Strong and weak readings

If pressed to explain my way out of a tight corner in English, I find that the distinction between the strong and weak reading of some English structures is often a very handy tool. Once in that mode, I further discover that its application can be far wider than is usually suggested in logic courses.

The textbook example is that of a disjunction in propositional logic. The inclusive sense of ‘or’ traditionally gets a weak reading; the exclusive sense of ‘or’ – a strong reading. The standard reading in the inference mechanism is that of the inclusive ‘or’. Reasoning with the exclusive ‘or’ leads to fallacies.

p or q
p
Therefore, not q.

If the argument is: Either the coin comes up heads or it comes up tails. It has come up heads. Therefore, it hasn’t come up tails; the reasoning works. But if the argument is: Either a cat or a fox has been getting at the chickens. A cat has been getting at the chickens. Therefore, a fox hasn't; we cannot be absolutely sure. Exclusive disjunction is non-validating.

Another example is the choice of quantifier in predicate logic. If we choose to turn the sentence: If something is good, it is forbidden, into the language of FOL, we get:

(x)(x is good ⊃ x is forbidden)

and the reading is that if ‘anything’ is good, it is forbidden. If we choose the existential quantifier:

(∃x)(x is good ⊃ x is forbidden)

the reading is that either there is something that is not good, or it is forbidden – a much weaker reading by all accounts.

But aside from these examples, there are sentences which seem to hover on the border between well-formed and ill-formed, as the second one in this pair:

There will be complaints until someone does something about it.
There will be complaints before someone does something about it.

The first sentence clearly gets a strong reading. It seems to say that someone doing something about it, whatever that ‘it’ is, is a necessary condition for the complaints ceasing. The second sentence is merely a temporal sequence of events: complaints first, someone doing something about it later.

Or, take for example the pair:

I have nearly finished.
I’m not far off finishing.

In neither case do we actually indicate completion, nor is it possible to say that in one case we are further along in getting to the end than in the other, yet the first sentence seems to have more force.

A classic case is double negation, which needs little explanation:

The result was to be expected.
The result was not unexpected.

The difficulty is in defining ‘strong’ and ‘weak’ without getting entangled in the semantics. If we assume that ‘strong’ means definitive, categorical or conclusive, then I should be able to explain the difference between the active and passive structures in such terms, but I can’t decide which of these two sentences gets a strong reading and which weak:

Someone will do it.
It will get done.

A separate issue involves instances where some speakers of English give a weak reading to certain conjunctions, such as as well as, where the conjunction in fact suggests a strong reading.

Power plants trade in energy as well as in emission credits.

The purpose of as well as is to introduce ‘known information’ rather than ‘new information’. On current knowledge, it would make more sense to say:

Power plants trade in emission credits as well as in energy.