Hilbert and Ackermann asked for a method to consistently extend incomplete theories to complete theories. G\"odel essentially proved that any theory capable of encoding its own statements and their proofs contains statements that are true but not provable. Hilbert did not accept that G\"odel's construction answered his question, and in his late writings and lectures, G\"odel agreed that it did not, since theories can be completed incrementally, by adding axioms to prove ever more true statements, as science normally does, with completeness as the vanishing point. This pragmatic view of validity is familiar not only to scientists who conjecture test hypotheses but also to real estate agents and other dealers, who conjure claims, albeit invalid, as necessary to close a deal, confident that they will be able to conjure other claims, albeit invalid, sufficient to make the first claims valid. We study the underlying logical process and describe the trajectories leading to testable but unfalsifiable theories to which bots and other automated learners are likely to converge.

翻译：希尔伯特与阿克曼曾寻求一种方法，能将不完备理论一致地扩展为完备理论。哥德尔本质上证明了，任何能够编码自身陈述及其证明的理论，都包含真实但不可证明的陈述。希尔伯特并不接受哥德尔的构造回答了其问题，而在其晚期的著作与演讲中，哥德尔也认同这一观点——因为理论可以通过逐步添加公理来证明更多真实陈述从而被增量式地完备化，正如科学通常所做的那样，以完备性作为趋近目标。这种实用主义的有效性观点，不仅为提出可检验假设的科学家所熟悉，也为房地产经纪人及其他交易者所运用：他们为促成交易而编造（尽管无效的）主张，并确信自己能再编造其他（尽管无效的）主张，以使最初的主张成立。我们研究了其背后的逻辑过程，并描述了导致机器人及其他自动化学习者可能趋近于可检验但不可证伪的理论的演化路径。