There are two types of people. Those who say that the decimal notation 0.999… is not equal to 1, and then there are mathematicians who have proven that 0.999… is equal to 1.
The Catholic theologian Bernard Lonergan developed a theory of what it means to understand – a theory of knowledge – much like the Catholic apologist and saint, John Henry Newman’s theory of knowledge, which is fully capable of dealing with this. These men present theories of knowledge to respond to the extreme skepticism of men like David Hume who present a radically negative view of knowledge that surpasses even Descartes (the father of modern philosophy) and Socrates, whose skeptical claim that he knew nothing is differentiated from Hume’s skepticism very well in Peter Kreeft’s book, “Socrates Meets Hume.”
Not a lot of people I have met are up for this sort of discussion, but I am always game. But if we are going to begin reading Lonergan, we should perhaps also take a look at the Catholic philosopher, Alasdaire MacIntyre, who is very influenced by St. Thomas Aquinas.
So we have before us a study of all of mathematics, an inquiry of “what is number,” an investigation into the history of the several theories of epistemology from Socrates to Descartes to Hume and on to Lonergan and MacIntyre and perhaps much more. In other words, an investigation for a lifetime. And meanwhile we shall ever ask, where are you, God, Lord of all? And shall we not ever hear, “I AM.”
And in all of this, I am always delighted to find souls who delight in discussing the mystery that is number, the mystery that is knowledge, the mystery that is being, the mystery that is God, and any other mystery that seizes the soul, which are legion.