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```Ontology
The Case for Properties
“Some”, “All”, and “The”
 Some dogs are nice.
 There is a thing that’s a dog and it’s nice.
 All dogs are nice.
 It’s not the case that: there’s a thing that’s a
dog and that isn’t nice.
“Some”, “All”, and “The”
 Some president is nice.

There is a thing that’s a president and it’s nice.
 The president is nice.

There is a thing that is a president and it’s nice
(and it’s the only such thing).
“Some”, “All”, and “The
We dealt in the preceding chapter with the words all
and some; in this chapter we shall consider the word
the in the singular, and in the next chapter we shall
consider the word the in the plural. It may be thought
excessive to devote two whole chapters to one word,
but to the philosophical mathematician it is a word of
very great importance… I would give the doctrine of
this word if I were “dead from the waist down” and not
merely in prison.
-Bertrand Russell, Introduction to Mathematical
Philosophy
The Average Family Argument
1) The average family has 1.8 children.
2) If (1), then there is a thing that is an average
family and that has 1.8 children.
3) [So] There is a thing that is an average
family and that has 1.8 children.
4) [So] There is an average family.
Loose Talk?
 The average family has 1.8 children.

The number of children divided by the number
of families equals 1.8.
 The Death Star was blown up by rebel forces.
 The space in my garage is empty.
 The number of Wasserman children is at
least two.
Loose Talk?
 The average family has 1.8 children.

The number of children divided by the number
of families equals 1.8.
 Wisdom is had by Socrates.
 Ryan has some nice features, like being tall.
 The relation of father to son is really special.
Properties
 Properties are “that which is said of a
subject”.



Socrates is wise (the property of wisdom)
Ryan is tall (the property of tallness)
Ryan is the father of Benjamin (the two-place
property being smarter than).
Properties
Ryan is tall
INSTANTIATES
TALLNESS
The Argument for Properties
1) Wisdom (the property of being wise) is had
by Socrates.
2) If (1), then there is a property (of being wise)
and it is had by Socrates.
3) [So] There is a property (of being wise) and