Below, find a few remarks made on this paper by the reviewers
of Cybernetics and Human Knowing, followed by my replies.
This paper is a discussion of computing and Turing machines from a somewhat
"second order" perspective. I am not too excited about it. It seems more or
less journalistic to me, without any really new ideas. It does discuss
issues that should be discussed in this journal, and it may stimulate
Since the journal is quite popular and concerning the philosophy
of "second-order cybernetics" rather than any formal issues,
it would be strange if my submission were of a different kind.
The paper was not intended to be an ordinary mathematical publication,
with much technicality and poor understanding of the sense of
the results derived. Rather, it had to suggest an alternative
to the blind manipulation with symbols, up to the necessity
of employing a way of reasoning different from the traditional
deductive scheme. The reviewer did not notice that in the text,
since he shared the common prejudices about "science-like"
discourse and could not conceive any other forms of reasoning
that are as precise, and more adequate for the subject under
The end of the paragraph is a contradiction to the previous sentence:
if the paper contained nothing new, how could it stimulate
The author airs ideas which in general are of interest to
the readership. However he is unable to simultaneously be
precise and understandable, that is, he takes pains to
provide (reasonable) mathematical definitions, but as soon
as the conceptual terrain gets rough, he retreats to vague
and airy prose. Moreover, I find serious problems in his
discussion of and arguments regarding extendible Turing
machines. But even if I'm mistaken here, he has a lot of
explaining to do.
Yes, the text is not readily understandable, since it is
based on the notions far from the mathematical tradition,
which could not be described in full in a paper subject to
the usual size limitations (<5000 words). Moreover,
this new approach can hardly ever be formulated completely,
since self-development is one of its basic principles.
There is a lot of explaining to do — but one of the
ideas discussed in the paper is exactly that there can be
no completely explicit formalism, and any
mathematical paper is bound to contain something implicit
in it, thus requiring a lot of explaining too. My paper
is more honest than the bulk of other "scientific" works,
since it does not try to hide the narrow places "under the
Indeed, I did not "take pains to provide (reasonable)
mathematical definitions" — the definitions in the
beginning of the paper just describe the usual notions, to
fix the terms. There are no mathematical definitions in
the paper, quite intentionally. The paper says that
mathematical defitions are a very particular case of
definition in general — so, I tried to avoid too
much dependence on the traditional formalism, to stress the
basic ideas. What seems "vague and airy prose" to the reviewer
is actually never less precise than the usual mathematical
methods, accounting for the implicitness inherent to all
the mathematical knowledge. I explicate what mathematicians
try to hide behind the superficial formality.
Furthermore, what sense would there be in publications which
do not leave room for further development? Why not first
announce a viewpoint. and then get engaged in explanations?
The demand to present a "ready-to-consume" work looks
most strange, since it is the basic mechanism of science
to suggest hypotheses which are to be verified later on.
Of course, I can agree that my style is not too crisp and
clear — but I read many papers written in a language
much more obscure and heavy, and this cannot be the true
reason of the reviewer's negative attitude.
Although I appreciate from my own experience how difficult
this topic is, I don't feel that the author, in the final
analysis, succeeds in presenting anything genuinely new.
That is, anyone who has thought seriously about this topic
arrives at much the same thoughts as the author, which
accomplishment is not to be denigrated, but the problem is
to get further.
If the views I present are that obvious, why there are so
few traces of them in the literature, and why there are
so many quite opposite views, indicating a rather poor
understanding of the problems related to development?
Where are those who "thought seriously about this topic"
and "arrived at much the same thoughts"? Are these thoughts
forbidden to publicly discuss? I'm afraid, the reviewer's
awareness of these issues was the result of reading the
paper, rather than his own achievement — and his
desire to get further was an intended effect. This is
what I wrote the paper for.
I have suggested that the middle of the paper be deleted,
and the author concentrate on his opening theme. But whether
this suggestion is of any use or not, the paper as it stands
must be rejected.
The suggestion to delete the parts of the text that contain
the new ideas might be an indication of the reviewer's fear
of them. I am advised to do nothing beyond the scope of
traditional mathematics, and to never try to point to its
insufficiency. But my interpretation of the traditional
line seems too dangerous to the reviewer as well, and he says
that the paper should not be published even if I removed any
"bad" ideas from it. No further comment is needed.