The sentence
"The sentence
"The sentence
·'The sentenceis infinitely long"
is infinitely long··
is infinitely long"
is infinitely long.elc., etc.But this cannot work for finite sentences. For the same reason, Codel's
string C could not contain the explicit numeral for its Codel number: it
would not fit. No string of TNT can contain the TNT-numeral for its own
Codel number, for that numeral always contains more symbols than the
string itself does. But you can get around this by having C contain a
description of its own Codel number, by means of the notions of "sub" and
"arithmoquinification".
One way of achieving self-reference in an English sentence by means
of description instead of by self-quoting or using the phrase "this sentence"
is the Quine method, illustrated in the dialogue Air on C's String. The
understanding of the Quine sentence requires less subtle mental processing
than the four examples cited earlier. Although it may appear at first to be
trickier, it is in some ways more explicit. The Quine construction is quite
like the Codel construction, in the way that it creates self-reference by
describing another typographical entity which, as it turns out, is isomorphic
to the Quine sentence itself. The description of the new typographical
entity is carried out by two parts of the Quine sentence. One part is a set of
instructions telling how to build a certain phrase, while the other part
contains the construction materials to be used; that is, the other part is a
template. This resembles a floating cake of soap more than it resembles an
iceberg (See Fig. 85).
FIGURE 85.Quine sentenceSelf-Ref and Self-Rep 497
water