A modifier-based philosophy of whole number

• Main Author: Martin, James V.
• Other Authors: Philosophy
• Format: Others
• Language: en
• Published: Virginia Tech 2014
• Subjects: Compositionality; Adverbial Modifiers; Arithmetic; Number
• Online Access: http://hdl.handle.net/10919/42796; http://scholar.lib.vt.edu/theses/available/etd-05252007-094340/

This paper offers an alternative philosophy of whole number in which number-words are treated as being of the semantic-type modifier. Other accounts of number in which number-words are treated as names, syncategoremata, determiners, and predicates are considered and rejected based on their failure to provide number-words with the necessary compositional semantics. This leaves only modifiers as plausible candidates to play number-words' role in natural language. After the semantic-type modifier is chosen, a decision between number-words' being adjectival or adverbial modifiers must then be made. I argue that due to a lack of entities to be ascribed adjectival numerical properties we must settle on an adverbial treatment. After developing this treatment, I close with an attempt to explain seemingly singular-term uses of number-words in arithmetical statements like '2 + 2 = 4' in terms of these claims' stating the rules for substituting equivalent modifier-phrases in non-mathematical usages. === Master of Arts