Predicate Logic
A Note on Interpretation of "Some"
"Some integers are odd" was interpreted as "There are objects in the universe that are
integer and odd"
and it was translated as
x [ I(x) 
O(x)].
It can also be interpreted as "For some object in the universe,
if it is integer, then it is odd".
In that case it becomes
x [ I(x) 
O(x)].
The difference here is that the former asserts that an odd integer exists, while the later
does not assert the existence of such an object. It is a hypothetical statement.
This difference would be clearer in the following statement:
"Some Martians are 10 foot tall".
Assuming that the universe is the set of all objects, this can be transcribed as
x [ Martian(x) 10_ft_tall(x)]
or
x [ Martian(x) 10_ft_tall(x)]
The former asserts that a 10 foot tall Martian exists, while the latter does not say whether or not a Martian exists.
It is not addressing the question of existence of Martian. If a Martian does not exist, the latter statement is still true
while the former is false in that case.
back to "Transcribing English to Predicate Logic wffs".
Back to Schedule
Back to Table of Contents