Free will Lucas (1961) began a lengthy and heated
debate over the implications of
Gödel's incompleteness theorems for the
anthropic mechanism thesis, by arguing that: •
Determinism ↔ For any human
h there exists at least one (deterministic)
logical system L(
h) which reliably predicts
h's actions in all circumstances. • For any logical system
L a sufficiently skilled
mathematical logician (equipped with a sufficiently powerful computer if necessary) can construct some statements
T(
L) which are true but unprovable in
L. (This follows from Gödel's first theorem.) • If a human
m is a sufficiently skillful mathematical logician (equipped with a sufficiently powerful computer if necessary) then if
m is given
L(
m), he or she can construct
T(
L(
m)) and determine that they are true—which
L(
m) cannot do. • Hence
L(
m) does not reliably predict
m's actions in all circumstances. • Hence
m has
free will. • It is implausible that the qualitative difference between mathematical logicians and the rest of the population is such that the former have free will and the latter do not. His argument was strengthened by the discovery by
Hava Siegelmann in the 1990s that sufficiently complex analogue recurrent neural networks are more powerful than
Turing Machines.
Space, time and causality Lucas wrote several books on the philosophy of science and space-time (see below). In
A treatise on time and space he introduced a transcendental derivation of the Lorenz Transformations based on Red and Blue exchanging messages (in Russian and Greek respectively) from their respective frames of reference which demonstrates how these can be derived from a minimal set of philosophical assumptions. In
The Future Lucas gives a detailed analysis of tenses and time, arguing that "the
Block universe gives a deeply inadequate view of time. It fails to account for the passage of time, the pre-eminence of the present, the directedness of time and the difference between the future and the past" and in favour of a tree structure in which there is only one past or present (at any given point in spacetime) but a large number of possible futures. "We are by our own decisions in the face of other men's actions and chance circumstances weaving the web of history on the loom of natural necessity" ==Timeline==