writer’s choice
Instructions
Type and double-space your assignment. Number your pages. Use a 12-point font,
and leave at least 1-inch margins on all sides. Your assignment should be 5 or 6
pages long.
You (absolutely, positively) must write up your answers on your own. Failure to do
so may result in catastrophic consequences. The policy on academic misconduct
stated on the syllabus applies to this assignment.
You are not required to consult sources other than the readings assigned in class. In
fact, you are discouraged from doing so. You are not absolutely forbidden from
doing so; but, if you do consult additional sources, you must cite them. Again,
failure to do so may result in catastrophic consequences.
Answer one of the following questions.
1. On Byeong-Uk Yi’s view in “Numbers and Relations,” a natural number is a
property that is collectively instantiated by some things. Is this a plausible view about
the natural numbers? Why or why not?
2. In “Structuralism and the Notion of Dependence,” Øystein Linnebo says, “It is of
limited use to be told that mathematical objects are identical with positions in
abstract structures before an account has been given of the nature of these positions”
(p. 61). On one view, abstract structures are universals, and positions in abstract
structures are slots in universals. Spell out what such a view might look like in the
case of the natural numbers. (You’ll need to say a bit about what the universal would
be like and about what it would be instantiated by.) Is this a plausible view about the
natural numbers? Why or why not?
3. In “Structuralism and the Notion of Dependence,” Øystein Linnebo says, “I
suspect it is possible to defend … [a] view of the natural numbers, according to
which one natural number depends on its predecessors but not vice versa” (p. 73,
italics in original). Spell out what such a view might look like. (You’ll need to say a
bit about the sort of dependence in question. Does it have to do with essence, or
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grounding, or perhaps something else?) Is this a plausible view about the natural
numbers? Why or why not?
