Nietzsches
Overhuman is an Ideal Whereas Posthumans Will be Real Bill Hibbard University
of Wisconsin Madison test@ssec.wisc.edu Journal of Evolution and Technology - Vol. 21 Issue 1 January 2010 - pgs 9 - 12
Abstract Sorgner
recently wrote in this journal that Nietzsches overhuman and the posthuman
envisioned by transhumanists are similar at a fundamental level. However, the
overhuman is an ideal limit of human progress that can never be reached,
whereas posthumans will be a reality, the next stages in human progress. Some
transhumanists are concerned that human improvement technologies will create
radical inequality. Hobbess
prescription for a social contract to bring stability and security to human
society makes him more a useful antecedent than Nietzsche for those
transhumanists. Introduction Sorgner
wrote significant
similarities between the posthuman and the overhuman can be found on a
fundamental level
(Sorgner 2009, 1), in reaction to Bostroms claim that there are only
"surface-level similarities" between these concepts (Bostrom 2005,
4). While there certainly must be some similarity between the posthuman and the
overhuman, there is a fundamental difference that posthumans will be a reality,
whereas the overhuman is an ideal limit that can never be reached. Nietzsches
overhuman Nietzsche
described the overhuman as follows: Here
man has been overcome at every moment; the concept of the overman has here become the greatest
reality whatever was so far considered great in man lies beneath him at an
infinite distance. (Nietzsche 1888, 305.) The
important point is the infinite
distance
between human and overhuman. As envisioned by the transhumanist community,
posthumans are a finite improvement on humans. Nietzsches overhuman is closely related to
his concept of eternal
recurrence. Faced
with the prospect of living ones
life again endlessly, with every detail and misery replicated exactly, the
ordinary human says no but the overhuman says yes. Nietzsche believed in human
improvement, driven by a human will
to power. But
the overhuman has no need for improvement, having achieved satisfaction with
life. The overhuman is an ideal rather than an achievable reality. Posthumans,
as envisioned by most transhumanists, will be real successors to humans and
still struggling to improve. Analogy
with fixed point theory The
notion of human and posthuman improvement suggests a partial order relation
among sentient beings. The notion of beings wanting to improve suggests a
function from beings to the beings they want to become. And the notion of the
overhuman being satisfied with eternal recurrence of its life suggests a fixed
point of this function. Taken together, these suggest an analogy with the
mathematical theory of fixed points over partially ordered sets, as used in the
denotational semantics of programming languages (Scott 1972). We should not
take this analogy too seriously because of the lack of rigorous definitions of
posthuman, overhuman and other terms, but it is nevertheless interesting. Let S represent the set of possible sentient
beings, including humans, posthumans and the overhuman. We define a partial
order relation on S, writing s < s' for s and s' in S, to mean that s' is an
improvement on s. This is a partial
order because it may be the case that neither s < s' nor s' < s is true (e.g., neither my wife nor I am an improvement on the
other, in the interest of domestic tranquility). We also define a function F: S
→ S where F(s) is the being that s wants to become. Humans want to
improve, so for all human s, s < F(s). Similarly a
posthuman s as envisioned by the
transhumanist community will want to improve, so for these posthumans s < F(s). This assumes that
all humans and posthumans agree on what constitutes improvement, which may not
be true. Nietzsche discussed how different people had different moralities but
he imposed on this discussion his own standard of strength and weakness among
humans, which was his real definition of improvement. And there is a general
consensus among humans on at least certain types of improvement, so perhaps we
can restrict S to those sentient
beings who subscribe to this consensus. An objective mathematical measure of
intelligence has been proposed and might contribute to a definition of
improvement (Legg and Hutter 2007). The
sentient being called the overhuman would happily relive its life in eternal
recurrence, so overhuman = F(overhuman).
That is, overhuman is a fixed point of F.
Under certain assumptions about S,
the order relation and F, the Kleene
fixed point theorem tells us that a least fixed point of F exists and is defined as the limit of the infinite sequence: ^ ≤ F(^)
≤ F(F(^))
≤ F(F(F(^))) ≤ etc. (Manes and Arbib 1986).
Here ^
indicates the least member of S,
whose existence is one of the theorem's assumptions. Since we are looking for a
fixed point greater than humans (i.e., the overhuman) rather than a least fixed
point, we can replace ^
by any human s_{1} (if we
restrict S to those s such that s_{1} ≤ s,
then s_{1} is the least
member). Another
assumption of Kleenes
theorem is that S is a complete
partial order, which means that every directed subset (every pair of members of
a directed subset has an upper bound in the subset) of S has a least upper bound in S.
Since S is a set of possible rather
than actual beings, it is plausible that there exists a possible being that is
a least upper bound for every directed subset of S. The
final assumption of Kleenes
theorem is that F is continuous,
which means that it preserves least upper bounds. That is, given a directed
subset D of sentient beings then F(D)
is the set of beings that each being in D
wants to become. We can also define d
and d' as the least upper bounds of D and F(D). Continuity of F means that d' is the being that d
wants to become (i.e., d' = F(d)).
If F satisfies this assumption, and
if S is complete, then Kleenes theorem says we can define the
overhuman as the limit of the infinite sequence of improving humans and
posthumans: s_{1} ≤ s_{2} = F(s_{1}) ≤ s_{3} = F(s_{2}) ≤ s_{4} = F(s_{3}) ≤
etc. We are
assuming that all humans and posthumans want to improve, so this sequence
should be strictly increasing: s_{1}
< s_{2} = F(s_{1})
< s_{3} = F(s_{2})
< s_{4} = F(s_{3})
< etc. Thus the analogy with fixed point theory suggests that the overhumans satisfaction with eternal
recurrence implies that the overhuman must be the result of an infinite
sequence of improving humans and posthumans. This is consistent with the
Nietzsche quote that humans are infinitely far beneath the overhuman. However,
according to current physics the universe has a finite information capacity
(Lloyd 2002), so there cannot be an infinite sequence of strict improvement.
Some s_{n} in the sequence of
improving posthumans must reach the maximal improvement possible in our finite
universe. Assuming that this s_{n}
is intelligent enough to realize that it has reached the maximum, it will not
want to improve (violating our assumption that all posthumans want to improve),
so s_{n}_{+1} = F(s_{n})
= s_{n}. That is, s_{n} is a fixed point of F. If current physics is right that our
universe is finite, then it is possible that some posthuman would say yes to
eternal recurrence. But nineteenth century physics did not derive any finite
limit on the information capacity of the universe and a finite limit on the
overhuman is inconsistent with the Nietzsche quote. The
posthuman s_{n} that reaches
maximal improvement is reminiscent of Tiplers prediction of human
intelligence spreading to employ all the matter and energy in the universe
(Tipler 1994). But the goal of Tiplers
work was to derive Christian theology from physics, so Nietzsche would probably
have denied any connection with his overhuman (perhaps This
analogy with fixed point theory is one interpretation of Nietzsches overhuman and eternal
recurrence. His romantic writing style is open to many interpretations. Radical
inequality Sorgner
writes about social issues including the dangers of genetic engineering, peoples concern for their children, and
eugenics (Sorgner 2009). But he does not address the issue of the radical
inequality that could result from technological change to human bodies and
brains. Some transhumanists think that this is a critical issue (Hughes 2004;
Hibbard 2008a), whereas others focus only on individual improvements without
regard for the effects of unequal access to the technologies of improvement.
When humans can simply buy greater intelligence and use that intelligence to
earn more money, this positive feedback cycle will lead to an unstable arms race in intelligence (Hibbard 2008b).
Intelligence levels among humans will diverge to the extent that less
intelligent humans will be unable to understand or learn the languages spoken
by the most intelligent humans, leading to different laws for people of
different intelligence. This must have a destructive effect on the sense of
meaning in the lives of less intelligent people. Nietzsche
thought that strength was the ultimate good and expressed little sympathy for
measures to oblige the strong to subsidize the weak. Thus Nietzsche is not a
good antecedent for transhumanists concerned with the issue of radical
inequality. Hobbes is a more useful antecedent than Nietzsche for such
transhumanists. Hobbes was a materialist with a practical writing style who
wrote By
reasoning, however, I understand computation (Hobbes 1981, 177). So Hobbes
would probably not be surprised that 350 years later humans are approaching the
construction of machines surpassing the human mind. More important for
transhumanism is Hobbess
observation that humans need stability and security, but that society will
degenerate into chaos without a social contract and an authority to enforce
that contract (Hobbes 1968). The technology of mind will invalidate assumptions
underlying our society and lead to instability and insecurity unless we modify
our social contract to regulate that technology (Hibbard 2008a). Following
Hobbes, transhumanists should analyze this situation and ask what social
contract will create stability and security for people to live meaningful
lives. References Bostrom,
N. Hibbard,
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Walter Kaufmann, in On the genealogy of
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