[Fis] CONSILIENCE: When separate inductions jump together

From: Malcolm Forster <mforster@wisc.edu>
Date: Wed 15 Sep 2004 - 22:04:56 CEST

As far as the outside world is concerned, the philosophy of science began
with Popper and Hempel and ended with Kuhn. But there is one important
exception. In the mid 1800s, William Whewell wrote extensively on the
history and philosophy of science, and his writings were well known to
scientific greats such as Charles Darwin and James Clerk Maxwell. In my
opinion, Whewell's ideas lie at the heart of the very best general accounts
of science that exists today. Whewell's views are especially relevant to
this discussion, because he coined the term 'consilience' (as well as the
word 'scientist').

Whewell distinguishes four tests of scientific hypotheses. By 'instances'
he is referring to empirical data that can be fitted to the hypothesis in

(1) The Prediction of Tried Instances (used in the construction of the

(2) The Prediction of Untried Instances;

(3) The Consilience of Inductions; and

(4) The Convergence of a Theory towards Simplicity and Unity.

For Whewell, 'induction' refers to the process of applying or constructing a
scientific hypothesis to explain some empirical phenomenon. For example,
Newton explained the motion of a terrestrial projectiles in terms of
gravity, and he also explained the moon's motion in terms of gravity. These
are two different phenomena and their explanations can be seen as two
difference inductions. Whewell often used the term 'colligation of facts'
in place of 'induction'. A consilience of inductions occurs when two, or
more, colligations of facts are successfully unified in some way. Newton's
theory of gravity applied the same form of equation to celestial and
terrestrial motions (the inverse square law), and in the case of the moon
and the apple, both colligations of facts made use of the same adjustable
parameter (the earth's mass). Consequently, the moon's motion and an apple's
motion provide independent measurements of the earth's mass, and the
agreement of these independent measurements was an important test of Newton's
hypothesis. This test is more than a prediction of tried or untried
instances (tests (1) and (2)). It leads to the prediction of facts of a
different kind (facts about celestial bodies from facts about terrestrial
bodies, and so forth).

The consilience of inductions is accompanied by a convergence towards
simplicity and unity because unified theories forge connections between
disparate phenomena, and these connections may be tested empirically.
Simplicity and unity are necessary conditions for the consilience of
inductions, but not sufficient. A theory like 'everything is equal to
everything else' is highly unified, but not consilient. As Einstein once
said, science should be simple, but not too simple.

In the Novum Organon Renovatum, Whewell (1858) speaks of the consilience of
inductions in the following terms:

We have here spoken of the prediction of facts of the same kind as those
from which our rule was collected [tests (1) and (2)]. But the evidence in
favour of our induction is of a much higher and more forcible character when
it enables us to explain and determine cases of a kind different from those
which were contemplated in the formation of our hypothesis. The instances in
which this has occurred, indeed, impress us with a conviction that the truth
of our hypothesis is certain. No accident could give rise to such an
extraordinary coincidence. No false supposition could, after being adjusted
to one class of phenomena, exactly represent a different class, where the
agreement was unforeseen and uncontemplated. That rules springing from
remote and unconnected quarters should thus leap to the same point, can only
arise from that being the point where truth resides.

Accordingly the cases in which inductions from classes of facts altogether
different have thus jumped together, belong only to the best established
theories which the history of science contains. And as I shall have occasion
to refer to this peculiar feature of their evidence, I will take the liberty
of describing it by a particular phrase; and will term it the Consilience of
Inductions. (Quoted from p. 153 in Butts, Robert E. (ed.) (1989). William
Whewell: Theory of Scientific Method. Hackett Publishing Company,

Contemporary philosophers of science (including Popper, Hempel, and Kuhn)
have failed to place any special emphasis on the consilience of inductions
for the confirmation, verification, or corroboration of scientific theories,
partly because they have not been able to understand it within their
framework. (So much the worse for their framework.)

Here are three questions that might be discussed:

(1) Is the consilience of inductions a clear notion? What does it mean for
facts to be of a different kind? Why is this especially significant?

(2) Do examples of consilience occur in sciences outside of physics? One
might think not because disparate phenomena are never, or very rarely,
successfully unified by theories outside of physics. This may be true to
some extent, but it does seem that Darwin, for example, postulated
connections between disparate phenomena that were previously unforeseen and

(3) Is Whewell right to claim that the consilience of inductions belong
only to the best established theories that the history of science contains?
Does the consilience of inductions always point to the truth, as Whewell
claims? Or does it point to something else?

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Received on Wed Sep 15 22:06:43 2004

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