Meaning and Proscription in Formal Logic: Variations on the Propositional Logic of William T. Parry

Cham, Switzerland: Springer Verlag (2017)
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Abstract

This book aids in the rehabilitation of the wrongfully deprecated work of William Parry, and is the only full-length investigation into Parry-type propositional logics. A central tenet of the monograph is that the sheer diversity of the contexts in which the mereological analogy emerges – its effervescence with respect to fields ranging from metaphysics to computer programming – provides compelling evidence that the study of logics of analytic implication can be instrumental in identifying connections between topics that would otherwise remain hidden. More concretely, the book identifies and discusses a host of cases in which analytic implication can play an important role in revealing distinct problems to be facets of a larger, cross-disciplinary problem. It introduces an element of constancy and cohesion that has previously been absent in a regrettably fractured field, shoring up those who are sympathetic to the worth of mereological analogy. Moreover, it generates new interest in the field by illustrating a wide range of interesting features present in such logics – and highlighting these features to appeal to researchers in many fields.

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Chapters

Nonsense and Proscription

This chapter identifies as develops a few salient facets of the relationship between Parry-type deductive systems and the field of ‘logics of nonsense.’ Of particular importance is Dmitri Bochvar’s ‘internal’ nonsense logic $$\mathsf {\Sigma }_{0}$$ Σ 0, establishing a strong connection between such... see more

Faulty Belnap Computers and Subsystems of $$\mathsf{E}_{\texttt {fde}}$$ E fde

Cut-Down Operations on Multilattices

Of the interpretations of disjunction in which Addition fails discussed in Chap. 4, Melvin Fitting’s cut-down disjunction stands out as an interpretation with a plausible explanation for the failure. This chapter examines cut-down operations in more detail and with more rigor. In particular, we cons... see more

Metaphysical Considerations on State Space Semantics

In this chapter, we review elements of Kit Fine’s project of truth maker semantics, in which models are constructed on spaces of states—fine-grained semantical devices that can stand in for many objects, such as facts, truthmakers, situations, and so forth. Fine’s framework has rapidly borne fruit, ... see more

A Computational Interpretation of Conceptivism

In this chapter, we consider interpretations of disjunction that accord with a characteristic feature of Parry logics: the failure of Addition. In such a context, the evaluation of a disjunction $$A\vee B$$ A ∨ B requires not only the truth of one disjunct, but also that both disjuncts satisfy some ... see more

Introduction: The Proscriptive Principle

This chapter provides the necessary background for the broader investigation into deductive calculi related to William Parry’s logic of analytic implication. The properties that play a fundamental role in the are defined along with historical background. In particular, the philosophical intuitions d... see more

Concluding Remarks

This concluding chapter reflects on the import of the work as a whole. The concrete fruits of the work are surveyed alongside its limitations, leaving the reader with a list of important open problems remaining along with suggestions for how these problems might be addressed.

Correia Semantics Revisited

In this chapter, the correspondence between the present many-valued semantics for $$\mathsf {AC}$$ AC and those of Correia is revisited and studied in more details. The technique that plays an essential role in proving the completeness of the many-valued semantics for $$\mathsf {AC}$$ AC in Chap. 4 ... see more

Faulty Belnap Computers and Subsystems of $$\mathsf{E}_{\texttt {fde}}$$ E fde

This chapter continues the consideration of the potential for interpreting ‘nonsense’ values as catastrophic faults in computational processes, focusing on the particular case in which Nuel Belnap’s ‘artificial reasoner’ is unable to retrieve the semantic value assigned to a variable. This leads not... see more

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Thomas Ferguson
City University of New York

Citations of this work

Variable-Sharing as Relevance.Shawn Standefer - forthcoming - In Igor Sedlár, Shawn Standefer & Andrew Tedder (eds.), New Directions in Relevant Logic.
Meaningless Divisions.Damian Szmuc & Thomas Macaulay Ferguson - 2021 - Notre Dame Journal of Formal Logic 62 (3):399-424.
Negation as Cancellation, Connexive Logic, and qLPm.Heinrich Wansing - 2018 - Australasian Journal of Logic 15 (2):476-488.

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