[Fis] CONSILIENCE: When separate inductions jump together

Thank your for the very interesting discussion and questions. Let me try to
answer one of the questions: What is the difference between the prediction
of instances of the same kind (Whewell's test 2) and prediction of instances
of a different kind (consilience a la Whewell)?

It seems to me that there are at least two distinct goals of theory or model
building in science. One is to obtain a good picture or representation of
the way the world works-the causes or mechanisms lying behind empirical
phenomena. This is what philosophers refer to as a realist goal. Then
there is the goal of making accurate predictions. The goal of predictive
accuracy is often referred to as an instrumentalist goal of science.
Predictive accuracy is a truth-related goal (since accuracy depends on what's
true), but it is limited to what's directly observable. The realist goal
goes beyond that.

Reconsider the example in which we apply Kepler's laws (K) to the motion of
the moon and Galileo's law of projectile motion (G) to explain terrestrial
phenomena. In each case, there is a parameter that can be estimated by
fitting the laws to the data. For celestial phenomena we can measure Kepler's
constant, which is the period of motion squared divided by the mean radius
cubed. From the terrestrial phenomena, we can measure the constant g,
which is the acceleration due to gravity. Galileo thought that the
influence of the earth's gravity did not reach the moon (for Galileo, the
moon's circular motion was a kind of force-free inertial motion). So,
Galileo did not interpret Kepler's constant as a measure of the earth's
gravitational influence. Now, notice that Kepler's and Galileo's laws are
adequate for predicting instances of the same kind. That is, Kepler's laws
prediction new observations of the moon's motion, and Galileo's laws predict
new cases of terrestrial motions. The mere conjunction of K and G passes
all of the tests that fall under Whewell's test 2. But it does not unify
terrestrial and celestial motion in any way. It does not achieve the
consilience that is achieved by Newton's theory. That consilience is
achieved by the fact that Kepler's constant and g provide independent
measurements of the earth's mass, where these measurements agree
numerically. That agreement does not contradict K or G. K&G accommodates
this relational fact. But it does not predict it. So, maybe a clearer way
of making Whewell's distinction would be to say that unified theories
predict *relational* facts, and unified theories are confirmed (supported,
verified, corroborated) when such relational facts turn out to be true.

My intuition is that the observed consilience of Newton's theory gives us
some reason to believe that gravity, as measured by the earth's
gravitational mass, real does exist and the earth's gravity is influencing
the moon's motion. If this is right, then a (successful) consilience
provides some evidence that Newton's theory is actually succeeding in
capturing something deep about the underlying causes of motion. This is
evidence for a realist as opposed to an instrumentalist goal.

Notice that consilience can be achieved even when the sub-models (such as K
and G) are not very good at predicting instances of the same kind (just as
Kepler's laws are not very good at predicting the moon's motion, because the
fine details of the motion is fairly chaotic and unpredictable). Maybe
this is why oversimplified models (idealizations) have a useful role to play
in science? (Witness the fact that Kepler's laws are still widely used in
astronomy.)

If this is right, then it raises an important point about the methodology of
science, which I think is widely misunderstood. For example, Thomas Kuhn
(in The Copernican Revolution) claims that Copernicus's appeal to the
harmony of his theory nothing more than an appeal to an aesthetic virtue.
Kuhn supports this view by pointing out that Copernicus's published model
was less simple (had more circles) than Ptolemy's, and that Copernicus's
theory was not more successful at making predictions. All of this overlooks
Copernicus's argument that his theory predicts relational facts that Ptolemy's
theory does not. In particular, Copernicus's heliocentric theory predicts
that Mars will appear to move backwards (regress) if and only if the earth
is overtaking Mars if and only if the sun is in opposition to Mars (relative
to us). Ptolemy's earth-centered theory accommodates this relational fact
connecting the retrograde motion of Mars and the position of the sun, but
does not predict it.

It's no coincidence, in my view, that all subsequent theories, such as
Kepler's, Newton's, and Einstein's, make the same prediction.

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Received on Thu Sep 23 22:17:50 2004