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 CasesThe 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 CasesThe 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 CasesMost 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 1In 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 2Premise 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 2Premise 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?

EpistemicismFurther 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 VaguenessThe 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 LogicInstead, 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 LogicA 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 AttitudesShe 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

That Guy

She believes X is a criminal

Eddie Murphy

That Guy

She believes X is a criminal

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 Cases1. 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 PossibilitiesBruce 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 CasesSuppose 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 non-factual?

Two Possibilities

Lingens

Two Possibilities

Lingens

For Your *I*s OnlyDr. 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!