LGCS 99DR: Independent Study in Pragmatics Jesse Harris & Meredith Landman September 0, 203 Last class, we discussed the difference between semantics and pragmatics: Semantics The study of the literal meaning of words and phrases, and the way in which they combine to form more complex literal meanings. Pragmatics The study of how literal meaning gives rise to the intended meaning of an utterance in context. Philosopher H. Paul Grice introduced several terms of art, including a fundamental distinction between what was said and what was intended. Although these terms are a little vague, and sometimes disputed, we ll assume an intuitive distinction in this class: What was said The literal meaning of an sentence (semantics) In the sense in which I am using the word say, I intend what someone has said to be closely related to the conventional meaning of the words (the sentence) he has uttered. (Grice, 975: 25) H. Paul Grice What was intended The utterance meaning (pragmatics) How would you identify what was said and what was intended in Meredith s utterance? () A fictional conversation: Jesse: John is such a jerk, don t you think? Meredith: You know, I just can t believe this weather.
Pragmatics deals with the context dependent, non-truth-conditional interpretation of an utterance. To fully understand how pragmatics works, we first need to understand how truth-conditions relate to literal meaning in general. Meaning is notoriously elusive. We follow the advice of philosopher David Lewis, advice which we might (affectionately) call the Forest Gump approach (Meaning is what meaning does). In order to say what a meaning is, we may first ask what a meaning does, and then find something that does that. (Lewis, 970: 22) David Lewis This of course raises the issue what does meaning do? Whatever our theory of meaning ultimately looks like, it should honor the following intuitions: What does meaning do?. 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 think of the relationship between meaning and world in terms of truth conditions: Truth conditions You know the meaning of a sentence S from language L when you know under what conditions S is true. This is all to say that I know what a sentence S means when I know when it is true and when it is false. To know the truth conditions of S doesn t imply that S is true, just that you recognize how the world would look like if it were true. Let s take a look at a concrete, if absurd, example. 2
(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 such things as Martians, and most of them eat cotton candy and adore it, then I m prepared to say that the sentence (2) is true. If any of those conditions are false, e.g., Martians are serverly allergic to cotton candy, then I m confident that (2) is, in fact, false. Turning to the second criterion namely, that meaning allows relationships between expressions, let s turn to examples of semantic relations: contradition, entailment, and synonymy. (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 case illustrates a similar point: each clause in (4) cannot simultaneously be true. (4) Contradiction Dylan is brave and Dylan is not brave. Entailment is quite different than contradition. If sentence S entails sentence T, then T cannot 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 be true, neither one depends on the other. It s perfectly possible, for example, then although John 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? Definitely not! If John brought some fruit, he could have brought an orange instead. 3
When sentences S and T entail the other, then S and T are synonymous. Two sentences are 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 one over the other is arbitrary. The passive version (b) is non-canonical and might be used in special circumstances, for example to highlight Lydia over Sue. These considerations fall under the domain of Information Structure, a topic which we hope to discuss in a few weeks. In addition, terms like soda and pop may be synonymous, but carry different connotations 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 in nature. Logic is a system that is particularly good at treating such relations. There are many kinds of logic: propositional, predicate, modal, fuzzy, temporal, nonmonotonic, etc. These logics share a few things in common. A logic has a set of primitive symbols, rules for generating formulas (expressions) of the language, and rules of inference. We ll focus on propositional logic here. Propositional logic trades in propositions. Just how to define the term proposition is no simple matter, especially among philosophers of language. Let s avoid that debate and settle on a vague, but simple, definition. Proposition A bearer of truth or falsity. Sentences express propositions, but not uniquely so. For example, synonymous sentences will express the same proposition. We might also think that an English sentence might share a proposition with its translation in, say, Hindi. So, though propositions are expressed by sentences, they are also independent of sentences. The sentence Reginald opened the refrigerator only to find an elephant dancing about in the butter expresses a proposition, even if the sentence is never uttered. In the Tractatus, Ludwig Wittgenstein famously proposed that the world is everything that is the case. That is, we could give a complete description of the world if only we cared to list all the true propositions (facts) about the world. 4
But this world could have turned out differently. I ll rely on your commonsense intuitions here to make my point. For example, this class could have been taught by someone else, Jay Atlas say, rather than us. Or I could have worn a different shirt than I did. Or you could have decided to skip class and lay out in the sun. The world is what it is, but you probably think that it could have turned differently than (unless you re a predeterminist or a fatalist). Think of a proposition as something that is potentially true or false depending on how the world actually is. Assume that we have just two types of truth the True (represented as 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 to your left was born in. Here s a proposition: (0) The person sitting next to you was born in March. You re going to be right () or wrong (0) about this there are only two possibilities. So much for propositions. The language of propositional logic consist of a basic vocabulary (atomic propositions) and a syntax for generating well-formed expressions (complex propositions) via sentential connectives. Sentential connective Logical connective (Additional symbols) not and & or if... then... if and only if () Syntax for propositional logic L i. Propositional letters standing for atomic propositions p, q, r, etc. in the vocabulary 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) are formulas in L, too. iv.only that which can be generated by the clauses (i) (iii) in a finite number of steps is a formula in L. 5
Ex.. 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 form all kinds of fascinating fomulas: Ex. 2. Translate the formula into English: (2) 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 use your intuitions. (3) 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 gives us. Truth tables provide a snapshot of all various ways in which the world might be, and allows to evaluate a complex proposition. p 0 Simple truth table All the possibilities for some proposition p. For example, if p = Padma is sick, then p is either true, in which case she is sick, or false, in which case she s not. Truth tables come in handy when considering more complex expressions. A truth table must specify every possible combination. Since we have two values (true and false), the number of rows in a truth table equals 2 n, where n is the number of unique propositions p, q, r and so on. 6
p q r 0 0 0 0 0 0 0 0 0 0 0 0 Hint on specifying truth tables Start with the leftmost atomic proposition, p, and write alternating s and 0 s. Then move to the next atomic proposition, q, in the table and write two s, followed by two 0 s. You have a third proposition, r, so write four s, followed by four 0 s. And so on for 2 n rows. Here we have 3 propositions, p, q, r and so 2 3 = 2 2 2 = 8 rows. You can give the table a rough check by making sure that each column of atomic propositions has the same number of s and 0 s. We can define the sentence operators above (,,,, ) by defining the conditions in which they are true for arbitrary propositional letters p and q. Let s use our natural language intuitions to guide us. p p 0 0 Negation (4) Padma isn t sick Note: Treated as equivalent to It s not the case the Padma is sick. p q p q 0 0 0 0 p q p q 0 0 0 0 Conjunction (5) Padma is sick and Quincy left early Disjunction (6) Padma is sick or Quincy left early 7
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 by logicians. 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 intuition is to translate if as something like supposing that. If the supposition in the antecedent fails, we can t really blame the conditional. Since we re working with a two-valued truthconditional theory, each statement must be either true or false. And to many logicians, we simply 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? Most logicians would say that your prediction is not false at least and given the lack of other options, are content to call it true. At any rate, I ve gone ahead and filled in the relevant rows in advance. p q p q 0 0 0 0 Material conditional (7) If Padma is sick, then Quincy left early The material conditional also gives us a chance to acknowledge that logic does not map onto language use perfectly. Statements of the if... then form are often used in very different ways, for example, to express a causal relationship between antecedent and consequent. There are, as a result, many different proposals for treating conditional statement which are argued to better fit natural language. p q p q 0 0 0 0 Biconditional (8) Padma is sick if and only if Quincy left early Speakers tend not to use the biconditional in this form very often. common locution would be just in case or only if. Perhaps a more 8
Here s another case where propositional logic doesn t totally converge with natural language: p p p 0 Law of double negation (9) Padma is sick It s not the case that Padma isn t sick Finally, we get to cases of logical constancy: tautology and contradiction. p p p p 0 p p p p 0 Tautology A formula φ is a (logical) tautology iff φ is true in all possible situations. (20) Padma is sick iff it s not the case that Padma is not sick Contradiction A formula φ is a (logical) contradiction iff φ is false in all possible situations. (2) Padma is sick and Padma is not sick Ex. 4. How would you test whether two propositions are truth-conditionally equivalent 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. 9