Naive set theory with exclusive interpretation of quantifiers

• Thesis title in Czech: Naivní teorie množin s výlučnou interpretací kvantifikátorů
• Thesis title in English: Naive set theory with exclusive interpretation of quantifiers
• Key words: Naivní teorie množin|Exkluzivní interpretace|Kvantifikátor|Spornost|Bludný kruh
• English key words: Naive set theory|Exclusive interpretation|Quantifier|Inconsistency|Vicious circle
• Academic year of topic announcement: 2021/2022
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Department of Logic (21-KLOG)
• Supervisor: Mgr. Vít Punčochář, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 26.09.2022
• Date of assignment: 26.09.2022
• Administrator's approval: not processed yet
• Confirmed by Study dept. on: 25.10.2022
• Date and time of defence: 16.06.2023 09:00
• Date of electronic submission: 10.05.2023
• Date of proceeded defence: 16.06.2023
• Submitted/finalized: committed by student and finalized
• Opponents: Mgr. Šárka Stejskalová, Ph.D.

Guidelines

In his Tractatus Logico-Philosophicus Wittgenstein claimed that the sign of identity is not an essential constituent of correct logical notation and should be eliminated and replaced with an exclusive interpretation of quantifiers. The goal of the thesis is to investigate to what extent this move is feasible. In particular, possibilities of having a naive set theory (i.e. a set theory with unrestricted comprehension and axiom of extensionality), in which quantifiers are interpreted exclusively, will be explored. One can formulate various versions of such a theory differing especially in how parameters are used in the comprehension schema. The technical part of the thesis will analyze which versions lead to a contradictory system (this is related to an open problem formulated by Jakko Hintikka). The philosophical part will discuss what the inconsistent versions have in common and which basic principles are responsible for the contradiction. The thesis should also reflect the broader philosophical context of this problem and related discussion from Ludwig Wittgenstein to modern philosophers like Kai Wehmeier.

References

Hintikka, J. (1956). Identity, variables, and impredicative definitions. Journal of Symbolic Logic, 21, 225-245.
Hintikka, J. (1957). Vicious circle principle and the paradoxes. Journal of Symbolic Logic, 22, 245-249.
Lampert, T., Säbel, M. (2021). Wittgenstein's elimination of identity for quantifier-free logic. The Review of Symbolic Logic 14, 1-21.
Wehmeier, K. (2012). How to live without identity – and why. Australasian Journal of Philosophy 90, 761-777.
Wehmeier, K., Rogers, B. (2012) Tractarian first-order logic: identity and the N-operator. Review of Symbolic Logic 5, 538–573.
Wehmeier, K. (2017). Identity and quantification. Philosophical Studies 174, 759-770.
Wehmeier, K. (2019). Frege's Begriffsschrift theory of identity vindicated. In: E. Lepore and D. Sosa (eds.) Oxford Studies in Philosophy of Language vol. 1, Oxford University Press, 2019, 122–147.
Wittgenstein, L. (1922). Tractatus Logico-Philosophicus. London: Routledge & Kegan Paul.