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.

Motion and the Infinite

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

(St. Thomas Aquinas Oratio ante studium)
02/29/12

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Infinity is a Live Contemporary Issue
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Empiriological method tends toward reductionism.

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Is mobile being really an infinite collection of parts?

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Does infinity account for motion?
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And not matter-form-privation triads?

Zeno said motion is impossible because it would require
traversing an infinity.
∵ infinity = “unbounded” or “without limits.”

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Infinity is a Live Contemporary Issue
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Descartes defined matter as
quantity.
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Pythagoras: Infinity in sensible qualities

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Newton: universe finite, but Law of Inertia requires an
infinite chain of movers
Kant: Two lines of reasoning, one arguing for and the
other against the infinitude of matter, can both be true.
Among mathematicians:
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Dedekind & Cantor: numbers points on a line

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Cantor: “Trans-finite numbers” (‫)א‬
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Infinity is a Live Contemporary Issue

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“Each portion of matter may be
conceived as like a garden full of
plants, and like a pond full of fish.
But every branch of a plant, every
member of an animal, and every
drop of the fluids within it, is also
such a garden or such a pond.”

Aristotle declared motion eternal (infinite in
time).

02/29/12

From Leibniz’s Monadology:
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Democritus: Matter an infinity of identical atoms
that form matter only by different geometrical
arrangements
Plato: Infinity existed in his “realm of forms.”

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Thus, nature can have
mathematical infinities

Anaxagoras: “Mind” separated infinite matter
into parts.

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Infinity is a Live Contemporary Issue
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Etymologically: in- = “not”, finis = “end” or “bound”

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Creates impression infinite division in matter actually possible, not
just potentially

Is there a “finality in our knowledge of matter,” or is
matter “essentially infinite” as Bridgman thought?

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Infinity is a Live Contemporary Issue
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Traditional notions of infinity (McWilliams table):
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Absolute infinity: God as fullness of being

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Relative infinity:
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Realism says form terminates matter’s potencies.

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Matter cannot be composed of both finite and infinite components.

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Also called “privative infinite”
Aristotle’s definition of it: “that to which something more can
always be added”
Bolzano’s definition: “a quantity in which the parts are similar to
(equal to) the whole”

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Order is stability, so infinitely divided matter would be
chaotic.
Quantum physics says law of chance is basic law of
nature.
Indeterminate particle or universe is purely potential.

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Potency (matter) is the principle of individuation;
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Non regreditur in infinitum.

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Aristotle arrived at Prime Mover.

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∃ relatively prime movers (natures)

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An infinitely divided neutron would be:
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Purely potential

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Purely indeterminate
The only one ∵ all material reality would be appropriated to
it!

Infinity in matter, according to Aristotle, “will be at
home everywhere, then it will not be moved; or it will
be moved everywhere, then it will not come to rest.”

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Modern idea of inertia contains a contradiction:
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It says: Nothing can move itself from within.
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As opposed to inertias

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There is No Regression into Infinity

If there are an infinitely number of intermediate
movers between A and B, A cannot move B
because its influence would have to stretch an
infinite divide ( ∃ no proportion between finite and
infinite); thus, it cannot move B. Since we observe
motion, there cannot be an infinite regression.

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∴, a pluralistic universe is chaotic.

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Example: infinitely divided proton + finite electron =
hydrogen atom?

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There is No Regression into Infinity

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But it never really gets there, so there’s neither motion nor rest!
It is indeterminate.

Infinity in Matter Would Forbid Its
Motions

Dividing being you get being and non-being; ∴,
being = non-being‽

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The limit of mn, where n goes to infinity, is R!

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Indeterminacy of infinite regressions applied to being:
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m1 is state between M and R, m2 is between R and m1, m3 is between R
and m2, ad infinitum.

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Principled by the Infinite, the World
Would Be Homogeneous, Potential,
and Chaotic
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Aristotle: impossible for finite air to mix with infinite fire.

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Matter cannot be composed of infinitely many components ∵ it
would be undetermined (i.e., “not terminated”).

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Formally infinite (e.g., human intellect and will)
Materially infinite (e.g., prime matter unterminated or “unfinited” by form, second matter, and number)
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Principled by the Infinite, the World
Would Be Homogeneous, Potential,
and Chaotic

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So movement requires outside forces.
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This is a denial of natures.
Empiriological physicists call this order.

But where do these come from? Thus we have an
infinite regress.

Another argument against infinite regress:
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If there is no first mover, there cannot be
subsequent movers.
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Matter is Potentially, Not Actually,
Infinite

There is No Regression into Infinity
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A third rejection of an infinite series in matter:

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Instrumental cause (causa vitalis)

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Finitism: rejection of the infinite in motions
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If no first mover, everything is an instrumental
cause.

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Imagine a paintbrush painting the Mona Lisa on its
own!

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Einstein: universe is “finite but unbounded”
Finitists say: Motion is not continuous; ∃ a greatest
and smallest number; etc.

“Middle way” between finitist and infinitist
extremes:

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“Everything would be wholly for something else.”

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“reception itself would be a form of transmission.”

Change is potentially or materially infinite.

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Actually or formally finite.

Instrumentalism: everything is for another and
nothing in itself

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∄ a “completed infinity.”

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The Mathematical Infinite is the
Potential Infinite
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Is an irrational number like π or e infinite?

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Number line:

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Actual Infinity in Matter is a
Substitute for Form

Cantor’s sets: are there really “orders of
infinity”? ∃ more rational than irrational
numbers?

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Can potential points on a line uniquely map to
every real number?

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As V. E. Smith says: “Scientism [i.e.,
empiriological physics taken as philosophical
physics] has made matter’s actual infinity into a
shadowy substitute for the Aristotelian notion of
unity, nature, relation, number, and order.”
Since Descartes and Bacon, teleology and form
have been abandoned.
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Where is order, then?

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It must be sought in the indeterminacy of matter.

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Actual Infinity in Matter is a
Substitute for Form
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lim v / C = ∞

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lim C v = ∞

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lim C / v = 0

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V. E. Smith’s Philosophical Physics
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Please read ch. 4 (Motion and the Infinite).
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Lastly, empiriological physics tends toward
studying prime matter.
A.M.D.G.

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

Further reading:
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Modern mathematical infinity is simply a rule for
“determining the indeterminate.”

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References

Consider the following limits as v → ∞, where C
is a constant:
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02/29/12

Aristotle, Physics, Bk. III, chs. 4-8.
Aquinas, St. Thomas, Summa contra gentiles, Bk.
1, ch. 13.
McWilliams, J., Physics and Philosophy
(Washington, 1945), pp. 8, 135
A.M.D.G.

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