Assertion and Negotiation

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Contents:

1 Assertion and negotiation

1.1 Assertion

1.2 Negotiation

1.2.1 Problems with the Stalnakerian picture

1.2.2 Expanding the Stalnakerian picture

1.3 Probabilistic common ground

1.3.1 Why probability?

1.3.2 What is probability?

1.3.3 Probabilities of probabilities

1.3.4 Probability spaces

1.3.5 Probabilistic context update

1.3.6 Assertion operator

1.3.7 Mixture model

1.3.8 Negotiation Zone

1.3.9 The aim of assertion

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"There are times I almost think I am not sure of what I absolutely know.

Very often find confusion in conclusion I concluded long ago.

In my head are many facts, that, as a student I have studied to procure.

In my head are many facts, of which I wish I was more certain I was sure."

(Rodgers & Hammerstein: The King and I, A puzzlement)

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Chapter 1

Assertion and negotiation

This chapter is divided into 3 parts. The first deals with the speech act of assertion,

opening with Stalnaker's (1978) Assertion and continuing with the speech act theories

of Austin (1962) and Searle (1969) and illocutionary logic of Searle & Vanderveken

(1985). This part introduces the distinction between propositional content and

illocutionary force which serves as the basis for the theory propsed in this dissertation,

which distinguishes between the propositional content of assertion and the degree of

strangth by which the assertion is performed. Another elenent of importance is

Stalnaker's notion of context update.

The second part of this chapter deals with negotiation in conversation. This section

discusses conversational elements which are not addressed in Stalnaker's theory, such

as the state of assertions that are not accepted into the common ground, yet not

rejected either. In order to deal with negotiation in conversation, this section proposes

a conversational theory in which such assertions are placed within a Negotiation

Zone, a conversational element complimenting the common ground in which

assertions reside from the moment they are performed until the moment they are

either accepted or rejected.

The third part presents the framework of the expanded conversational theory proposed

in the second part, via a probabilistic expansion of the common ground and the

introduction of the Assertion Operator. The assertion operator is the means by which

assertion are represented and inserted into the negotiation zone. It distinguishes

between the propositional content of the assertion and the degree of strength by which

the assertion is performed. In default conditions this degree of strength is the degree

of strength of the sincerity condition of assertion which is belief, but there are

conditions, e.g. asserting clarity (cf. chapter 4) in which this degree of strength is

more general and represents objectivized belief. This section also deals with the nature

of probability and distinguishes between expressive and descriptive probability. The

former relates to the personal probability assigned by the speaker to various events

and is based on belief, and the latter relates to a more objective notion of probability,

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relating to the manner by which the available evidence affects the likelihood of

events. The chapter concludes with a discussion about the aim of assertion and a

novel proposal.

1.1 Assertion

What's a better place to start a discussion on assertion than Stalnaker's (1978) seminal

paper Assertion? Stalnaker's paper opens with the following four truisms:

"First, assertions have content; an act of assertion is, among other things, the

expression of a proposition – something that represents the world as being a certain

way. Second, assertions are made in a context – a situation that includes a speaker

with certain beliefs and intentions, and some people with their own beliefs and

intentions to whom the assertion is addressed. Third, sometimes the content of the

assertion is dependent on the context in which it is made, for example, on who is

speaking or when the act of assertion takes place. Fourth, acts of assertion affect, and

are intended to affect, the context, in particular the attitudes of the participants in the

situation; how the assertion affects the context will depend on the content."

Starting with the first truism, assertion is an act. More specifically, it is a speech act

(cf. Austin, 1962; Searle, 1969). To paraphrase Austin, speakers do not only say

things but also do things with words. This act has an effect on hearers, i.e. how they

perceive the world and furthermore how they act themselves. Thus speech acts affect

not only conversational participants but also the world that surrounds them. The type

of effect speech acts have is called speech act or illocutionary force (cf. Austin, 1962;

Frege, 1956). Questions, for example, have interrogative force, commands have

commanding force and assertions assertoric force. The force is an important

component of performing a speech act since it distinguishes between different ways

that the same proposition can be used:

(1) a. The dog is on the lawn.

b. Is the dog on the lawn?

c. The dog – to the lawn!

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The first example, an assertion, adds assertoric force to the proposition 'the dog is on

the lawn' thereby guaranteeing to the hearer that this proposition is true. The second

example, a question, adds interrogative force to the proposition 'the dog is on the

lawn' thereby indicating to the hearer that she1 is under obligation to state whether the

proposition is true or not and the third example, a command with the corresponding

force, obliges the hearer to perform an act that will make this proposition true2.

The proposition itself, without speech act force, is inert. This is the reason that early

speech-act theorists (e.g. Stenius, 1967) use Wittgenstein's analogy in which an

utterance's propositional content is like a chemical radical which does not have

independent existence and the force or mood by which the utterance is performed is

like the functional group that gives the radical substance. The distinction between

propositional content and illocutionary force plays a large role in the theory presented

in this work, as will be discussed ahead3.

Assertion is a most basic speech act, being simply a claim about how things are in the

world. When performing an assertion, the speaker provides information about the

world which passes on to the hearer. This information has to be accurate in order for

an assertion to be successful, i.e. the words spoken have to fit the world. This is the

'words to world' direction of fit (cf. Anscombe, 1957; Searle, 1976) demonstrated by

the following scenario:

"Let us consider a man going round a town with a shopping list in his hand. Now it is

clear that the relation of this list to the things he actually buys is one and the same

whether his wife gave him the list or it is his own list; and that there is a different

relation where a list is made by a detective following him about. If he made the list

itself, it was an expression of intention; if his wife gave it to him, it has the role of an

order. What then is the identical relation to what happens, in the order and the

intention, which is not shared by the record? It is precisely this: if the list and the

things that the man actually buys do not agree, and if this and this alone constitutes a

mistake, then the mistake is not in the list but in the man's performance (if his wife

1 In this work referring pronouns alternate randomly between masculine and feminine. 2 This work adopts a 'normative theory' of speech acts (cf. Cohen & Krifka, 2011; Searle, 1969)

according which the performance of speech acts relates to commitments speaker take upon themselves

or impose upon others. 3 This distinction is further divided within illocutionary force into the degree of strength of this force,

specifically of the sincerity condition of assertion, which is belief.

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were to say: “Look, it says butter and you have bought margarine”, he would hardly

reply: “What a mistake! we must put that right” and alter the word on the list to

'margarine'); whereas if the detective's record and what the man actually buys do not

agree, then the mistake is in the record." (Anscombe, 1957)

The content of an assertion, the proposition expressed by virtue of performing the

speech act of assertion, is like the list that the detective holds. The list has to fit the

items that the man bought in order to be a successful account of how things are. This

differentiates assertion from other speech-acts such as requesting or promising which

have a 'world to words' direction of fit. Using Searle's (1969) taxonomy, requesting is

of the directive speech-act types. It is performed by the speaker in order to get the

addressee to do something, and promising, of the commissive types, is performed by

the speaker in order to commit to do something. Both requests and promises fit the list

that the man holds - a request made by the man's wife will lead him to search for the

items on the list and to make the world fit the words written on it, as will a promise

performed by the man to bring these items back home.

While assertions need to fit the state of the world, the direction of fit between

assertions and the state of discourse is not so clear. On the one hand, the propositional

content conveyed by an assertion has to be consistent with the state of discourse, but

on the other hand successful assertions change the state of discourse by virtue of their

assertive force. This is where Stalnaker's second truism comes in: assertions are made

in a context, which is a situation that includes a speaker with certain beliefs and

intentions, and hearers with their own beliefs and intentions. Stalnaker represents this

conversational context in terms of mutually shared presuppositions held by

conversational participants to be true. As stated in the truism, each conversational

participant has certain beliefs. Beliefs are standardly represented by propositions,

when a proposition corresponds to a set of possible worlds in which it is true i.e. a

function from possible worlds to truth values. Thus, each conversational participant

has a set of propositions he holds to be true. A subset of this set of beliefs is the set of

beliefs that each conversational participant holds to be true and to be shared with all

the other conversational participants. This set constitutes the speaker presupposition.

As Stalnaker puts it:

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"A proposition is presupposed if the speaker is disposed to act as if he assumes or

believes that the proposition is true, and as if he assumes or believes that his audience

assumes or believes that it is true as well". (Stalnaker, 1978, pp. 321).

These presuppositions constitute the Common Ground, the set of propositions all

conversational participants (ideally) share with one another. Being a set of

propositions, the common ground is a set of sets of possible worlds. The intersection

of this set, therefore, provides the set of possible worlds in which all the propositions

of the common ground are true – the Context Set. Each world in the context set is thus

considered by the conversational participants to be a “live option” relevant to the

conversation. That is – each world in the context set can, for all the conversational

participants know, be the actual world.

This leads us to the fourth truism:4 assertions affect the context, in particular the

attitudes of the participants in the situation. In this regard, it is important to

distinguish between two notions of context that exist in the literature. The first notion,

notably used in Kaplan (1989) is the situation in which discourse occurs, i.e. the time,

location, conversational participants etc. The second notion of context is the totality of

information that has been accumulated throughout conversation(s) and is treated by

all conversational participants as a given. This second sense is the one used by

Stalnaker, and the one that is referred to in this work.

The fourth truism deals with the effect of assertion on the context, i.e. context update.

The force of assertion is its main effect on the context, which according to Stalnaker

is achieved by changing the attitudes of conversational participants towards the

propositional content of the assertion, from an attitude of disbelief or indifference to

an attitude of belief – this is when the assertion is said to be accepted. And, as

recalled, the common ground is composed of the presuppositions of conversational

participants, i.e. the set of propositions all conversational participants hold to be true.

Therefore, if an assertion is accepted, the propositional content of this assertion is

added to the set of propositions in the common ground and since the context set is the

intersection of the common ground, adding a proposition to the common ground

causes worlds to be eliminated from the context set. This is the process of context

4 The third truism deals with indexicals and therefore doesn't concern the purposes of this chapter, but

cf. chapter 5 on predicates of personal taste for a discussion of Kaplan's (1989) theory of indexicality.

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update which is the main effect and the force of assertion. Using Wittgenstein's

(1953) language game term, Stalnaker provides the following description of context

update:

"One may think of a non-defective conversation as a game where the common 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". (Stalnaker, 1978: 325).

This concept also echoes David Lewis' (1979) view of assertion as a way to change

the shared 'conversational scoreboard', a common register of the progress of

discourse.

Stalnakerian context update can be represented in the following manner:

Figure 1.1: Stalnakerian context update

As seen in the figure above, the initial context set is CS0, and it contains both and

worlds. An addition of into the common ground eliminates the from the

context set by intersecting CS0 with the proposition i.e. the set of worlds.

The next section discusses problems with the Stalnakerian picture and proposes a way

to expand this picture while preserving its qualities.

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1.2 Negotiation

1.2.1 Problems with the Stalnakerian framework

There are two ways to look at the update process – one is cooperative, the other is

dominative. The cooperative notion of context update is that conversational

participants work together in order to pass meaning from one to the other. This is

conveyed by Grice's well known cooperative principle (Grice, 1975): "Make your

contribution such as it is required, at the stage at which it occurs, by the accepted

purpose or direction of the talk exchange in which you are engaged". If everyone

adheres to this principle, communication will be successful. This is, of course, so long

as the mutual goal of conversational participants is to exchange information about the

world in the best possible way. However, this is not the only conceivable goal –

conversational participants might also strive to establish their view of the world

regardless of whether this view is considered true or not by other interlocutors. This is

the dominative notion of context update, which is that every speaker aims to reach a

conversational state in which his beliefs are shared by all other conversation

participants.

The cooperative and the dominative principles exist in every conversation to various

degrees, and therefore both need to be represented. This representation, however, is

not easily done in a Stalnakerian framework because of the nature of the common

ground. As defined, the common ground requires that conversational participants

share beliefs and have mutual expectations, but this is not the case if every

conversational participant has a different agenda that possibly has nothing to do with

beliefs, which she wishes to be accepted by the others. Thus, the Stalnakerian

framework as it is can't adequately represent the dominative principle at work.

Another problem stems from the limited number of moves in the 'language game'

proposed by Stalnaker – either attempts to reduce the size of the set in certain ways or

rejections of such moves by others. Thus, this system allows for a speaker to assert a

proposition like 'the dog is on the lawn' and for the hearer to either accept or reject

this proposition. But what happens if things are not so clear, as is usually the case?

When the hearer does not have enough information at her disposal to either rule out or

accept the proposition, Stalnaker's system doesn't have a way to deal with it. This

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relates to the third problem, which stems from the definition of the context set as “the

set of possible worlds recognized by the speaker to be the ‘live options’ relevant to

the conversation” (Stalnaker, 1978; pp. 321–2). This is a good way to view the

possible worlds in the context set, and it should not be abandoned, but in everyday

conversation there are always propositions which are asserted and are very much 'live

options' even though they are not accepted and thus not part of the context set.

Consider the following example of a dialog from Ginzburg (1996: 3):

(2) A: Bill left.

B: Are you sure?

A: I saw his car drive away.

B: That's impossible: I hear his voice upstairs.

A: Look, his secretary just told me he's left.

The last step in our motivation to expand the Stalnakerian picture comes from the

proposal nature of assertion, which, as argued in Farkas & Bruce (2010), is not much

dealt with in the Stalnakerian account. Although assertion according to Stalnaker is a

proposal to change the common ground, the Stalnakerian system does not really

specify what it means for an assertion to be a proposal and how this proposal status

manifests. Farkas & Bruce argue that theories of context update should not disregard

this proposal nature since asserted propositions affect the context in significant ways

even if they are not accepted, but only proposed.

All of the abovementioned problems seem to stem from the same underlying cause,

which is that the Stalnakerian system tells us how assertions affect the context, and

what happens when assertions are proposed and then accepted or rejected. But it does

not tell us what happens to an assertion from the moment it is performed until the

moment it is accepted or rejected. This is an important part of conversation; it may

last for a long time during which the status of the assertion in the Stalnakerian system

is unclear. However, it is clear that the force of assertion is still in effect, i.e. the

assertion is not inert, even when it is in this 'limbo' state.

Thus, there is a need to expand the Stalnakerian framework, which is the topic of the

next section.

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1.2.2 Expanding the Stalnakerian framework

Expansions and revisions to the Stalnakerian framework are suggested by many

theories. For example, dynamic theories of meaning (inter alia Dekker, 1993;

Groenendijk & Stokhof, 1990; Heim, 1983; Kamp, 1981; Landman, 1984; Veltman,

1996) develop the Stalnakerian idea of context update into a semantic system that

deals with the non-static development of discourse information as a consequence of

the addition of new information by discourse participants, with the underlying

conception of meaning as context change potential. Reinhart (1981) discusses a

structure paralleling the common ground in terms of discourse topics, Carlson

(1982)also talks about discourse topics in an account of dialogue games, and

Erteschik-Shir (1997) views the common ground as a set of file cards representing

discourse topics. Roberts (1996) and Ginzburg (1996a) offer a new discourse entity,

Questions Under Discussion, Gunlogson (2013) offers the new discourse entity public

commitments, and Farkas & Bruce (2010), propose the table. This work combines

features from the abovementioned theories, with a focus on Ginzburg (1996a), and

Farkas and Bruce (2010).

Ginzburg (1996a) proposes a Lewis (1979) style conversational scoreboard termed

gameboard which contains, in addition to a set of known facts corresponding to the

propositions in the Stalnakerian common ground, a set of Questions Under Discussion

(QUD). This set contains issued that are brought up during conversation and need to

be resolved, in the form of questions. Thus, if a certain proposition p is accepted into

the common ground, it gets updated into facts but if this proposition is under dispute

then until it is fully resolved it's added into QUD as the question whether p. The

process of context update, according to Ginzburg (1996a) is that the speaker asserts p,

and the hearer then has the option of accepting p and updating it into the common

ground, or to discuss whether p. In the latter option, the hearer adds the question

whether p as a topmost element in her QUD, and produces an utterance that is

relevant to a discussion of this question.

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Ginzburg's QUD is a good place to start, but it is unsuitable for the purpose of this

work, that deals with degree based assertion-modifying expressions, as such degrees

are not represented in Ginzburg's theory. Thus, the discourse element of discussion

needs a different representation here. Such a representation is found in Farkas and

Bruce (2010), who discuss a transitory discourse stage, the table, upon which

discourse items that the speaker publicizes her commitment to (based on Gunlogson's

(2013) public commitments) are placed before they are accepted by other participants

in conversation. Placing an item on the table is a way of proposing a new addition to

the common ground. This action affects the context by projecting a set of the future

context state called a projected set, which has the potential of replacing the current

context state and becoming the new common ground.

Similarly to Farkas and Bruce, the proposed account incorporates a transitory stage in

which assertions that are performed and not yet accepted or rejected reside, termed

Negotiation Zone (cf. section 1.3.8). While Farkas and Bruce do not discuss the

mechanism by which interlocutors decide whether or not to accept propositions that

are on the table, the proposed theory offers an account of this process. Moreover, this

theory assigns an important role to the degree of strength of the assertion which is an

element that is lacking from the abovementioned previous accounts.

1.3 Probabilistic common ground

1.3.1 Why probability

This work is done within a probabilistic framework. A question that immediately

comes to mind (cf. Cohen, 2009 for further discussion of this question): why should

we abandon formal logic and replace it with probability?

The short answer to this question is that we do not have to. Formal logic is a powerful

and helpful tool whose worth is tried and tested and there's no reason to abandon it.

The long answer is that while we do not have to completely abandon logic and the

principle of bivalence, there is a lot to benefit from adding probability to our

theoretical toolkit.

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The first motivation for probability comes from its use as a tool in many different

disciplines. As Hajek (2011) puts it: "Probability is virtually ubiquitous. It plays a role

in almost all the sciences. It underpins much of the social sciences - witness the

prevalent use of statistical testing, confidence intervals, regression methods, and so

on. It finds its way, moreover, into much of philosophy. In epistemology, the

philosophy of mind, and cognitive science, we see states of opinion being modeled by

subjective probability functions, and learning being modeled by the updating of such

functions. Since probability theory is central to decision theory and game theory, it

has ramifications for ethics and political philosophy. It figures prominently in such

staples of metaphysics as causation and laws of nature. It appears again in the

philosophy of science in the analysis of confirmation of theories, scientific

explanation, and in the philosophy of specific scientific theories, such as quantum

mechanics, statistical mechanics, and genetics. It can even take center stage in the

philosophy of logic, the philosophy of language, and the philosophy of religion".

But perhaps we should not infer from the successful use of probability in non-

linguistic disciplines that it should be applicable to linguistics as well. In that case,

there is also plenty of linguistic motivation, starting with the simple fact that

probability is used in everyday language. If we wish to represent utterances involving

probability such as the following, we need to incorporate probability into our

semantics in one way or another:

(3) a. There is a low/high/80% probability that the Bulls win the game.

b. The chances of Jordan making it as a golfer are slim to none.

c. In this time of year, any given day is 80% likely to be rainy.

In addition to everyday use, there are many linguistic phenomena that benefit from a

probabilistic explanation. Cohen (2009) discusses some of these, e.g. generics and

frequency adverbs, vagueness, and conditionals, and argues that this use needs not

even be too intrusive as to rule out formal logic. In fact, probability can be employed

while preserving the Tarskian biconditional.

Gradable adjectives are another phenomenon in which the use of probability is very

beneficial. The most widely held semantic theory of adjectives today is based on

Kennedy (2007), in which these adjectives are represented in terms of degrees on a

scale. More specifically, adjectives such as long, cold, smart, deep, fast, good, happy,

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popular etc. are taken to be measure functions, from entities to the appropriate

degrees. This type of semantics, which is very much at use in standard current

semantic theories, provides initial motivation to the use of degrees in semantics. And,

as probability is another type of a measure function, it is not so farfetched now to

conceive of probabilistic semantics as a representation of human cognition and at the

very least suggests that probability, too, has an important role to play in semantics and

pragmatics.

Moreover, as argued by Yalcin (2010) and Lassiter (2011) among others, possible,

probable, certain and likely are gradable adjectives which convey epistemic modality,

and since gradable adjectives are already represented as degrees it is natural to have a

probabilistic degree scale for epistemic gradable adjectives. And, once it is

established that certain types of epistemic modals are best represented by probability,

a unified account of all epistemic modals in terms of probability is much more

desirable.

1.3.2 What is probability

The question to deal with before going forward with a probabilistic account is the

nature of probability, i.e. what does it mean to say that a certain event has a

probability of 0.7?

The answer is not a simple one. The philosophical literature on probability is vast and

complex, and there are many different theoretical ways to define what probability is

(for an overview, cf. L. J. Cohen, 1989; Gillies, 2000; Hacking, 2001; Hajek, 2011;

Mellor, 2005). Not only are there many ways to define probability, but the terms vary

as well. Thus, even the task of partitioning the theories is not an easy one. For

example, Gillies (2000) categorizes probability theories into classical, logical,

subjective, frequency and propensity. Mellor's (2005) categories are chances,

epistemic probabilities, and credences, and Hacking (2001) simply divides

probabilities into belief-types and frequency-types.

I will follow Hajek (2011) and divide probability theories into three main concepts:

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A. A quasi-logical concept that measures the degree of evidential support a claim

about the world has. For example, “in light of the relevant seismological and

geological data, it is probable that California will experience a major

earthquake this decade”.

B. The subjective concept of an agent's degree of belief. For example, “I am not

sure that it will rain in Canberra this week, but it probably will.”

C. An objective metaphysical concept that applies to how the world is like,

independently of what anyone thinks. For example, “the probability that a

particular radium atom will decay within 10,000 years is high”.

Of these three concepts, the first two are of importance to this work as they deal with

different notions of belief, the 'objective' evidence-based belief and the 'subjective'

which is based on more than evidence alone. The third concept of probability,

corresponding to objective reality, is irrelevant to this work.

Assigning the first two probability concepts to two types of belief is not something

idiosyncratic to this work. For example, Halpern & Fagin (1992) differentiate

between two types of probabilistic belief functions – the first is as a generalized

probability function, and the second is as a way of representing evidence via mapping

from probability functions to probability functions. They show how several puzzles

raised in the literature can be solved once belief functions are not treated as uniform

but rather divided into either measures of evidence or generalized probability. The

former pertains to the first abovementioned concept of probability and the latter to the

second. I will term the first type of probability, which pertains to belief as evidence,

descriptive and the second type of probability which pertains to belief as subjective

degree of confidence in the truth of a proposition expressive, a terminology which will

be clarified ahead, and will used throughout the course of this dissertation5.

1.3.3 Probabilities of probabilities

5 Note that this view, i.e. the distinction between expressive and descriptive probability and the two

types of belief is not shared by Ariel Cohen.

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The use of probability is usually done with regards to some event, but interestingly,

probabilities can also be applied to other probabilities, as in the next example from

(Kyburg, 1988):

"I might say that the probability that a coin will yield heads on a certain toss is

"almost certainly" a half, i. e. that the probability that the probability is a half is very

close to one. In contrast, I might say that the probability that a certain person will

choose a blue tie, given that she is wearing a blue suit, is 0.8, but I may be no more

than 50% confident of my probability judgment. That is, I might say that the

probability that the probability is 0.8 is less than 0.5. " (Kyburg, 1988 : 31)

The matter of whether probabilities of probabilities, i.e. higher order probabilities

constitute a qualitatively different type than 'lower order' ones is under dispute. de

Finetti (1977) for example claims that such a concept as a probability of a probability

is meaningless, Pearl, (1987) accepts the notion but claims that there is no need to

posit two different probability types since both higher and lower order probabilities

can be accounted for by classical probability. Kyburg (1988), on the other hand, finds

the notion of probabilities of probabilities having a different type quite natural:

"Higher order probabilities, if they are given a different interpretation from that given

to first-order probabilities, make more sense. The most natural view discussed by

Brian Skyrms … is that first-order probabilities represent propensities or frequencies-

objective facts about the word and second-order probabilities represent degrees of

belief. I may have a certain degree of belief that the propensity of this die to land five

in the long run is .3. The degree of belief (the second-order probability) and the long-

run relative frequency (the first-order probability) are clearly distinct."

I will use the abovementioned Skyrms (1980) as a stepping stone to the claim that just

as probability as propensities or frequencies can be embedded by probability as

degrees of belief, so can probability as a measure of evidence6. Thus, probability as a

measure of evidence is more subjective than probability as propensity or frequency,

but still more objective than probability as degrees of belief. For the technicalities of

how probabilities of probabilities are computed, cf. Kyburg (1988). For the purposes

of this work, the details of how this is done are less important than the hierarchical

6 Note that this view is not shared by Ariel Cohen, cf. Cohen (2012).

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order. The hierarchy goes from the most subjective to the most objective types of

probability, when the latter scope over the former:

(4) Belief-type probability >> evidence-type probability >> objective probability

1.3.4 Probability spaces

Following Yalcin (2012) probability spaces are formally defined as a tuple <W,s,A,f>

such that:

(5) a. W is a sample space, i.e. the set of all possible worlds.

b. s W is a probability domain.

c. A is a Boolean algebra of subsets of W including s.

d. f is a probability measure defined over A.

e. P() is a propositional function such that for any set of worlds W, model M,

world w and assignment function g:

[|P()|]M,w,g = f ( {wW | (M,w,g) |= } )

f. P(s)=1

Each probability space is akin to an information state7, i.e. a cognitive state of some

conversational participant containing his beliefs about the world and his

representation of discourse including the information states of other discourse

participants. As stated in Groenendijk, Stokhof, & Veltman (1995): "Information

states contain two kinds of information: information about the world, and discourse

information. In the end, it is information about the world that counts, but in acquiring

such information through discourse, one also has to store information pertaining to the

discourse as such".

In order to have a formal account of the context update effects of probabilistic

assertions the context set can no longer be simply a set of possible worlds since

possible worlds by themselves do not carry probabilistic information. Yalcin's (2012)

7 This relates to the dynamic semantics perception of context as a set of information states.

18

context probabilism approach is therefore adopted, i.e. the view that the common

ground admits of probabilistic landscaping.

The common ground can be viewed in two compatible ways – either as the set of

propositions shared by all conversational participants, or as the set of information

states in which all the propositions in the common ground have the same probability

value. As discussed above, each information state is a probability space, the domain

of which is the set of possible worlds determined by the intersection of all the

propositions a given conversational participant believes.

By this view every proposition is defined in probabilistic terms, thus probabilistic

propositions are similar to non-probabilistic propositions. For example:

(6) The dog is on the lawn.

(7) The probability that the dog is on the lawn is 0.2.

The truth conditions of the proposition in (6) are that it has a probability of 1, hence

an assertion of (6) has the following propositional content:

(8) [| P (on-the-lawn (the-dog)) = 1 |]

The truth conditions of the proposition in (7) are that it has a probability of 0.2, hence

an assertion of (6) has the following propositional content:

(9) [| P (on-the-lawn (the-dog)) = 0.2 |]

The next section discusses the context update effect of probabilistic and non-

probabilistic assertions.

1.3.5 Probabilistic context update

Recall that in the standard Stalnakerian context update an assertion of a proposition

adds to the common ground and eliminates all worlds in which is false from the

context set.

19

Following and modifying Yalcin (2012)8 a probabilistic context update is one in

which an assertion of a probabilistic proposition such as 'P() = x' adds 'P() = x' to

the list of propositions in the common ground. Once this proposition is added, all

conversational participants agree that the probability of is at least x9, therefore all

the probability spaces in which P() < x are removed from the common ground.

Thus, for a non-probabilistic assertion:

(10) The dog is on the lawn.

The update will be the set of probability spaces in which:

(11) [| P (on-the-lawn (the-dog)) = 1 |]

And worlds in which the probability is lower than 1 are removed from the common

ground. As for a probabilistic assertion:

(12) The probability that the dog is on the lawn is 0.2.

The update will be the set of probability spaces in which:

(13) [| P (on-the-lawn (the-dog)) = 0.2 |]

And probability spaces in which this probability is lower than 0.2 are removed from

the common ground, leaving of course probability spaces in which the probability is

higher since it entails a probability of 0.210.

Thus, in this system, both probabilistic and non-probabilistic assertions are

represented by propositions and updated into the common ground in the same way.

The standard Stalnakerian context update is now a special case of probabilistic

context update – the case in which the probability of the asserted proposition is 1.

However, for the sake of simplicity, whenever the propositional content is P() = 1

the representation will simply be , unless otherwise required.

8 Yalcin's context update process is expressive, i.e. unlike in the account proposed here, the common

ground in Yalcin's account is not updated directly. Instead, when a speaker asserts a proposition, she

expresses her credal state with regards to this proposition and proposes that other conversational

participants adopt the same state towards it. If this happens, the speaker presuppositions change,

thereby updating the common ground. 9 Since every probability space in which 'P() ≥ x' entails 'P() = x'. 10 Similarly to an update of numerically quantified propositions such as 'John has 3 children', where all

the worlds in which John has less than 3 children are removed.

20

1.3.6 Assertion operator

As previously discussed, the speech act of assertion contains, in addition to

propositional content, various other elements. Searle and Vanderveken (1985) divide

illocutionary force into 7 components:

1. Illocutionary point: The point and purpose of the speech act, i.e. what speakers

aim to do when they perform the speech act. The point of assertion is

presumingly to convey information about the nature of the world11.

2. Degree of strength of the illocutionary point: The same illocutionary point can

be achieved with varying degrees of strength. For example, the illocutionary

point of getting the addressee to do something can be achieved by requesting

or by insisting. The latter has a greater illocutionary strength.

3. Mode of achievement: Some speech acts require a special mode by which the

illocutionary point can be achieved. For example, the illocutionary point of

performing marriage is achieved via the mode of being appropriately licensed

to marry people.

4. Propositional content conditions: There are certain restrictions on the

propositional contents appropriate for various speech acts. For example, the

propositional content of an apology can't contain actions that the speaker is not

responsible for, it's inappropriate to apologize for something you had nothing

to do with.

5. Preparatory conditions: Restrictions on the conditions that need to be fulfilled

before the speech act can be adequately performed. For example, in order to

marry two individuals the person performing the speech act of declaring has to

have the appropriate license.

6. Sincerity conditions: In order for a speech act to be performed the speaker has

to possess the appropriate psychological state corresponding to the speech act.

For example, in order to request something the speaker has to want it,

11 For a discussion about the aim of assertion, see section 1.3.9.

21

otherwise the speech act is not sincere. The sincerity condition for assertion is

belief, since in order to perform an assertion sincerely the speaker has to

believe in the asserted propositional content.

7. Degree of strength of the sincerity conditions: The same sincerity condition

can exist with varying degrees of strength. For example, the speaker can be

sincere while either requesting or imploring, i.e. in both cases the speaker

wanted the thing she asked for. However, the degree of this sincerity condition

is higher in the case of imploring. As for assertion, the speaker can believe in

the asserted propositional content with varying degrees of strength, ranging

from skepticism to total conviction.

The account proposed here minimally divides the assertion into two components12,

propositional content and degree of strength. This degree of strength corresponds by

default to the seventh abovementioned speech-act component i.e. the degree of

strength of the sincerity conditions, which in the case of assertion is belief. However,

there are cases in which this degree of strength is generalized and becomes the second

abovementioned speech-act component, i.e. the Degree of strength of the

illocutionary point. One of these cases is discussed in chapter 4 that deals with clarity,

and the other case discussed in section 2.4 of chapter 2 that deals with modal concord.

The following assertion operator is proposed:

(14) Ax <S,C>

The first argument, S, stands for the degree of strength by which the assertion is

performed and the second argument C is the assertion's propositional content. The

order of arguments stands for relative scope, i.e. the degree of strength scopes over

the propositional content. Thus, a shorthand representation13 of this assertion operator

in probabilistic terms, i.e. the assertion of propositional content with a degree of

strength that is the value v of a probability function P, is:

(15) Ax P() = v

12 I remain agnostic regarding the other components. They are not used in the current account as they

are not needed in order to explain the linguistic phenomena discussed. 13 Given that the asserted propositional content is the same as the propositional content that the degree

of strength is applied to.

22

As recalled, it is important for speech acts to be performed sincerely, and the sincerity

condition for assertion is belief. This is the reason why an utterance such as the

following seems like a contradiction even though logically it isn’t:

(16) #I went to the pictures last Tuesday, but I don't believe that I did. (Moore,

1942)

Of course, it is not a logical contradiction that it is true that the speaker went to the

pictures and that it is true that the speaker does not believe it. But it is inappropriate to

assert such a thing, and speech act theory has a straightforward explanation in terms

of a violation of the sincerity condition - the speaker has to believe in what she

asserts. And, since the theory proposed in this work deals with degrees of belief, a

belief norm of assertion14 is adopted and modified to a degree based account:

(17) One must assert that p only if one believes to a high degree that one knows

that p.

Thus, standard unmodified assertions carry by default a degree of strength which is

equal to or greater than high, which stands for some numerical degree close to 1.

Thus, an assertion of:

(18) The dog is on the lawn.

Is represented by the following formula:

(19) Ax P (on-the-lawn(the-dog)) ≥ high

The speaker x asserts the propositional content 'the dog is on the lawn' with the default

degree of strength for assertion which is equal to or greater than high.

And an assertion of:

(20) The probability that the dog is on the lawn is 0.2.

Is represented by the following formula:

(21) Ax P ( P (on-the-lawn(the-dog)) = 0.2) ≥ high

14 cf. Lackey (2007) for a survey of norms of assertion.

23

The speaker x asserts the propositional content 'the probability that the dog is on the

lawn is 0.2' with the default degree of strength for assertion which is equal to or

greater than high. As can be seen, this is a case in which expressive probability i.e. the

degree of belief of the speaker, has wide scope over descriptive probability i.e. the

statement that the world is such that there is a 0.2 probability that the dog is on the

lawn.

1.3.7 Mixture model

As recalled, the context update process involves a speaker who performs an assertion

and a hearer who has to decide whether to accept, reject, further discuss, or agree to

disagree on it. The hearer's decision process takes into account various sources of

evidence at the hearer's disposal. These sources may include direct knowledge (e.g.

perception), deductive processes (e.g. inference), or reported information (e.g.

hearsay).15

The evidence provided by each source is not, in general, conclusive, for two reasons.

One is that some sources are more reliable than others. For example, the accuracy of

perception will depend on the reliability of the sense organ (e.g. eyes) or sensing

device (e.g. camera); the weight of hearsay evidence will depend on the reliability of

the reporter, etc. The second reason why the evidence is not conclusive is that the

evidence provided by the source is generally, by its nature, graded and not certain. For

example, one possible source of evidence is inference—but inference is often

probabilistic. Even if the calculation of probabilities is entirely accurate, the result is

still only a probability measure, not a definite result. What is less often acknowledged

is the fact that reported evidence is also graded: the speaker may believe what she

says to various degrees, and, consequently, make statements with varying

illocutionary strengths. A speaker who utters (22) expresses more confidence than a

speaker who utters (23) who, in turn, expresses more confidence than a speaker who

utters (24)16:

(22) The dog is certainly on the lawn.

15 If this classification of knowledge sources brings evidentials to the mind of the reader, this is not a

coincidence. 16 At this stage, the claim is based on the reader's intuition, but cf. chapter 2 for a formal explanation.

24

(23) The dog is on the lawn

(24) The dog is possibly on the lawn

The different illocutionary strength of the utterances must be taken into account by

the hearer in deciding whether or not to accept their propositional content.

In order to formalize the two factors that affect the relative strengths of different

sources of evidence, we assign two values to each source of evidence i: a probability

measure, Pi(), indicating the strength of the evidence for according to source i, and

a weight wi, indicating the reliability of the source. Of particular interest here is a

specific type of reported information: an unmodalized assertion made by the speaker.

Thus, if the speaker asserts (23), the probability value will be high, and the weight will

reflect how reliable the speaker is considered to be.

The probability that the hearer assigns to a proposition is a weighted sum of the

probabilities assigned to it by the various sources. The sum of the weights is equal to

1, so that the result can be easily shown to be a probability measure itself:

(25) n

=i

ii )(Pw=)P(1

The formula states that the probability of is the sum of weighted probabilities

assigned to by all available sources of evidence pertaining to .

This type of probability measure is often referred to as a mixture model (cf.

McLachlan & Peel, 2000). Note that because the sum of the weights is 1, the value of

the probability does not necessarily increase if the number of sources increases.

If P() exceeds the hearer’s threshold of acceptance17, the proposition is accepted; if

P() exceeds this threshold, the proposition is rejected. Otherwise it is left in the

negotiation zone – which is discussed in the next section.

1.3.8 Negotiation Zone

17 The assumption is that, by default, the threshold of acceptance is the same degree as the default for

standard assertion, i.e. high. However, this threshold can change, cf. Davis, Potts, & Speas, (2007) and

Davis (2009).

25

The Negotiation Zone (NZ) is a discourse entity similar to Farkas and Bruce's table,

but unlike the table, the NZ hosts propositions coupled with degrees of strength, the

first argument of the assertion operator.

The NZ is a set of assertion operators. Whenever a conversational participant

performs an assertion, the appropriate assertion operator containing the identity of the

speaker, the degree of strength and the propositional content, is added to the NZ. For

example, the speaker performs the following standard assertion:

(26) The dog is on the lawn.

This assertion is based on the speaker's information state, i.e. the speaker's

information state is such that the asserted proposition has a degree of probability of

equal to or greater than high.

Now, the hearer has to take this proposition under consideration. She inspects her own

information state, which contains various evidential sources available to her which

pertain to the asserted proposition. i.e. the hearer activates a mixture model.

While this happens the speaker's assertion is neither accepted nor rejected. Both the

speaker and hearer have a representation of the speaker's assertion,18 but even though

this representation is part of the common ground, the propositional content of this

representation can't be as long as it is not accepted and updated. What happens to it?

As discussed in example (2), repeated here, even in this state of 'limbo' assertions still

have effect on the discourse Ginzburg (1996: 3):

(27) A: Bill left.

B: Are you sure?

A: I saw his car drive away.

B: That's impossible: I hear his voice upstairs.

A: Look his secretary just told me he's left.

Moreover, assertions can stay in this indefinite state for a very long period of time:

18 The common ground and the information states within it contain a register of discourse that includes

details of assertions performed during discourse (cf. Groenendijk et al., 1995; Stalnaker, 1978).

26

(28) B(1): after all your father's a generation younger than my father isn't he,

basically

a(2): well I should think so

B(3): cos your father's now SEVENTY is he

a(4): seventy two or (simultaneous with next turn:) seventy three

B(5): SEVENTY TWO. yes. well father would have been seventy eight I

suppose. if he had been alive still

C(6): good lord

a(7): that all

?(8): goodness

C(9): my father would have been a hundred and twenty seven

B(10): no, not seventy eight, eighty eight

a(11): (coughs)

B(12): yes. (simultaneous with next turn:) no. yes

a(13): as bad as Charlotte's

B(14): no, not seventy eight. yes, eighty eight. no, I'm sorry, sixteen years, yes

eighty eight, that sort of thing

C(15): a half generation then

(Ginzburg, 1996b)

The issue raised in step (1), i.e. the proposition (or question whether) 'your father's a

generation younger than my father', is resolved only in step (15). Of course, it is still

very much relevant to conversation, and thus must be stored in a form that can be

examined by other discourse participants in order to reach a conclusion about it. The

form is the assertion operator, the place of storage is the NZ and the examination is

done via the mixture model.

27

After the activation of the mixture model there are three possible results –

a) A probability value of greater than high – the assertion is accepted by the

hearer.

b) A value of lower than low – activation of a mixture model to check if the

negation exceeds high, and if it does the assertion is rejected by the hearer.

c) Any other value – the assertion is under negotiation, i.e. neither accepted nor

rejected by the hearer.

If the result is a probability value of greater than high, the hearer utters an acceptance

phrase that enables the speaker to understand that the hearer accepts the assertion. The

speaker than incorporates the hearer's response as a new source of evidence and

activates a new mixture model that includes the hearer, her weight and her judgment.

If the result is greater than high the speaker utters some acceptance phrase back and

the proposition is updated into the common ground, conversational participants

update their beliefs in the asserted proposition to a full degree of 1, and the

proposition is removed from the NZ.

Note that even if a proposition is accepted and as a result updated into the common

ground, belief is corrigible, i.e. conversational participants are always prepared for the

possibility that their beliefs may turn out to be false. In this regard, following Cohen

(1996), I adopt an action analysis of belief (cf. Braithwaite, 1932) according which a

belief that p is a disposition to act as if p were true, with respect to some practical

objective. This accords well with Stalnaker's (1978) claim that: "A speaker

presupposes that P at a given moment in a conversation just in case he is disposed to

act, in his linguistic behavior, as if he takes the truth of P for granted, and as if he

assumes that his audience recognizes that he is doing so".

It is also important to note the difference between probability update and probability

revision. As discussed in Wang (1993), probability update occurs when a previous

degree of probability assigned to a proposition p is assigned new value. This is what

happens when a proposition is added to the common ground. If the proposition is non-

probabilistic, e.g. 'the dog is on the lawn' then the update is from any previous degree

of probability to 1. If the proposition is probabilistic, e.g. 'there is 20% probability

that the dog is on the lawn' then the update is from any previous degree of probability

28

to 0.2. Probability revision, on the other hand, is when a previous degree of

probability assigned to a proposition p is affected by various factors and changes to a

new value accordingly. This is what happens when the mixture model is activated – a

previous degree of belief is affected by various evidential sources and information

states with varying degrees of belief with regards to the same proposition as will be

discussed shortly.

In the second option, in which the result is a probability value of 0, the hearer utters a

rejection phrase that enables the speaker to understand that the hearer rejects the

assertion. The speaker than incorporates the hearer's response as a new source of

evidence and activates a new mixture model that includes the hearer, her weight and

her judgment. If the new result is lower than high the speaker can retract the assertion,

and the item stays in the NZ pending new evidence.

Let's go through a scenario of assertion and acceptance that will help understand the

process:

Tom and Jerry go out to an evening in Tel-Aviv and have to return back to Beer-

Sheva before the last train leaves. Tom remembers looking at a train schedule

according which the last train leaves at 23:00. He therefore asserts to Jerry: 'the last

train leaves at 23:00'. In order to sincerely and felicitously perform this assertion,

Tom's degree of belief in the asserted proposition has to be at least equal to or greater

than high.

Jerry hears Tom's assertion, activates his mixture model, which results in a probability

which is also greater than high. He therefore accepts Tom's assertion, uttering 'OK',

indicating to Tom that the result value of Jerry's mixture model is greater than high.

Jerry's acceptance phrase is also, of course, an assertion, and every assertion places

the asserted item into the NZ and triggers an activation of the mixture model by the

hearer in order to revise probabilities. Thus, Tom activates the mixture model and

revises the probability he assigns to his previous assertion in light of Jerry's

acceptance. This is actually a redundant step in this case, since Tom's mixture model

has already surpassed the threshold of acceptance, but there are cases in which this

step is not redundant. The next step is an utterance of some acceptance phrase by

Tom. The last step is context update – both conversational participants update their

29

belief in the asserted proposition to a full degree of 1, and the proposition is added to

the common ground19. The following is a discourse table of the steps described above:

Discourse steps Speaker: Tom Negotiation Zone Hearer: Jerry

Step 1: Assertion Tom1 = {PTom() =

MIX1Tom() ≥ high}

NZ1 = NZ0

{ATom P() ≥high}

Jerry1 = {PJerry() =

MIX1Jerry() =

undefined }

Step 2: Mixture-Jerry Tom2 = Tom1 NZ2 = NZ1 Jerry2 = { PJerry() =

MIX2Jerry() ≥ high}

Step 3: Acceptance-

Jerry

Tom3 = Tom2 NZ3 = NZ2

{AJerry P() ≥high}

Jerry3 = Jerry2

Step 4: Mixture-Tom

(redundant)

Tom4 = {PTom() =

MIXTom() ≥ high}

NZ4 = NZ3 Jerry4 = Jerry3

Step 5: Acceptance-

Tom

(redundant)

Tom5 = Tom4 NZ5 = NZ4

{ATom P() ≥high}

Jerry5 = Jerry4

Step 6: Context

update

Tom6 = {PTom() =

MIXTom() = 1}

NZ6 = NZ5 -

{Ax <S,C> | C = }

Jerry6 = { PJerry() =

MIXJerry()=1}

Result: CG' = CG

Figure 1.2: Discourse table

1.3.9 The aim of assertion

19 This model is perhaps somewhat idealized in assuming that once a proposition is accepted all doubts

disappear and it gets a value of 1. Whether this is in fact the case is a matter of further empirical study.

30

As recalled from section 1.3.6, the speech act of assertion is composed of

propositional content and illocutionary force, when the latter is divided into seven

components. The first of which, the Illocutionary point stands for the aim of assertion.

But what is the aim of assertion? The literature has several answers for this question.

Macfarlane (2010), surveying the philosophical literature divides the answers into

four main categories:

(29) a. To assert is to express an attitude.

b. To assert is to make a move defined by its constitutive rules.

c. To assert is to propose to add a proposition to the common ground.

d. To assert is to undertake a commitment to the truth of the asserted

proposition.

The theory proposed in this work suggests a fifth option – to assert is to 'refresh' the

discourse state. The speaker who performs the assertion introduces a new piece of

evidence with regards to the asserted proposition. This, in turn, brings about an

activation of a mixture model by every conversational participant, which causes a

revision of previously assigned probabilities. As a consequence, this can bring about

an update of the asserted proposition to a new probability value by every

conversational participant and the addition of the proposition into the common

ground, but it doesn’t have to. The essential effect of assertion is, thus, not the

addition of a proposition into the common ground, but rather a feasibility check of a

proposition in light of new information. This effect is achieved by virtue of expressing

an attitude, as in (29), with the addition of gradability, i.e different degrees this

attitude may be expressed by.

31

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