Robert C. Stalnaker: Assertion

Graham Katz, Introduction to Semantics SS03 

University of Osnabrück 

Robert C. Stalnaker: Assertion 

by Jan Scholz

Part I: Semantics & Modal 

Logic

Robert C. Stalnaker: Assertion 3 

Assertions (Behauptungen) 

• have a content (propositions) 

• are made in a context 

• content depends on the context 

• acts of assertion affect the context

Questions 


• How do content and context interact? 

• How do assertions act on the context in 

which they are made?

Proposition 


• is a function from possible worlds into 

truth values 

• and thereby determines a set of 

possible worlds: W = { w | φ is true in w}

Possible Worlds 


• ~ distinction among alternative ways 

that things might be, or might have 

been 

• every set of possible worlds determines 

the proposition φ, which is true for every 

w ∈ W. 

• Note: If several propositions fullfill this constraint, 

they are the same.


⇒ one-one correspondence between sets 

of possible worlds and propositions


Two-Dimensional Modal Logic 

We might represent a proposition by enumerating the 

truth values that it has in the different possible worlds 

i, j, k. 

A 

i 

T 

j 

F 

k 

T 

different 

possible sets 

of facts that 

determin the 

truth value of 

the proposition


Two-Dimensional Modal Logic 

There is a second way that the facts enter into the 

determination of the truth value. They can affect the 

proposition, too. 

imaging the following situation...

name 

I 

O‘Leary 

Daniels 

facts 

fool(O‘Leary) 

¬ fool(Daniels) 

¬ fool(O‘Leary) 

fool(Daniels) 


¬ fool(Daniels) 

Accusations 

(what the person believes) 

utterance 



fool(Daniels) 


utterance‘s 

truth value 

T 

F 

F


2D Modal Logic: Matrix 

• the vertical axis represents possible worlds in their 

role as context – as what determines what is said 

• the horizontal axis represent possible worlds in their 

role as the arguments of the functions which are the 

propositions expressed 

utterances 

B 

i 

j 

k 

possible worlds 

i 

T 

T 

F 

j 

F 

F 

T 

k 

T 

T 

F


Diagonal Proposition 

• is the proposition that is true at l for any l iff what is 

expressed in the utterance at l is true at l. 

B 

i 

j 

k 

i 

T 

T 

F 

j 

F 

F 

T 

k 

T 

T 

F


Propositional Concept 

• We will call what a matrix like B represents a 

propositional concept 

• A propositional concept is a function from possible 

worlds into propositions 

• or a function from an ordered pair of possible worlds 

into a truth value (remember the definition of a 

proposition)

Operator 

~ 

, 

†, † 

Modal Operators 

Name 

existential negation 

operator 

possibility, necessity 

dagger, square-dagger 


Type 

{T,W} → {T,W} 

φ→φ 

P → P 

Each kind of operator is a generalization of the kind 

preceding it.

B 

†-Operator 


• The dagger takes the diagonal proposition and 

projects it into the horizontal. 

i 

j 

k 

i 

T 

T 

F 

j 

F 

F 

T 

k 

T 

T 

F 

†B 

i 

j 

k 

i 

T 

T 

T 

j 

F 

F 

F 

k 

F 

F 

F

B 

†-Operator 


• The square-dagger says that the diagonal proposition 

is necessary. This can be understood as a priori truth 

operator. 

i 

j 

k 

i 

T 

F 

F 

j 

F 

T 

F 

k 

F 

F 

T 

†B 

i 

j 

k 

i 

T 

T 

T 

j 

T 

T 

T 

k 

T 

T 

T

Part II: Conversational 

Pragmatics


Speaker Presupposition 

• the set of propositions whose truth the 

speaker takes for granted 

• or better: the set of possible worlds, 

which are compatible with what is 

presupposed ⇒ context set

Conversation 


• To engage in conversation is, 

essentially to distinguish among 

alternative possible ways that things 

might be. The purpose of expressing 

propositions is to make such 

distinctions.


Nondefective Context 

• a context in which the presuppositions 

of the participants in the conversation 

are all the same

Defective Context 


• unnoticed discrepancies between the 

presuppositions of speaker and 

addressees is likely to lead to a failure 

of communication

1. form 


How does an assertion 

change the context? 

• the fact that a speaker is speaking... 

• ...in a certain physical surrounding 

2. content 

• an assertion reduces the context set 

(all possible situations incompatible with what is said are 

eliminated)


Conversation is a Game 

• where the common context set is the 

playing field and the moves are either 

attempts to reduce the size of the set in 

certain ways or rejections of such 

moves by others 

• think about: exchange of information, 

arguments, briefings...


Interaction of Context & 

Content 

1. A proposition asserted is always true in 

some but not all of the possible worlds in the 

context set 

2. Any assertive utterance should express a 

proposition, relative to each possible world 

in the context set 

3. The same proposition is expressed relative 

to each possible world in the context set


Interaction of Context & 

Content 

Each principle can be used in three ways: 

• to interpret what is said 

• as a clue to what is presupposed 

• to evaluate the action of a speaker

† 

Robert C. Stalnaker: Assertion 26

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