＜余録＞
小平先生が 怠け数学者の記 のP164で ヒルベルトの幾何学基礎論 公理で
「点」、「直線」などは意味の無い無定義語で
「鯨」、「豚」などに置き換えても良いとあるのを 厳しく批判していますね
（やっぱり 線、直線など まずは普通の意味であるべき？）

おそらく コテコテの 形式主義や公理主義を 小平先生は批判していますね （＾＾
なお、”「鯨」、「豚」などに置き換えても良い”は
英語系では 下記 en.wikipediaなどでは ”tables, chairs and beer mugs”らしいが
後に付けた ”The Foundations of Geometry BY DAVID HILBERT”の英訳には 見つからなかった
（ひょっとして HILBERTがどこかでしゃべったことで 都市伝説ができたかもです）

＜アマゾン＞
怠け数学者の記(岩波現代文庫)2000/8/17
小平邦彦(著),上野健爾(解説)
レビュー 北狐
5つ星のうち5.0 実在論と比類無き計算力
20200817
この本を読むと、小平邦彦を斯くの如く在らしめたものは、彼の正確無比の
計算力と数学に対する楽天的実在論(詳しくは小平著『解析入門Ⅰ』の初めに書いてある。『数学のすすめ(筑摩書房)』の«数学の印象»の中で夏目漱石の『夢十夜』を実在論の喩えに挙げている。)に在ったことが良く分かる

https://en.wikipedia.org/wiki/Foundations_of_geometry
Foundations of geometry is the study of geometries as axiomatic systems.
There are several components of an axiomatic system
1.Primitives (undefined terms) are the most basic ideas. Typically they include objects and relationships. In geometry, the objects are things like points, lines and planes while a fundamental relationship is that of incidence – of one object meeting or joining with another. The terms themselves are undefined. Hilbert once remarked that instead of points, lines and planes one might just as well talk of tables, chairs and beer mugs. His point being that the primitive terms are just empty shells, place holders if you will, and have no intrinsic properties.

https://scispace.com/pdf/hilbert-s-synthesis-on-foundation-of-geometry-dbanopt5ac.pdf
Journal of Humanities and Education Development Vol-1, No6,2019
Hilbert Synthesis on Foundation of Geometry Andrea Battocchio
P10
Virtually, all types of objects that possess the characteristics given by the axioms can equally be taken into account as geometric entities. To describe Hilbert's approach, it is always appropriate the famous anecdote according to which at the end of a Wiener lesson, on foundations of geometry, he said “One must be able to say at all times - instead of points, straight lines, and planes - tables, chairs, and beer mugs”' [65, p. 39].
[65] Reid, C.(1996). Hilbert. Springer, New York.

https://math.berkeley.edu/~wodzicki/160/Hilbert.pdf
The Foundations of Geometry BY DAVID HILBERT,
AUTHORIZED TRANSLATION BY E. J. TOWNSEND, PH. D. UNIVERSITY OF ILLINOIS
REPRINT 1950 The Open Court Publishing Co.1902.