David Lewis, Attitudes De Dicto and De Se: Outline

I Content of Desire

What is the content of our expectation/desire?

Option 1: Miscellaneous objects; particular objects(this cat)/Meinongian incomplete objects(unspecified cat)/proposition
Option 2: Unified Propositional Object

Defending 2: There are several advantages of adopting 2

Avoid suspicious Meinongian objects
Our attitudes are characterized more fully
- Example: If the content of “I want a cat” is a cat, it is still unclear whether I want to be an owner of a cat, or I want to be accompanied by a cat.
Explains the causal roles of attitudes better than miscellaneous framework why?

Option 3: Unified properties

Lewis will argue that, option 3 is better than option 2 because

it has all the features that option 2 has, and
sometimes does better than option 2

II proposition vs. property

Definition (proposition): A proposition is a set of possible worlds, a region of logical space.

There are other ways to understand propositions, Lewis does not intend to quarrel with them.
Possible world semantics has obvious problem, and there are various way to respond. Lewis will ignore the problem for now. We may imagine ourselves talking about hyper-rational creatures who treats all propositions with the same extension as equal.

Definition (property): The set of exactly those possible beings, actual or not, that have the property in question.

Proposition (Correspondence): For any proposition $P$ , i.e. set of world $W_{P}$ , it corresponds a property of inhabiting in some world $x$ such that $x \in W_{P}$ .

Hidden Proposition (Symmetry of Correspondence): Correspondence is symmetric: If a proposition corresponds with a property, then the property also corresponds with the proposition

Remark: The proposition “The snow is white” is a set of world where snow is white. It corresponds with the property of “being in one of the world where snow is white.” This property is turn defined as everything in the set of worlds.

Proposition (Injective Correspondence): If a property corresponds to some proposition, it corresponds exactly one proposition

Proof: We prove this by reductio. Assume a property $℘$ corresponds to both $X$ and $Y$ , and $X$ is not $Y$ . Since $℘$ is one, $℘_{X} = ℘_{Y}$ . But since $X \neq Y$ , $℘_{X} \neq ℘_{Y}$ . Contradiction.

Remark: We can understand the correspondence relation as an injective mapping. Let $A$ be the set of all propositions $A$ and $B$ the set of all properties. We have an injective function $f : A \to B$ .

Given this injective relation, we can defend the thesis that, properties can express more things than propositions.

III propositional belief

Stage Setting:

When we quantify over the subjects of attitudes, we quantify over subjects spread out in space, time and possible worlds.
A subject is defined within a world, i.e. their counterparts are not the subject themselves.

Definition (S believes that P): S believe that P means that, S ascribe themselves the property of being in the world that satisfies P

Example: Smith believes that cyanoacrylate glue dissolves in acetone means that, Smith is locating himself in one of the world where cyanoacrylate glue dissolves in acetone. That is to say, Smith is ascribing the property of being in some specific world to himself.

Remark: Another way to put this is that, S believes that P is for S to locate themselves in the population who lives in the world that satisfies P

IV de dicto and de se

John Perry’s puzzle

An amnesiac, Rudolf Lingens, is lost in the Stanford library. He reads a number of things in the library, including a biography of himself, and a detailed account of the library in which he is lost…. He still won’t know who he is, and where he is, no matter how much knowledge he piles up, until that moment when he is ready to say, “This place is aisle five, floor six, of Main Library, Stanford. I am Rudolf Lingens.”

Lewis’ explanation:

Reading book will make Lingens believe he is in the world that has some specific structure. But this is not enough. He also ascribe himself some properties of being in a certain perceptual situation, which does not correspond with any proposition. By believing a non-propositional belief and a propositional belief, Lingens eventually transformed the propositional belief from book reading to the non-propositional belief about himself.

Another Example: Two Gods

Two gods may know every proposition that is true at their world. In so far as knowledge is a propositional attitude, they are omniscient. However, it is still possible that they suffer from ignorance: they cannot tell which one of the two is me.

Upshot of the example:

They do not lack propositional knowledge
They lack knowledge
Therefore, they lack non-propositional knowledge

Therefore, sometimes property objects will do and propositional objects won’t

Definition (Attitude De Dicto): When the content of belief/knowledge/etc has a propositional object, it ha an attitude de dicto
Definition (Attitude De Se): Self-ascription of properties is belief/knowledge/etc. with an attitude de se.

Disagreement with Perry: Perry makes self-locating vs. Fregean belief distinction. Lewis argues that all beliefs are self-locating. The difference lies in that, de dicto beliefs locate oneself in some logical space; de se beliefs locate oneself with respect to ordinary time and space, or with respect to the population.

V answer to Haecceitists’ objection

Let the god in the tallest mountain in world $W$ be called $T a l l y (w)$ , and the god in the coldest mountain in world $W$ $C o l d y (w)$ . And assume there is a qualitatively identical world $V$ , except the gods swap their places. Therefore, $T a l l y (v)$ is on the coldest mountain, and $C o l d y (v)$ is on the tallest mountain. We can draw the following table:

	$W$	$V$
On the tallest mountain	$T a l l y (w)$	$C o l d y (v)$
On the coldest mountain	$C o l d y (w)$	$T a l l y (v)$

Haecceitist would would say, the reason why $T a l l y (w)$ don’t know where he is is that, he knows the statement “I am on the tallest mountain” is true at $W$ and false at $V$ , but $T a l l y (w)$ does not know if he is in $W$ or $V$ . If $T a l l y (w)$ knows he is in $W$ , then he would know he is on the tallest mountain.

However, this is false. Even if we grant that Tally knows:

His is in $W$ ,
“I am on the tallest mountain” is true at $W$ and false at $V$

$T a l l y (w)$ still does not know where he is. This is because “I am on the tallest mountain” is true when $T a l l y (w)$ utters it at $W$ , but false when $C o l d y (w)$ utters at $W$ . Since $T a l l y (w)$ does not know which one is him, he still does not know who he is.

Remark: This is due to the indexicality of the word “I”

VI Problems with propositional belief

In Perry’s example of the mad Heimson, there will be two problems if we consider belief as propositional attitude. These two problem will vanish if we think of belief as self-ascription properties

The first problem (Empty belief): There can’t be an in-world identity for Hume and Heimson, since they are stipulated to be different. Even they have transworld identity, the proposition that “I am Heimson” is an empty set of worlds. Therefore, the content of the belief is empty. But having an empty belief is absurd (for an hyper-rational agent) I don’t understand. How is this a problem??

This can be explained by saying Heimson is attributing himself the property of being Hume

The Second Problem: A belief (in Lewis’ term) must be something in the head, so Hume and Heimson have the same belief; But how could it be that Hume and Heimson have the same mental state but one has true belief while the other one is false? (Meaning may be external, but it does not mean that beliefs also include external entities. Instead, it would just mean that belief is ill-presented by meaning in this sense) If you think belief is purely in the head, why would you think it must be truth-apt?

This can be explained by saying Heimson is attributing himself a property that he does not have.

VII self-attributing to time slice

Sometimes, belief de se can be better understood if we take the person as a time slice. For example, realizing now is the time is to locating the current time slice of me at some time.

VIII Value of knowledge de dicto

We need to distinguish the view that knowledge de dicto incompletely presents the world, from the view that knowledge de dicto misrepresents the world.

IX Desire de se and de dicto

So far we’ve only covered belief and knowledge. Now let’s show the content of desire is also properties and desire de se subsumes de dicto ones.

Examples:

De se desire: wanting to be healthy, wanting to visit Swindon
De dicto desire: want cyanoacrylate to dissolve in acetone

Explanation:

To want cyanoacrylate to dissolve in acetone is to want the property of being in a world where cyanoacrylate dissolves in acetone;
To want to be healthy is simply want the property of being healthy

Problem (infinite Regress): If someone desires $X$ , and this desire can be expressed by a proposition $Y$ , then they at the same time desire the property of being in the world where $Y$ holds. If this property is different from $X$ , then there will be an infinite regress.

Answer: Desire de se cannot be expressed by desire de dicto. For example, Tally could desire all the true proposition, therefore Tally can desire “Tally lives in world $W$ .” But they cannot desire “I lives in world $W$ ” because Tally do not know who am I. Therefore, the desire of “I live in world $W$ ” is not a propositional desire. Similarly, Lingens will not desire to live in the world where someone who has the property of Lingen managed to find the way out unless Lingens realizes “that guy is me!”

Problem with the proposition account (Empty content): I may want to be a poached egg, but there is no such world where I am a poached egg. Therefore, if my desire is a proposition, it would be an empty desire.

Time-slice attribution: I wouldn’t want something bad to be over at some time $t$ unless I realize $t$ ’s relative position to my current time slice (e.g. now)

An interesting analogy: To make the world a better place is similar to wanting to live in a better part of a town huh?

X Quine’s Solution

Quine’s problem: A cat is being chased by a dog. If we take the content of the cat’s fear and desire as propositions, we can represent them as sets of possible worlds: the cat fears the set of possible worlds where it is eaten by the dog, while it desires the set of possible worlds where it is on the roof. Now, if we have a world where a similar cat is on the roof and another similar cat is being eaten by a dog, does the cat desire this world or fear it?

Quine’s solution: The set of possible worlds have centers; In the cat’s case, it desire the world where it is centered on the cat’s pineal gland, and a cat is safely on the roof; and it fears the world where it is centered on the cat’s pineal gland, and a cat id being eaten.

Lewis’ Remark: The concept of “possible world centered on oneself” is just another way to say “self-attributing property.”

The main dispute between Quine and Lewis is that, Lewis is treating possible worlds as real, concrete worlds; Quine is treating possible worlds as logical constructions. But it would lead to the fact that the actual world is necessarily actual, but it seems that the actual world is only actual contingently.

XI Argument From Rational Action

Proposition: De se attitude is compatible with Bayesian decision theory.

Proposition: Bayesian decision theory needs properties (de se attitudes) as the objects of belief and desire, not propositions (de dicto attitudes), because propositions are not fine-grained enough to capture differences in cases of self-locating uncertainty.

Proof: There are two amnesiacs, one in Stanford (needs to go down to get out) and one in Widener (needs to go up to get out). Lingens knows he is one of the two but doesn’t know which one he is. In the table, Case 1 (Lingens is the Stanford amnesiac, both go down) and Case 3 (Lingens is the Widener amnesiac, both go down) occur in the same possible world. However, they are functionally different for Lingens: Case 1 is good (he gets out if he is the Stanford amnesiac), and Case 3 is bad (he stays lost if he is the Widener amnesiac). If propositions (sets of possible worlds) were the objects of attitudes, Case 1 and Case 3 would be indistinguishable because they occur in the same world. Properties (de se attitudes), which involve self-ascription (e.g., “I am the Stanford amnesiac and I go down”), can distinguish these cases. Therefore, propositions are inadequate as objects of attitudes in cases of self-locating uncertainty, and properties are needed.

	He is the Stanford amnesiac		He is the Widener amnesiac
	Stanford amnesiac goes down	Stanford amnesiac goes up	Stanford amnesiac goes down	Stanford amnesiac goes up
Widener amnesiac goes down	Case 1, Good	Case 2, Bad	Case 3, Bad	Case 4, Bad
Widener amnesiac goes up	Case 5, Good	Case 6, Bad	Case 7, Good	Case 8, Good

XII Other Alternatives

Proposition: Only properties can serve as uniform objects of attitudes.

Alternative 1 (Sentential objects/meaning): appeals to hypothetical language of thought or sentence structures what?

Objection: This ignores indexicality, open sentences, etc

Alternative 2 (Two-layers): From Perry, a belief has two objects: (1) a pair of an individual and a property; and (2) a function that takes the subject as argument and outputs 1, i.e. the way of believing 1.

The first object determines whether one’s belief is true, and it explains agreement in belief (e.g. Heimson believes “I am Hume” and another person believes “Heimson is Hume”).

Objection: Too complex. Perry’s solution includes self-ascription, but also allows other ascriptions, i.e. ascribing properties to others (belief de re). Lewis denies that de re beliefs are beliefs at all, but “states of affairs that obtain in virtue of the relations of the subject’s beliefs to the res in question,” explained in XIII

XIII Belief De Re

A related case: Attributing “rectitude” to the individual under description of “Lord High Auditor”

Remark:

X in “Under the description of X” does not need to be verbal. X could be visual image
Description here means property, not expressions of properties

Definition (preliminary, de re ascription) A subject ascribes property $X$ to individual $Y$ under description $Z$ iff

$Y$ uniquely has the property $Z$
the subject believes that $P$ , i.e. there is something which uniquely has $Z$ and also has $X$

Remark: This preliminary definition is not general enough because the second condition is propositional. Therefore it would by definition restrict the possibility of ascribing relational properties like “the mountain I live on the top of” because this is not propositional. We need to modify the definition.

Definition (de re ascription): A subject ascribes property $X$ to individual $Y$ under description $Z$ iff

the subject bears the relation $Z$ uniquely to $Y$
the subject self-ascribes the property of bearing relation $Z$ uniquely to something which has property $X$

Remark on Z:

$Z$ is now expressed by a relation characterized by a function with two arguments, the subject and the object, i.e. $f (s, o)$ ; A property is just a special kind of relation where the output does not change when you changes the subject in the argument.
$Z$ has certain restrictions. For example, ascribing espionage to someone under the description “the shortest spy” will not generate a de re belief. What restrictions, then?

Definition (restriction for modality de re): It is necessary de re of individual $Y$ that $Y$ has property $X$ if and only if for some property $Z$ , (1) $Z$ is the essence of Y, and (2) the proposition that whatever has $Z$ also has $X$ is the necessary proposition.

Definition (restriction for belief de re): A subject ascribes property $X$ to individual $Y$ if and only if the subject ascribes $X$ to $Y$ under some description $Z$ such that either (1) $Z$ captures the essence of $Y$ , or (2) $Z$ is a relation of acquaintance that the subject bears to Y

Remark: For belief de re, it is very hard to say that anyone know the essence of some person, even if we grant that there is such an essence. But arguably we do have belief de re. Therefore, $Z$ does not need to be essence in order to form belief de re.

Tentative sufficient conditions for $Z$ in order to form belief de se: acquaintance, public figures, famous people, people with traces, myself, etc. The cases in common is that, it has a relation of acquaintance, which may be defined by a reliable causal chain of evidence for the transmission of information.

XIV Identity De Re vs De Se

When you are watching yourself in the Mirror, you may have a de re belief about yourself, but it does not necessarily follow that you have a de se belief. But de se belief entails de re. Therefore, there’s something more to de se than to de re.

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