Logic in the Tractatus

Review of Symbolic Logic 10 (1):1-50 (2017)
Download Edit this record How to cite View on PhilPapers
I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably infinite, then the property of being a tautology is \Pi^1_1-complete. But third, it is only granted the assumption of countability that the class of tautologies is \Sigma_1-definable in set theory. Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects.
PhilPapers/Archive ID
Upload history
Archival date: 2017-01-15
View other versions
Added to PP index

Total views
519 ( #12,749 of 65,694 )

Recent downloads (6 months)
38 ( #22,375 of 65,694 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.