Phil 105: Science and Philosophy - Fall 2004 Lectures
!You will be sorely disappointed if you think that these are a
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Topic Three. What is Space?
Previous Lecture
Lecture 11 – Space and Matter (10/4/04) pp 52-55
1. Physics Before Descartes and Newton
- Copernicus (1473-1543), Brahe (1546-1601) and Kepler (1571-1630)
– the motions of the planets
- Galileo (1564-1642): amongst his other contributions
- Observations of sun spots, phases of Venus and moons of Jupiter
– 1610s, especially The Starry Messenger.
- Motion under a uniform force and the ‘Law of Odd Numbers’: if
an object accelerates
due to a constant force then the distances traveled in a series of
equal
intervals (1 second say) are proportional to the numbers 1, 3, 5, …
(equivalently,
distance travelled is proportional to the square of the time) –
Proposition
II of Two New Sciences, 1638.
- Some outstanding problems
- Laws of collision – what will happen when two given objects
with
given motions collide?
- Explanation of the motions of the planets – why do they have
elliptical motions around the Sun?
2. Space is Just Matter – Descartes in the Principles
of Philosophy (1644)
- II.4: The nature of matter – the stuff of all material bodies
– is not any property like hardness, heaviness, colour or temperature,
but having volume (‘extension’). Consider a stone, and ask which of its
properties are essential to its being material:
"In the first
place, then, hardness may be rejected, because if the stone were
liquefied or reduced to powder, it would no longer possess hardness,
and yet would not cease to be a body; colour also may be thrown out of
account, because we have frequently seen stones so transparent as to
have no colour; again, we may reject weight, because we have the case
of fire, which, though very light, is still a body; and, finally, we
may reject cold, heat, and all the other qualities of this sort, either
because they are not considered as in the stone, or because, with the
change of these qualities, the stone is not supposed to have lost the
nature of body. After this examination we will find that nothing
remains in the idea of body, except that it is something extended in
length, breadth, and depth; and this something is comprised in our idea
of space, not only of that which is full of body, but even of what is
called void space. " (G M Ross trans)
- Hence space = matter!
- And so there can be no vacuum – a supposed empty region is
a body too.
- The
universe is completely full of matter – a plenum – arranged according
to
Euclidean geometry.
Descartes’ universe is full of vortices carrying the planets
around their
Suns – ours is labelled S. (Source; Descartes,
Principles of
Philosophy,
V.R.Miller and R.P.Miller (trans): Reidel Publishing, Dordrecht
1983.Plate
VI.)
- A puzzle – how can a body move from one place? If
a body and its place are the same thing then in some sense they move
together. Descartes' answer: motion is motion relative to some
‘reference’
bodies.
The man is at rest relative to the boat, but moving towards
one shore
and away from another, and if the boat moves at the same speed in the
opposite
direction to the Earth, both boat and man are at rest in the heavens.
3. Matter is Just a State of Space – Newton in De Gravitatione (or 'On the
Gravity and Equilibrium of
Fluids')
- Couldn't matter simply be a an impenetrable (i.e., infinitely
hard) region of space?
"God by the sole
action of
thinking or willing could embrace any defined space by certain
limits that some
bodies not advance [penetrate] into it.
What if he were
to exercise this very power, and he should cause that
some space should
arise in the image of a mountain or whatever body being
terminated above
the earth impervious to bodies, and thus light and all
pressing things
would stop or would rebound; it seems impossible that with
the aid of our
senses (which should be constituted judges in this matter
only) we will
disclose this space not actually to be body; it were indeed
tangible on
account of the impenetrability, and visibly opaque and colored on
account of the
reflection of light, and a blow would resonate for the reason
that the
neighboring air would be moved by the blow." (trans W. B. Allen)
4. Space is Separate From Matter – Newton in the Principia (or 'Mathematical
Principles of Natural Philosophy' – i.e., 'of Physics') 1687.
- 'Absolute' space (for Newton, infinite Euclidean space) exists
separately from matter (so even where there is no matter), and all
bodies occupy – are coincident with – regions of space.
"Absolute space, in its own nature,
without relation to anything external, remains always similar and
immovable. ... Place is a part of space which a body takes up... I say,
a part of space; not the situation, nor the external surface of the
body." (Rob Rynasiewicz trans)
For Descartes and Leibniz (top) there is only matter, and
space is not a
separate
thing – for Newton (bottom) there is matter and there is space, and
bodies
and their places coincide.
5. Space is a Mental or Logical 'Construct' (from Matter) – Leibniz in
the Leibniz-Clarke Correspondence
(1715-1716)
- What if space is simply the system of all locations relative to a
reference body (or bodies):
V. 47 "I will here show, how men come
to form to themselves the notion of space. They consider that
many things exist at once and they observe in them a certain order ...,
their situation or distance. When it happens that one of those
co-existent things changes its relation to a multitude of others, which
do not change their relation among themselves; and that another thing,
newly come, acquires the same relation to the others, as the former
had; we then say, it is come into the place of the former; .... And
supposing or feigning, that among those co-existents, there is a
sufficient number of them, which have undergone no change; then we may
say, that those which have such a relation to those fixed existents, as
others had to them before, have now the same place which those others
had. And that which comprehends all those places, is called space....
In like manner, as the mind can fancy to itself an order made up of
genealogical lines, whose bigness would consist only in the number of
generations, wherein every person would have his place: and if to this
one should add the fiction of a metempsychosis , and being in the same
human souls again; the persons in those lines might change place; he
who was a father, or a grandfather, might become a son, or a grandson,
etc. And yet those genealogical places, lines, and spaces, though they
should express real truth, would only be ideal things." (S Clarke trans)
- A particular 'relative space' is then a ‘reference
frame’ = a system of coordinates 'attached' – by us – to a
reference body.
- To attach a frame to a reference body, specify locations
according to how far
above
or below, to the left or right and in front or behind they are.
A reference frame!
- But in this case space is not a thing, separate from bodies at
all – the way another body is a separate thing. Instead, space is
'constructed' logically or in our minds from relations – an 'idea' –
like 'genealogical space'.
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