Abstract
We treat the problem of reasoning with ambiguous propositions. Even though ambiguity is obviously problematic for reasoning, it is no less obvious that ambiguous propositions entail other propositions, and are entailed by other propositions. This article gives a formal analysis of the underlying mechanisms, both from an algebraic and a logical point of view. The main result can be summarized as follows: sound reasoning with ambiguity requires a distinction between equivalence on the one and congruence on the other side: the fact that \ entails \ does not imply \ can be substituted for \ in all contexts preserving truth. Without this distinction, we will always run into paradoxical results. We present the sequent calculus \, which we conjecture implements sound and complete propositional reasoning with ambiguity, and provide it with a language-theoretic semantics, where letters represent unambiguous meanings and concatenation represents ambiguity.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s10849-020-09324-5
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 60,044
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
The Proper Treatment of Quantification in Ordinary English.Richard Montague - 1973 - In Patrick Suppes, Julius Moravcsik & Jaakko Hintikka (eds.), Approaches to Natural Language. Dordrecht. pp. 221--242.

View all 9 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Ambiguity in Architecture.Christoph Baumberger - 2009 - In G. Ernst, O. Scholz & J. Steinbrenner (eds.), Nelson Goodman: From Logic to Art. Ontos. pp. 293--319.
Ambiguity and Zeugma.Emanuel Viebahn - forthcoming - Pacific Philosophical Quarterly.
Deductive Reasoning.Joshua Schechter - 2013 - In Hal Pashler (ed.), The Encyclopedia of the Mind. SAGE Reference.
Jaffray’s Ideas on Ambiguity.Peter P. Wakker - 2011 - Theory and Decision 71 (1):11-22.
Religious Ambiguity in Hick’s Religious Pluralism.Amir Dastmalchian - 2009 - International Journal of Hekmat 1:75-89.
On Religious Ambiguity.Robert Mckim - 2008 - Religious Studies 44 (4):373-392.
Moral Reasoning.Gilbert Harman, Kelby Mason & Walter Sinnott-Armstrong - 2010 - In John Michael Doris (ed.), The Moral Psychology Handbook. Oxford University Press.

Analytics

Added to PP index
2021-02-25

Total views
2 ( #1,388,204 of 2,433,567 )

Recent downloads (6 months)
2 ( #298,411 of 2,433,567 )

How can I increase my downloads?

Downloads

My notes