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：希尔伯特和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。希尔伯特不认为哥德尔的构造回答了他的问题，而在其晚期著作和讲座中，哥德尔也认同这一点，因为理论可以通过逐步添加公理来证明更多真实陈述而渐进完成——正如科学通常所做的那样——以完备性作为消失点。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熟知：他们会凭空编造主张（即便无效）以促成交易，并确信自己能够再编造其他主张（即便无效）足以使最初的主张成立。我们研究了这一底层逻辑过程，并描述了机器人及其他自动化学习者可能收敛于可检验但不可证伪理论的发展轨迹。