- If religion and philosophy are views of the same thing — the ultimate
nature of the universe — then the true religion and the true philosophy must
coincide, though they may differ in the vocabulary which they use to express
the same facts. - E.G. Collingwood,
Faith and Reason, p. 55.
On Abstract Thinking
by R. G. Collingwood
31.26: The symbiosis
of factual thinking with abstract thinking which I have metaphorically
described by saying that the science rests on two legs might be
alternatively described by saying that its body consists of two parts: an
armature of abstractions reinforcing a concrete whose aggregate consists of
31.27: A still
better metaphor is one of Bacon's. The scientist is neither an 'ant',
storing what it finds lying about ready-made, nor a 'spider', spinning a web
out of what its entrails secrete. He is a bee, visiting innumerable flowers
and collecting the nectar it finds in them; but storing not this nectar in
its crude state but the honey into which it turns it (Novum Organum, I. XCV).
31.28: The scientist
collects crude facts, but he stores only what he has converted them into:
laws. Laws are the body of a science. Laws are what it is a scientist's
business to come at. Laws are what a master-scientist has to teach. Laws are
what a pupil-scientist has to learn.
31.29: A law is
neither a crude fact nor (as some anti-logicians pretend) a collection of
crude facts. It cannot be established by an observation or an experiment, or
many of them. Nor is it a theorem in pure mathematics, to be established by
a mathematical operation. It is midway between the two: a hybrid. It is what
the scientist can breed from facts by crossing them with pure abstractions,
which is another way of saying what Bacon said. It is what he can breed from
pure abstractions by crossing them with facts. If any reader knows too
little of scientific work to understand the metaphor, I willingly apologize
for its obscurity.
31.3: Modern science
needs two different kinds of raw material: crude facts and pure
abstractions. To combine these into science is called 'interpreting' the
crude facts and 'applying' the abstractions.
31.31: To interpret
a set of crude facts is to get at what is called their 'law'. To apply a
pure abstraction is to think of it as the law of a set of crude facts.
science (31.24) is two different processes arriving at the same result. One
process is interpreting facts; a conversion of crude facts into laws by
mixing the nectar you get from flowers with the acid you secrete in your own
inside and thus turning it into honey.
31.33: The other is
applying abstractions: starting with pure abstractions and converting these
into laws by bringing them into relation with the facts whose laws they
henceforth are. 'Are',I say, not 'are thought to be'; the Newtonian law of
gravitation is (not 'is thought to be') the law of direct variation as the
product of the masses and inverse variation as the square of the distance
between the centres. In formulating this law Newton was applying ideas in
pure mathematics that had long been familiar.
facts and applying abstractions are really not two processes but one. If you
keep your eye on the factual element you think of this process as a process
which the facts undergo by having abstractions mixed with them.
31.35: If you keep
your eye on the abstractions you think of it as a process which the
abstractions undergo by having facts mixed with them.
fixations of the eye have their uses; but they must not become obsessions.
You can fix your eye on the bicarbonate of soda and think of baking-powder
as made by adding to it double its amount in cream of tartar: or you can fix
you eye on the cream of tartar and think of yourself as adding half its
amount in bicarbonate of soda.
31.37: Only a very
cretinous pupil will fancy these rival methods of making the powder, or the
'rationalism' and 'empiricism' ascribed to seventeenth-century thinkers,
rival theories of scientific method.
31.38: Double or
single, the process is richly illustrated by Galileo and Newton and the many
physicists who were working on it about the same time (to mention physicists
only); and theoretically expounded partly by Galileo himself, less so by
Newton; whose theoretical exposition interested himself but little and, to
tell the truth, interests his readers even less.
31.39: If Galileo's
practical work awaited completion by Newton, his theoretical work awaited
completion by Bacon and Descartes.
The New Leviathan, (Oxford, 1942), p. 247-49.