The problem of negative truth is the problem of how, if everything in the world is positive, we can speak truly about the world using negative propositions. A prominent solution is to explain negation in terms of a primitive notion of metaphysical incompatibility. I argue that if this account is correct, then minimal logic is the correct logic. The negation of a proposition A is characterised as the minimal incompatible of A composed of it and the logical constant ¬. A rule based account of the meanings of logical constants that appeals to the notion of incompatibility in the introduction rule for negation ensures the existence and uniqueness of the negation of every proposition. But it endows the negation operator with no more formal properties than those it has in minimal logic. There is implanted in the human breast an almost unquenchable desire to find some way of avoiding the admission that negative facts are as ultimate as those that are positive.

中文翻译：

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最小逻辑论证

否定真理的问题是，如果世界上的一切都是肯定的，我们如何能用否定命题真正谈论这个世界。一个突出的解决方案是根据形而上学不兼容的原始概念来解释否定。我认为，如果这个帐户是正确的，那么最小逻辑就是正确的逻辑。命题 A 的否定被表征为由它组成的 A 与逻辑常数 ¬ 的最小不相容。对逻辑常数含义的基于规则的解释在否定的引入规则中诉诸不相容的概念，确保每个命题的否定的存在性和唯一性。但它赋予否定运算符没有比它在最小逻辑中具有的形式属性更多的形式属性。