Logic & Conversation – H.P. Grice

•	There appears to be a divergence between the formal devices of logic (i.e. ~, ^, v, (x), etc.) and their natural language counterparts, “not”, “and”, “or”, “all”, etc.

•	Grice holds that this assumption is a common mistake that “arises from an inadequate attention to the nature… of the conditions governing conversation” (p. 166)

•	Conversations (a.k.a. “talk exchanges”) are generally cooperative efforts between participants who constrain their “moves” (i.e. utterances on their “turn”) according to a mutually accepted purpose, topic, (+last utterance)

•	Pay particular attention to conversational implicature, where what is literally said is not what is actually meant (which can be represented with generative semantics..?)
•	
Cooperative Principle (a.k.a. CP): “Make your conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged.” (p. 167)

•	The four maxims of conversational cooperation:
o	Quantity: Be as informative as is required without being too informative (i.e. Goldilocks: not too little or too much, but juuust right)

o	Quality: Say only what you believe to be true and only what you have adequate evidence for

o	Relation: Be relevant to the topic at hand

o	Manner: Be perspicuous 
•	I.e. don’t be ambiguous, obscure, etc.
•	Grice’s fundamental question:
o	What basis do we have for assuming that people follow the Cooperative Principle & 4 maxims?

o	He wants to show that, not only do we do it, but it is reasonable for us to follow them insofar as, 
•	Given that people care about the goals of communication (e.g. exchanging information, influencing beliefs, etc.) 
•	Some talk exchanges can only be understood to meet such goals if exchanges assumed to be following the CP & 4 maxims

o	Specifically, Grice is trying to show a connection between (1) the CP & 4 maxims, and (2) conversational implicature, such that (2) can only be understood in terms of (1)

•	
Conversational Implicature: Someone who says that p may be said to have conversationally implicated that q through the failure, or potential failure, to uphold one or more of the maxims in such a way that…

•	She is presumed to at least be following the CP

•	She, the speaker, thinks that the implication is required to make what she actually said be an utterance that upholds the Cooperative Principle

•	She thinks that (i) the hearer can work out the implication that q, and (ii) the hearer can expect the speaker to think that he can work out the implication that q

•	
Distinction between conversational & conventional implicature: conversational implicature must be capable of being worked out 
o	I.e. intuitive understanding must be replaceable by an argument
o	Otherwise, it’s conventional implicature
o	E.g. “It’s raining cats and dogs” (Quality?)
- (vs. “It’s raining tigers and wolves.”)
- (What about an ironic usage? 2 violations…)

•	General pattern for “working it out” (p. 170):
o	She said that p
o	No reason to suppose she’s not following CP
o	She would therefore have to think that q
o	She knows, etc. that I can see that q is required
o	She hasn’t tried to stop me from thinking that q
o	She is intending/willing to have me think that q
o	Therefore, she has implicated that q	

3 Kinds of Examples
•	A-type: no violation
o	S1 is in her car and sees S2 walking by.

S1: “I’m out of gas.”  
S2: “There’s a garage around the corner.”
•	It would be a violation of the maxim of Relation (+Quality?) if S2 didn’t think that the garage was likely open and selling gas

•	B-type: a clash between maxims
o	S1 is planning to visit France and would like to see his friend X while he’s there if he can.

S1: “Where does X live?”
S2: “Somewhere in the south of France.”
•	Maxim of Quantity is violated because S2 isn’t detailed enough

•	Implication is that S2 can’t be more specific without violating the Maxim of Quality (i.e. he doesn’t know where X lives, specifically)

3 Kinds of Examples, cont’d
•	C-type: “flouting”/blatantly violating maxim(s)
o	Quantity: Prof. writes a letter of reference for his student saying, “X attends class regularly.”
•	Prof. can’t be unable to say more
•	Implies X is a bad student
o	Quality: 
•	Irony: S says, “X is a fine friend,” when X betrayed the speaker.

•	Metaphor: “You’re the cream in my coffee / apple of my eye.”
o	Can’t mean the opposite, as in Irony, because it’s a truism, so it’s probably a fanciful feature of the substance discussed

•	Hyperbole:
o	Every nice girl loves a sailor
o	That hike gave me a stroke!

3 Kinds of Examples, cont’d
•	C-type: “flouting”, cont’d
o	Relation:
•	S1: “Mrs. X is an old bag.”
S2: “What fine weather!”
o	Manner:
•	Ambiguity: General captures city of Sind, writes back to HQ, “Peccavi” = “I have sinned.”

•	Obscurity: Speaking in front of a child about something you don’t want them to understand

•	Brevity: (How about under Quantity?)
o	“X sang Jingle Bells.”
o	“X produced a series of sounds that corresponded closely with the score from Jingle Bells.”
•	Implies X can’t sing.

Conversational Postulates – Gordon & Lakoff

•	Purpose: Formalize & incorporate conversational postulates into a theory of generative semantics

•	Call the logical structure of a sentence L 

•	Call the conversational postulates CoP

•	The application of conversational postulates depends on contexts, so we conceive of ‘conversational implication in a class of contexts, CONi’ as follows:
o	L conversationally implies P in CONi    IFF CONi U CoP U {L} ╟ P 
o	I.e. (‘In context CONi, given the conversational postulates, CoP, L entails P.’)

•	
Consider the following meaning postulates:
a.	SINCERE(a,REQUEST(a,b,Q))  WANT(a,Q)
b.	SINCERE(a,REQUEST(a,b,Q)) 
 ASSUME(a,CAN(b,Q))
c.	SINCERE(a,REQUEST(a,b,Q)) 
 ASSUME(a,WILLING(b,Q))
d.	SINCERE(a,REQUEST(a,b,Q))  ASSUME(a,~Q)
Where Q is of the form FUT(DO(b,R))=[‘b will do act R’]

•	In other words, if a sincerely requests of b that b do R, then (a.) a wants b to do R, (b.) a assumes that b can do R, (c.) a assumes that b would be willing to do R, and (d.) a assumes that b will not do R without a request.

•	These determine a set of conversational postulates for English (and other languages, too)
•	
Consider the following sentences:
a.	I want you to take out the garbage.
b.	Can you take out the garbage?
c.	Would you be willing to take out the garbage?
d.	Will you take out the garbage?
•	One can convey a request by (a.) asserting a speaker-based sincerity condition, or (b-d.) questioning a hearer-based sincerity condition.

•	So, we get the following conversational postulates
a.	SAY(a,b,WANT(a,Q))*  REQUEST(a,b,Q)
b.	ASK(a,b,CAN(b,Q))*  REQUEST(a,b,Q)
c.	ASK(a,b,WILLING(b,Q))*  REQUEST(a,b,Q)
d.	ASK(a,b,Q)*  REQUEST(a,b,Q)
Where Q is of the form FUT(DO(b,R))=[‘b will do act R’]

•	Asserting the appropriate speaker-based sincerity condition can extend to other performatives
a.	SINCERE(a,SAY(a,b,Q))  BELIEVE(a,Q)
b.	SINCERE(a,PROMISE(a,b,Q))  INTEND(a,Q)
Question “Can you take out the garbage?” is ambiguous.
o	It could be a real question.
o	It could convey a request to do so.
o	But, it can only convey a request if it is assumed by the hearer that the sentence is NOT a literal question.

•	This is the meaning of the asterisk (*), used previously

•	So we get:
Vp(a,b,S)* = Vp(a,b,S) AND ~INTEND(a,CONVEY(a,b,Vp(a,b,S))) AND ASSUME(b,~INTEND(a,CONVEY(a,b,Vp(a,b,S))))
Where Vp is a performative predicate.

•	Then we have something like: 	
ASK(a,b,Q) AND ~INTEND(a,CONVEY(a,b, ASK(a,b,Q))) AND ASSUME(b,~INTEND(a, CONVEY(a,b,ASK(a,b,Q))))  REQUEST(a,b,Q)
•	
Suppose I meet a friend on the street and say:
i.	Your wife is faithful.

•	If one is in a conversational situation where statements are meant to inform (i.e. not making small talk), one normally says a thing only if one assumes the other person doesn’t already know or take it for granted.

We can derive this:
•	Part of what it means to intend to inform is:
o	SAY(a,b,Q)*  INTEND(a,CAUSE(a,COME-ABOUT(KNOW(b,Q))))

•	Given the meaning postulate for CAUSE:
o	CAUSE(a,S)  S
•	And given an informal meaning of INTEND:
o	INTEND(a,COME-ABOUT(R)) ASSUME(a,~R)
•	We get the result:
o	SAY(a,b,Q)*  ASSUME(a,~KNOW(b,Q))
So, in Conclusion…
•	Don’t tell your friend that his wife is faithful!
o	It should be part of your understanding of the [social] context that this is taken for granted
o	Therefore, you can’t help but create the implication that you mean something else

•	We developed an outline of a Gricean explanation of the divergence between formal and natural languages using the Cooperative Principle and the four maxims, with conversational implicature as our subject material
•	Then we took it one step further and tried to apply conversational postulates to a formal semantics, with a look at forms of request and a particular social gaffe

•	Do you see any difficulties with this approach? 
- Representing the context(s)? (E.g. problem of common sense: wives are faithful, etc.) 
- Size of the rule-base and search space?
•	Any other questions, thoughts, or comments?