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Modal LogicAn Introduction to its Syntax and Semantics$
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Nino B. Cocchiarella and Max A. Freund

Print publication date: 2008

Print ISBN-13: 9780195366587

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780195366587.001.0001

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Second-Order Modal Logic

Second-Order Modal Logic

(p.183) Chapter 9 Second-Order Modal Logic
Modal Logic

Nino B. Cocchiarella

Max A. Freund

Oxford University Press

This chapter extends the systems to the level of second-order modal predicate logic, where the notion of existence that is central to the actualism-possibilism distinction is given deeper and finer-grained analysis in terms of existence-entailing concepts, as opposed to concepts that do not entail existence. By existence in this context means actual, or concrete, existence in the sense of being part of the material, causal order. In contrast, concepts such as being an ancestor of everyone now existing, etc. may have objects falling under them at a time when those objects do not exist. In possibilism, but not in actualism, there are concepts such as possibly being a physical object that moves faster than the speed of light, etc. that might have objects falling under them that do not exist in the actual world. These concepts do not entail (concrete) existence unlike e-concepts.

Keywords:   second-order modal predicate logic, actualism, possibilism, existence-entailing concepts, existence

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