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. Born: 356 AD Died: 427 AD Lived in N. Africa, spoke Latin
Could God have created a world in which
2 + 2 4
without changing the meanings of
2, +, =, and 4?
For Augustine, mathematical objects (well, at least the natural numbers) are ideas in the mind of God and have been such from eternity.
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.
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.
“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.
The ability to form and operate upon abstract concepts
For Augustine, it’s how we learn anything and includes deductive reasoning, i.e., logic
…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.
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.
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.
…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
+ + =
“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.”
“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…”
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.
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
Augustinian view of mathematics: