Below are my understandings. Some come from all the inductive school
(Russel, etc), some could be totally wrong.
There are two approaches to know the world: induction and deduction.
Logic is above all. It is neither induction nor deduction. Logic (like
syllogism) gives the rules/laws to do deduction. There are surely
classifications of logic, like proposition logic, predicate logic, etc. But
in general, Logic does not KNOW the world directly, but gives us tools to
know the world.
Math = Axioms + Deduction. Axioms come from induction. From parallel axiom,
you get Euclidean Geometry. Here, parallel axiom is from induction, and all
the others are from deduction. U can get rid of parallel axiom, then you get
non-euclidean geometry. Neither euclidean nor Non-euclidean geometry is a
physical existence. It is our knowledge of the world. In old ages,
experience shows euclidean describes our world accurately. Late, people
realize that our world is non-euclidean, but Riemann. This does not change
logic and deduction at all. This just changes our induction!
Science = induction. All the most basic laws are from induction, like
Newton's Law. You can make deductions after some basic laws (which come from
induction), but essentially, science is induction. Therefore, there is no
ABSOLUTELY TRUE in science. Science, like math axioms, can only be
falsified. With more observations of the world, we may induct new basic
laws, which contradicts old basic laws. This is falsification. We can
replace Newton's gravity law by General Relativity. But the deduction from
the gravity laws is NEVER changed.
One world, in human history, we keep changing inductive knowledges, but
NEVER changed logic and deduction laws.
Above are my understandings. Criticisms to these understandings are
welcomed.
Back to Three Body III. Higher level of intelligence can change the science,
or math, or logic. Or in another word, change induction and deduction. I
cannot image a universe with a different logic (deduction rules), and I do
not believe (it is faith) that is possible.
However, it is very possible that all the axioms, science observations,
which all come from induction, are changed by higher level of intelligence.
Actually, it is very possible that, those basic rules from induction (like
constant light speed C) can change at different stage of the universe (see
Dirac's conjecture).
So I think Liu Cixin made a not bad job not changing the logic, but changing
the inductive knowledge of the universe.