[FOM] FOM: Set theory and ordinary language

[Dean Buckner]

Consider ordinal descriptions, such as "the first man", "the second man",
"the third man" and so on, as they are used in ordinary language.

Suppose we can show that any sequence of such expressions (a) has a linear
ordering (b) has a first member (c) has a "last" member (d) contains no
"limit ordinal", ie. contains no ordinal without a direct predecessor.

Does this then guarantee that the sequence determines a finite set, and thus
a
set which is well-ordered, and thus a set to which for which finite
induction is automatically valid)?


Dean