SHOULD METHODOLOGY OF SCIENCE CHANGE?

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.

Pentcho Valev

On Dec 12, 4:54*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.

Pentcho Valev


xxein: "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 frequency. The speed of light is not determined by the speed
of the source. However, it is affected by a gravitation. Ask a BH.

Otherwise a good post.

On Dec 12, 4:54*am, Pentcho Valev wrote:

Unless EXPERIMENTAL verification of theories is replaced by LOGICAL
verification, science has no future. "Building up logically" should be
tested, not the final results.

That is a reversion to Aristotelian authoritarianism. Aristotle's
"science" was perfectly logical (given what was known at the time) and
almost invariably wrong, but nobody questioned it because he was the
"Great Aristotle."

It also sounds vaguely like religion, philosophy, and folklore, and
especially like "alternative medicine."

"If if makes sense, it must be right."

Logical consistency in a theory may be nice, and is often necessary,
but it is never sufficient.

For example, in the chemical physics of electrolyte solutions, the
"ionic atmosphere" of P. DeBye is logically consistent, and certainly
wrong, but it gives results that are consistent with observations.
For this reason it is still used. Similarly, the model of aerodynamic
lift based on the Bernoulli Principle is logically correct and
absolutely wrong (none of the assumptions are applicable!), but it is
still useful in designing airfoils.

It is far more important for a scientific theory to be accurately
descriptive (which makes it *useful*) than logically correct (which
makes it *satisfying*).

Tom Davidson
Richmond, VA

Tom Davidson "tadchem" wrote:

Pentcho Valev wrote:
Unless EXPERIMENTAL verification of theories is replaced by LOGICAL
verification, science has no future. "Building up logically" should be
tested, not the final results.

Tom Davidson wrote:
That is a reversion to Aristotelian authoritarianism. Aristotle's
"science" was perfectly logical (given what was known at the time)
and almost invariably wrong, but nobody questioned it because
he was the "Great Aristotle."
It also sounds vaguely like religion, philosophy, and folklore, and
especially like "alternative medicine."
"If if makes sense, it must be right."
Logical consistency in a theory may be nice, and is often necessary,
but it is never sufficient.
For example, in the chemical physics of electrolyte solutions, the
"ionic atmosphere" of P. DeBye is logically consistent, and certainly
wrong, but it gives results that are consistent with observations.
For this reason it is still used. Similarly, the model of aerodynamic
lift based on the Bernoulli Principle is logically correct and
absolutely wrong (none of the assumptions are applicable!), but it is
still useful in designing airfoils.
It is far more important for a scientific theory to be accurately
descriptive (which makes it *useful*) than logically correct (which
makes it *satisfying*).
Tom Davidson, Richmond, VA

hanson wrote:
I hear you say, in short: "The story (theory) of/about an event
or process has to be of practical use, rather then just 'making
sense' "...

If so, then this is borne out by example of the investigation
after the 1, Feb. 2003 Columbia orbiter broke apart during
reentry because of Wing damage sustained during launch
by a chunk of fuel tank foam insulation. --- For months the
probing physicists came up with "it couldn't be the cause, for
logical reasons, "proving" their logic with all kinds of theories,
computer simulations, spreadsheets and animations... and
kept on arguing... and arguing.. and arguing...ahahaha...

Finally, someone managed to arrange for an ***experiment***
to replicate the events with a chunk of gossamer foam being
shot at the leading edge of the SV wing.... Sure enough, the
impossible happened.
Against all logic and prognostications of physics arguments,
the feeble foam tore a 2x3 foot hole into the wing!!....

This fall there aired an impressive 2 hrs TV show about
this investigation, detailing what I sketched above.

BTW, what was stated above was advocated in ~1894
by Max Planck, Einstein's mentor, who said:
=P= "Experiments are the only means of knowledge
=P= at our disposal. The rest is poetry, imagination."

Happy Festivities to you, Tom
hanson

http://tinyurl.com/586k35

On Dec 14, 12:49*pm, "hanson" wrote:
Tom Davidson "tadchem" wrote:

Pentcho Valev wrote:
Unless EXPERIMENTAL verification of theories is replaced by LOGICAL
verification, science has no future. "Building up logically" should be
tested, not the final results.

Tom Davidson wrote:

That is a reversion to Aristotelian authoritarianism. *Aristotle's
"science" was perfectly logical (given what was known at the time)
and almost invariably wrong, but nobody questioned it because
he was the "Great Aristotle."
It also sounds vaguely like religion, philosophy, and folklore, and
especially like "alternative medicine."
"If if makes sense, it must be right."
Logical consistency in a theory may be nice, and is often necessary,
but it is never sufficient.
For example, in the chemical physics of electrolyte solutions, the
"ionic atmosphere" of P. DeBye is logically consistent, and certainly
wrong, but it gives results that are consistent with observations.
For this reason it is still used. *Similarly, the model of aerodynamic
lift based on the Bernoulli Principle is logically correct and
absolutely wrong (none of the assumptions are applicable!), but it is
still useful in designing airfoils.
It is far more important for a scientific theory to be accurately
descriptive (which makes it *useful*) than logically correct (which
makes it *satisfying*).
Tom Davidson, Richmond, VA

hanson wrote:

I hear you say, in short: "The story (theory) of/about an event
or process has to be of practical use, rather then just 'making
sense' "...

If so, then this is borne out by example of the investigation
after the 1, Feb. 2003 Columbia orbiter broke apart during
reentry because of *Wing damage sustained during launch
by a chunk of fuel tank foam insulation. --- For months the
probing physicists came up with "it couldn't be the cause, for
logical reasons, "proving" their logic with all kinds of theories,
computer simulations, spreadsheets and animations... and
kept on arguing... and arguing.. and arguing...ahahaha...

Finally, someone managed to arrange for an ***experiment***
to replicate the events with a chunk of gossamer foam being
shot at the leading edge of the SV wing.... Sure enough, the
impossible happened.
Against all logic and prognostications of physics arguments,
the feeble foam tore a 2x3 foot hole into the wing!!....

This fall there aired an impressive 2 hrs TV show about
this investigation, detailing what I sketched above.

BTW, what was stated above was advocated in ~1894
by Max Planck, Einstein's mentor, who said:
=P= "Experiments are the only means of knowledge
=P= *at our disposal. The rest is poetry, imagination."

Happy Festivities to you, Tom
hanson

http://tinyurl.com/586k35

....and to you, too, Sir.

Thank you for all the laughs!

Tom Davidson
Richmond, VA

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.

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

On Dec 16, 6:24*am, Pentcho Valev wrote:
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".


This is *FLAT* wrong. The history of science puts the lie to this
statement. There is NO requirement that an axiom needs to "fit into
the preexisting system of knowledge about Nature". The entire history
of science is *littered* with fundamental shifts that marked the
occasion of the introduction of axioms that were completely
inconsistent with the preexisting system of knowledge:

- Galileo: No force is required to compel a body in motion to remain
in motion.
- Copernicus: The heavens are not geocentric.
- Columbus: There is no edge to the world.
- Carnot: Perfect engine efficiency is not possible, even in
principle.
- Darwin: Species are created by natural diversification and natural
selection.
- Maxwell: Electricity and magnetism are the same phenomenon, and
light is electromagnetism.
- Planck: Energy is not continuous.
- Bohr: Angular momentum is not continuous.
- Heisenberg: Infinitely precise specification of a state's conjugate
variables is not possible, even in principle.
- Feynman: Particles do not follow definite trajectories through
space.


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

On Dec 16, 2:24*pm, Pentcho Valev wrote:
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).

http://www.online-literature.com/orwell/1984/
George Orwell "1984": "In the end the Party would announce that two
and two made five, and you would have to believe it. It was inevitable
that they should make that claim sooner or later: the logic of their
position demanded it. Not merely the validity of experience, but the
very existence of external reality, was tacitly denied by their
philosophy. The heresy of heresies was common sense. And what was
terrifying was not that they would kill you for thinking otherwise,
but that they might be right. For, after all, how do we know that two
and two make four? Or that the force of gravity works? Or that the
past is unchangeable? If both the past and the external world exist
only in the mind, and if the mind itself is controllable what then?"

This is only a partial development in Big Brother's world that can be
summarized as:

Two and two make five; two and two do not make four

Next development (not described by Orwell):

Two and two make five; two and two make four

Two developments in Einstein's world:

1) The bug is dead; the bug is alive:

http://hyperphysics.phy-astr.gsu.edu.../bugrivet.html

2) The speed of light is constant; the speed of light is variable:

http://www.astronomynotes.com/relativity/s4.htm
"Prediction: light escaping from a large mass should lose energy---the
wavelength must increase since the speed of light is constant.
Stronger surface gravity produces a greater increase in the
wavelength. This is a consequence of time dilation. Suppose person A
on the massive object decides to send light of a specific frequency f
to person B all of the time. So every second, f wave crests leave
person A. The same wave crests are received by person B in an interval
of time interval of (1+z) seconds. He receives the waves at a
frequency of f/(1+z). Remember that the speed of light c = (the
frequency f) (the wavelength L). If the frequency is reduced by (1+z)
times, the wavelength must INcrease by (1+z) times: L_atB = (1+z)
L_atA. In the doppler effect, this lengthening of the wavelength is
called a redshift. For gravity, the effect is called a gravitational
redshift."

http://helios.gsfc.nasa.gov/qa_sp_gr.html
"Is light affected by gravity? If so, how can the speed of light be
constant? Wouldn't the light coming off of the Sun be slower than the
light we make here? If not, why doesn't light escape a black hole?
Yes, light is affected by gravity, but not in its speed. General
Relativity (our best guess as to how the Universe works) gives two
effects of gravity on light. It can bend light (which includes effects
such as gravitational lensing), and it can change the energy of light.
But it changes the energy by shifting the frequency of the light
(gravitational redshift) not by changing light speed. Gravity bends
light by warping space so that what the light beam sees as "straight"
is not straight to an outside observer. The speed of light is still
constant." Dr. Eric Christian

http://www.math.ucr.edu/home/baez/ph..._of_light.html
"Einstein went on to discover a more general theory of relativity
which explained gravity in terms of curved spacetime, and he talked
about the speed of light changing in this new theory. In the 1920 book
"Relativity: the special and general theory" he wrote: ". . .
according to the general theory of relativity, the law of the
constancy of the velocity of light in vacuo, which constitutes one of
the two fundamental assumptions in the special theory of relativity
[. . .] cannot claim any unlimited validity. A curvature of rays of
light can only take place when the velocity of propagation of light
varies with position." Since Einstein talks of velocity (a vector
quantity: speed with direction) rather than speed alone, it is not
clear that he meant the speed will change, but the reference to
special relativity suggests that he did mean so."

http://www.physlink.com/Education/AskExperts/ae13.cfm
"So, it is absolutely true that the speed of light is not constant in
a gravitational field [which, by the equivalence principle, applies as
well to accelerating (non-inertial) frames of reference]. If this were
not so, there would be no bending of light by the gravitational field
of stars....Indeed, this is exactly how Einstein did the calculation
in: 'On the Influence of Gravitation on the Propagation of Light,'
Annalen der Physik, 35, 1911. which predated the full formal
development of general relativity by about four years. This paper is
widely available in English. You can find a copy beginning on page 99
of the Dover book 'The Principle of Relativity.' You will find in
section 3 of that paper, Einstein's derivation of the (variable) speed
of light in a gravitational potential, eqn (3). The result is,
c' = c0 ( 1 + V / c^2 )
where V is the gravitational potential relative to the point where the
speed of light c0 is measured."

Pentcho Valev

On Dec 16, 8:53*am, PD wrote:
On Dec 16, 6:24*am, Pentcho Valev wrote:





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".

This is *FLAT* wrong. The history of science puts the lie to this
statement. There is NO requirement that an axiom needs to "fit into
the preexisting system of knowledge about Nature". The entire history
of science is *littered* with fundamental shifts that marked the
occasion of the introduction of axioms that were completely
inconsistent with the preexisting system of knowledge:

- Galileo: No force is required to compel a body in motion to remain
in motion.
- Copernicus: The heavens are not geocentric.
- Columbus: There is no edge to the world.
- Carnot: Perfect engine efficiency is not possible, even in
principle.
- Darwin: Species are created by natural diversification and natural
selection.
- Maxwell: Electricity and magnetism are the same phenomenon, and
light is electromagnetism.
- Planck: Energy is not continuous.
- Bohr: Angular momentum is not continuous.
- Heisenberg: Infinitely precise specification of a state's conjugate
variables is not possible, even in principle.
- Feynman: Particles do not follow definite trajectories through
space.

Well, a lot of those have already been reserved, though.
Since the people today who study Digital Systems, A.I. computers,
robotics, solar energy,
wind energy, Pv cells, satellites, Fiber Optics, Holograms,
masers, and lasers have already
proven that most of the failling of Carnot engines is merely
because of science idiots who think
Maxwell wrote a bible, and Galileo invented History.












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
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