Posted on 01/10/2009 3:10:02 PM PST by NYer
From Sandro Magister of Chiesa, a piece about Pope Benedict XVI's interest in the nature of mathematics within the relationship of faith and science:
Scientists of worldwide fame, like Richard Dawkins of England and Piergiorgio Odifreddi of Italy, insistently link mathematics with the profession of atheism. Spread through conferences, articles, and best-selling books, their theories aspire to become a common language and philosophy.In simple terms, the objections to these atheist mathematicians are the ones expressed by a 17-year-old Roman high school student, Giovanni, during a question-and-answer session with the pope in St. Peter's Square, crowded with young people on April 6, 2006:
"Holy Father, we are often led to believe that knowledge and faith are each other's enemies; that it was through mathematical logic that everything was discovered; that the world is the result of an accident, and that if mathematics did not discover the theorem-God, it is because God simply does not exist."
Benedict XVI responded to these objections as follows:
"The great Galileo said that God wrote the book of nature in the form of the language of mathematics. He was convinced that God has given us two books: the book of Sacred Scripture and the book of nature. And the language of nature – this was his conviction – is mathematics, so it is a language of God, a language of the Creator.
"Let us now reflect on what mathematics is: in itself, it is an abstract system, an invention of the human spirit which as such in its purity does not exist. It is always approximated, but as such is an intellectual system, a great, ingenious invention of the human spirit. The surprising thing is that this invention of our human intellect is truly the key to understanding nature, that nature is truly structured in a mathematical way, and that our mathematics, invented by our human mind, is truly the instrument for working with nature, to put it at our service, to use it through technology.
"It seems to me almost incredible that an invention of the human mind and the structure of the universe coincide. Mathematics, which we invented, really gives us access to the nature of the universe and makes it possible for us to use it. Therefore, the intellectual structure of the human subject and the objective structure of reality coincide: the subjective reason and the objective reason of nature are identical. I think that this coincidence between what we thought up and how nature is fulfilled and behaves is a great enigma and a great challenge, for we see that, in the end, it is 'one' reason that links them both. Our reason could not discover this other reason were there not an identical antecedent reason for both.
"In this sense it really seems to me that mathematics – in which as such God cannot appear – shows us the intelligent structure of the universe. Now, there are also theories of chaos, but they are limited because if chaos had the upper hand, all technology would become impossible. Only because our mathematics is reliable, is technology reliable. Our knowledge, which is at last making it possible to work with the energies of nature, supposes the reliable and intelligent structure of matter. Thus, we see that there is a subjective rationality and an objectified rationality in matter which coincide. Of course, no one can now prove – as is proven in an experiment, in technical laws – that they both really originated in a single intelligence, but it seems to me that this unity of intelligence, behind the two intelligences, really appears in our world. And the more we can delve into the world with our intelligence, the more clearly the plan of Creation appears.
"In the end, to reach the definitive question I would say: God exists or he does not exist. There are only two options. Either one recognizes the priority of reason, of creative Reason that is at the beginning of all things and is the principle of all things – the priority of reason is also the priority of freedom –, or one holds the priority of the irrational, inasmuch as everything that functions on our earth and in our lives would be only accidental, marginal, an irrational result – reason would be a product of irrationality. One cannot ultimately 'prove' either project, but the great option of Christianity is the option for rationality and for the priority of reason. This seems to me to be an excellent option, which shows us that behind everything is a great Intelligence to which we can entrust ourselves.
"However, the true problem challenging faith today seems to me to be the evil in the world: we ask ourselves how it can be compatible with the Creator's rationality. And here we truly need God, who was made flesh and shows us that he is not only a mathematical reason but that this original Reason is also Love. If we look at the great options, the Christian option today is the one that is the most rational and the most human. Therefore, we can confidently work out a philosophy, a vision of the world based on this priority of reason, on this trust that the creating Reason is love and that this love is God."
the great option of Christianity is the option for rationality and for the priority of reason
Heavey stuff but the Holy Father makes a masterful statement.
...and Carl Olsen is right on top of everything. I am very impressed with what he does at Ignatius Insight! ;-))))
read later
Indeed! Thanks for joining the conversation :-)
A slight misquotation, but perhaps of significance in these careful formulations.
In The Assayer, Galileo wrote, "Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics ... "
Regarding mathematics itself, Galileo seemed to have the Platonic view, that mathematics concerned itself with an abstract reality distinct from material reality. Pope Benedict is careful to say that mathematics is an "invention of our human intellect."
Near the end of "The First Day" in The Dialogues Concerning the Two Chief World Systems, Salviati expands on this theme. Regarding mathematical propostions he says, "... I say that the human intellect does understand some of them perfectly, and thus in these it has as much certainty as Nature itself has. Of such are the mathematical sciences alone; that is geometry and arithmetic, in which the Divine intellect indeed knows infinitely more propositions, since it knows all. But with regard to those few which the human intellect does understand, I believe that its knowledge equals the Divine in objective certainty ..."
In a footnote, Stillman Drake notes that this passage was cited as representing one of eight points offensive to the Church - "6. That he asserted some equality between the Divine and the human mind in geometrical matters."
So it would seem that we might still feel a little frisson when we read "the great Galileo".
Without making too much of it, I perceive some equality between human and angelic intelligence in geometric matters.
I think “angelic” is a cop-out. When he spoke of the “Divine intellect” Galileo was clearly referring to God.
He acknowledges, BTW, the controversial nature of these remarks right in the Dialogue, with Simplicio remarking, “This speech strikes me as very bold and daring.” Of course Salviati duly denies it.
Angelic
math ping
Sc.B Applied Math here ...
“God ordered all things by measure, number, weight”.
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