Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

psychological and artistic infinities 13Denys Turner’s chapter, “A (Partially) Skeptical Response to Hart and Russell,”takes issue with the two chapters that I just discussed. His issue seems to be that sayingthat God is infinite is not really the same kind of thing as saying that God is good.Roughly speaking, he feels that “being good” has some positive content that we canunderstand, while “being infinite” is in the nature of a negative statement akin to “notbeing finite,” with no positive content of its own. In his words:To get at the infinity of God, we would have to “get at” some intelligible content to thenotion of an infinite being. And that we cannot get at. For we possess no concepts and nolanguage, except that of negation, for doing so. Such a notion is utterly incomprehensible,beyond any power of expression. . . .(Turner, Chapter 14)The best response to this kind of remark is not so much a counterargument, but ademonstration. My feeling is that the mathematical science of set theory has indeedshown that we can form positive and meaningful ideas about infinite entities. And todeny this is perhaps only to reveal one’s unfamiliarity with the discipline in question.On the other hand, I myself have but the slightest familiarity with the fine pointsof theological discourse. Reading these chapters, I felt new kinds of thought patternsemerging in my mind. I’m still not quite sure what to make of them, but I’ll be happyto leaf through the final form of this book and ponder it all again.Psychological and Artistic InfinitiesCan we, in fact, think about infinite things? In the nineteenth century, the mathematicianBernard Bolzano formulated an argument for the infinitude of the class of all possiblethoughts. If T is a thought, suppose we write T ∗ to stand for the thought, “T is athought.” T and T ∗ are distinct thoughts, so if we start with any thought T, we can getan endless sequence of possible thoughts: T, T ∗ ,T ∗∗ ,T ∗∗∗ , and so on. Some, such asthe philosopher Josiah Royce, have viewed this as evidence that the mind has accessto infinity. One might say that the T series is only potentially infinite, that is, wedon’t literally think it all at once. But we do understand the idea of the T series all atonce.We can present something like the T series as a mental loop, along the lines of ameditation such as “I know that I know that I know . . .” But, rather than trying tohandle an infinitely long sentence, why not just think, “I know,” or perhaps “I am”?People who meditate on these kinds of things may experience moments of illumination.Perhaps they’ll even have a vision of a blinding white light. Are they seeing infinity?Or seeing God? Are these visions real?Perhaps. Those who’ve had a strong mystical experience are often very insistentthat their vision had some objective content. But how, one might ask, could a finitebrain hold infinity? Well, perhaps it is not that the mind actually contains the vision ofinfinity – any more than an eyeball contains a mountain. Perhaps the vision of infinitylies somehow outside the brain, let us say, in another dimension or at another level ofbeing.