De Se Attitudes
the paradox of the heap
Sorites
1. 1 grain of sand is not a heap.
2. For all numbers n: if n grains of sand are not a heap, then n + 1
grains of sand are not a heap.
3. Therefore, 200 trillion grains of sand are not a heap.
The Other Way
1. 200 trillion grains of sand makes a heap.
2. For all numbers n: if n + 1 grains of sand make a heap, then n grains
of sand make a heap.
3. Therefore 1 grain of sand makes a heap.
Paradox
Neither of these sorites arguments results in a
contradiction… until you add in the obvious fact that
the conclusion of each is false.
Borderline Cases
The paradox seems to arise whenever we have a term that admits of
borderline cases.
There are some people that I don’t know whether they’re rich out of
uncertainty: because I don’t know how much money they have. These
are not borderline cases.
Borderline Cases
The paradox seems to arise whenever we have a term that admits of
borderline cases.
But there are other people that I don’t know whether they are rich
even though I know exactly how much money they have. These are
borderline cases.
Borderline Cases
Most of our ordinary language admits of borderline cases:
Big, tall, short, rich, fast, slow, smart, dumb, funny, long, flat, narrow…
Also: mountain, car, tree, horse…
What To Do?
Neither of these sorites arguments results in a
contradiction… until you add in the obvious fact that
the conclusion of each is false.
To deny the conclusion, we need to deny either
premise 1 or premise 2 or logic.
Denying Premise 1
In the first argument, premise 1 is:
1 grain of sand is not a heap.
In the second it’s:
200 trillion grains of sand is a heap.
Denying Premise 2
Premise 2 (Argument 1) says: For all numbers n: if n grains of sand are
not a heap, then n + 1 grains of sand are not a heap.
The negation of this is: There exists a number n such that: n grains of
sand are not a heap, but n + 1 grains of sand are a heap.
Denying Premise 2
Premise 2 (Argument 2) says: For all numbers n: if n + 1 grains of sand
make a heap, then n grains of sand make a heap.
The negation of this is: There is a number n such that: n + 1 grains of
sand make a heap, but n grains of sand do not make a heap.
No Sharp Boundaries
Premise 2 in both cases asserts No Sharp Boundaries.
It’s never true that one grain of sand makes the
difference between a heap and not a heap.
No Sharp Boundaries
• One hair doesn’t make the difference between being bald and not
bald.
• One micrometer doesn’t make the difference between being tall and
not tall.
• $0.10HKD does not make the difference between being rich and not
rich.
• One nanosecond does not make the difference between being old
and not old.
Solutions
1. Accept Sharp Boundaries.
2. Introduce more truth-values.
Epistemicism
One solution is to claim that there ARE sharp boundaries, but we can
never know where they are.
Acquiring $0.10 can make someone go from not rich to rich, but we
can’t ever know when this happens.
Epistemicism
Basic problem: What determines the boundary if not how we use the
words?
What determines how we use the words if not what we (can) know?
Epistemicism
Further problem: the epistemicist says we can’t know where the Sharp
Boundary is, but that it exists. However, he has to admit that we can:
• Guess where the Sharp Boundary is.
• Wonder where the Sharp Boundary is.
• Fear that we are crossing the Sharp Boundary (e.g. for getting old).
But all these seem silly!
Many-Valued Logics
Another solution is to introduce a new truth-value: True, False, and
Undefined.
There’s No Sharp Boundaries, because there’s no point at which adding
one hair moves someone from truly bald to falsely bald.
Many-Valued Logics
More hairs →
tttttttttttttttttttttttuuuuuuuuuuufffffffffffffffffff
Higher-Order Vagueness
The problem is that now there are sharp boundaries between being
truly bald and undefinedly bald, and between being undefinedly bald,
and falsely bald.
Intuitively, adding one hair to a truly bald person can’t make them
undefinedly bald.
Many-Valued Logics
More hairs →
tttttttttttttttttttttttuuuuuuuuuuufffffffffffffffffff
Two sharp boundaries!
Fuzzy Logic
Instead, we might try having infinitely many truth-values: 1 is fully true,
0 is fully false, and any number in between is less than fully true.
More hairs →
1 1 1 1 1 1 .99 .98 .98 .97… .12 .11 .1 .1 0 0 0 0 0
Fuzzy Logic
A fuzzy logician has to explain how to calculate the truth-values of
complex expressions from the truth values of their parts. Common
rules:
• The truth-value of “~P” is 1 minus the truth-value of P
• The truth-value of “P & Q” is the lowest of the truth-values of P and
Q.
• The truth-value of “P or Q” is the highest of the truth values of P and
Q.
Problems
“P & ~P” should always be fully false: 0.
But if P = 0.5, then “P & ~P” = 0.5
De Se Attitudes
The Other Disquotation Principle
Our earlier disquotation principle was: P = “P” is true.
Here’s a very different principle:
If a rational speaker sincerely asserts “P” then the speaker believes P. If
a rational speaker won’t sincerely accept an assertion of “P” then the
speaker does not believe P.
De Dicto Attitudes
Let’s call these your de dicto attitudes. “De dicto” means “concerning
what is said.” These are the propositional attitudes you have that
match what you would say. For example:
Lois Lane believes de dicto that Superman can fly.
Lois Lane does not believe de dicto that Clark Kent can fly.
De Re Attitudes
Sometimes we use the word “believe” in a way that is not consistent
with “believe de dicto.”
De Re Attitudes
I once knew a woman who told
me the following story.
She went to Las Vegas and won
lots of money in the slot
machines. She got into an elevator
with several black men, a number
of whom were large and
intimidating.
De Re Attitudes
The woman thought “these men
on the elevator are criminals and
they are going to rob me!”
De Re Attitudes
She would never have asserted or
accepted the sentence “Eddie
Murphy is a criminal,” so she did
not believe de dicto that Murphy
was a criminal.
BUT… the man on the elevator
was Eddie Murphy (and his
bodyguards). He had millions of
dollars and no need to rob.
De Re Attitudes
This case is quite naturally
described in the following way:
The woman believed that Eddie
Murphy was a criminal.
Eddie Murphy
She believes X is a
criminal
That Guy
Eddie Murphy
She believes X is a
criminal
That Guy
De Re Attitudes
“De re” means “concerning the thing.” They’re a way we have of
reporting propositional attitudes that people have about things,
regardless of what people would say about those things.
Another example: Dr. Baker says “that guy wanted to pee on my car”–
the guy didn’t know it was Baker’s car, or he wouldn’t have tried to pee
on it!
Frege Cases
We saw before a class of cases where people:
• Had an attitude de dicto that X was F
• Did not have an attitude de dicto that Y was F
• Even though X = Y
Frege Cases
1. John believes Benjamin
Franklin liked Belgian waffles.
2. Mary discovered that
Benjamin Franklin liked potato
salad.
3. Sam doubts that Benjamin
Franklin liked deep dish pizza
Frege Cases
1. John believes that the inventor
of bifocals liked Belgian
waffles.
2. Mary discovered that the first
postmaster general liked
potato salad.
3. Sam doubts that the author of
Poor Richard’s Almanac liked
deep dish pizza.
Factual Errors
In cases where our de dicto beliefs correspond to contradictory de re
beliefs, it seems reasonable to say that this is because we are lacking
some factual information.
There are things regarding how the world is that we are simply ignorant
of.
Two Possibilities
Bruce Wayne
Clark Kent
The Messy Shopper
“I once followed a trail of sugar on
a supermarket floor, pushing my
cart down the aisle on one side of
a tall counter and back the aisle
on the other, seeking the shopper
with a torn sack to tell him he was
making a mess…”
The Messy Shopper
“…With each trip around the
counter, the trail became thicker.
But I seemed unable to catch up.
Finally it dawned on me. I was the
shopper I was trying to catch.” –
John Perry, “The Essential
Indexical”
De Se Cases
Suppose Ada sees herself in the
mirror, unaware that it’s her
who is in the mirror.
She believes what she’d express
by saying “I am pretty.”
But she also believes what she’d
express by saying “she is not
pretty.”
De Se Attitudes
“De se” means “concerning the self.” These are attitudes we have
about ourselves… but only a special sort of attitudes.
(NOT: that person in the mirror/ that person on TV/ etc… attitudes
about me.)
Rudolf Lingens
Perry imagines another case:
Rudolf Lingens has lost his memory. He doesn’t know who he is or
where he is or why he’s there. As a matter of fact, he’s in the library at
Stanford Univeristy.
Where am I?
Who am I?
Rudolf Lingens
In the library, Lingens finds a biography of himself. He reads the entire
life story of Rudolf Lingens. The biography even says, “Lingens is
currently wandering around the Stanford Library without his memory.”
Lingens knows that Lingens did X, Y, and Z. But he does not know that
he did X, Y, and Z. (He does not know what he’d express by saying “I
know that I did X, Y, and Z.”)
Non-Factual Problem
Lingens seems to know all the relevant facts. He knows everything
there is to know about Lingens EXCEPT that he is Lingens.
Is this a further fact? Or are there things you can know that are nonfactual?
Two Possibilities
Lingens
Two Possibilities
Lingens
For Your *I*s Only
Dr. Evil is a criminal
mastermind who
constructs a base of
operations on the moon.
On the base he has built a
giant “laser” with which
he intends to destroy all
the human inhabitants of
Earth
License to Laser
The combined military might of
the nations of the world are
unable to stop Dr. Evil’s moon
laser (shown right).
In desperation they turn to Adam
Elga, who suggests…
You Only Live Twice
First, we create, on Earth, a molecule-for-molecule duplicate of Dr.
Evil’s moon base– one that actually works and will destroy the Earth if
the red button within is pushed.
Then, we create a complete duplicate of Dr. Evil himself and place the
duplicate inside the duplicate moon base.
Evil’s Twin
Die Another Day
Crucially, we make sure to announce to both the real Dr. Evil and his
doppelganger everything we have just done.
Elga suggests that in this circumstance, Dr. Evil will refrain from
destroying Earth, because he will be uncertain as to whether he is the
real Dr. Evil or instead the recently-created but psychologically-identical
double on Earth.
One Possibility!