The Science of Mobile Being (part
2)

O Creator ineffable, who of the riches of Thy wisdom didst
appoint three hierarchies of Angels and didst set them in
wondrous order over the highest heavens, and who didst
apportion the elements of the world most wisely: do Thou,
who art in truth the fountain of light and wisdom, deign to
shed upon the darkness of my understanding the rays of
Thine infinite brightness, and remove far from me the twofold
darkness in which I was born, namely, sin and ignorance. Do
Thou, who givest speech to the tongues of little children,
instruct my tongue and pour into my lips the grace of Thy
benediction. Give me keenness of apprehension, capacity for
remembering, method and ease in learning, insight in
interpretation, and copious eloquence in speech. Instruct my
beginning, direct my progress, and set Thy seal upon the
finished work, Thou, who art true God and true Man, who
livest and reignest world without end. Amen.

Regina Cœli Academy
Natural Philosophy – Physics
Lecturer: Mr. Alan Aversa

(St. Thomas Aquinas Oratio ante studium)
02/01/12

A.M.D.G.

1

02/01/12

Empiriological physics does not
attain being.
●

–

●

●

The parts of a broken glass do not spontaneously reassemble into a whole glass.

Law of Inertia
Does it show that moving things tend to be constantly in flux (á la
Heraclitus) or that change is an illusion (á la Parmenides)?

●

–

A.M.D.G.

●

3

02/01/12

–
●

●

Y = F(x)
–

●

F is a function.
x is the independent variable.
Y is the dependent variable.

They in no way imply one quantity causes another
–

●

∵ correlation doesn’t necessarily imply causation.

A.M.D.G.

A.M.D.G.

4

Concept of a limit is very important in calculus.
V. E. Smith’s definition of limit: “y is a limit of x if,
when x increases indefinitely, the difference
between y and x gradually becomes smaller
than any assignable value.”
Examples:
●

●

02/01/12

Newton, in his Philosophiæ Naturalis Principia
Mathematica, & Leibniz co-invented

Empiriological physics does not
attain motion.

Functions relate one quantity to another. E.g.:
–

In other words: calculus!
–

Empiriological physics does not
attain motion.
●

Diogenes disproved this simply by walking!

Henri Poincaré and Bertrand Russell, e.g.,
thought that empiriological physics is the
description of the world via differential
equations.

Viz., does this the law of inertia imply empiriological physics studies ens
mobile like philosophical physics?

02/01/12

●

Zeno argued motion is impossible
●

Heat cannot pass from a cold to a hot body.
Things in nature do not spontaneously become more ordered without an
input of work.

Does it prove causality or presuppose it?

●

●

●

Many equivalent formulations of it; here are two examples:
–

2

Empiriological physics does not
attain motion.

2nd Law of Thermodynamics
●

A.M.D.G.

5

02/01/12

If # of sides of a regular polygon → ∞, then the limit
of the polygon is a circle.
If the function N(t) is how much radioactive material
you have at time t, limit of N(t) as t → ∞ is 0.
A.M.D.G.

6

Empiriological physics does not
attain motion.
●

Empiriological physics does not
attain motion.

Archimedes computed π to be the limit of the
areas of polygons with increasing numbers of
sides.
●

●

π is the ratio of any circle’s circumference to its
diameter.

●

Let y be a function of x, so y = f(x).

●

Δx = a small change in x.

●

Δy = a small change in y.

●

Calculus measures the limit of this ratio:

π ~ 3.1415926....
●

02/01/12

A.M.D.G.

7

Let y be a function of x, so y = f(x).

●

Δx = a small change in x.

●

Δy = a small change in y.

●

Calculus measures the limit of this ratio:

●

●

●

(Δy / Δx) as Δx → 0.

●

This limit is the derivative of f with respect to x.

●

●

A.M.D.G.

●

A.M.D.G.

9

“But quantity is not motion; change is not a ratio or
relation.”
It isn’t a succession of events
or potency becoming act insofar as it is in potency.

Remember: Mathematics is the 2nd degree of
abstraction.
●

02/01/12

Boethius: “Mathematics does not deal with motion…for
it investigates forms of bodies apart from matter…and
therefore apart from movement.”
A.M.D.G.

10

MOTION AND ITS PRINCIPLES:
Motion is given in experience.

Philosophical physics studies what follows from
being and motion.

●

Parmenides thought motion is an illusion.

●

Heraclitus thought everything was in flux.

●

Empiriological physics ignores being and
motion.
It assumes whatever is meaningful is measurable.

●

Being cannot be measured because there is
nothing outside of being to which to compare it.
A.M.D.G.

8

Derivatives tell about instantaneous rates of
change of one quantity with respect to another.

–

Empiriological physics evolves rapidly over
time.

02/01/12

Equations with derivatives are called differential
equations.

●

Equations with derivatives are called differential
equations.

●

This limit is the derivative of f with respect to x.

Empiriological physics does not
attain motion.

Philosophical physics does not
suppose the empiriological.
●

●

–

●

02/01/12

(Δy / Δx) as Δx → 0.

02/01/12

Empiriological physics does not
attain motion.
●

●

11

St. Thomas says in his First Way of proving
God’s existence: “It is certain, and evident to
our senses, that in the world some things are in
motion.”
Distinction: mutatio (change proper) and motus
(continuous, successive change)
●

02/01/12

Will be important later.
A.M.D.G.

12

Motion is determined by act and
potency.

Motion is not deducible.
●

●

Aristotle: motion is known by induction.
Can we deduce motion from something more
known? Is anything more known in nature than
motion?
●

●

●

●

How is motion defined?

●

It’s definition more difficult than its discovery.

●

Can the more evident be proven by the less evident?

●

Motion cannot be measured because motion is
not quantity.

A.M.D.G.

13

02/01/12

Motion is determined by act and
potency.

●

●

●

●

Being is; non-being is not.
There cannot be anything between being and nonbeing, and motion is the passage from being to
non-being or vice versa.
Nothing can come from being because it already is,
and nothing can come from nothing, either: ex nihilo
nihil fit.
Therefore, motion is impossible.

02/01/12

A.M.D.G.

15

References
V. E. Smith’s Philosophical Physics
●

Please read finish ch. 1 (The Science of Mobile
Being) and begin ch. 2 (Motion and Its Principles).
–

●

We will send out a scanned PDF of this necessary
reading.

Next time we will see how motion is a mixture
of act and potency.

02/01/12

A.M.D.G.

A.M.D.G.

14

Motion is determined by act and
potency.

Parmenides argued motion is impossible, an
illusion:
●

●

We will discuss Zeno’s argument later because it
deals with infinity.

The static can only be known in reference to the
moving.

02/01/12

●

Parmenides & Zeno (Eleatics) versus
Heraclitus

17

●

Heraclitus denied being and thought everything
is in motion.
●

Fire represented something always changing.

●

So did the flow of time.

●

E.g.: No man can swim in the same stream twice.

Aristotle reconciled Parmenides’s and
Heraclitus’s views.
●

Act = existence

●

Potency = capacity to be actual

02/01/12

A.M.D.G.

16