Saturday 24 April 2010

Only P if Q v P only if Q

Am I thick or are they doing it on purpose? Here is a sentence from a case brief summarizing a court’s ruling which I was challenged to explain this week:

The recent Court of Appeal case of Sagal v Atelier Bunz GmbH held that an agent with the authority to contract (as opposed to simply the authority to negotiate) is only a commercial agent for the purposes of the Commercial Agents Regulations 1993 if they contract in the name of the principal.

The ambiguity is captured by the following pair of sentences:

(1) A person is only a grease monkey if he has failed school.
(2) A person is a grease monkey only if he has failed school.

Sentences (1) and (2) present two non-equivalent readings. Sentence (1) is false just in case a person is not a grease monkey having earlier failed school. Sentence (2) is false just in case a person is a grease monkey having earlier finished school, and true otherwise.

The position of the adverb ‘only’ in a sentence does make a difference then. In the first sentence ‘only’ modifies the noun, suggesting that being a grease monkey is a lowly job. In the second sentence ‘only’ is part of the expression ‘only if’, which introduces a necessary condition. This means that one doesn’t become a grease monkey without failing school. Another way of looking at sentence (2) is this: A person is not a grease monkey unless he has failed school. Paraphrased again, the sentence says: If a person has not failed school, he is not a grease monkey. Stripped down to Boolean grammar, sentence (2) is equivalent to: Either a person has failed school or he is not a grease monkey. The last paraphrase may sound too radical too many speakers, but the meaning is preserved.

The original sentence then seems to imply that, if one contracts in the name of the principal, one is a commercial agent as opposed to some ‘other’ kind of agent who enjoys a higher status or more privileges.

This is not what was intended though, as we learn from the rest of the case summary. Mr Sagal was seeking to fall within the definition of a commercial agent precisely because commercial agents can claim compensation or indemnity on termination of the agency. The court looked at the evidence and found that, on balance, Mr Sagal was trading in his own name, denying him the status of a commercial agent.

To round off the point, let us return to the sentences about a grease monkey, but let us rewrite them like this instead:

(3) You will be a grease monkey if you fail school.
(4) You will have failed school if you are a grease monkey.

Again, sentence (3) is false when the antecedent (you fail school) is true and the consequent (you will be a grease monkey) is false. Under the same circumstances sentence (4) is true (false antecedent, true consequent). Suppose ‘you are a grease monkey’ is true and ‘you failed school’ is true. Suppose also that ‘you failed school’ is false and it is equally false that ‘you are a grease monkey’. What then? Then we have a biconditional, or material equivalence:

(5) You will be a grease monkey if and only if you fail school.

- a statement which is true when antecedent and consequent have the same truth value: both true or both false.

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