In Chapter 9 we presented evidence in support of Grice’s analysis of the English words and and or. Grice suggested that the lexical semantic content of these words is actually equivalent to their logical counterparts (∧ and ∨), and that apparent differences in meaning are best understood as conversational implicatures. This approach seems to work fairly well for those two words; could a similar approach work for English if ? Grice argued that it could, specifically proposing that the lexical semantic content of English if is equivalent to the material implication operator (→). However, there are a number of reasons to believe that this approach will not work for if.
First, if if really means material implication, then the truth table for material implication predicts that the sentences in (21) should all be true. (Recall that p→q is only false when p is true and q is false.) However, this does not match our intuitions about these sentences; most English speakers are very reluctant to call any of them true.
(21) a. If Socrates was a woman then 1 + 1 = 3.17
b. If the Amazon flows through Paris then triangles have three sides.
c. If the Chinese invented gunpowder then Martin Luther was German.
What makes these sentences seem so odd is that there is no relationship between the antecedent and consequent. Whatever if means, it seems to require that some such relationship be present. Grice argued that this inference of relationship between antecedent and consequent is only a conversational implicature. Several other authors have also proposed that the semantic content of if is simply material implication, and that the apparent differences between the two are pragmatic rather than semantic in nature. Other authors have tried to account for the requirement of relationship between antecedent and consequent by suggesting that if p then q expresses the claim that p→q is true in all possible worlds, i.e., under any imaginable circumstances.18 But any attempt to derive the meaning of if from material implication must deal with a number of problems.
As discussed in Chapter 4, the meaning of the material implication operator is entirely defined by its truth table. We need to know the truth values for both p and q (but nothing else) before we can determine the truth value for p→q. But this does not match our judgments about the truth of English conditionals. It would be entirely possible for a competent native speaker to believe that sentence (22) is true without knowing whether either of the two clauses alone expresses a true proposition. What is being asserted in (22) is not a specific combination of truth values, but a relationship between the meanings of the clauses.19
(22) If this test result is accurate, your son has TB.
This point is further demonstrated by the fact that, in addition to statements, questions and commands may also appear as the consequent clause of a conditional, as illustrated in (23). This is significant because questions and commands cannot be assigned a truth value.
(23) a. If you are offered a fellowship, will you accept it?
b. If you want to pass phonetics, memorize the IPA chart!
Finally, as we will argue in more detail below, the antecedent in a speech act conditional like (24) does not specify conditions under which the consequent is true, but rather conditions under which the speech act performed by the consequent may be felicitous.20
(24) a. If you have a pen, may I please borrow it?
b. If you want my advice, don’t invite George to the party!
c. If I may say so, you do not look well.
Even if we focus only on truth values, the logical properties of → make predictions which do not seem to hold true for English if. For example, it is easy to show (from the truth table for →) that ¬(p→q) logically entails p. So if the semantic value of if is material implication, anyone who believes that (25a) is false is committed to believing that (25b) is true. However, it does not seem to be logically inconsistent for a speaker to believe both statements to be false.
(25) a. If I win the National Lottery, I will be happy for the rest of my life.
b. I will win the National Lottery.
Counterfactuals raise a number of special problems for the material implication analysis. We will mention here just one famous example, shown in (26).21 It is easy to show that p→q logically implies (p∧r) → q. So if the semantic value of if is material implication, anyone who believes that (26a) is true should be committed to believing that (26b) is true. However, it does not seem to be logically inconsistent for a speaker to believe the first statement to be true while believing the second to be false.
(26) a. If kangaroos had no tails, they would topple over.
b. If kangaroos had no tails and they used crutches, they would topple over.
Many other similar examples have been pointed out, and various solutions have been proposed.22 As we noted in §19.1 above, even if material implication is not logically equivalent to English if, that does not mean that it is irrelevant to natural language semantics. It will always be an important part of the logical metalanguage that semanticists use. But in view of the many significant differences between material implication and English if, it seems reasonable to look for some other way of capturing the meaning of if.
17 http://en.Wikipedia.org/wiki/Material_conditional
18 C. I. Lewis (1918), cited in von Fintel (2011).
19 The material in this paragraph and the next are based on observations made by Podlesskaya (2001).
20 In order to account for such examples under the assumption that if is equivalent to the material implication operator, we could interpret them as conditional speech acts; so (24c) would have an interpretation something like: “If I am permitted to say so, then I hereby assert that you do not look well.” But in fact someone who says (24c) seems to be asserting the consequent unconditionally; it is only the felicity of the assertion that is conditional.
21 This example comes from D. Lewis (1973b).
22 See Von Fintel (2011) for a good summary; see also Gazdar (1979: 83–87); Bennett (2003: ch2–3).
