LGCS 199DR: Independent Study in Pragmatics

Jesse Harris & Meredith Landman

September 10, 2013

Last class, we discussed the difference between semantics and pragmatics:

Semantics The study of the literal meaning of wordsand phrases, and the way in which theycombine to form more complex literalmeanings.

Pragmatics The study of how literal meaning gives riseto the intended meaning of an utterance incontext.

Philosopher H. Paul Grice introduced several terms of art, including a fundamentaldistinction between what was said and what was intended. Although these terms are alittle vague, and sometimes disputed, we’ll assume an intuitive distinction in this class:

H. Paul Grice

What was said The literal meaning of an sentence (semantics)

“In the sense in which I am using the word say, I intendwhat someone has said to be closely related to the con-ventional meaning of the words (the sentence) he hasuttered.” (Grice, 1975: 25)

What was intended The utterance meaning (pragmatics)

How would you identify what was said and what was intended in Meredith’s utterance?

(1) A fictional conversation:

Jesse: John is such a jerk, don’t you think?

Meredith: You know, I just can’t believe this weather.

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Pragmatics deals with the context dependent, non-truth-conditional interpretation of anutterance. To fully understand how pragmatics works, we first need to understand howtruth-conditions relate to literal meaning in general.

Meaning is notoriously elusive. We follow the advice of philosopher David Lewis, ad-vice which we might (affectionately) call the Forest Gump approach (Meaning is whatmeaning does).

David Lewis

“In order to say what a meaning is, we may first askwhat a meaning does, and then find something thatdoes that.” (Lewis, 1970: 22)

This of course raises the issue what does meaning do? Whatever our theory of meaningultimately looks like, it should honor the following intuitions:

What does meaning do?

1. Meaning describes the world.2. Meaning allows relationships between expressions: contradiction, entailment, and

synonymy.3. Meaning is productive. Once you know the meaning of two things, you usually

have a darn good chance of knowing what they mean when combined.

The first criterion can be taken in a couple of different ways. Semanticists tend to thinkof the relationship between meaning and world in terms of truth conditions:

Truth conditions You know the meaning of a sentence S fromlanguage L when you know under whatconditions S is true.

This is all to say that I know what a sentence S means when I know when it is trueand when it is false. To know the truth conditions of S doesn’t imply that S is true, justthat you recognize how the world would look like if it were true. Let’s take a look at aconcrete, if absurd, example.

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(2) Most Martians feast on cotton candy.

I’ll be honest: I have no idea if Martians actually eat cotton candy, let alone feast on it(let alone whether there are actually such things as Martians). But if there were suchthings as Martians, and most of them eat cotton candy and adore it, then I’m preparedto say that the sentence (2) is true. If any of those conditions are false, e.g., Martians areserverly allergic to cotton candy, then I’m confident that (2) is, in fact, false.

Turning to the second criterion – namely, that meaning allows relationships betweenexpressions, let’s turn to examples of semantic relations: contradition, entailment, andsynonymy.

(3) Contradiction

a. All Martians feast on cotton candy.

b. Some Martians don’t eat cotton candy.

I know that this is a contradiction, even without knowing whether each sentence is true.Relationships between sentences holds by virtue of their form. The more subdued caseillustrates a similar point: each clause in (4) cannot simultaneously be true.

(4) ContradictionDylan is brave and Dylan is not brave.

Entailment is quite different than contradition. If sentence S entails sentence T, then Tcannot be true without S also being true. So, if S is true, then T must also be true.

(5) Entailment

a. Three detectives failed to find the killer.

b. Two detectives failed to find the killer.

(6) Entailment

a. John brought an apple for lunch.

b. John brought a fruit for lunch.

It’s not enough for both sentences to be true. Although both sentences in (7) might betrue, neither one depends on the other. It’s perfectly possible, for example, then althoughJohn brought an apple, Cindy has brought nothing at all.

(7) John brought an apple for lunch and Cindy brought some crackers.

Further, just because S entails T, doesn’t necessarily mean that T entails S. For example,switch (a) and (b) in (6) above. Does bringing fruit entail bringing an apple? Definitelynot! If John brought some fruit, he could have brought an orange instead.

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When sentences S and T entail the other, then S and T are synonymous. Two sentencesare synonymous just in case one cannot be true with the other also being true.

(8) Synonymy

a. Sue hugged Lydia.

b. Lydia was hugged by Sue.

These sentences describe the exact same scenario. But this is not to say that picking oneover the other is arbitrary. The passive version (b) is non-canonical and might be usedin special circumstances, for example to highlight Lydia over Sue. These considerationsfall under the domain of Information Structure, a topic which we hope to discuss in afew weeks. In addition, terms like soda and pop may be synonymous, but carry differentconnotations or be preferred for reasons of dialect:

(9) Synonymy

a. Sam drank a soda.

b. Sam drank a pop.

Again, the semantic relations of contradiction, entailment, and synonymy are semantic innature. Logic is a system that is particularly good at treating such relations.

There are many kinds of logic: propositional, predicate, modal, fuzzy, temporal, non-monotonic, etc. These logics share a few things in common. A logic has a set of primitivesymbols, rules for generating formulas (expressions) of the language, and rules of infer-ence. We’ll focus on propositional logic here.

Propositional logic trades in propositions. Just how to define the term proposition is nosimple matter, especially among philosophers of language. Let’s avoid that debate andsettle on a vague, but simple, definition.

Proposition A bearer of truth or falsity.

Sentences express propositions, but not uniquely so. For example, synonymous sen-tences will express the same proposition. We might also think that an English sentencemight share a proposition with its translation in, say, Hindi. So, though propositionsare expressed by sentences, they are also independent of sentences. The sentence Regi-nald opened the refrigerator only to find an elephant dancing about in the butter expresses aproposition, even if the sentence is never uttered.

In the Tractatus, Ludwig Wittgenstein famously proposed that “the world is everythingthat is the case.” That is, we could give a complete description of the world if only wecared to list all the true propositions (facts) about the world.

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But this world could have turned out differently. I’ll rely on your commonsense in-tuitions here to make my point. For example, this class could have been taught bysomeone else, Jay Atlas say, rather than us. Or I could have worn a different shirt than Idid. Or you could have decided to skip class and lay out in the sun. The world is whatit is, but you probably think that it could have turned differently than (unless you’re apredeterminist or a fatalist).

Think of a proposition as something that is potentially true or false depending on howthe world actually is. Assume that we have just two types of truth – the True (representedas 1 or >) and the False (represented as 0 or F or sometimes even ⊥).

For example, chances are good that you don’t know what month the person sitting toyour left was born in. Here’s a proposition:

(10) The person sitting next to you was born in March.

You’re going to be right (1) or wrong (0) about this – there are only two possibilities.

So much for propositions. The language of propositional logic consist of a basic vocabu-lary (atomic propositions) and a syntax for generating well-formed expressions (complexpropositions) via sentential connectives.

Sentential connective Logical connective (Additional symbols)not ¬ ∼and ∧ &or ∨

if . . . then . . . → ⊃if and only if ↔ ≡

(11) Syntax for propositional logic L

i. Propositional letters standing for atomic propositions p, q, r, etc. in the vocabu-lary of L are formulas in L.

ii. If p is a formula in L, then ¬p is a formula in L, too.

iii.If p and q are formulas in L, then (p ∧ q), (p ∨ q), (p → q), and (p ↔ q) areformulas in L, too.

iv.Only that which can be generated by the clauses (i)–(iii) in a finite number ofsteps is a formula in L.

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Ex. 1. Which of the following are well-formed formulas of L?

a. ¬(¬p ∨ q) e. p→ ((p→ q))b. p ∨ (q) f. (p→ (p→ q)→ q)c. ¬(q) g. (¬p ∨ ¬¬p)d. ((p→ p)→ (q→ p)) h. (p ∨ q ∨ r)

For example, let p represent Padma is sick and q represent Quincy left early. We can formall kinds of fascinating fomulas:

Ex. 2. Translate the formula into English:

(12) a. p ∨ q

b. ((p ∧ ¬q)→ p)

c. (p↔ (q ∨ (p ∧ ¬p)))

Ex. 3. Translate the English sentences into propositional logic. You may have to useyour intuitions.

(13) a. If Padma isn’t sick, then Quincy didn’t leave early.

b. Padma is sick or Padma isn’t sick but Quincy left early.

c. Because Padma is sick, Quincy left early.

We also need a way to interpret all the expressions that our propositional language givesus. Truth tables provide a snapshot of all various ways in which the world might be,and allows to evaluate a complex proposition.

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Simple truth tableAll the possibilities for some proposition p. For example, ifp = Padma is sick, then p is either true, in which case she issick, or false, in which case she’s not.

Truth tables come in handy when considering more complex expressions. A truth tablemust specify every possible combination. Since we have two values (true and false), thenumber of rows in a truth table equals 2n, where n is the number of unique propositionsp, q, r and so on.

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p q r1 1 10 1 11 0 10 0 11 1 00 1 01 0 00 0 0

Hint on specifying truth tablesStart with the leftmost atomic proposition, p, and write alter-nating 1’s and 0’s. Then move to the next atomic proposition,q, in the table and write two 1’s, followed by two 0’s. Youhave a third proposition, r, so write four 1’s, followed by four0’s. And so on for 2n rows. Here we have 3 propositions,p, q, r and so 23 = 2× 2× 2 = 8 rows.

You can give the table a rough check by making sure thateach column of atomic propositions has the same number of1’s and 0’s.

We can define the sentence operators above (¬,∨,∧,→,↔) by defining the conditionsin which they are true for arbitrary propositional letters p and q. Let’s use our naturallanguage intuitions to guide us.

p ¬p1 00 1

Negation

(14) Padma isn’t sick¬

Note: Treated as equivalent to It’s not the case the Padma is sick.

p q p ∧ q1 10 11 00 0

Conjunction

(15) Padma is sick and Quincy left early∧

p q p ∨ q1 10 11 00 0

Disjunction

(16) Padma is sick or Quincy left early∨

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So far so good. The next one is tricky. Consider the case where Padma isn’t sick (p = 0).What do we say about the conditional? This situation has been heavily debated bylogicians. The classical view is that when the antecedent (on the left of the conditional)is false, the entire conditional statement is true, regardless of whether the consequent(on the right side of the conditional) is true or false. One way to justify this intuitionis to translate if as something like supposing that. If the supposition in the antecedentfails, we can’t really blame the conditional. Since we’re working with a two-valued truth-conditional theory, each statement must be either true or false. And to many logicians, wesimply can’t call these kinds of statements false if the supposition doesn’t come through.

A related way to view this decision is to think of the conditional as a kind of wager,“When p happens, I’ll bet that q”. If p doesn’t happen, do we lose the bet? Mostlogicians would say that your prediction is not false at least – and given the lack of otheroptions, are content to call it true.

At any rate, I’ve gone ahead and filled in the relevant rows in advance.

p q p→ q1 10 1 11 00 0 1

Material conditional

(17) If Padma is sick, then Quincy left early→

The material conditional also gives us a chance to acknowledge that logic does not maponto language use perfectly. Statements of the if . . . then form are often used in verydifferent ways, for example, to express a causal relationship between antecedent andconsequent. There are, as a result, many different proposals for treating conditionalstatement which are argued to better fit natural language.

p q p↔ q1 10 11 00 0

Biconditional

(18) Padma is sick if and only if Quincy left early↔

Speakers tend not to use the biconditional in this form very often. Perhaps a morecommon locution would be just in case or only if.

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Here’s another case where propositional logic doesn’t totally converge with natural lan-guage:

p ¬p ¬¬p10

Law of double negation

(19) Padma is sickIt’s not the case that Padma isn’t sick

Finally, we get to cases of logical constancy: tautology and contradiction.

p ¬¬p p↔ ¬¬p10

TautologyA formula φ is a (logical) tautology iff φ is true in all possiblesituations.

(20) Padma is sick iff it’s not the case that Padma is not sick

p ¬p p ∧ ¬p10

ContradictionA formula φ is a (logical) contradiction iff φ is false in allpossible situations.

(21) Padma is sick and Padma is not sick

Ex. 4. How would you test whether two propositions are truth-conditionally equiva-lent using truth tables? Take the following case as an example:

¬(p ∨ q) and (¬p ∧ ¬q)

Next week: We’ll talk about how Grice proposed to treat cases in which the logical,literal meaning diverged from what was conveyed by an utterance.

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