The classical definition of the phoneme runs something like this: a set of sounds in complementary (noncontrastive) distribution and phonetically similar. To this one may append Trager's statement, ‘The criterion of complementary versus contrasting distribution is first, then that of phonetic similarity.‘ While it may be generally admitted that the criterion of phonetic similarity is of secondary importance, the question can be raised: is it of any importance at all? Here, as in everything else, the answer depends upon the level of analysis. The phoneme qua phoneme exists only by virtue of its distribution on a higher level, in the morpheme. On the phonetic level the phoneme is only a metaphysical possibility, on the morphemic level it is reality. Phonemes are phonemes because of their function, their distribution, not because of their phonetic similarity. Most linguists are arbitrary and ad hoc about the physical limits of phonetic similarity.

Recently, in a workshop of members of the Summer Institute of Linguistics in Peru, working with about twenty-one languages from nine language families of the area, I had an opportunity to observe the fruitfulness of one set of exploratory concepts postulated in Part II of my Language in relation to a unified theory of the structure of human behavior. The relevant section of Part II states: ‘Our empirical data, however, suggest that we must assume contrastive differences in abdominal pulses of types not postulated by Stetson. ... I am convinced, on kinesthetic evidence, that we must for the abdominal pulse, as for the syllable pulse, postulate types which are (a) ballistic, (b) controlled, (c) beginning ballistic and ending controlled, (d) beginning controlled and ending ballistic’ (57a).

Linguists, like many other people who feel called upon to talk about language, are in the habit of saying that speech activity is continuously variable in nature. Having said this, they proceed to describe particular samples of speech as sequences of events which they isolate on the basis of either articulatory definitions or acoustic definitions, or both. In carrying out this operation they are not seriously inconvenienced by the continuous aspect of speech: the fact that boundaries between any two of the elementary events composing an utterance cannot be fixed with exactness does not constitute a problem for them. They may occasionally use metaphoric expressions such as ‘overlapping phones’ and ‘slurring’, by way of acknowledging the continuously varying character of speech; but the function of such expressions is to justify the keeping of a discrete representation in the face of any demonstration that the physical segmentation of speech is hopeless. (That it is in fact not hopeless at all is beside the point here.) Speech may indeed be continuously varying when looked at in the laboratory, but the basic fact about speech is that human beings can hear it as a sequence of auditory fractions. Linguists may divide an utterance into a larger number of fractions than other listeners do, but even linguists have never been forced to concede the inadequacy of a discrete representation on the ground that it did not account explicitly for the physical continuous character of speech.

A free allophone is that allophone of any phoneme for which no feature or articulatory movement is determined by its environment. By extension, an allophone may be said to be free with respect to any undetermined feature or phase even though some other of its features or phases may be determined.

It is partly a matter of terminology. It seems advantageous under certain circumstances, including the pedagogical, to use 'free' as the antonym of 'determined'. If one wants to press the concept of determination to such minute detail as to include all allophones, i.e. to say that no two realizations of a phoneme can be same except in identical environments, then 'determined' has no antonym. But there is ample precedent for drawing a line, perhaps best defined as that between perceptible and nonperceptible. The difference between the /w/s in a queen and chickweed is readily perceptible; the difference between the /k/s, if not so clearly hearable, is certainly perceptible in the proprioceptive sense of the observer's empathic analysis. The difference between the /w/s in a queen and between or in chickweed and shirtwaist is not, however, perceptible, nor, as a matter of labialization, that between the /k/s in a queen and a quart or in chickweed and backwards.

[A problem which arises in the course of research on mechanical translation is the prediction of dictionary size. This article investigates the relation between empirical frequency laws and the function V(n)—the expected number of different words in an n-word sample of text. It is found that the probability-law proposed by Joos (1936) yields results which do not check well with experiments, and it is concluded that some modification of it is necessary for the purpose of vocabulary prediction.]

Thanks to the means available for speech analysis and synthesis, there is at present considerable knowledge of the acoustic differences whereby we distinguish among the various sounds of English. We know, for example, what the more important acoustic cues are by which listeners decide whether a stop sound is velar, alveolar, or bilabial. In the case of the stops, moreover, we know by and large what the acoustic differences are between the members of each of the homorganic pairs p-b, t-d and k-g (in other words, between the so-called voiced and voiceless stops). But we are as yet unable to state with any exactness the extent to which each of these acoustic differences separately affects our ability to discriminate between the two kinds of stops. Moreover, where progress has been made in this direction it is certainly in some measure due to the fact that we have dealt chiefly with the stops in those positions where the voiced-voiceless contrast is phonetically maximal, that is, in initial and final positions.

In recent years there have appeared in linguistic publications a number of explicit references to the methodology and concepts of mathematical logic. In the abstract of one provocative article, Martin Joos writes, 'Physicists describe speech with continuous mathematics, such as Fourier analysis or the autocorrelation function. Linguists describe language instead, using a discontinuous or discrete mathematics called “linguistics”.' Joos spells out what he means by the identification 'linguistics—discrete mathematics' at a number of points in his article. ‘Ordinary mathematical techniques fall mostly into two classes, the continuous (e.g. the infinitesimal calculus) and the discrete or discontinuous (e.g. finite group theory). Now it will turn out that the mathematics called “linguistics” belongs in the second class. It does not even make any compromise with continuity as does statistics, or infinite-group theory. Linguistics is a quantum mechanics in the most extreme sense. All continuity, all possibilities of infinitesimal gradation, are shoved outside of linguistics in one direction or the other’ (702).