142 IV. STRUCTURAL FACTORS IN A LANGUAGES
said that 'all A's are B', it is assumed that there are A's. It is obvious that always assuming existence leaves no place for non-existence; and this is why the old statements were supposed to be true or false. In practical life, collections of noises (spell-marks) which look like words, but which are not, are often not suspected of being meaningless, and action based on them may consequently entail unexplicable disaster. In our lives, most of our miseries do not originate in the field where the terms 'true' and 'false' apply, but in the field where they do not apply; namely, in the immense region of propositional functions and meaning-lessness, where agreement must fail.
Besides, this sweeping and unjustified structural assumption makes the-system less general. To the statement, 'all A's are B', the mathematician adds 'there may or may not be A's'. This is obviously more general. The old pair of opposites, true and false, may be enlarged to three possibilitiesstatements which might be true, or false, and verbal forms which have the appearance of being statements and yet have no meaning, since the noises used were spell-marks, not symbols for anything with actual or 'logical' existence.
Again a-system shares with theandsystems a useful and important methodological and structural innovation; namely, it limits the validity of its statements, with weighty semantic beneficial consequences, as it tends from the beginning to eliminate undue, and often intense, dogmatism, categorism, and absolutism. This, on a printed page, perhaps, looks rather unimportant, but when applied, it leads to a fundamental and structurally beneficial alteration in our semantic attitudes and behaviour.
In the present work, each statement is merely the best the author can make in 1933. Each statement is given definitely, but with the semantic limitation that it is based on the information available to the author in 1933. The author has spared no labour in endeavouring to ascertain the state of knowledge as it exists in the fields from which his material is drawn. Some of this information may be incorrect, or wrongly interpreted. Such errors will come to light and be corrected as the years proceed.
A great source of difficulty and of possible objections is that science is, at present, so specialized that it is impossible for one man to know all fields, and that, therefore, the use of a term such as 'science 1933'> might be fundamentally unsound. This objection should not be lightly dismissed, as it is serious. Yet it can, I believe, be answered satisfactorily. At this early stage of our enquiry, a large number of the facts of knowledge does not affect my investigation; therefore, it has not proved im-