AN AUGUSTINIAN PERSPECTIVE ON
MATHEMATICS
A dilemma
Could God have created a world in which
2+24
without changing the meanings of
2, +, =, and 4?
Augustine
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Born: 356 AD
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Died: 427 AD

Lived in N. Africa, spoke Latin

Probably the most influential Christian thinker
outside the biblical writers

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Much influenced by Plato; the “gold of the
Egyptians”
Wrote On Free Choice of the Will, c. 395 AD
Philosophy of Mathematics
Four basic themes:
1. Ontology
2. Epistemology
3a. Meaning of truth
3b. How do we account for the certainty of
mathematical truth?
4. Effectiveness
Ontology
For Augustine, mathematical objects (well, at
least the natural numbers) are ideas in the mind
of God and have been such from eternity.
Epistemology
Elementary truths of mathematics are present
to all who think - neither deduced nor induced
but perceived.
Not perceived by bodily senses - our
understanding of infinity is enough to prove that
Are more foundational than bodily senses.
Accessible to anyone who uses reason.
Concept of truth
Def’n: A truth is a necessary and therefore
immutable proposition.
Distinctive characteristics of all truths:
•necessity
•immutability
•eternity
•common to all minds that contemplate them
Some items of rational knowledge are truths.
Examples of truths
One ought to live justly.
Like should be compared with like.
Everyone should be given what is rightly his.
The uncorrupted is better than the corrupt, the eternal than the
temporal, the invulnerable than the vulnerable.
A life that cannot be swayed by any adversity from its fixed and
upright resolve is better than one that is easily weakened and
overthrown by transitory misfortunes.
Mathematical truths
Mathematical truths are instances of truths and
hence are:
- necessary
- immutable
- eternal
- and they transcend human minds
Effectiveness
“Every material object, however mean, has its
number.”
Augustine says things have form because they have
number - take away their number and they cease to
be.
Math is effective because the number of things
existed in the mind of God at creation and because
we are created in the image of God.
Reason
The ability to form and operate upon abstract
concepts
For Augustine, it’s how we learn anything and
includes deductive reasoning, i.e., logic
Benedict
…the faith of the Church has always insisted that
between God and us, between his eternal Creator
Spirit and our created reason there exists a real
analogy, in which - as the Fourth Lateran Council in
1215 stated - unlikeness remains infinitely greater
than likeness, yet not to the point of abolishing
analogy and its language.
Logos
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John 1 – “In the beginning was the logos…”
The Greek concept of “logos” includes reason
and order.
Colossians 1 – all things were made by and for
him
So all mathematics finds its origin and its
meaning in Christ – that is, he is the alpha and
omega of mathematics.
Kepler
I was merely thinking God's thoughts after him.
Since we astronomers are priests of the highest
God in regard to the book of nature, it benefits
us to be thoughtful, not of the glory of our minds,
but rather, above all else, of the glory of God.
Galileo
Philosophy is written in this grand book, the
universe, which stands continually open to our
gaze. But the book cannot be understood
unless one first learns to comprehend the
language and read the letters in which it is
composed. It is written in the language of
mathematics, and its characters are triangles,
circles, and other geometric figures without
which it is humanly impossible to understand a
single word of it; without these one wanders
about in a dark labyrinth.
BUT
Descartes
…the essence of the Enlightenment was the
belief that the world could now be seen in
mechanical terms and defined in mathematical
language…all reality…acts by natural laws , if
we had eyes to see them. The world of human
affairs, in sum, is the same as the natural world
because the same laws that govern each govern
all. The task for Enlightenment thinkers, then
was to ascertain those general laws that
governed reality and then apply them to the
various cases that came up, whether political,
economic, social, or religious.
Ronald Wells, History Through the Eyes of Faith
th
19

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Century England
George Boole – called the “father of pure
mathematics” by Bertrand Russell
Mary Boole – “Mathematics had never had more than
a secondary interest for him; and even logic he cared
for chiefly as a means of clearing the ground of
doctrines imagined to be proved, by showing that the
evidence on which they were supposed to give rest
had no tendency to prove them. But he had been
endeavoring to give a more active and positive help
than this to the cause of what he deemed pure
religion.”
The secularization of mathematics

Poor apologetics

Events within mathematics
Apologetics
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Oliver Byrne (1839) The Creed of Saint
Athanasius Proved by a Mathematical Parallel
++=
Within mathematics
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Rigorization
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Professionalization
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Non-Euclidean geometry
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Logicism – Russell
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Formalism - Hilbert
Russell
“It has gradually appeared, by the increase of
non-Euclidean systems, that Geometry throws
no more light on the nature of space than
Arithmetic throws on the population of the
United States…Whether Euclid’s axioms are
true, is a question as to which the pure
mathematician is indifferent…The [modern]
geometer takes any set of axioms that seem
interesting and deduces their consequences.”
Hilbert
“The fundamental idea of my proof theory is none
other than to describe the activity of our
understanding, to make a protocol of the rules by
which our understanding actually proceeds …
Already at this time, I would like to assert what
the final outcome will be: mathematics is a
presuppositionless science. To found it, I do not
need God or a special faculty of our
understanding…”
What are we to make of this effort to establish the
autonomy of mathematics?
If we grant that reason is rooted in the nature of
God, the secular position on mathematics has
fundamental intellectual and spiritual problems.
1. Autonomy

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The assertion of human autonomy from
God is the essence of sin.
“The gold of the Egyptians”
2. It starts from a false premise
Science / religion debate.
Atheistic perspective starts with the premise:
If science can explain x, then we don’t need
God.
Russell and Hilbert:
If mathematics can be cut loose from
moorings in anything external to itself, then it
doesn’t need God or anything external to
human thought.
Reason

The saying is sure:
If we have died with him, we shall also live with him;
If we endure we shall also reign with him;
If we deny him, he will also deny us;
If we are faithless, he remains faithful– for he cannot deny
himself.
2Tim 2: 11-13 RSV
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( p  p )
3. It doesn’t account for:

The fact that we have these incredible
capabilities

The certitude mathematics provides

Effectiveness of mathematics in describing
physical reality
4. Fractures human thought

Enlightenment defines reason as empiricism
and mathematics; Russell sees his view as
glorifying human thought.
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But these views exclude
 Ethics
 Culture
 Religion
Some implications
Augustinian view of mathematics:
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Is inspiring – the capacity to do math is a gift of
God, its content originates in God, a
mathematical career is a calling to think about
God’s wonders, it leads to service of his
kingdom, and to worship
Leads us to work for a more holistic view of
mathematics – one that includes history,
philosophy, ethics, and culture
Our calling
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Restoration – to reestablish the vision of
mathematics as rooted in the mind of God,
given to us that we might worship God and
build God’s kingdom
Transformation – to counter the turn away
from reason in popular culture by helping
our students value, trust, and use reason