An artificial language
described in the book
LINCOS: Design of a Language for Cosmic Intercourse: Part I
by Hans Freudenthal, Professor of Mathematics, University of Utrecht
North-Holland Publishing Company, Amsterdam, 1960.
This is a volume in the series
Studies in Logic and The Foundations of Mathematics
L. E. J. Brouwer,
E. W. Beth,
and A. Heyting.
So far as I know, subsequent parts of this work never appeared -- do tell me if I am wrong!
The Introduction begins:
Scientists, artists and artisans tend to develop a terminology of their own.
They use common language as a vernacular that will be enriched,
impoverished, and modified in order to serve special purposes.
The transformation may affect not only the vocabulary but also the syntax of the
though essential syntactical modifications are rather unusual.
It is certain, though far from generally admitted, that the meaning of a
linguistic term should be determined by its contexts, it is a matter of fact that
there cannot be any reasonably uniform opinion about the meaning of a word,
if people cannot agree about the truth of the majority of contexts in which the word occurs.
It is a common historical feature of many sciences, that their first representatives
tried to create a terminology before the stock of known facts was large enough to provide a sufficiently large context
for the elements of that terminology. Even now this is a serious drawback for philosophy and the arts.
When people do not understand each other, this is usually said to be because
'they speak different languages'.
This may be correct as long as "understanding" means a mere linguistic phenomenon.
If understanding means intelligence, one may posit the inverse thesis with at least as much justification:
People speak different languages because they do not understand each other.
(Note that the word language has here a rather unusual meaning).
As long as there is no reasonable agreement about facts and terminology among those who work in a given field,
it seems wise to stick as closely as possible to the vernacular,
and not to create any new term until it has become possible to define it in a satisfactory way by a sufficiently rich
In any case, one should try to abstain from playing upon words as contexts.
In the following pages I shall use common English as a vernacular, and I shall endeavour
not to use technical terms that are not generally agreed upon or else to provide for a sufficiently rich context or
even something of a definition if I use technical terms of my own.
So verbs like "to designate" and "to mean" will have the same meaning as they have in the vernacular
and not that given them in recent publications which might be characterized by the term
The use of a few words will be explained below.
0 02. The meaning of the word "language" is fairly unambiguous as long as there is no reference
to any special language. Generally people agree that somebody who uses English words when he explains
some astronomical experiments, is speaking English, but sometimes, especially if one wishes to stress some
divergences between the vernacular and the more
technical idiom, one says that he uses a special astronomical language.
Though borderlines may always be disputed (one may quarrel about the question whether as early
as 1250 the monk
Robert of Gloucester wrote English and whether nowadays
"Beach-la-mar" is still English)
"language" in the first sense is one of the best defined notions of contemporary English,
whereas in the second sense it is extremely vague. So I will provisionally stick to the customary
unsophisticated use of the word "language".
(Emphasis added by bertilak
The notation for this artificial language will remind the reader of that of
Russell and Whitehead's
Principia Mathematica, but an encoding is described by means of which LINCOS messages
might be transmitted via electromagnetic or other pulses.
The most interesting part of the book for me is the discussion of how the language could be
bootstrapped from elementary arithmetic and from itself.