Type of Document	Master's Thesis
Author	Martin, James V.
Author's Email Address	jvmartin@vt.edu
URN	etd-05252007-094340
Title	A modifier-based philosophy of whole number.
Degree	Master of Arts
Department	Philosophy
Advisory Committee	Advisor Name Title Epstein, Brian Committee Chair Klagge, James C. Committee Member Ott, Walter R. Committee Member
Keywords	Compositionality Adverbial Modifiers Arithmetic Number
Date of Defense	2007-05-10
Availability	restricted
Abstract 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.
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