this string a theorem of TNT?" Now you are used to such questions; for
instance, if you had been asked that question about 50=0, you would have a
ready explanation: "Its negation, ~50=0, is a theorem." This, together with
your knowledge that TNT is consistent, provides an explanation of why the
given string is a nontheorem. This is what I call an explanation "on the
TNT -level". Notice how different it is from the explanation of why MU is
not a theorem of the MIU-system: the former comes from the M-mode, the
latter only from the I-mode.
Now what about G? The TNT-level explanation which worked for
50=0 does not work for G, because --G is not a theorem. The person who
has no overview of TNT will be baffled as to why he can't make G according
to the rules, because as an arithmetical proposition, it apparently has
nothing wrong with it. In fact, when G is turned into a universally quan-
tified string, every instance gotten from G by substituting numerals for the
variables can be derived. The only way to explain G's nontheoremhood is to
discover the notion of Godel-numbering and view TNT on an entirely
different level. It is not that it is just difficult and complicated to write out
the explanation on the TNT -level; it is impossible. Such an explanation
simply does not exist. There is, on the high level, a kind of explanatory
power which simply is lacking, in principle, on the TNT-level. G's non-
theoremhood is, so to speak, an intrinsically high-levelfact. It is my suspicion
that this is the case for all undecidable propositions; that is to say: every
undecidable proposition is actually a Godel sentence, asserting its own
nontheoremhood in some system via some code.
Consciousness as an Intrinsically High-Level PhenomenonLooked at this way, Godel's proof suggests-though by no means does it
prove I-that there could be some high-level way of viewing the mindlbrain,
involving concepts which do not appear on lower levels, and that this level
might have explanatory power that does not exist-not even in
principle-on lower levels. It would mean that some facts could be ex-
plained on the high level quite easily, but not on lower levels at all. No
matter how long and cumbersome a low-level statement were made, it
would not explain the phenomena in question. It is the analogue to the fact
that, if you make derivation after derivation in TNT, no matter how long
and cumbersome you make them, you will never come up with one for
G-despite the fact that on a higher level, you can see that G is true.
What might such high-level concepts be? It ha~ been proposed for
eons, by various holistically or "soulistically" inclined scientists and
humanists, that consciousness is a phenomenon that escapes explanation in
terms of brain-components; so here is a candidate, at least. There is also the
ever-puzzling notion of free will. So perhaps these qualities could be "emer-
gent" in the sense of requiring explanations which cannot be furnished by
the physiology alone. But it is important to realize that if we are being
guided by Godel's proof in making such bold hypotheses, we must carry the708 Strange Loops, Or Tangled Hierarchies