Plato Links:
Study questions on Plato (Timaeus and
commentary
- Huggett, Chapter 1)
1.
|
What are the three types
of things that Plato mentions? |
2.
|
Why must the thing upon
which the imprints are to be formed
be
totally
devoid of any characteristics? |
3.
|
Which of the three things
mentioned in (1) does Plato
identify
with
space? (Note: the reading has been edited in a slightly
misleading
way here.) |
4.
|
What are some
characteristics of space, according to Plato? |
5.
|
According to Plato, can
space act on physical objects? |
6.
|
How does Huggett define a
valid argument? |
7.
|
What is Huggett's
definition of a scientific theory?
According
to Huggett, what makes a theory good? |
Euclid Links:
Study questions on Euclid (The Elements
and
commentary
- Huggett, Chapter 2)
1.
|
How does Euclid define a
point? A line? A right
angle? |
2.
|
What are Euclid's five
postulates? |
3.
|
According to Postulate
32, the interior angles of any
triangle
are equal to what? |
4.
|
What does it mean to say
that a line is a dense collection
of
points? |
5.
|
How can Euclidean geometry
be thought of as a theory of
space?
In what sense can it immediately be said to be a "good" theory of
space? |
6.
|
How can Gauss' Experiment
be thought of as a confirmation
of
Euclidean
geometry thought of as a theory of space? Suppose you think
Euclidean
geometry is not true of the actual world. How could you respond
to
the outcome of Gauss' Experiment? |
Study questions on Zeno (Huggett, Chapter 3)
1.
|
Describe Zeno's first
argument against the possibility of
motion
(the Dichotomy argument). |
2.
|
According to Aristotle,
what are the two ways in which a
time
interval
or a line segment can be infinite? |
3.
|
How does Aristotle use the
distinction made in #2 as a
response
to
Zeno's first argument against the possibility of motion? Why does
Aristotle think this is not an adequate response? |
4.
|
How does Aristotle argue
for the possibility of having a
finite
length
of time composed of an infinite number of time intervals? |
5.
|
Describe Zeno's "Achilles"
argument against the possibility
of
motion. |
6.
|
According to Zeno, why is
a flying arrow motionless?
Why
does
Aristotle think this is false? |
7.
|
Describe Zeno's fourth
argument against the possibility of
motion.
(Note: the translation is a bit misleading.) |
8.
|
Describe the argument Zeno
gives against plurality (Fr.
13). |
9.
|
Which premise in Huggett's
reconstruction of the Dichotomy
argument
can we reject without having to reject Euclidean geometry? |
10.
|
What is Cauchy's
definition of an infinite sum? How
does
this
resolve the Dichotomy argument? |
11.
|
Why can't we use Cauchy's
definition of an infinite sum to
conclude
that the length of a line segment comprised of dimensionless points is
zero? |
12.
|
Why can't the length of a
finite line segment depend on
the
number
of points that make it up? |
13.
|
According to Huggett's
reconstruction of Zeno's Arrow
Paradox,
why
is motion during an instance impossible? |
14.
|
How does the "at-at"
theory of motion reconcile the claim
that
motion
during an instance is impossible with the claim that motion in general
is possible? |
15.
|
At any given instant t,
how can the "at-at" theory of
motion
distinguish
between an arrow in motion versus an arrow at rest? |
Study questions on Aristotle (Physics, On
the Heavens - Huggett, Chapter 4)
Physics
1.
|
What two reasons does
Aristotle give for why the concept of place
is so important? |
2.
|
Why does Aristotle think
the place an object occupies must
be
different
from the object itself? |
3.
|
In what way does place
exert an influence on objects? |
4.
|
According to Aristotle, in
what sense could place be the
form of
an object? In what sense could place be the matter comprising an
object? |
5.
|
Why does Aristotle think
place cannot be either the form or
the
matter
associated with an object? |
6.
|
Why does Aristotle think
place cannot be the "extension
between
the
extrimities" of an object? |
7.
|
What, finally, does
Aristotle take place to be? |
8.
|
What does it mean to say
that the place of a thing is the
"innermost
motionless boundary" of what contains it? |
9.
|
According to Aristotle,
why does the World have no place |
On the Heavens
10.
|
Why does Aristotle think
there cannot be a fourth
dimension? |
11.
|
According to Aristotle,
what movements constitute simple
locomotion? |
12.
|
What two simple bodies
move by nature away from the
center?
What two simple bodies move by nature toward the center? |
13.
|
Why must there be, in
addition to the four simple bodies
in #12,
a fifth simple body whose natural motion is in a circle? |
14.
|
Why is the fifth simple
body whose natural motion is in a
circle
"more divine and prior to" the other four simple bodies? |
15.
|
According to Aristotle,
why can't there be more than one
World? |
16.
|
Why does Aristotle claim
there is no such thing as
infinite
(i.e.,
unlimited) motion? |
17.
|
According to Aristotle,
why is the world (i.e., the
universe)
spherical
and not egg-shaped? |
18.
|
According to Aristotle,
why is the Earth motionless and at
the
center
of the universe |
Study questions on Descartes (Principles of
Philosophy
and commentary - Huggett, Chapter 4)
1.
|
Why don't we have to worry
about being decieved by "clear
and
distinct"
perceptions, according to Descartes? |
2.
|
What is the essence of
corporeal substance? What is
the
essence
of thinking substance? |
3.
|
Is there a difference
between an extended body and an
extended
space,
according to Descartes? |
4.
|
Why does Descartes think
that, in relation to different
bodies,
we
may say that the same thing is both changing and not changing its place
at the same time? |
5.
|
What is the distinction
between "internal place" and
external
place",
according to Descartes? |
6.
|
What do variation and
diversity in matter depend on? |
7.
|
How does Descartes define
"motion"? |
8.
|
Does Descartes think it
takes more action to move a body
than to
keep it at rest? |
9.
|
What is Descartes' first
law of motion? |
10.
|
How does Descartes' first
law of motion resolve
Aristotle's
problem
of describing projectile motion? |
11.
|
What is Descartes' second
law of motion? |
12.
|
How does Descartes avoid
Aristotle's objection to the
identification
of place with matter? |
Study questions on Newton (De Grav and Principia
- Huggett, Chapter 5)
De
Gravitatione
1.
|
Why is the tendency of the
Earth to recede from the Sun hard to
explain on Descartes' relational theory of motion? |
2.
|
According to Newton, how
can the following two situations
be
distinguished? (a) Earth at rest and stars revolving around
the Earth; (b) Earth rotating on its axis and stars at
rest. |
3.
|
According to Descartes,
can the two situations in #2 be
distinguished? |
4.
|
Why does Newton think
that, on Descartes' account of
motion, a
moving
body has no determinate velocity and no determinate line in which it
moves? |
5.
|
For Newton, are body and
extension identical? |
6.
|
What are some
characteristics of extension (i.e., space),
according
to Newton? |
7.
|
Why does Newton claim that
the parts of space are
motionless? |
8.
|
What does Newton mean when
he says, "Whatever is neither
everywhere
nor anywhere does not exist"? |
Principia
9.
|
How does Newton define
absolute time? |
10.
|
How does Newton define
absolute space? |
11.
|
How does Newton define
place? How does this differ
from
the
accounts of Plato, Aristotle and Descartes? |
12.
|
How does Newton define
absolute motion? |
13.
|
According to Newton, how
can we distinguish absolute rest
and
motion
from relative rest and motion? |
14.
|
What are the causes by
which true and relative motions can
be
distinguished? |
15.
|
What does Newton's bucket
experiment demonstrate? |
16.
|
Why are true motions
difficult to distinguish from
apparent
(relative)
motions? |
17.
|
What does Newton's globes
experiment demonstrate? |
Study questions on Leibniz and Clarke (The
Leibniz-Clarke
Correspondence - Huggett, Chapter 8)
1.
|
What is Leibniz's
Principle of Sufficient Reason? |
2.
|
What is space, according
to Leibniz? |
3.
|
According to Leibniz, how
would the existence of absolute
space
violate
the Principle of Sufficient Reason? |
4.
|
How does Clarke respond
Leibniz's "Static Shift" argument
described
in #3? |
5.
|
How do Clarke and Leibniz
differ over what the Principle of
Sufficient
Reason entails about God's actions? |
6.
|
What is Leibniz's
Principle of the Identity of
Indiscernibles? |
7.
|
According to Leibniz, how
would the existence of absolute
space
violate
the Principle of the Identity of Indiscernibles? |
8.
|
Leibniz considers the
following claim: "God can cause
the
whole
universe to move forward in a right line, or in any other line, without
making otherwise any alteration in it." Why does the existence of
absolute space entail this claim? Why does Leibniz think that
this
claim violates the Principle of Sufficient Reason? Why does he
think
it violates the Principle of the Identity of Indiscernibles? |
9.
|
Why does Clarke disagree
with the Principle of the Identity
of
Indiscernibles? |
10.
|
According to Clarke, does
a motion have to be observed in
order
to be real? |
11.
|
What type of motion of the
universe does Clarke think
would be
discernible
and thus would not violate the Principle of the Identity of
Indiscernibles? |
12.
|
According to Leibniz, does
a motion have to be observed in
order
to be real? |
13.
|
According to Leibniz, how
is absolute true motion
distinguished
from relative motion? |
Study questions on Berkeley and Mach (De Motu
and The Science of Mechanics - Huggett, Chapter 9)
1.
|
Why does Berkeley think
absolute space is "mere nothing"? |
2.
|
Why does Berkeley think it
makes no sense to speak of the
rotational
motion of two globes in an otherwise empty universe? |
3.
|
According to Berkeley,
what causes the water to recede from
the
axis
of rotation in Newton's spinning bucket? Why is this an
inadequate
response? |
4.
|
According to Berkeley,
with respect to what is the water in
Newton's
spinning bucket rotating? |
5.
|
According to Mach, why
should mechanics be concerned only
with
relative
motions and not absolute motions? |
6.
|
According to Mach, what
"twofold error" do we commit when
we
attempt
to talk of the motion of a body K in the absence of other reference
bodies? |
7.
|
Why does Mach think it is
"not permitted [of] us to say how
things
would be if the earth did not rotate"? |
8.
|
What conclusion about the
motion of the water in Newton's
spinning
bucket does Mach think it is legitimate to draw? How is this
conclusion
different from the conclusion that Newton draws? |
9.
|
Instead of Newton's
absolute space, what does Mach suggest
we use
as a frame of reference from which to judge intertial motions? |
Study questions on Kant - Part 1 (Huggett,
Chapter
11)
Concerning the Ultimate Foundation of the
Differentiation of
Regions
of Space
1.
|
According to Kant, what
does a region of space consist of? |
2.
|
According to Kant, how do
we determine the position of
places in
nature? |
3.
|
According to Kant, what
does the "complete principle of
determining
a physical form" rest on? |
4.
|
According to Kant, what
distinguishes a right hand from a
left
hand? |
5.
|
What is Kant's definition
of an "incongruent
counterpart"?
Give an example. |
6.
|
Kant refers to an "inner
principle" by which incongruent
counterparts
can be distinguished. Why can't this inner principle be
associated
with the different ways in which the parts of an object are connected
to
each other? |
7.
|
Suppose the only thing in
the universe was a human
hand.
Does
Kant think it necessarily would have to be a right hand or a left hand? |
8.
|
Suppose the only thing in
the universe was a human right
hand.
What does Kant think this would entail about the reality of space? |
Commentary
9.
|
What does it mean to say
that mirror images are incongruent? |
10.
|
In 2-dimensional space,
does the letter "F" have an
incongruent
counterpart? Explain. |
11.
|
Why does the definition of
incongruent counterparts in
2-dimensional
space need to be restricted to local regions of space? |
12.
|
How are the concepts of
"handedness" and "incongruence"
related? |
13.
|
How can a relationist
respond to the charge that there are
no
relational
differences between right and left hands? |
14.
|
According to Kant, would
reflecting the entire universe to
produce
a mirror image result in a different universe? Would such a
mirror
image count as a different universe for a relationist? |
15.
|
How can the "reflected
universe" example be used as an
argument
against absolute space? |
Study questions on Kant - Part 2 (Huggett,
Chapter
12)
The Critique of Pure Reason
1.
|
Does Kant think all
knowledge begins with experience? Does
he think all knowledge arises purely out of experience? |
2.
|
What characteristics must
knowledge have to be considered a
priori
for Kant? |
3.
|
Give an example of a
priori knowledge. |
4.
|
What is an analytic
judgement? Give an example. |
5.
|
What is a synthetic
judgement? Give an example. |
6.
|
Are judgements of
experience analytic or synthetic? |
7.
|
What is the "pure form of
sensibility"? In what sense
is it
a priori? |
8.
|
What is space, according
to Kant? |
9.
|
If knowledge of space were
a posteriori (aquired through
experience
alone), what would this entail about truths like "there is only one
straight
line between any two points"? |
10.
|
What does it mean to say
that Euclidean geometry consists
of
synthetic
a priori knowledge? |
11.
|
What does Kant mean when
he says, "It is therefore solely
from
the
human standpoint that we can speak of space"? |
Commentary
12.
|
What does the existence of
consistent non-Euclidiean geometries
entail about Kant's claim that Euclidean geometry consists of synthetic
a priori truths? |
13.
|
Is it a necessary and
universal truth that through any
point
only
one line can be drawn that is parallel to another line? |
14.
|
How does elliptical
geometry differ from Euclidean
geometry? |
15.
|
How does hyperbolic
geometry differ from Euclidean
geometry |
Study questions on Poincare (Huggett, Chapter 13)
Space
and Geometry
1.
|
Why does Poincare claim
that, if there were no solid bodies in
nature,
there would be no geometry? |
2.
|
According to Poincare,
what does it mean to say that space
is
homogeneous
and isotropic? |
3.
|
What does Poincare mean
when he says that geometry is only
the
summary
of the laws by which images we experience succeed each other? How
is this different from Kant's conception of geometry? |
4.
|
In what sense is
Poincare's sphere world a non-Euclidean
world? |
5.
|
According to Poincare,
what is the role of experiment in
determining
the geometric properties of physical space? |
Experiment and Geometry
6.
|
According to Poincare,
will astronomical observations of, say, the
parallax of distant stars ever enable us to decide what the geometrical
properties of space are? |
7.
|
How can Poincare claim
both that no experiment will ever be
in
contradiction
with Euclidean geometry and that no experiment will ever be in
contradiction
with Lobatschewskian geometr |
Commentary
8.
|
In discussing Poincare's
heated disk, why should we replace his
heat deformation force with a "universal" deformation force that
affects
all things in the same way? |
9.
|
Why do the surveyors in
the disk world believe their space
is
infinite? |
10.
|
Why do the surveyors in
the disk world believe the
geometrical
properties
of their space are Lobatschewskian (hyperbolic)? |
11.
|
How might other disk
scientists argue against the
conclusion of
the surveyors in #10? |
12.
|
According to Poincare,
what factors influence any attempt
at
conducting
surveying measurements? |
13.
|
What does it mean to say
that the choice of geometry is a
convention? |
Study
questions on Einstein (Huggett, Chapter 14)
1.
|
What are two ways of
regarding concepts, according to Einstein? |
2.
|
What does the concept of
space presuppose? |
3.
|
According to Einstein,
does Newtonian absolute space affect masses? Do masses affect it? |
4.
|
What role did the ether
have for 19th century physicists? |
5.
|
According to Einstein,
what is the relationship between a physical field and physical space
(i.e., the ether)? |
6.
|
What is the significance
of Lorentz transformations? |
7.
|
What is the principle that
characterizes the heuristic method of the special theory of relativity?
|
8.
|
What does the empirical
equivalence of inert and gravitational masses entail?
|
9.
|
What must be done to the
principle in #7 above in order to arrive at the general theory of
relativity?
|
10.
|
How are Riemannian spaces
different from Euclidean space?
|
11.
|
The metric field gmn
determines the structure of a Riemannian space. What did Einstein
assume about the metric field?
|
12.
|
In what sense is space no
longer absolute in general relativity?
|
|