The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony

Studia Logica ◽  
2014 ◽  
Vol 102 (6) ◽  
pp. 1185-1216 ◽  
Author(s):  
Peter Schroeder-Heister
Keyword(s):  
Propositional Quantification

scholarly journals Relative Necessity and Propositional Quantification

2019 ◽  
Vol 49 (4) ◽  
pp. 703-726
Author(s):  
Alexander Roberts
Keyword(s):  
Mathematical Logic ◽  
Propositional Logic ◽  
Recent Article ◽  
Symbolic Logic ◽  
Philosophical Logic ◽  
Alternative Account ◽  
Standard Account ◽  
Current Article ◽  
Modal Propositional Logic ◽  
Propositional Quantification

AbstractFollowing Smiley’s (The Journal of Symbolic Logic, 28, 113–134 1963) influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Humberstone (Reports on Mathematical Logic, 13, 33–42 1981) and others have highlighted various flaws with Smiley’s now standard account of relative necessity. In their recent article, Hale and Leech (Journal of Philosophical Logic, 46, 1–26 2017) propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech’s account suffers from its own defects, some of which Hale & Leech are aware of but underplay. To supplement this criticism, the article offers an alternative account of relative necessity which overcomes these defects. This alternative account is developed in a quantified modal propositional logic and is shown model-theoretically to meet several desiderata of an account of relative necessity.

scholarly journals Translatable Self-Reference

2011 ◽  
Vol 10 ◽  
Author(s):  
Hartley Slater
Keyword(s):  
Alternative Analysis ◽  
Quantification Theory ◽  
Semantic Paradoxes ◽  
The Third ◽  
Referential Form ◽  
Propositional Quantification ◽  
Self Reference

Stephen Read has advanced a solution of certain semantic paradoxes recently, based on the work of Thomas Bradwardine. One consequence of this approach, however, is that if Socrates utters only ‘Socrates utters a falsehood’ (a), while Plato says ‘Socrates utters a falsehood’ (b), then, for Bradwardine two different propositions are involved on account of (a) being self-referential, while (b) is not. Problems with this consequence are first discussed before a closely related analysis is provided that escapes it. Moreover, this alternative analysis merely relies on quantification theory at the propositional level, so there is very little to question about it. The paper is the third in a series explaining the superior virtues of a referential form of propositional quantification.

Belief, propositional quantification, and the liar

Philosophia ◽  
1985 ◽  
Vol 15 (1-2) ◽  
pp. 123-132
Author(s):  
Michael Pendlebury
Keyword(s):  
The Liar ◽  
Propositional Quantification
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