On Dec 12, 11:54*am, Pentcho Valev wrote:
Philosophers of science dealing with axiomatic (deductive) systems
have devised what may be called the hat-of-the-magician model of
science.
Einstein: "Guided by empirical data, the investigator rather develops
a system of thought which, in general, is built up logically from a
small number of fundamental assumptions, the so called axioms."
The problem is that "building up logically" is taken to constitute the
interior of magician's hat where you put ties which are then turned to
rabbits. Then Popper only worries when a wolf rather than a rabbit
jumps out of the hat, Feyerabend vindicates the existence of the hat
in a world where "anything goes" etc.
The magician is free to rearrange the interior of the hat so that
always rabbits and never wolves jump out of it. For instance, Einstein
initially introduces his false postulate of constancy of the speed of
light, deduces miracles from it (time dilation, length contraction
etc.) and becomes "Divine Einstein". Later he introduces the
postulate's true antithesis (the speed of light varies with both the
speed of the light source and the gravitational potential) and obtains
results confirmed by experiments.
That is, by combining the thesis and the antithesis, the theory
becomes an INCONSISTENCY: a malignant formation that experiments do
confirm:
W. H. Newton-Smith, The rationality of science, Routledge, London,
1981, p. 229: "A theory ought to be internally consistent. The grounds
for including this factor are a priori. For given a realist construal
of theories, our concern is with verisimilitude, and if a theory is
inconsistent it will contain every sentence of the language, as the
following simple argument shows. Let 'q' be an arbitrary sentence of
the language and suppose that the theory is inconsistent. This means
that we can derive the sentence 'p and not-p'. From this 'p' follows.
And from 'p' it follows that 'p or q' (if 'p' is true then 'p or q'
will be true no matter whether 'q' is true or not). Equally, it
follows from 'p and not-p' that 'not-p'. But 'not-p' together with 'p
or q' entails 'q'. Thus once we admit an inconsistency into our theory
we have to admit everything."
Unless EXPERIMENTAL verification of theories is replaced by LOGICAL
verification, science has no future. "Building up logically" should be
tested, not the final results.
Contrary to what Popper and Einstein taught, in natural sciences, the
introduction of an axiom only apparently marks the beginning of a
theory building. Essentially, the introduction of an axiom marks the
beginning of the process of fitting the axiom into the preexisting
system of knowledge about Nature. For that reason the introduction of
a false axiom automatically converts the respective theory into an
inconsistency, insofar as the true alternative of the false axiom is
already present, implicitly, in "the preexisting system of
knowledge".
Consider a mathematical system (analogous to but much simpler than the
"system of knowledge about Nature") where all statements are
unambiguous and true, except for the result of the operation 2+2.
There are two hypotheses: 2+2=4 and 2+2=5. One somehow chooses the
false hypothesis 2+2=5 (it is now an axiom) and obtains:
(A) 3(2+2) = 3*5 = 15
(B) 3(2+2) = 6 + 6 = 12
Note that the true conclusion 3(2+2)=12 belongs to the theory
initiated by the false axiom 2+2=5, so if an experiment somehow tests
this particular conclusion, the theory (rather, the inconsistency)
would prove deceptively correct.
Since the experimental verification is unreliable in the case of
inconsistency, REDUCTIO AD ABSURDUM (forgotten in the era of
Postscientism) remains the only reasonable procedure leading to
falsification. If it were used, the following case of trapping a long
pole inside a short barn would have led to an immediate refutation of
Einstein's theory:
http://www.math.ucr.edu/home/baez/ph...barn_pole.html
"These are the props. You own a barn, 40m long, with automatic doors
at either end, that can be opened and closed simultaneously by a
switch. You also have a pole, 80m long, which of course won't fit in
the barn....So, as the pole passes through the barn, there is an
instant when it is completely within the barn. At that instant, you
close both doors simultaneously, with your switch. Of course, you open
them again pretty quickly, but at least momentarily you had the
contracted pole shut up in your barn."
If Einsteinians fail to reopen the doors "pretty quickly", the length
L of the pole trapped inside the barn would be:
(A) L = 40 because the trapped pole cannot be longer than the barn.
(B) L = 80 because that is the proper length and the pole is no longer
in motion.
Both conclusions, L=40 and L=80, belong to Einstein's theory (rather,
Einstein's inconsistency).
Pentcho Valev