Last Update: 24 September 2010
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Index to all lecture notes
…Previous lecture
In the interest of completeness, here I repeat all of the examples from
last time,
and add some new ones.
Let Dog(x) = (x) is a dog
Let Fish(x) = (x) is a fish
Let Glitters(x) = (x) glitters
Let Gold(x) = (x) is gold
Let Mammal(x) = (x) is a mammal
Let Man(x) = (x) is a man
Let Pet(x) = (x) is a pet
Let Wise(x) = (x) is wise
Let mark-twain =
Mark Twain
Let sam-clemens =
Samuel Langhorne Clemens (as in
Clemens Hall)
i.e., even if there were no dogs, but only cats,
"∃x[Dog(x) → Pet(x)]" would be T,
but the English would be false.
See "On the Translation of ‘Some Dogs Are Pets’" for further explanation.
"Some dogs are pets" becomes:
where the "restriction" on x that Dog(x) is like a type declaration.
"All dogs are pets" becomes:
For more suggestions on how to translate, see:
"There is exactly one dog" can be represented as:
(read "There is a unique x in the domain such that x is a dog".)
… and I will tell you more about this on Monday