Lancelot Fletcher (lance.fletcher@freelance-academy.org)
Sun, 19 Sep 1999 19:22:29 -0500
Dear Hitoshi,
> The word "falsifiable" is a difficult one for me. I tried to
> find it in my
> on-line English-Japanese dictionary, but there is no such word. Instead I
> found the word "falsify" that means: "A falsifies B" is "A
> proves that B is
> wrong." From this I imagine "falsifiable" means: "A theory T is
> falsifiable"
> is "There is a possibility that someone is able to prove that
> the theory T is
> wrong." Is this interpretation correct? Or are there any other
> and/or deeper
> meanings in the word "falsifiable."
Your interpretation is correct, but there is a long history attached.
The terms "falsifiable" and "falsifiability" were introduced by Karl Popper
in 1934 in his Logik der Forschung (The Logic of Scientific Discovery).
His discussion of falsifiability occupies section 6 of Chapter I and all of
Chapter IV.
Popper advanced the notion of falsifiabilty as a criterion of acceptable
theory construction in response to the so-called "verifiability criterion
of meaning" which had been postulated a few years earlier by the
positivists of the Wiener Kreis (Carnap, Waismann and Schlick) and
popularized in the English-speaking world by A.J. Ayer. [This is the
verifiability criterion, as stated by Ayer in Language, Truth and Logic,
p.35: "We say that a sentence is factually significant to any given person,
if, and only if, he knows how to verify the proposition which it purports
to express -- that is, if he knows what observations would lead him, under
certain conditions, to accept the proposition as being true, or reject it
as being false."] Since that time the notion of falsifiability has occupied
a central place in debates about the nature of scientific method as most
prominently represented in the works of Thomas Kuhn, Imre Lakatos and Paul
K. Feyerabend.
Here is a sample of what Popper said about falsifiability:
>>>The criterion of demarcation inherent in inductive logic -- that is the
positivistic dogma of meaning -- is equivalent to the requirement that all
the statements of empirical science (or all "meaningful" statements) must
be capabile of being finally decided, with respect to their truth and
falsity; we shall say that they must be "conclusively decidable". This
means that their form must be such that to verify them and to falsify them
must both be logically possible. Thus Schlick says: "...a genuine
statement must be capable of conclusive verification"; and Waismann says
still more clearly: "If there is no possible way to determine whether a
statement is true then that statement has no meaning whatsoever. For the
meaning of a statement is the method of its verification."
Now in my view there is no such thing as induction. Thus inference to
theories, from singular statements which are "verified by experience"
(whatever that may mean), is logically inadmissable. Theories are,
therefore, never empirically verifiable. If we wish to avoid the
positivist's mistake of eliminating, by our criterion of demarcation, the
theoretical systems of natural science, then we must choose a criterion
which allows us to admit to the domain of empirical science even statements
which cannot be verified.
But I shall certainly admit a system as empirical or scientific only if it
is capable of being tested by experience. These considerations suggest
that not the verifiability but the falsifiability of a system is to be
taken as a criterion of demarcation. In other words: I shall not require
of a scientific system that it shall be capable of being singled out, once
and for all, in a positive sense; but I shall require that its logical form
shall be such that it can be singled out, by means of empirical tests, in a
negative sense: it must be possible for an empirical scientific system to
be refuted by experience.<<<
Popper goes on to consider a number of objections. I will omit the first
two and skip to the third, which has been the focus of a copious
literature:
>>>...It might be said...it is still impossible, for various reasons, that
any theoretical system should ever be conclusively falsified. For it is
always possible to find some way of evading falsification, for example by
introducing ad hoc an auxiliary hypothesis, or by changing ad hoc a
definition. It is even possible without logical inconsistency to adopt the
position of simply refusing to acknowledge any falsifying experience
whatsoever. Admittedly, scientists do not usually proceed in this way, but
logically such a procedure is possible;...<<<
Showing that this last statement -- that scientists do not usually proceed
in this way -- is historically inaccurate is what formed virtually the
whole career of Thomas Kuhn. In The Structure of Scientific Revolutions,
which is by far the most widely-read book on the history and philosophy of
science published in this century, Kuhn argued convincingly that, far from
being an aberration, the practice of constructing auxiliary and ad hoc
hypotheses to defend theories that have been confronted with disconfirming
evidence is overwhelmingly the standard practice in the scientific world --
so much so that Kuhn characterized this practice as part of what he called
"normal science."
The behavior of the scientific establishment with respect to the Big Bang
theory is a good example of what Kuhn was talking about, where the
retention of the theory depends on accepting ad hoc ideas of inflation and
dark matter, or on simply disregarding disconfirming evidence, such as
Segal's work indicating the non-linearity of the Hubble relationship, the
work of Tifft, et al. demonstrating periodicities in galactic redshift data
that are hard (or impossible) to account for on the basis of the
cosmological interpretation of the redshift, or Halton Arp's observations
indicating what appear to be gravitational interactions between large light
sources with such radically differing redshifts that, based on the
conventional interpretation, they could not be near enough to have any
significant local interaction.
Now, to get back to my response to Stephen:
Stephen said that he understands my objections to Pratt (I had told Stephen
in a private message that I thought Pratt had misunderstood the nature of
Cartesian mind-body dualism and also that I thought Pratt's use of
mathematics was more cosmetic than in the service of rigorous argument) and
concluded "...but we do need some falsifiability in our models of the
world!." From this I took Stephen to be saying that, in his opinion,
notwithstanding my objections, Pratt's article on "rational mechanics"
contains empirically falsifiable statements and therefore satisfies Karl
Popper's criterion for the construction of decidable scientific theories.
I replied by saying that "the claim that a model or theory is falsifiable
is a strong claim." By that I meant to refer to the extensive controversy
about whether or not any theory is genuinely falsifiable. My intended
implication was that one must have a very strong argument if one claims
that a particular statement is falsifiable, in the face of the literature
indicating that the falsifiability criterion cannot be counted on the
ensure decidability.
And I concluded by challenging Stephen to cite at least one falsifiable
proposition contained in Pratt's paper.
Stephen then replied to this challenge with a private message. I hope he
will not mind if I quote from it the following:
>>>You are not being unfair! ;-) I must be able to back up my claims. The
difficulty is that within the specific context of Pratt's paper, it is
difficult to "cite at least one falsifiable proposition". I would
tanatively propose this statement as being falsifiable:
"Identifying and adjoining are canonically denotational tasks that
mathematicians are accustomed to performing on their spaces, groups, and
other algebraic objects. This is the realm of the physical.
Copying and deleting are canonically operational tasks that logicians
and computer scientists are accustomed to performing on their proofs,
spreadsheets, and other symbolic objects. This is the realm of the
mental." page 4-5<<<
To this proposal, I respond with a further challenge to Stephen: Please
describe an observation which you, or Pratt, would accept as demonstrating
that this collection of statements (or any part thereof) is false.
Lance Fletcher, President
The Free Lance Academy Foundation
http://www.freelance-academy.org
lance@interactive.net
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