Stephen P. King (stephenk1@home.com)
Mon, 20 Sep 1999 15:56:16 -0400
Dear Lance and Hitoshi,
Lancelot Fletcher wrote:
>
> Dear Hitoshi,
[HK]
> > 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."
[LF]
> 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.
It would be illustrative to apply the logic implicit in the statement
to the statement itself, viz a viz, is the sentence "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"
capable of verification?
We discover that the class of propositions vastly exceeds the class of
observables of an entity (person, etc.) that is capable of "accepting"
or "rejecting" such! This is the start of problems! It is noteworthy to
realize that the set theoretic logic that is used by Peter Wegner can
easilty deal with such circularity! (non-well founded set theory
http://www.acsu.buffalo.edu/~lizhang/Thesis/ ) We really need to remove
the blinkers that our "classical" education has implanted!
> 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.
I completely agree! This is why I try to weight my thinking toward
observabible implications, e.g. I try to always consider the
experienciable consequences of a hypothesis...
> 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:
That is fine! :-)
> >>>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.
Well, let us see. Is it observationally true that
a) Identifying and adjoining are canonically denotational tasks that
mathematicians are accustomed to performing on their spaces, groups, and
other algebraic objects.
b) Copying and deleting are canonically operational tasks that logicians
and computer scientists are accustomed to performing on their proofs,
spreadsheets, and other symbolic objects.
These seem trivially true... Is the problem in the definition of the
words used?
Lance, I think that we are getting sidetracked here! Pratt et al, are
offering us an alternative way of, at least, thinking about the
mind-body problem and also time and causality. Just because the writting
does not conform to the "standards" of people like Spinoza, etc. is not
a reason to dismiss it! The fact that it is hard if not impossible to
understand it is an indication of the difference in the paradigms
involved.
Yes, I know that we need to have some criteria with which to evaluate
the utility of some persons ideas, but Pratt is not operating in a
vacuum! He is merely pushing an existing body of work (computational
complexity, distributed computing theory, etc.) to the "next level". Can
we dispence with this and examine what he is triyng to tell us? If
Spinoza's work has some bearing on this discussion I will be happy to
read your posts and think about it. I of course can only speak for
myself and do not claim any sort of authority. I am a mere amateur after
all!
Kindest regards,
Stephen
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