Philosophy 226f: Philosophy of Science

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Philosophy 226f Philosophy of Science Prof.
Robert DiSalle (rdisalle_at_uwo.ca) Talbot College
408, 519-661-2111 x85763 Course Website
http//instruct.uwo.ca/philosophy/226f/
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The nature of scientific explanation What is it
that we understand when we have a scientific
account of some phenomenon? Does scientific
explanation have a different character from
explanation in other forms of thought, or in
common-sense human reasoning? Is the scientific
way of explaining privileged in some way? Or is
it too severely restricted to give us the kind of
deeper understanding that we expect in certain
other ways of thinking?
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A Kuhnian question Did the adoption of the
Copernican-Galilean viewpoint involve abandoning
a degree of understanding for the sake of greater
predictive power? Did Galileos work reflect the
replacement of understanding why with merely
describing how as the ultimate aim of
science? René Descartes, 1638 Galileo only
described particular cases of motion, without
inquiring into their first causes.
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In general, why do bodies in motion tend to
persist in motion? Aristotle As a matter of
fact, they dont tend to persist the little
persistence that they do manage can be explained
by the medium. Galileo Assume that they do
persist in motion then explain what forces are
cause them to speed up, slow down, or change
direction. What keeps the planets in
motion? Aristotle Planets are carried by
spheres, each of which executes the rotational
motion that is naturally suited to its spherical
form. Galileo Suppose that the planets
naturally persist in their rectilinear motion.
Explain their curved orbits by the forces that
cause them to deviate from the straight path.
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A deductive-nomological theory of scientific
explanation (cf. Rudolph Carnap Carl Hempel,
1950's and 1960's). Deductive Implies that
explanation is a kind of deduction from given
premises. Nomological Implies that the given
premises are universal or statistical laws of
nature. The point that to explain an event,
ideally, is to provide what suffices to deduce
logically that the event must have
occurred. Explanation is symmetric with
prediction.
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Why did event E occur (the explanandum)? Becau
se it is logically deducible from the
explanans Some set of laws of nature L1,
L2,...LN , and a set of initial conditions C1,
C2,CN, If laws of nature L1, L2,...LN hold
And initial conditions C1, C2,...CN obtain Then
event E necessarily follows. If L1, L2,...LN are
merely statistical laws rather than universal
laws, then given L1, L2,...LN and C1, C2,...CN ,
event E follows with probability P.
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The philosophical idea behind the D-N model To
give a conceptual analysis of what we mean by
explanation, and to show that our commonsense
idea of explanation is implicitly based on the
D-N structure. Explanations that dont (at
least implicitly) have these ingredients turn out
to be pseudo-explanations. Explanations that
claim to provide more than what the D-N model
provides are delusions.
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Keplers early model of the solar system
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Keplers model the inner planets
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• Empirical laws of planetary motion discovered by
  Kepler
• Planets orbit the sun in ellipses, with the sun
  at their common focus. This accounts for the
  inability of previous astronomers to find a
  circle, or combination of circles, that accounts
  for their irregular motions
• 2. A radius drawn from the sun to a planet sweeps
  out equal areas in equal times. This rule
  governs the way in which planets speed up as they
  approach the sun and slow down as they recede
  from it.
• 3. The square of the time it takes a planet to
  complete one orbit (the period t) is proportional
  to the cube of its average distance from the sun
  (the mean radius r). So t2 ? r3 for each planet.

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Keplers ellipse law Planets orbit the sun in
ellipses with the sun at their common focus.
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Keplers area law The radius drawn from the sun
to a planet sweeps out equal areas in equal times.
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Keplers harmonic law The periodic time t and
the mean radius r of any planetary orbit are
related as t2 ? r3. Or, t ? r3/2
Or, for any two planets a and b, Ta2 / Tb2
Ra3 / Rb3
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Keplers physical astronomy
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Newtons laws of motion (The Mathematical
Principles of Natural Philosophy, 1687) Law 1.
Every body, left to itself, maintains its state
of uniform motion or rest until acted upon by a
force. Law 2. Acceleration is in the direction
in which a forced is impressed, and is
proportional to the magnitude of the force and
the mass of the body. Law 3. To every action
there is an equal and opposite reaction.
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Corollaries to Newtons Laws Corollary 1. A
body moved by two forces will follow the diagonal
of the parallelogram formed by the motions that
those bodies would separately produce. Corollary
2. Every motion can therefore be described as the
composition of motions according to Cor.
1. Corollary 3. The total quantity of motion in a
system of bodies is not changed by the mutual
interactions of those bodies, because every
action will be balanced by an equal and opposite
reaction. Corollary 4. The center of gravity of a
system of bodies is not changed by the mutual
interactions of those bodies therefore it will
always remain at rest or moving uniformly in a
straight line (unless the entire system is acted
upon by some force originating outside the
system).
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Corollary 1 at work The projectiles motion
combines inertial motion with free fall according
to the parallelogram of forces.
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Corollaries 5 and 6 The Newtonian theory of
relativity Corollary 5. The motions of the
bodies in a given space are the same among
themselves whether that space is at rest or
moving uniformly in a straight line (Newtons
precise formulation of the Galilean principle
of relativity). I.e., because force is determined
by acceleration, no experiment can measure the
velocity of the system in which it takes place.
Acceleration is absolute, but velocity is
relative. Corollary 6. The motions of the bodies
in a given space are the same among themselves
whether that space is at rest, moving uniformly
in a straight line, or accelerated uniformly in
parallel directions, by forces that act equally
and in parallel directions on all the bodies in
the system.
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Examples of Corollary 6 The system of Jupiter
and its moons behaves (almost) as if it is at
rest or moving uniformly in a straight line,
because the attractive force of the sun acts
(almost) equally on every part of the system. In
an orbiting spacecraft, bodies behave as if no
forces were acting on any of them (as if they
were weightless) because the attraction of the
earth acts equally on all of them.
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The system of Jupiter and its moons, considered
as an isolated system
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Descartes on the origin of centrifugal forces
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Descartes vortex theory of planetary motion
The universe is completely filled with vortices,
each surrounding a rotating star
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Descartes What motion is, taking the term in its
common use. But motionin the ordinary sense of
the term, is nothing more than the action by
which a body passes from one place to another.
And just as we have remarked above that the same
thing may be said to change and not to change
place at the same time, so also we may say that
the same thing is at the same time moved and not
moved. Thus, for example, a person seated in a
vessel which is setting sail, thinks he is in
motion if he look to the shore that he has left,
and consider it as fixed but not if he regard
the ship itself, among the parts of which he
preserves always the same situation. Moreover,
because we are accustomed to suppose that there
is no motion without action, and that in rest
there is the cessation of action, the person thus
seated is more properly said to be at rest than
in motion, seeing he is not conscious of being in
action.
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Descartes What motion is properly so called
(motion in the philosophical sense) But if,
instead of occupying ourselves with that which
has no foundation, unless in ordinary usage, we
desire to know what ought to be understood by
motion according to the truth of the thing, we
may say, in order to give it a determinate
nature, that it is THE TRANSPORTING OF ONE PART
OF MATTER OR OF ONE BODY FROM THE VICINITY OF
THOSE BODIES THAT ARE IN IMMEDIATE CONTACT WITH
IT, OR WHICH WE REGARD AS AT REST, to the
vicinity of other bodies. By a body as a part of
matter, I understand all that which is
transferred together, although it be perhaps
composed of several parts, which in themselves
have other motions.
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Newton It is indeed a matter of great
difficulty to discover, and effectually to
distinguish, the true motion of particular bodies
from the apparent because the parts of that
immovable space, in which those motions are
performed, do by no means come under the
observation of our senses. Yet the thing is not
altogether desperate for we have some arguments
to guide us, partly from the apparent motions,
which are the differences of the true motions
partly from the forces, which are the causes and
effects of the true motion. For instance, if two
globes, kept at a given distance one from the
other by means of a cord that connects them, were
revolved about their common center of gravity, we
might, from the tension of the cord, discover the
endeavor of the globes to recede from the axis of
their motion, and from thence we might compute
the quantity of their circular motions.
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Newtons bucket experiment The Cartesian
definition of motion vs. the dynamical measure of
motion
The bucket and water are at rest No motion in
Descartes sense, and no dynamical effect
The bucket spins Now the water moves in
Descartes sense, but no dynamical effect
The water spins along with the bucket No motion
in Descartes sense, but an evident dynamical
effect
The bucket stops and the water continues The
water moves in Descartes sense, with the same
dynamical effect
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Newtons thought-experiment on rotation Even if
there is nothing else in the universe-- therefore
no relative motion-- the rotation of these
spheres about their common centre of gravity can
be known from the tension on the cord joining
them.
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• Newtons argument for universal gravitation
• Theoretical premises of the argument
• 1. The laws of motion and their corollaries.
• 2. Propositions on centripetal forces,
  mathematically derived from the laws of motion
• Empirical premises of the argument
• That all the planets, with respect to the Sun,
  obey Keplers 2nd and 3rd laws
• 2. That the satellites of Jupiter, Saturn, and
  Earth obey Keplers 2nd and 3rd laws with respect
  to their central planets

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Methodological premises Rules of Reasoning in
Philosophy I. We are to admit no more causes of
natural things than such as are both true and
sufficient to explain their appearances. II.
Therefore to the same natural effects we must, as
far as possible, assign the same causes. III. The
qualities of bodies, which admit neither
intensification nor remission of degrees, and
which are found to belong to all bodies within
the reach of our experiments, are to be esteemed
the universal qualities of all bodies whatsoever.
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IV. In experimental philosophy we are to look
upon propositions inferred by general induction
from phenomena as accurately or very nearly true,
notwithstanding any contrary hypotheses that may
be imagined, till such time as other phenomena
occur, by which they may either be made more
accurate, or liable to exceptions. In
experimental philosophy we are to look upon
propositions inferred by general induction from
phenomena as accurately or very nearly true,
notwithstanding any contrary hypotheses that may
be imagined, till such time as other phenomena
occur, by which they may either be made more
accurate, or liable to exceptions.
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Propositions from Principia, book I

• The areas which revolving bodies describe
  by radii drawn to an immovable centre of
  force do lie in the same immovable planes, and
  are proportional to the times in which they are
  described.
• II. Every body that moves in any curve line
  described in a plane, and by a radius, drawn to a
  point either immovable, or moving forward in a
  uniform rectilinear motion, describes about that
  point areas proportional to the times, is urged
  by a centripetal force directed to that point.
  This is the converse of Proposition I.
• III. Proposition II can be generalized to the
  case of a centre of force in any sort of motion.

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• The centripetal forces of bodies, which by
  equable motions describe different circles, tend
  to the centres of the same circles and are one
  to the other as the squares of the arcs described
  in equal times applied to the radii of the
  circles. In other words, F ? ?2/R, where F
  centripetal force, ? arc of the circle, and R
  radius of the circle.
• Corollary 1. Since the arcs described are
  proportional to angular velocity (V), i.e. ??V,
  then F?V2/R.
• Corollary 2. Since the periodic time around the
  circle (T) is proportional to R/V (and V ? R/T),
  then F ?R/T2.
• Corollary 6. If T ? R3/2, then F ? 1/R2. This is
  the case of the planets orbiting the sun.
• Corollary 7. In general, if T ? Rn, then F
  ?1/R2n-1.

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Proposition 2, Book I
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(No Transcript)
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The argument for universal gravitation
(Principia, Book III) I. The force that draws
Jupiter's moons out of rectilinear motion and
into their orbits (a) tends to Jupiter's centre,
and (b) is an inverse-square force i.e., it
varies as 1/D2, where D is the distance from the
centre of Jupiter. Proof (a) Phenomenon I and
Proposition II and III (b) Corollary 6,
Proposition IV. The same proposition holds for
Saturn and its moons. II. The forces that draw
the planets into their orbits (a) tend to the
centre of the sun and (b) are inverse-square
forces. Proof (a) Phenomenon V, and Propositions
II and III (b) Corollary VI, Proposition
IV. III. The force that holds the moon in orbit
around the earth (a) tends to the centre of the
earth and (b) is an inverse-square force. Proof
(a) Phenomenon VI, and Propositions II and III
(b) observations of the moons distance and
motion.
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IV. The moon gravitates toward the earth, and by
the force of gravity is continually drawn off
from a rectilinear motion and retained in its
orbit. Proof Since the force on the moon is
inversely proportional to the square of the
distance from the earth, and since its distance
from the earths centre is 60 times the radius of
the earth, then the force acting on the moon is
1/602, i.e. 1/3600, as powerful as the same force
acting at the earths surface (i.e., at one
radius from the centre). And it turns out that
the acceleration of the moon is exactly 1/3600 of
the acceleration of a falling apple at the
earths surface. Hence the force acting on the
moon is just gravity, attenuated by distance.
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V. Jupiters moons gravitate toward Jupiter
Saturns moons gravitate toward Saturn the
planets gravitate toward the sun, and are held in
their orbits by gravity. Proof Rule of
Reasoning II states that to like effects, we
should assign like causes. The force that urges
Jupiters moons toward Jupiter, and Saturns
moons toward Saturn, obeys the same law as the
force that urges the moon toward the earth, so
they must be the same force but by Proposition
4, this force is gravity.
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Corollary 1. All planets have gravity (i.e. a
gravitational force directed toward their
centres) for, doubtless, Venus, Mercury, and
the rest are bodies of the same sort with Jupiter
and Saturn. Furthermore, by Law III, all
attraction must be mutual, so these planets must
in turn gravitate towards their
satellites. Corollary 2. The power of gravity
towards any planet varies inversely as the square
of the distance from that planet. Corollary 3.
It follows from Corollaries 1 and 2 that all
planets gravitate towards each other. And hence
it is that Jupiter and Saturn, when near their
conjunction, by their mutual attractions sensibly
disturb each others motions. So the sun disturbs
the motions of the moon and both the sun and the
moon disturb our seas....
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VI. All bodies gravitate toward every planet, and
the weights of bodies toward any given planet, at
equal distances from the centre of that planet,
are proportional to their respective
masses. Proof This follows from Galileo's
demonstration that bodies fall at the same rate
regardless of composition, which Newton proved to
great accuracy using pendulums of different
kinds. Further demonstration is the fact that
the accelerations of Jupiter's moons (or
Saturn's, or of the planets around the sun)
depend only on their distances from Jupiter (or
Saturn or the Sun).
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VI. That there is a power of gravity tending to
all bodies, proportional to the several
quantities of matter which they severally
contain." i.e.,gravitation is universal, and the
force of gravity toward any body is proportional
to its mass. Proof The previous propositions
and proposition LXIX and its corollaries (book I)
jointly show that all planets have a power of
gravity and that this power is proportional to
their respective quantities of matter. Moreover,
since all the parts of any planet A gravitate
towards any other planet B and the gravity of
the part is to the gravity of the whole as the
matter of the part to the matter of to the matter
of the whole and (by Law III) to every action
corresponds an equal reaction therefore the
planet B will, on the other hand, gravitate
towards all the parts of the planet A, and its
gravity towards any one part will be to the
gravity towards the whole as the matter of the
part to the matter of the whole.
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The system of the world what is really moving,
and what is really at rest? Hypothesis I. That
the centre of the system of the world is
immovable. This is acknowledged by all, while
some contend that earth, others that the sun, is
fixed in that centre. Let us see what from hence
may follow. XI. That the common centre of
gravity of the earth, the sun, and all the
planets is immovable. Proof By Corollary 4 of
the Laws of Motion, that centre is either at
rest or moving uniformly in a right line but if
that centre moved, the centre of the world would
move also, against the Hypothesis. i.e., if
that centre moved, all bodies in the system would
share its motion, and nothing would be at rest.
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XII. That the Sun is agitated by a perpetual
motion, but never recedes far from the common
centre of gravity of all the planets. Proof The
ratio of the mass of the sun to the mass of
Jupiter is 1067 to 1 of the sun to Saturn is
3021 to 1 therefore, the centre of gravity of
the sun and Jupiter is just outside the surface
of the sun, while the centre of gravity of the
sun and Saturn is just inside the surface of the
sun. And, pursuing the principles of this
computation, we should find that though the earth
and all the planets were placed on one side of
the sun, the distance of the common centre of
gravity of all from the centre of the sun would
scarcely amount to one diameter of the sun.the
sun, according to the various positions of the
planets, must perpetually be moved every way, but
will never recede far from that centre.
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Corollary. Hence the common centre of gravity of
the earth, the sun, and all the planets, is to be
esteemed the centre of the world....
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To put the Earth in the centre makes as much
sense as thinking that the Earths mass can
balance all the other masses together.
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That makes as much physical sense as this picture