It has long been a familiar view among students of language that writing is not and cannot be anything other than a record of speech. It is recognized that the particular speech in question may never have been audibly uttered. But marks on paper, in order to be writing, must according to this view correspond at least to potential speech-sounds existing in the mind of the writer (if he has a mind) or represented by observed or assumed movements of the writer's vocal organs or other portions of his anatomy (if he has no mind), and must in either case enable any reader who knows both the system of writing and the dialect to utter the particular series of phonemes intended by the writer. I do not know how old this view may be. I have the impression that it is too old to have originated in any of those schools of thought which deny the existence, or the accessibility to scientific investigation, of human consciousness, but I am not prepared to document this impression. It seems clear that these schools of thought provide important support for the view at the present time. This opinion of writing seems to be the only one reflected in Edward Sapir, Language: an Introduction to the Study of Speech (New York, 1921, reprinted 1939; see especially pp. 19-21) or in Leonard Bloomfield, Language (New York, 1933; see especially Chapter 17, Written Records). A recent expression of the same view appears in Bloomfield, Linguistic Aspects of Science (International Encyclopedia of Unified Science 1.4; Chicago, 1939): 'Writing is a device for recording language by means of visible marks. By "recording" we mean that the beholder, if he knows the language of the writer and the system of writing, can repeat the speech which the writer uttered, audibly or internally, when he set down the marks' (6). The last-named work, however, contains other statements which seem to me to contradict this view. Thus Bloomfield states (7) that mathematical discourse (described as the 'most characteristic and powerful form' of 'the language' of science') 'can be transmitted only by means of a written record.' With reference to certain mathematical procedures he writes (30), 'The result is a system of writing which cannot be paralleled in actual speech.' Again (43), 'The ancient Greeks carried on mathematical demonstrations largely in ordinary language; it was the development, in the early modern period, of arithmetic and algebra, with its box-within-box markings of scope, that divorced scientific calculations not only from ordinary language but, to all practical purposes, from vocal