ȁȈȁ Partʺʺ: Politics and Philosophy
thatȀȃȂprime numbers, no more and no fewer, exist in the range ofȀǿǿto
Ȁǿǿǿ. Euclid already proved the infinitude of prime numbers: no largest
one exists. But is there a largestpairoftwinprimes (likeȀȆandȀȈ,ȄȁȀ
andȄȁȂ,ȀȃȄȀandȀȃȄȂ)? No one, the last I heard, has actually proved either
a “yes” or a “no” answer. Ļe problem objectively exists as a challenge to
human intelligence.
Ļe autonomous objects of WorldȂinteract with WorldȀthrough
the human perceptions, feelings, dispositions, and decisions of Worldȁ.
Ļe challenges of pure mathematics lead to results that find applications
in computer hardware and software, which in turn function in changing
the physical world. Some challenges of her field lead a mathematician
to results that enhance her reputation and win her an appointment at a
prestigious university, where she has a house—a physical object—built in
accordance with her tastes and increased income.
WorldȂis intrinsically open or emergent, says Popper (ȀȈȆȁ/ȀȈȇȁ,
p.Ȅ); any theory holding scientific and artistic creation ultimately explain-
able by physics and chemistry seems absurd to him. Moreover, interrela-
tions among the three Worlds render the whole universe partly open and
emergent.
I am not sure that Popper would agree, but his concept of WorldȂin
particular, the world of things like scientific theories, does help underline
how preposterous it is to suppose that each later state of affairs is totally
specified by earlier states. Scientific progress does occur. New knowledge,
by its very meaning, was not available in advance; the notion of some-
thing being known before it is known is self-contradictory. Is it plausible,
then, to maintain that all the mathematical and physical knowledge not
yet achieved but that will be achieved in the next hundred years somehow
already exists in latent form, already somehow coded into the current state
of the universe, along with the date and other details of the discovery of
each bit of that future knowledge? (Many of the associated challenges
already exist as problems belonging to Popper’s WorldȂ, but this is not
the same as the preexistence of solutions both to unsolved problems and
to problems not yet even formulated.)
ŏŔōŚŏő
Gerd Gigerenzer and coauthors (ȀȈȇȈ/ȀȈȈȂ, esp. pp.ȄȈ–ȅȇ,ȁȆȅ–ȁȇȄ) review
apparent and supposed implications of probability theory and statistics
for free will versus determinism. Ļese disciplines have been successfully