Academic journal article Style

# Disjunctive Numerals of Estimation

Academic journal article Style

# Disjunctive Numerals of Estimation

## Article excerpt

1. Introduction

English contains a number of expressions of the form m or n, where m and n are numerals, with the meaning 'from m to n.' I call such expressions disjunctive numerals of estimation, or DNEs. Examples 1-4 illustrate the use of these expressions:

(1) My family's been waiting four or five hours for a flight to Florianopolis.

(2) This saying has fifteen or twenty meanings.

(3) Let me have thirty or forty dollars.

(4) Your call will be answered in the next ten or twenty minutes.

Example 1 may be used to assert that my family has been waiting from 4 to 5 hours, not for either exactly 4 or exactly 5 hours. More precisely, one should say that the expression is ambiguous between, on the one hand, an exactor literal interpretation of four or five, in which my family is said to have been waiting either 4 or 5 hours and not some intermediate amount of time (such as 4 hours and 30 minutes) and, on the other hand, an idiomatic "estimation" interpretation of four or five, in which my family is said to have been waiting from 4 to 5 hours; and one should also say that the second interpretation is much more likely to be given to the sentence than the first. The range interpretation of DNEs is even clearer in examples 2-4, where the interval between m and n is greater than 1. For example, sentence 2 under this interpretation is true if the number of meanings of the saying in question has any value from 15 to 20 and is false otherwise, similarly for examples 3 and 4.

The literal and idiomatic interpretations of a DNE coincide in truth value if the interval between m and n equals 1 and the DNE modifies a noun that is normally enumerated in discrete (integral) values, as in 5:

(5) There are four or five people ahead of us in line.

In such cases, nevertheless, the literal and idiomatic interpretations of DNEs should be distinguished. Under the latter, 5 is understood as providing an estimate of the number of people ahead of us in line, whereas under the former, it is understood as specifying a disjunction of exactly how many people are ahead of us in line.

DNEs have been around for a long time in English. The following excerpt is from a report written shortly after the British takeover of New Amsterdam in 1664, quoted in Keller. DNEs are italicized:

(6) There are about nine or ten three Mast Vessels of about eighty or a Hundred tons burthen, two or three ketches and Barks of about forty Tun, and about twenty Sloops of about twenty or five and twenty Tun belonging to the Government--all of which Trade for England, Holland and the West Indies, except five or six, sloops that use the river Trade to Albany and that way. (34)

Not all expressions of the form m or n, qualify as DNEs, however, as the following examples show:

(7) My family's been waiting two or five hours for a flight to Florianopolis.

(8) This saying has eleven or twenty-two meanings.

(9) Let me have forty or thirty dollars.

Example 7 would be used to say only that my family has been waiting either 2 or 5 hours, and not for an intermediate period of time, such as 3 hours. Thus the expression two or five in that example behaves only as an ordinary disjunction, not as a DNE. Similarly, example 8 would be used to say that the saying in question has either 11 or 22 meanings, not some intermediate number, such as 16. Finally, example 9 would be used to request either \$40 or \$30, not any amount of money in between.

2. Principles of Interpretation for DNEs

Genuine DNEs in English conform to certain principles of formation. For convenience in stating these principles, let M and N be the numbers that the numerals m and n respectively stand for; let D be the difference between N and M; and let R be the ratio of M to N. The principles are given in 10-12. (1)

(10) D is a nonnegative power of 10 or is 1/2 or 1/5 of a nonnegative power of 10 (i. …

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