Title page for ETD etd-05252007-094340


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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