Re: [Fis] CONSILIENCE: When separate inductions jump together

Dear Aleks, and All,

Aleks has raised some issues of great interest to philosophers of science.
I thank him for raising them. Here are some brief responses, off the cuff.
They may expose my ignorance more than they enlighten, but that is useful to
me.

> 1. Entropy
>
> Entropy is an interesting example of attempted consilience. Entropy was
> shown to correspond to thermodynamics for models of molecules. Entropy in
> the sense of quantifying dispersion proved useful for any kind of a
> statistical model. However, if entropy can be defined for a particular
> model, it doesn't imply that the laws of thermodynamics will apply to that
> model. In that sense, we have consilience in the notion of "dispersion"
> but
> not consilience of the notion of "the arrow of time". Since entropy is
> connected with both notions, there is mess. The solution is to split
> "arrow
> of time" entropy and "dispersion".

Yes, it seems plausible that extension of a concept to a new situation does
not imply that the associated laws will also apply to the new situation. So
why assume that the arrow of time is tied to the arrow of entropy? Why
assume that the arrow of dispersion has anything to do with time? I gather
this is what you are saying here, Aleks. In which case, I agree
wholeheartedly.

> 2. Bell's theorem
>
> Isn't using Bell's theorem as an example of consilience dangerous, as it's
> loaded with assumptions? See for example: Karl Hess and Walter Philipp. A
> possible loophole in the theorem of Bell. PNAS. vol. 98. no. 25.
> 14224-14227
> December 4, 2001. Briefly, Bell's theorem indicates that if there are two
> separated measurement stations measure an entangled pair of particles,
> moving one station will influence the readings on the second station. This
> is inconsistent with the view that the particles can be measured
> independently. Operators are just one way of explaining this, often quite
> confusing. But you get the same effect if you measure the waving of water
> in
> a pond with your hands: if you move one hand in the pond, the waves at the
> second hand will be affected. But note that the water in the pond can be
> modelled causally. Would you want to model the pond with quantum
> operators?

Alice measures the spin of one electron in an entangled pairs of electrons,
and Bob measures the spin of the second electron. Each controls the
measurement setting (the orientation of the Stern-Gerlach magnet), but not
the outcome of the measurement ('up' or 'down'). There is nothing that Bob
sees that tells him what measurement setting Alice has chosen. The
conclusion that Alice's choice affects the outcomes that Bob sees cannot be
derived from quantum theory--it is only derived from the assumption that
there exist hidden variables, and this assumption leads to false
predictions, and therefore should be rejected. That is Bell's argument.

The stuff about loopholes concerns ways in which hidden variable can be
saved from refutation. Let's assume, for the sake of argument, that there
are such loopholes, and the prediction is blocked. Then hidden variable
theory is saved from a false consilience, and ends up with no consilience at
all.

In the meantime, quantum mechanics is making true predictions, and is
achieving genuine consiliences. The loophole program, if successful, is not
doing very much by way of resuscitating hidden variable theories. So, why
not concede that quantum mechanics is the better theory.

> 3. Empirical test
>
> We might be trying to be too discriminating for our own good here. There
> is
> no such thing as a definitive test, there is no such thing as definitive
> consilience. Consilience is just an increase in experimental support for a
> theory outside the scope for which the theory was originally created. This
> doesn't mean that the theory is the best, or unquestionably true. It's
> just
> an increase of support and of generality. I may appear like an
> instrumentalist, but I'm not. There are many things one doesn't question,
> and they form the foundation for realism. Each concept can be truth today
> and theory tomorrow. When you instrumentalistically move one foot, the
> other
> needs to be on realistic solid ground, just for that moment.

Agreed. There is no such thing as a definitive test, there is no such thing
as definitive
consilience. Consilience is just an increase in experimental support for a
theory outside the scope for which the theory was originally created. And
it doesn't mean that the theory is unquestionably true. But it may mean
that the theory is the best of the rival theories currently on the table.

> 4. Kepler and Newton
>
> I have enjoyed Malcolm's example very much: consilience is about explicit
> equality, not just implicit equality. Of course, if we don't allow for
> explicit *approximate* equality, we might not be able to apply consilience
> in other domains. Even in physics, for that matter, approximate equality
> is
> used, as long as it is not systematically biased. For a real-life example,
> take a look at "SEARCH FOR A STANDARD EXPLANATION OF THE PIONEER ANOMALY"
> at
> arXiv:gr-qc/0107022: the Pioneer probes seem to be systematically slowing
> down as they exit the solar system. One of the tongue-in-cheek comments on
> internet forums about this phenomenon is "It's bumping against the crystal
> sphere with the stars painted on it." True equality is only in the domain
> of
> pure mathematics.

Agreed. True equality is only in the domain of pure mathematics. That is
also true in the Kepler example. Newton argued that Kepler's third law,
which says that the ratio of the mean radius cubed to the period squared is
the same for every planet, supported his theory of gravitation. This is
because the ratio of the mean radius cubed to the period squared for each
planet is approximately equal to the mass of the sun according to Newton's
theory, so the measurements are approximately equal because they are
approximate measurements of the same quantity. If Kepler's third law is
exactly true, then Newton would have 6 independent measurements of the sun's
mass that agree exactly. But Newton knew that Kepler's law is false, not
merely because the numbers did not agree exactly, but also because he could
only derive the law by assuming that the planets were "test particles" with
infinitely small mass. This enabled Newton to correct the measurements by
taking account of independent estimates of the masses of the planets. After
this correction, the agreement was better, but still not perfect.
Nevertheless, the agreement was impressive. It did support Newton's theory
(if we deny this, then we would have to conclude that no scientific theory
are supported by the evidence any better than any rival theory).

For details of this example, see:

Harper, William L., Bryce H. Bennett and Sreeram Valluri (1994):
"Unification and Support: Harmonic Law Ratios Measure the Mass of the Sun."
In D. Prawitz and D. WesterstDhl (eds.) Logic and Philosophy of Science in
Uppsala: 131-146. Dordrecht: Kluwer Academic Publishers.

Cheers,
Malcolm

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Received on Wed Oct 6 22:59:41 2004