According to Curtis Franks's preface, this book bundles his historical, philosophical, and logical research to center around what he thinks are ‘the most important and most overlooked aspects of Hilbert's program … a glaring oversight of one truly unique aspect of Hilbert's thought’, namely that ‘questions about mathematics that arise in philosophical reflection — questions about how and why its methods work — might best be addressed mathematically … Hilbert's program was primarily an effort to demonstrate that’. The standard ‘well-rehearsed’ story for these oversights is said to be that Hilbert's philosophical vision was dashed by Gödel's incompleteness theorems. But Franks argues to the contrary that Gödel's remarkable early contributions to metamathematics instead drew ‘significant attention to the then fledgling discipline’, a field that has since proved to be exceptionally productive scientifically (even through the work of such logicians as Tarski, who mocked Hilbert's program). One may well ask how...

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