A modifier-based philosophy of whole number

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.

Name thesis:degree_name

Master of Arts

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Philosophy

Department dc:contributor.department

Philosophy

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2007

Author dc:creator

• Martin, James V.

Chair dc:contributor.committeechair

• Epstein, Brian

Committee members dc:contributor.committeemember

• Ott, Walter R.
• Klagge, James C.

• Compositionality
• Adverbial Modifiers
• Arithmetic
• Number

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-05252007-094340

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/42796