[1] See (Tipler 1994). Tipler would add computing theory to nuclear power and rocketry as the sufficient conditions for permanent economic growth.

[2] Of course, certain sorts of objects will
  be objectively more suited to perform the function of
[3] The
  most recent strong argument for the non-specifiable
  nature of personal skills and even the ability to
  discover mathematical proofs is presented by Roger
  Penrose in Shadows of the Mind
  (Penrose 1994).
[4] One might say that the division
  into personal versus objective knowledge obscures the
  fact that some intentional states (e.g.,
  dispositional expectations) shade over into
  propositional intentional states, i.e., World 3
  status. Peoples' "constitutive" attitude to money is
  a good example, for it may only be a shock like a
  hyperinflation that jolts people into making their
  unconscious expectations explicit and placed in
  linguistic form. But we do need the distinction
  between Worlds 2 and 3 to talk about the transition
  from one state to the other.
[5] For example, from the
  law-like statement "At atmospheric pressure silver
  melts at 960 degrees centigrade." one cannot derive a
  statement predicting a melting of silver at some
  definite spatio-temporal coordinates, or indeed even
  a purely existential statement to the effect "that
  some silver at some place and time has melted at 960
  degrees centigrade at atmospheric pressure". But one
  can derive negative predictions, such as the
  statement "One will not observe the melting of silver
  below 960 degrees centigrade at spatio-temporal
  coordinates w,x,y,z at atmospheric pressure".
[6] The logical
  form of metaphysical doctrines may be of the all-Some
  variety. For example, determinism may be stated thus:
  for every event there is a cause. Or more
  informatively, for every event x there exist a y and
  a z such that y is a lawful relationship describable
  by some true universal law u, and z is an event (set
  of initial conditions) preceding x, and x is
  predictable (deducible) from z in the presence of y
  (or of u) (cf.  Popper 1982a, p. 196).
  This is
  clearly untestable by confrontation with a basic
  statement, for suppose someone presents the
  determinist with a putatively uncaused event. The
  determinist always has two defensive options. No
  matter how far you have searched for the cause of
  some unexplained event and failed, the determinist
  can say either that you failed to look hard enough
  for the initial conditions or that you have
  insufficient imagination to formulate the correct
  lawful relationship connecting the two events (the
  initial conditions and the event to be explained). He
  can say this because you cannot logically exclude the
  possibility that the very next search will identify
  the cause.
[7] Popper deals with the methodological
  problem of picking the best curve through some given
  graphical points in sections 32 & 38 of Logic
    of Scientific Discovery (Popper 1980). Popper argues
  that given that one wants the most informative, and
  therefore most falsifiable, theory one should opt for
  the (theory) curve that has the lower degree of
  dimensionality, i.e., the one whose statement
  requires the smaller number of parameters. Theories
  with higher dimensionality require a greater number
  of basic statements to falsify them. For example, to
  refute the theory that all planetary orbits are
  circles requires only 4 singular statements, whereas
  to refute the theory that all planetary orbits are
  ellipses would require six singular statements.
[8] With the spread
  of psychological knowledge, this is a little unfair
  to "everyday" explanations. The knowledge of visual
  illusions, for example, is quite wide spread, and
  with this knowledge one can make quite precise
  predictions about another person's subjective
  experience and possible introspective reports.
[9] I am
  talking about melodies that can be appreciated by
  humans. Thus I am talking about discernible note
  lengths and pitches, which will obviously be finite
  in number, and melodies of finite length.
[10] To deny the influence of logical
  relationships would be to imply something very
  strange indeed: that the way things are never has the
  slightest influence on what we think or are prepared
  to maintain.  Correctly identifying errors in
  reasoning is on this view a purely accidental affair.
  But if the set of hypotheses we maintain in science
  is controlled even slightly by the process of trial
  and error elimination, in which the false hypotheses
  are cast from the body of science because they
  contradict true observation reports, then the
  maintainance of some hypotheses after each period
  of elimination is partly explained by their being
  true and the rejection of false ones is partly
  explained by the fact that they are false.

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TCR Issue Timestamp: Tue Nov 26 17:14:18 GMT 1996