### Abstract

In 1987, George Boolos gave an interesting and vivid concrete example of the considerable speed-up afforded by higher-order logic over first-order logic. (A phenomenon first noted by Kurt Gödel in 1936.) Boolos's example concerned an inference $I$ with five premises, and a conclusion, such that the shortest derivation of the conclusion from the premises in a standard system for first-order logic is astronomically huge; while there exists a second-order derivation whose length is of the order of a page or two. Boolos gave a short sketch of that second-order derivation, which relies on the comprehension principle of second-order logic. Here, Boolos's inference is formalized into fourteen lemmas, each quickly verified by the automated-theorem-proving assistant Isabelle/HOL.

### License

BSD License

### Topics

- Logic/Philosophical aspects

### Session Boolos_Curious_Inference

- Boo1
- Boo2

## Cite

×

Boolos_Curious_Inference-AFP

    @article{Boolos_Curious_Inference-AFP,
      author  = {Jeffrey Ketland},
      title   = {Boolos's Curious Inference in Isabelle/HOL},
      journal = {Archive of Formal Proofs},
      month   = {June},
      year    = {2022},
      note    = {\url{https://isa-afp.org/entries/Boolos_Curious_Inference.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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