Often you hear people say that it's just plain commonsense to
believe something, for example, that a tax cut is good for the
country or that daffodil bulbs should be planted in the fall.
However, there are limits to commonsense. This is a story about
one of the limits to commonsense.
Aristotle believed what our senses appear to tell us: that the
stars above us rotate around a stationary Earth. Look up at night
and observe the stars. It is almost impossible to believe anything
else. Now, although it is clear the stars move in a regular way
across the vault of heaven, Aristotle often refers to the stars
as 'fixed'. The stars are 'fixed' in the sense that they keep
the same relation to one another: they stay put in their constellations
and the constellations remain in the same unchanging relation
to one another even as the sphere in which they are embedded
rotates around the earth. The many 'fixed' stars are distinguished
from the few 'wandering' stars: the planets.
II. A brief summary of Aristotle's analysis of motion.
Movement in the wider sense is divided into coming-to-be and
passing-away on the one hand…and…movement in the narrower
sense on the other. This latter…is to be divided into its
three kinds-qualitative movement…, quantitative movement…and
local movement… The first is…qualitative change, the
second…quantitative change, the third…motion in our
ordinary sense of the word.1
According to Aristotle a body can only be moved by a present mover
in contact with the moved.2
According to Aristotle the universe consists of two distinct
worlds-the superlunary and the sublunary. In the superlunary world
are the stars, which are imperishable and undergo no change other
than that of local motion, their motion being circular and not
rectilinear, as is the natural movement of the four elements.
Aristotle concludes that the stars are composed of a different
material element, aether, which is the fifth and superior
element, incapable of any change other than change of place in
a circular movement.
Aristotle maintained the view that the earth, spherical in
shape, is at rest in the centre of the universe, and that round
it lie the layers, concentric and spherical, of water, air and
fire or the warm… Beyond these lie the heavenly spheres,
the outermost of which, that of the fixed stars, owes its motion
to the First Mover. Accepting from Calippus the number of thirty-three
as the number of spheres which must be presupposed in order to
explain the actual motion of the planets, Aristotle assumed also
twenty-two backward-moving spheres, interposed between the other
spheres, in order to counteract the tendency of a sphere to disturb
the motion of the planet in the next encompassed sphere;…
3
III. The Statement of Aristotle's argument
This is Aristotle's argument that the absence of shift in relative
position of the fixed stars shows that the Earth does not move:
Again, everything that moves with the circular movement, except
the first sphere, is observed to be passed, and to move with more
than one motion. The earth, then, also, whether it move about
the centre or as stationary at it, must necessarily move with
two motions. But if this were so, there would have to be passings
and turnings of the fixed stars. Yet no such thing is observed.
The same stars always rise and set in the same parts of the earth.4
III. Explication of the argument
The following is my interpretation of the structure of the above
argument. I maintain that the argument is a logically sound deductive
argument. It has premises and it has conclusions that are supported
by those premises. The premises of the argument are themselves
a mixture of types.
The first premise is a statement of a law of dynamics: the result of Aristotle's analysis of motion.
Premise 1. Local motion, the way natural objects move, is motion
that is either circular, in a straight line, or a combination
of the two
The second premise is a common sense classification that seems acceptable
Premise 2. The Earth is a natural object
The third premise is a conclusion from premises one and two
Premise 3. If the Earth moves, it moves in one of the ways described
in premise one
The fourth premise is partly the result of empirical observation, but also partly a theological or metaphysical interpretation of those observations
Premise 4. The fixed stars are special objects
The fifth premise is purely empirical: a statement of the observed facts
Premise 5. The fixed stars are observed to move across the sky
but are also observed to have unchanging positions relative to
one another
The sixth premise is a statement of facts we encounter practically every day
Premise 6. In our ordinary experience, when we as persons move
in relation to objects that are in fixed position relative to
one another, we see that the objects shift their apparent position
relative to one another.
Consider a row of trees planted equal distance from one another
along a road and person standing relatively between the first
and second tree.
The visual angle between trees one and two is greater than the
visual angle between trees nine and ten. So, even though the
trees are all equally spaced, trees nine and ten appear to person
P at position 1 to be closer together than do trees one and two.
If the person then moved to a position 2 between trees eight and
nine, then the observed situation would change. Trees nine and
ten would appear to be farther apart than trees one and two.
This relative change in position is what we experience all the
time in observing 'fixed' natural objects.
The seventh premise applies this common feature of observation to the stars
Premise 7. If the Earth moved, we should be able to observe the
fixed stars shift in relation to one another as the Earth moves
and changes its position relative to those fixed stars
The eighth premise is an empirical statement of what we actually observe with our senses (our 'naked' or unaided eye)
Premise 8. When we observe the fixed stars, we observe that they
do not shift in relation to one another
It then follows that
Conclusion: The Earth does not move
In part this argument depends on a view of the kind of motion
a body like the Earth manifests. Aristotle says that if the Earth
moves, it must necessarily move with two motions. The sort of
motions he has in mind are stated in a passage from his writings
about physics:
"Every local motion, as we have said before [Chapter 8, 261b
28.], is either rotatory or rectilinear or a compound of the two.."
I take 'rotatory' to mean moving in a curve or arc like stars
in the night sky. And 'rectilinear' I take to mean movement in
a straight line. Aristotle apparently thought that local motion
could always be explained in terms of combinations of the two
fundamental types of motion.
Aristotle thought of the stars as entities embedded in a sphere
that encircles us, much the way we still today find it useful
to think of stars as points of light on the empirically obvious
dome of the night sky. It is not clear whether the sphere of
the fixed stars is one thin layer or whether it has depth. If
it is 'thin' then the fixed stars are all equidistant from us;
like dots painted on the inside surface of a perfectly round ball.
If it has depth, then some fixed stars could be closer to us
than others; that is, some fixed stars could be relatively 'in
front of' other fixed stars. I have seen no indication that the
sphere of the fixed stars has depth. It seems to be taken for
granted by Aristotle and many commentators that the sphere is
'thin': all the stars are like points of light painted on the
surface of the celestial dome; they are equidistant from us.
The 'thin' sphere has an important consequence for interpreting
Aristotle's argument. When mentioned at all in undergraduate
astronomy text books, the argument we are dealing with is usually
referred to (in terms of modern astronomical notions) as an argument
about parallax.
parallax (symbol ) The change in the relative positions of objects when they are viewed from different places. The actual angular shift measured when a viewpoint is changed is also described as trigonometric parallax. In the case of astronomical objects, such changes are measurable only for relatively nearby objects in relation to the more distant stars. However, the measurement of parallaxes, where possible, is important since it is one of the most direct methods of determining astronomical distances. In astronomy, the word 'parallax' is often used synonymously with 'distance'.
The rotation of the Earth produces a diurnal parallax
effect, and the Earth's orbital motion around the Sun causes
annual parallax, statistical parallax.6
annual parallax (heliocentric parallax) The difference between the position of a star as seen from the Earth and as seen by a hypothetical observer at the Sun. The effect of annual parallax is observed as a shift in the positions of relatively nearby stars against the background of more distant ones during the Earth's yearly journey in orbit round the Sun. If the position of a nearby star is plotted over a year, it appears to sweep out an ellipse on the sky, called the parallactic ellipse.
The annual parallax is formally defined as the difference
in position that would be measured by hypothetical observations
made from the centre of the Earth and the centre of the Sun.7
In a very historically aware undergraduate astronomy text we find
the following.
But Aristotle concluded that Earth is stationary and gave a very
powerful argument. If Earth were moving, we ought to be able
to see changes in the relative configurations of the various stars,
just as, if you walk down a path, you see changes in the relative
positions of nearby and distant trees. If you line up a tree
in the middle distance with a very distant tree and then step
to one side, the nearby tree will seem to shift to the side of
the distant one. Such a shift in position due to motion is called
parallax, or a parallactic shift. If Earth were
moving in a straight line, we would see a continuous parallactic
shift of the nearer stars with respect to more distant stars;
and if Earth were moving around some distant center, we would
see a periodic parallactic shift back and forth among the stars.
But a visual survey of the stars and the constellations over time
showed no evidence of such a shift. So, reasoned Aristotle, Earth
must not move.8
However, if the fixed stars are embedded in a 'thin' celestial
sphere and are all equidistant from us, then some stars cannot
be relatively 'in front of' other stars; there can be no "nearer
stars with respect to more distant stars". If so, then Aristotle's
argument cannot be construed the way undergraduate astronomy text
has done. I think Aristotle's argument relies only on 'trigonometric'
parallax (as illustrated in the above figures). It does not depend
on the modern conception of annular parallax with its dependence
on foreground and background stars.
The lack of empirical evidence, the lack of observation, of
the parallax effect was a problem for astronomy until 1837 when
Friedrich Bessel detected the parallax of 61 Cygni (star number
61 in the constellation Cynus).9 This lack of empirical
evidence of the motion of the Earth was a large part of the Catholic
Church's opposition to Galileo's heliocentric theory. The Church
argued that without this evidence, all that could factually be
claimed was that there was 'apparent' motion and that the supposition
that the Earth moved allowed useful calculations to be done. It
is interesting to note that lack of empirical evidence, while
acknowledged to be a problem, did not prevent astronomers from
adopting the heliocentric theory and coming to treat it as true.
Science apparently does not always proceed cautiously and conservatively,
empirically proving each proposition step by tiny step.
In any case, Aristotle's deductive argument based, in part, on
empirically established commonsense premises stood for over 1000
years. And yet it was wrong: the earth does move.
References