Non-meant or intended

On some tickets we bought the other day, the terms and conditions say: ‘Tickets are non-refundable or transferable’.

Now, I know what they meant to say, but they didn’t achieve it. They intended to say (1).

(1) Tickets are not refundable and not transferable.

They could also have expressed that meaning with (2).

(2) Tickets are not refundable or transferable.

(2) has the same meaning as (1) because refundable or transferable is within the scope of not. The structure is:

(2a) Tickets are not [refundable or transferable].

Not P or Q / Not P and not Q

In (2), or corresponds to the and appearing in (1). This is an example of one of De Morgan’s laws: the negation of a disjunction (or) is a conjunction of negations (and). Thus, the logical formula (3) has the same meaning as (4).

(3) ¬ (P ∨ Q)  meaning: Not (P or Q)

(4) ¬P ∧ ¬Q  meaning: Not P and Not Q

Our tickets didn’t say the same thing as (1) or (2). (5) shows what they said and (5a) shows the structure.  

(5) Tickets are non-refundable or transferable.

(5a) Tickets are [non-refundable] or [transferable]

In (5), as the structure in (5a) shows, transferable is not within the scope of not. That is because non– does not negate the entire phrase refundable or transferable. In fact, it only negates the adjective refundable.   

So, (5) says that either the tickets are non-refundable or they are transferable. Attaching non– to refundable forms a new adjective that negates refundable and that does not negate transferable.

An ambiguity in sentence (2)

I said above that (2) means the same as (1). Actually, that isn’t quite right. (2) is ambiguous. Its structure could be (2a), but the structure could be (2b). (2b) is essentially the same as (5).

(2) Tickets are not refundable or transferable.

(2a) Tickets are not [refundable or transferable].

(2b) Tickets are [not refundable] or [transferable].

The ambiguity arises in (2) because not– could negate either the whole phrase (as in (2a)) or just the adjective refundable, (as in (2b)). In contrast, (5) is unambiguous because the word-building prefix non­– can only negate the adjective.

Conclusion

My main message in this post is to be very careful whenever you write or review a text that contains a negation. It is always important to check that what you intend to negate is what you actually end up negating.

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