I survey Brouwer’s weak counterexamples to classical theorems, with a view to discovering (i) what useful mathematical work is done by weak counterexamples; (ii) whether they are rigorous mathematical proofs or just plausibility arguments; (iii) the role of Brouwer’s notion of the creative subject in them, and whether the creative subject is really necessary for them; (iv) what axioms for the creative subject are needed; (v) what relation there is between these arguments and Brouwer’s theory of choice sequences. I refute one of Brouwer’s claims with a weak counterexample of my own. I also examine Brouwer’s 1927 proof of the negative continuity theorem, which appears to be a weak counterexample reliant on both the creative subject and the concept of choice sequence; I argue that it provides a good justification for the weak continuity principle, but it is not a weak counterexample and it does not depend essentially on the creative subject.

中文翻译：

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Brouwer 的弱反例和创造性主题：一项批判性调查

我调查了 Brouwer 对经典定理的弱反例，目的是发现 (i) 弱反例做了哪些有用的数学工作；(ii) 它们是严格的数学证明还是合理性论证；(iii) Brouwer 的创作主体概念在其中的作用，以及创作主体对他们来说是否真的必要；(iv) 创意主题需要哪些公理；(v) 这些论证与布劳威尔的选择序列理论之间有什么关系。我用我自己的一个弱反例反驳了 Brouwer 的一项主张。我还检查了 Brouwer 1927 年对负连续性定理的证明，这似乎是一个依赖于创造性主体和选择序列概念的弱反例；我认为它为弱连续性原则提供了一个很好的理由，