逻辑主义、形式主义、直觉主义）来表示 20 世纪早期的三个基础流派现在是文学的一部分。然而，它们的数量和采用率在 20 世纪都不稳定。它们不是由每个学派的创始人介绍的：即，弗雷格和罗素都没有谈到“逻辑主义”；甚至希尔伯特也没有使用“形式主义”这个词来介绍他的基础程序。在某个时候，只有布劳威尔在他的科学作品中使用“直觉主义”标签来体现他的数学哲学，而他使用“形式主义”标签来代表希尔伯特的基本观点。本文将从 Brouwer 开始，分析使用三个标签来表示基本含义的起源。此后，将考虑 Brouwer 的学生 Arend Heyting 在基础标签的生产和使用中所扮演的角色。在比较这两位学者的态度的基础上，我将最终提出这样一个论点，即不仅创作而且标签的使用，绝不仅仅是一种学术参考文学的姿态，而是一种文化的标志。每个学者都想做的操作。