Truth and Proof without Models: A Development and Justification of the Truth-valuational Approach (2nd edition)

Abstract

I explain why model theory is unsatisfactory as a semantic theory and has drawbacks as a tool for proofs on logic systems. I then motivate and develop an alternative, the truth-valuational substitutional approach (TVS), and prove with it the soundness and completeness of the first order Predicate Calculus with identity and of Modal Propositional Calculus. Modal logic is developed without recourse to possible worlds. Along the way I answer a variety of difficulties that have been raised against TVS and show that, as applied to several central questions, model-theoretic semantics can be considered TVS in disguise. The conclusion is that the truth-valuational substitutional approach is an adequate tool for many of our logic inquiries, conceptually preferable over model-theoretic semantics. Another conclusion is that formal logic is independent of semantics, apart from its use of the notion of truth, but that even with respect to it its assumptions are minimal.

Links

PhilArchive

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Similar books and articles

A propositional semantics for substitutional quantification.Geoff Georgi - 2015 - Philosophical Studies 172 (5):1183-1200.
On the explanatory power of truth in logic.Gila Sher - 2018 - Philosophical Issues 28 (1):348-373.
On the Proof Theory of the Modal mu-Calculus.Thomas Studer - 2008 - Studia Logica 89 (3):343-363.
The modal logics of kripke–feferman truth.Carlo Nicolai & Johannes Stern - 2021 - Journal of Symbolic Logic 86 (1):362-396.
Grafted Frames and S1-Completeness.Beihai Zhou - 1999 - Journal of Symbolic Logic 64 (3):1324-1338.
Grafted frames and S1 -completeness.Beihai Zhou - 1999 - Journal of Symbolic Logic 64 (3):1324-1338.
Truth via anaphorically unrestricted quantifiers.Jody Azzouni - 2001 - Journal of Philosophical Logic 30 (4):329-354.
Proto-Semantics for Positive Free Logic.G. Aldo Antonelli - 2000 - Journal of Philosophical Logic 29 (3):277-294.

Analytics

Added to PP
2022-07-25

Downloads
263 (#70,294)

6 months
79 (#48,277)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Hanoch Ben-Yami
Central European University

Citations of this work

No citations found.

Add more citations

References found in this work

Ontological relativity and other essays.Willard Van Orman Quine (ed.) - 1969 - New York: Columbia University Press.
Naming and Necessity.Saul Kripke - 1980 - Philosophy 56 (217):431-433.
Naming and Necessity.Saul Kripke - 2003 - In John Heil (ed.), Philosophy of Mind: A Guide and Anthology. Oxford University Press.
Semantical Considerations on Modal Logic.Saul Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
Introduction to mathematical logic.Elliott Mendelson - 1964 - Princeton, N.J.,: Van Nostrand.

View all 38 references / Add more references