On Dec 12, 3:54*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 wolfs 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.


Several short comments --
-- Your last paragraph is windmill-tilting. Much as you'd like science
to operate this way, it does not.
-- Relativity is completely internally consistent. You have taken the
statements of *special* relativity and *general* relativity to be
absolute, without at all considering what constitutes the difference
between "special" and "general" -- that is, the implicit constraints
on the statements of the special theory that make that theory special
and not general.
-- Your comic-book-level understanding of relativity leads you
conclude that it states both p and not-p. It most certainly does not.
If it did, this theory would have been chucked on its ear in January
1906. The fact that it did not should give you pause as to whether
your grip on the theory is as deep as it needs to be.
-- There is no magician's hat here. In all the papers, the
presumptions of the model were clearly laid out, and then the explicit
steps to deduce the inevitable from those presumptions were laid out
one by one. There is no curtain behind which things are hidden. The
assembly of the theory is completely out in the open. The fact that
you find it incomprehensible even while the assembly is done in front
of your eyes reflects on something, but it ain't the theory.