# quantifiers and Pronouns

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The myriad problems with quantifiers and pronouns, of scope and reference, need a new look. In what follows I will attempt to start this look, beginning from the logical foundations and yet looking at the realities of a human language. I will start with indefinite expressions, where most of the problems lie, but will regularly look to definite expressions, where the solutions are usually clearer.

I begin with two apparently parallel cases:

• 1. Ever since I started reading a newspaper (1), I have had it (2) delivered in its (2) wrapper each morning, but today it (3) did not arrive, so I bought it (4) at a newsstand and read it (4) at the office.
• 2. Ever since I got a butler (1), he (1 or 2 = A) has come in his (A) pajamas to awaken me, but he (1 or 3 = B) did not come this morning, so I traced him (B) to the pantry and read him (B) the riot act.

And consider also

• 3. Ever since I got this butler (1), he (1) has come in his (1) pajamas to awaken me, but he (1) did not come this morning, so I traced him (1) to the pantry and read him (1) the riot act.

Any attempt to come up with a rule that will explain both 1 and 2, seems doomed: it will either cut off genuine anaphora where it applies (the two 2s and 4s in 1, the two As and three Bs in 2) or it will force one or another of the solutions in 2 onto the reading of 1 or the reading of 1 onto 2. On the other hand, as 2 shows, simple glorking is not particularly likely to get it right – short of the information that I have had only one butler, who is still with me (as of this morning, anyhow). And it is fairly clear that another example could be created to refute each rule suggested.

The Mr. solution – if coherent at all – only delays the problem. Yes, it is always Mr. butler involved, but we need – for most practical purposes – to know which avatar it is, or at least when it is the same one and when different. And that raises the exact same issues as the quantifier case.

Logic has, of course, an unambiguous solution: introduce a new quantifier/indefinite expression at each change and connect only to the latest of these at each anaphoric point. So:

Ever since I started reading a newspaper (1), I have had a newspaper (2) delivered in its (2) wrapper each morning, but today a newspaper (3) did not arrive, so I bought a newspaper (4) at a newsstand and read it (4) at the office.

Ever since I got a butler (1), he (1) has come in his (1) pajamas to awaken me, but he (1) did not come this morning, so I traced him (1) to the pantry and read him (1) the riot act.

Ever since I got a butler (1), a butler (2) has come in his (2) pajamas to awaken me, but a butler (3) did not come this morning, so I traced him (3) to the pantry and read him (3) the riot act.

Logically very clear, but linguistically unlikely, as witness the fact that 1 and 2 are normal colloquial English, while these rewrites are not (and in most other languages I know of, for that matter). Even changing “a butler” to “my then current butler” (2) and “my now current butler” (3) or the like is not something we would say until the questions started to come in – and even then later rather than sooner. That is, natural language is going in some cases to use anaphoric pronouns for repeating the same phrase even if not with the same reference – and not just once but several times on the same phrase (or, of course, every language has references to Mr.s – I wonder if the Trobrianders just had a normal language and Malinowski misread it. Quine, who introduced the issue into Philosophy, should approve.)

Although these examples use explicitly indefinite referentials, the problem can arise as well with definites given a sufficiently transformative shift of worlds:

• The President of the US (1) is a Republican but in 1993 he (1 or 2) was a Democrat.
• The tallest man in the world lives in Chicago but he used to live in Detroit.
• The tallest building in the world is in Kuala Lumpur but it used to be in Chicago.

In all these the passage of time is enough to perform the shift

A logical language, because it is logical, needs to keep track of the shifting references; because it is a language, it needs to make use of this superficial anaphora – or something like it. So far, the matter could be handled – as it is with tenses – by a mark that the matter has settled down for a while.

But further difficulties arise. Consider

Three men walked into a bar. Two of them ordered drinks and drank them at their table. The third went off to play pool. He called the others and the three moved the pool table. By one, they had all left.

Here the same (multiple) reference is repeated, divided, recombined in different forms and finally restored. Once again, logic can expand “three men” into a number of quantifiers, with separate variables, and keep track of most of these shifts by using the different variables. But the result is not usable language:

A, B and C are men and walked into a bar. A and B say ordered drinks (for themselves respectively) and drank each his respective drinks at the table of A+B. C went off to play pool. C called A and B and A+B+C moved the pool table. By one, A and B and C had left.

Whereas the original gets by with:

Three men (A) walked into a bar. Two of A (B) ordered drinks (of B)(C) and drank C at collective of B’s table (?B’). The third (of A)(D) went off to play pool. D called B (‘?) and collective of A (? or D+ B’) moved the pool table. By one, A had left.

That is, the original gets subdivided, each subdivision gives rise to a new anaphora and that gets reorganized before the original reappears, reorganized and then in its original form. Minimally, this seems to require – in English – that pronouns from indefinite descriptions can be requantified and have their statuses shifted – and shifted back.

And finally the relatively simple case:

A police officer (1) loved a police officer (2) and so he (1 – just possibly 2) bought a house where they (1+2) could live. Then he (whatever the last one was) hired a decorator (3) and they (1+3, 1+2, 1+2+3) went to buy curtains.

In trying to deal with these in a realistic way, a couple of further factors need to be taken into account (as they were not, apparently, in Loglan or Lojban). The first of these is that, once a sentence is finished and processed, it no longer exists in memory as a syntactic structures or even – with notable exceptions – as a linear string. It is rather a semantic structure -- and probably a stripped down one at that. Thus, a pronoun system that relies upon the position of its anaphorizes phrase in either the linear order or the syntactic structure rapidly becomes useless – in speech, merely difficult in writing. Appearances to the contrary are due to correlations between syntactic role or position with semantic role (passives, for example, tend to affect the results adversely). Backcounting systems – even with in single sentence – are not contenders at all. Secondly, successful systems tend to rely on semantic or quasi-semantic information: number and gender in English and similar systems in other languages (Swahili for a maximal use of this sort of system). This would seem to indicate that some features of the presentation carry over into the semantic recording. But this is of no use in Lojban-Loglan, since there are no such phenomenal categories in either the noun phrases or any existing pronouns.

What comes closest to this sort of thing in Lojban-Loglan are, first, some pronouns that seem to have semantic structure function: subject (but watch out for passives), direct object and the like, and, second, pronominal use of alphabetics, picking out the initial of the key part of the phrase (pronominal use of numbers might also help but is grammatically trickier). Going on from the first of these to phrases embedded in those select phrases is markedly less successful unless that phrase is striking for some other reason. Similarly, alphabetics driven to using initials of less central words (and what is central is very context-dependent, if not idiosyncratic) or non-initials work less well.

In the end, no system that meets reasonable economic restrictions will deal successfully with every case, so back references which are in principle communicable will simply not get picked up – and there seems to be no way to predict which ones will be problematic, to take counter measures (repetition if nothing else). This does not mean that we should give up the quest for a pronoun system, only that we should stick to means built on reliable principles and thus likely usually to succeed.