1. Review from long ago

2. Review from long ago
FOPC definition of “the” (Bertrand Russell):

3. Review from long ago
Truth tables for V (or) and  (material condition)
Vacuous truth
"For any integer x, if x > 5 then x > 3." This statement is true non-vacuously (since some integers are greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 then 2 > 3".
"All my children are cats." is a vacuous truth when spoken by someone without children.

4. Review from last class
Increase parameters (multiple coordinate approach)
When do we stop?
Intensionality
Understanding modal locutions requires two components:
The modal base: range of possibilities to be considered
An ordering source: ranks the modal base w/rt some standard(s)
Discourse is dynamic
Assertions: add propositional content to the common ground
Context
The lambda operator
Useful for “substituting in” individuals: λx.hungry(x)[John]

5. Why stop there? The lambda operator
Useful for “substituting in” individuals: λx.hungry(x)[John]
Useful for “substituting in” predicates too: λP.P(John)[hungry]
1st order logic: quantification over variables
2nd order logic: quantification over predicates
3rd order logic: quantification over sets of predicates …
nth order logic: quantification over sets that are nested n times
Higher-order logic: union of all of the above

6. Contextuality

7. Basic motivation Indexicals (I, here, etc.) are important
Truth value changes with context
Circumstances can be parameterized
Context is a crucial parameter for interpretation
Discourse participants
Common ground
Useful for explicitizing presuppositions, preconditions, entailments, effects, inferences, etc.

8. Examples of indexicality (deixis)
Pronominal reference
Spatial orientation
Perspective on a situation
Temporal adverbs, locatives
How many coordinates?
Just adding them to the model directly might get to be intractable

9. The role of quantification
Modals: quantifying over possible worlds or circumstances
Temporal adverbs: quantifying over times
IPC: add instants to a world
Close relation between context and perception; human perception is bounded

10. Levels of meaning Interpretation: sensitive to context
Intensionality: specifying set of worlds, times, contexts
Truth-value determination
Context-dependent properties
Truth
Validity
Entailment

11. Ambiguity and validity
Pragmatic validity: holds over every possible context
Necessary truth: fixed context, holds over every possible world
Semantic ambiguity: contextual mapping not a determining factor
I am hungry.  not sem. ambig.
Every woman loves some man.  is

12. Presupposition (again)
S  p iff:
S  p, and
S  (p is already part of background)
Context must agree for felicitous assertion
Empirical tests:
Being backgrounded: implications that survive negation, interrogation, and if->then (the S family)
Being taken for granted
Assumed truth is a precondition for felicitous utterance
Constrains set of applicable contexts for p
Entailment vs. presupposition

13. Factive verbs Introduce presuppositions
“x discovered p” is T  iff p is T

14. Implicature (again) Conventional implicature
Conventional in nature
Not strictly truth-conditional
Relies heavily on background
Relies on inherent meaning
Conversational implicature
Dynamically emerge in conversation
Gricean maxims

15. Triggering and projecting
Two ways of triggering presuppositions: conversationally and conventionally
What about presupposition projection?
i.e. accounting for presuppositions in a sentence from the “inside out”?
Filter: filters out presupp’s
If [Linda]i lost something, what [she]i lost was not valuable.
Hole: lets presupp’s survive (e.g. factive verbs)
Plug: block presupp’s and their inheritance (e.g. “said CP”)
[Melissa]i said that [she]i knows that Elvis lives.
Caveat: all plugs leak

16. A richer framework (attempt 1)
Model: as before, except new element: speakers
Proposition: <w,i,s>  T/F
2 stages for sem interp:
Relativize interpretation to contexts (i.e. characters of an expression)
Assign extensional value to each type
Generalize this to not just speakers, but whole contexts (w/ hearer, location, etc.)
Valuation function V does work of specifying appropriate extensions

17. A richer framework (attempt 2)
Context
Determines what is said
Tells us who is speaking, etc.
Factors relevant for interpreting indexicals
Circumstances
Alternatives to consider in determining the truth value of what is said
[[I am hungry.]]
We don’t consider all possible speakers in the universe of discourse.
We do consider all possible circumstances w/rt the particular speaker.
Call this the “two-stage” approach

18. The two stages (for attempt 2)
1) Relativize the interpretation to contexts
Assign each expression a function: determine for a given context an intensional value per the last chapter.
2) As before, intensions will assign extensional values of the appropriate type relative to each circumstance.
Intensions: mappings from circumstances (<w,i>) to extensions
Expression characters: mappings from contexts to intensions

19. Specifying contextual information
c: a new parameter for the context
sp(c): speaker ∈ U
adr(c): addressee ∈ U
locn(c): n’th location
demlocn(c): n’th demonstrative location
mdb(c): modal base for c
ordsrc(c): ordering source for c
g() can sort this all out (of course!)
For interpretation of variables (traces, pronouns, etc.)

20. Enriched model for attempt 2
Note: Context, circumstance are separate parameters for V.

21. Integrating context into the model
As usual, V assigns denotations for constants and predicates
But, of course, with the new context parameter too

22. Three levels of processing
1) Fix the utterer.
2) Determine the intension of the sentence.
Set of times and worlds where the predicate holds
3) Determine the truth value of the sentence.
Based on worlds, times being talked about

23. Semantics and pragmatics
Pragmatic validity: looks at every possible context
Necessary truth: keeps the context fixed and looks at every possible world

24. Classifying sentences
I am an alien. (pragmatically valid, not necessarily true)

25. Presupposition
Now we can revisit the notion with a more formal, objective means of specifying what it is
Before: S presupposes p if uttering S imples p, PLUS implies that p is already part of the background against which S is considered
A little bit hand-wavy
Now: presuppositions of S constrain/limit the class of contexts C relative to a felicitous utterance of S
Presuppositions of S must be satisfied be a context c in order to be assertible (i.e. for an utterance of S to be felicitous)
Otherwise, HWAM…

26. Presuppositions have to be:
Backgrounded
The P family: S presupposes p only if p is implied by S in: S.
It is not the case that S.
Is it the case that S?
If S, then S’.
Taken for granted
1 a) Lee kissed Jenny. b) Lee touched Jenny.
2 a) Mary has a child.
b) Mary has exactly one child.
b) implication is: an entailment (1b) vs. conversational implicature (2b).
Neither b) is backgrounded or taken for granted (i.e. not presupposition)

27. Implicatures Conventional Conversational
Depend on meaning (e.g. lexical meaning)
Conversational
Depend on conversational dynamics
A entails B (if A is true, B is true)
A presupposes B (B is backgrounded and taken for granted by A)
A conventionally or conversationally implicates B (B follows from the interaction of the truth conditions of A together with either linguistic conventions or the proper use of A or general principles of conversational exchange)

28. The context set Live possibilities left open in the common ground
As common ground grows, context set shrinks
But c* can never be empty

29. Accommodation
If, during a conversation, something is said that requires presupposition p to be acceptable, BUT it’s not presupposed at that point, THEN presupposition comes into existence.

30. Filters, holes, and plugs (again)
Filters: and, or, if…then
Projection: how do presuppositions get passed up to the whole sentence?
“p and q”: inherits all presuppositions from p and q except for any presuppositions of q that are contextually entailed by p
a) If Keith is married to Linda, then he has children. b) Keith is married to Linda, and all his children are asleep.
If a) is in the common ground, then b) filters out the presupposition that he has some children.

31. Filters, holes, and plugs (again) (2)
Hole: Allows all presuppositions to pass up freely.
Negation is a hole
Plug: Doesn’t allow any presuppositions to pass up.

32. Dynamic sentential semantics
Conversation (narrative, etc.) is dynamic
Review: c* is the context set
Uttering a sentence S in a context c leads to a new context c′.
Assume a function mapping c* to c* ∩ p
It would exclude from c* all situations where p is false.
Its effect: comgrd(c′) = comgrd(c) ∪ {p}
Let c + S designate the context produced by uttering S in c. Then the context-change potential function |S|g,c maps c* onto a new context set |S|g,c(c*).

33. Dynamic sentential semantics
New mapping function: |S|g,c
Called the context-change potential
Maps c* of its utterance onto a new context set |S|g,c(c*)

34. Who killed Kermit? (disjunction)
S1p: Kermit was killed by someone.
c*: Kermit was killed by either Ms. Piggy or the butler.
S1: It was the butler who killed Kermit.
S1i is the relevant proposition.
Shaded area: context set of c+S1 (i.e. |S1|(c*))

35. Who killed Kermit? (the butler’s regret)
S1 as before
c*: Kermit was killed by either Ms. Piggy or the butler.
S2: The butler regrets that he killed Kermit.
c*+S1 in included in S2p
i.e. S2 is admitted into c+S1 but not into the original c*
c*+S1 entails S2p; after S2 it is restricted to (c*+S1)+S2
S2 by itself would be infelicitous

36. Negation not S: subtract from c* the worlds where S is true
|not S|(c*) = c* - |S|(c*)
c* + [not S] = c* - [c*+S]
S0P: Ms. Piggy killed someone.
S0: It was Kermit that Ms. Piggy killed.
S1: It wasn’t Kermit who Ms. Piggy killed.
#S1 in c*
S2: It wasn’t Ms. Piggy who killed Kermit.
S3: Kermit was killed by someone.

37. Conjunction (Keith, Joan, and sleeping children)

38. Do the walkthrough for these in your own words: