(BAAL News Autumn 2007)
The starting point for this investigation was a book review which appeared some time ago on the internet Linguist List (LL posting 12.1536, 17 May 2001). The review began:
‘The issues of focus influence on quantification (which
can be illustrated by the truth-conditional difference
between "John always introduces Bill to SUE" and "John
always introduces BILL to Sue") have been widely
discussed by formal semanticians during the last decade
(e.g., Rooth 1996, Benedicto et al. 1998, Hajicova et
al. 1998).’
While this generated little discussion at the time, recent work in pragmatics, and the consequent availability of more delicate analytical instruments than were in use when the review was posted, have brought to the surface several difficult questions relating to the examples used. In particular:
1. Why does John keep introducing Bill and Sue to each other?
2. Why is it always Sue that John introduces Bill to?
3. Why is Bill the only person that gets introduced to Sue?
Problems like this, at first sight insoluble, often yield surprisingly easily to the more rigorous approaches to hypothesis construction which have become widely used over the last decade, thanks largely to the work of Dieter Bauchweh vom Fass and his colleagues in the Abteilung für Heikle Fragen at the Remscheider Berufshochschule. Hypotheses, the keystone of the scientific method, are now no longer paradoxically the product of art rather than science, but can be systematically generated and assessed using standard statistical procedures. Applying the generalised vom Fass probability tables, adjusted for mode and dimensionality, to the questions outlined above, I have been able to construct the following provisional solution.
Bill and Sue are both institutionalised in the Florence Parker Home for the Bewildered, Clacton-on-Sea, and John is their nurse. In such a context, it is of course normal that each resident of the institution should be introduced on a daily basis to every other resident. The reason why, exceptionally, John does not introduce Bill to other inmates besides Sue – for instance Captain Potschinsky, the delightful Grace Haunch, or friendly old Mr Sackbottle – is a simple one. Bill, a former zoo keeper, likes to imitate the mating cry of the white rhinoceros whenever he meets people. Since Sue is stone deaf, this troubles her less than the others.
So far, so good. But how do we explain the third anomalous element in the situation: the fact that nobody except Bill gets introduced to Sue? Though past her first youth, she has retained much of the physical charm that led to her gaining the title of Miss Yarmouth 1923, and one would expect many of the residents to be anxious to make her acquaintance at regular intervals. As so often in these matters, it turns out that there are two conspiring causal factors at work. In the first place, Sue has a habit of hitting her fellow-inmates with the large spiked Tyrolean goat-herd’s umbrella that she insists on taking everywhere with her. While the other residents do not react well to this, Bill, who was brought up by a succession of strict Austrian nannies, is entranced by the memories conjured up by Sue’s behaviour. More importantly, however, Bill has himself taken steps to consolidate his favourable position vis-à-vis Sue, by bribing John with rhinoceros horn shavings to allow him sole access to the elderly siren.
That, I feel, pretty well clears matters up. Once a hypothesis of this kind is generated, evaluation is a relatively straightforward business. Applying a form of the normalised Caller-Herring calculus, now standard in this type of assessment, to the Bauchweh vom Fass figures, I assigned 1) probability matrix values A–H to each of the key elements in the projected scenario, and 2) vector-neutral functions z, z1, z2 … to the relationships between them. While the calculations are beyond the scope of an ordinary desktop computer, a close approximation can be achieved by using Markov analysis to collapse the probability values and vector-neutral functions into a single pair of real-number variables a and b. The coefficient (h) of the hypothesis can then be derived by representing all three variables in graphic form as the sides of a right-angled triangle, and applying a familiar formula (h2 = a2 + b2), according to which the square of the hypothesis is equal to the sum of the squares on the other two sides. Inserting the calculated Markov values for a (1.37) and b (2.94) into the formula, we find that h = √(1.372 + 2.942) = 3.24.
This is a reasonably robust hypothesis coefficient, comparing well with others in our field: the Noticing Hypothesis, for instance, has a coefficient of 0.71, the Learnability Hypothesis 1.46, and the Failed Functional Features Hypothesis 0.43. None the less, a hypothesis is only a hypothesis, and we cannot take the scenario outlined above as being the last word on the matter. In this case as in others, alternative hypotheses with higher coefficients may be possible, at least in principle. Readers are invited to attempt to generate such hypotheses. The best submission will be awarded a ticket for the Didcot Railway Museum. Second prize is two tickets.