Re: Bayesianism makes Falsification Obsolete?

[enigl@aol.com (Davin C. Enigl)]

>In a thread (which I'm abandoning) in sci.logic we
>discussed the logical form of various types of claims about the world:

>    1. Observational Claim: If true, it is possible to know that
>    it is true, and if false, it is possible to know that it is
>    false.

Advantage:  Everything is observable, in principle, on the surface,
there is no "deep" (unobservable) reality to complicate explanations.

Problem: Theoretical names (atom) do not connect directly to
observations (complex collection of points (and QED singularities) of
subatomic particles).  Therefore, all observations are interpreted
based on existing theories, based on limited numbers of past successes
of those theories.  Example 1: I could be dreaming right now.  How do
I know that I an not dreaming?  I don't know via observation.  Example
2:  A mirage is not explained by observing (what appears to be) wavy
black water.  


>    2. Verifiable Claim: If true, it is possible to know that it
>    is true, but if false, one may never come to know that it is
>    false. These claims have the form "There exists x such that
>    Phi(x)" where Phi(x) is an observational claim about x. If
>    someone witnesses a single x such that Phi(x), the verifiable
>    claim is proved true.

Advantage:  Only a few right predictions proves the theory is true.
Predictions that turn out wrong are not used to disprove the theory.
This is the main pseudo-scientific strategy.

Problem:  As pointed out many times before, existential statements are
never conclusively disprovable.  Therefore, wrong theories cannot be
culled out.  Error correction is impossible with this type of
reasoning.   Existential statement formulations can not be used to
formulate hypotheses because of irrefutability.  Every existential
statement could be true.  Example:  Unicorns exist.

>    3. Falsifiable Claim: If false, it is possible to know that it
>    is false, but if true, one may never come to know that it is
>    true. These claims have the form "For all x, Phi(x)" where
>    Phi(x) is an observational claim about x. If someone witnesses
>    a single x such that not Phi(x), the falsifiable claim is
>    proved false.

Note the (correct) formulation: a negation of an existential statement
is used here.  Existential formulations can not be used to formulate
hypotheses because of irrefutability.  Inductive falsification (one
~x, is inductive since a limited number of wrongs equals a global
conclusion) is called Naive Falsification.

Problem:  An observational claim might still be explained inside the
theory that is under test.  Jovian moons 8 minutes last or 8 minutes
early, was explained by a finite speed of light.  Neptune was
discovered by a "wrong" Einsteinian prediction of the observation of
Uranus, yet, was still explained within Einstein's theory.

Answer:  Fortunately, Popper rejected this form of what is called
"Naive Falsification" in his (1934/tr.1959/ed.1999) Logic of
Scientific Discovery (p. 42, 50) and he explained the difference
between "Naive" and his "Sophisticated" Falsification  (and the
falsifiability requirement) in his (1982) Realism and the Aim of
Science, p. xxii.   Inter-subjectivity is assumed to be just as good
as objectivity.  Subjectivity and inductively reasoned falsifications
are rejected.  Deduction is used to solve Hume's Problem of Induction.
William Warren Bartley III reformulated and improved this (Popper's)
with his pan-critical rationalism (Cf. David Miller's (1994) book,
Critical Rationalism, and Bartley's (1984) The Retreat to Commitment)

>    4. Metaphysical Claim: none of the above. These claims either
>    involve things that are inherently non-observable, or else
>    require more than one quantifier, such as "For all x, there
>    exists y such that Phi(x,y)". No finite collection of observations
>    can prove or disprove such claims.

Yet, (according to Popper, in his (1982) Quantum Theory and the Schism
in Physics) there *are* things that can be done to improve this
formulation:

a)  Find criterion of demarcation within metaphysics that separates
those worth discussing (and thinking about) and those rationally
worthless metaphysical systems.  

b)  Gather all scientific and non-scientific aspects of the world into
a worthwhile unifying metaphysical theory that can be improved upon
later:  "Evolutionary Metaphysics."

[This is basically what Benjamin Gal-Or tried to do in his book
Cosmology, Physics and Philosophy -- an aesthetics theory of
metaphysics, I think.  Has anyone read this book?]

>Karl Popper argued that to be considered a "scientific theory",
>a theory had to make falsifiable claims. In other words, a scientific
>theory must be capable of being disproved.

And, that any fruitful explanatory theory must connect, in some way,
to reality, to observation.  Popper was not only a Critical
Rationalist,  he was also a Critical Empiricist.  

>Now, it seems to me that there actually is a problem with
>this criterion: no scientific theory is actually falsifiable
>by itself.

Popper rejected Naive Falsification.

Here is a summary of Popper's more sophisticated approach:

Summary of non-authoritarian pan-critical rationalism:

(1) There are no ultimate sources of knowledge. (Human Fallibility)

(2) All we can do is ask if an assertion is true in that it agrees
with the facts (Cp. Tarski's Correspondence Theory of Truth).

(3) Previously held beliefs that agreed with the facts continue to be
held by tradition.

(4) Anti-traditionalism is not important for its own sake -- in
principle.  But all tradition is open to critical examination and may
be over thrown if found to be wrong.

(5) Knowledge cannot start from nothing (i.e., not from tabula rasa)
and knowledge cannot start from observation.  The advancement of
knowledge comes from modification and correction of earlier knowledge
(the basis for traditional beliefs).

(6) Neither knowledge nor reason is beyond criticism (nor are they
sources of ultimate authority).

(7) Absolute precision is impossible.  Definitions and meanings lead
to the fallacy of infinite regress, therefore cannot be important.
Clarity is achieved by understanding illustrative examples. (Ostensive
definitions, examples, etc.)

(8) Every solution creates new problems.  This makes our knowledge
finite and our ignorance not only intractable but also infinite -- in
principle. (Fruitfulness)

(9) The above numbered theses are open to criticism (Bartley's
Pan-Critical Rationalism)

>The problem is that any purported falsification
>can be explained away as experimental error or as due to
>unknown forces. (For example, the deviation of a planet from
>the orbit predicted by the law of gravity can be explained by
>proposing an unseen extra planet. This was how Pluto was
>discovered.)

This was covered and explained in Popper's L. Sc. D. , Conjectures and
Refutations, Realism and The Aim of Science, and many other places.
Do you *really* think Popper would not have addressed that problem?

>What we can do is to try to quantify the likelihood
>that experimental error or unknown forces caused the discrepancy,
>using Bayesian probability.

Popper considered that, but rejected it as subjective and because it
abandoned the search for truth (verisimilitude)!  

For instance according to I. J. Good in (1971) American Statistician
vol. 25, p.62 and (1983) Good Thinking (U. of Minn. press), there are
46,656 interpretations of Bayesiamism  For a good explanation of why
Bayesianism is not very good, please read David Miller's Critical
Rationalism p. 125-132, or any of the other critics -- and think about
the problems they pose.

>Then we can say that, for all
>practical purposes a theory is falsified if its adjusted
>probability following an observation is significantly small.

>However, once we start using probabilistic arguments, theories
>become falsifiable in practice even if they are not logically
>falsifiable. For example, the theory that there exists unicorns
>is not falsifiable (it is verifiable). But we can make a statistical
>argument that if unicorns existed, it is very likely that someone
>would have seen one by now. 

And, that is a big part of what is wrong with Bayesianism:  Hume's
Problem of Induction.  No finite number of *none-existing
observations* (logical problem: you cannot count something that does
not exist) says anything about what is true or false.  Example:  "I
don't see an x, so x probably doesn't exist." It is form of
self-delusion,  because, it neither changes the probability of x
existing, nor makes x less likely.   

Einstein said that the success of his Brownian motion theory,
nevertheless showed conclusively that Newtonian Classical mechanics
always offered trustworthy observational results whenever it was
applied to motions in which the higher time derivatives of velocity
were negligibly small.  This was a paradox.  How could a theory that
never incorrectly predicted an observation be wrong?  

I am glad Einstein was not a Bayesian.  Einstein said that he
"despaired" because Newton's theory had so much in its favor.  

"The myth, that is still prevalent today, is faith that the
observational facts alone, can yield scientific knowledge -- that is,
without theoretical or mathematical construction.  The misconception
comes due to long-use of successful theories, where one does not
become aware that theoretical concepts are not connected with the
empirical observation data the theory predicts.  The theoretical
concepts are a 'free-choice' and can change at any time, yet the
observations remain unchanged.  Theory and observation are not
connected.  If they were, no theories could ever change or improve."

Einstein knew "probably right" is meaningless when it comes to
scientific theories.  It does not change the probability.  [Einstein
had long discussions with Popper about many topic such as this.]

>So while observations can't logically
>disprove the existence of unicorns, they can decrease the likelihood
>of their existence to the point where we need not worry about them.

If that *were* true,  we would not have to "worry" about Einstein's
theory of Relativity, because the Eddington data could not have
decided that Newton's predictions were not as close to reality as
Einstein's.  . . . Because Newton's theory would be "probably" right
and Einstein's would be "probably" wrong.  

Popper's said, that it was acceptable to "intuitively feel" that a
theory was "probably" right or "probably" wrong, in the everyday
understanding of "probably."   . . . The danger was giving up a
regulatory mechanism, that culls-out wrong theories by observations
(of reality) that clash with a theory.  

>It seems to me that statistical analysis of theories and their
>predictions is a much more powerful way to discuss theories than
>in terms of falsifiability. Of course, the problem is that any
>notion of likelihood must inherently involve subjective guesses,

Exactly the problem with Bayesianism.  It is neither objective nor
even, inter-subjective.

>but those sorts of guesses are involved in deciding whether an
>experiment has actually falsified a theory, anyway. We may as
>well come clean about the subjectivity (try to be objective
>about our subjectivity).

You are forgetting that inter-subjectivity is just as good as
objectivity.  Falsification has it and Bayesianism does not have it.