A stimulating four-way discussion between mathematicians David Berlinski, Sergiu Klainerman, and philosopher of science Stephen Meyer, mediated by Peter Robinson, proposes that the existence of mathematics is a likely defeater for naturalist materialism, and a strong argument for theism.
The argument runs that mathematical truths are indisputably real, and yet immaterial, conceptual realities. The suggestion that mathematics is an invention of the human mind is denied by mathematicians, who see their task as discovering what is already there. The example of Euclidean geometry was raised in the discussion. Long before there were human minds, including Euclid’s, all circular things still had a circumference of πd, and would in principle have done so even before the actual existence of anything circular, or anything at all, come to that.
Klainerman emphasised that even advanced maths unreasonably predicts the real world. Einstein employed the esoteric developments in the maths of complex numbers, and the like, to predict his theory of general relativity, and it was only later confirmed experimentally. Extrapolating the maths beyond Euclid showed non-Euclidian space-time to be inevitable.
But Berlinski, characteristically incisive, said that one doesn’t need to go so deep. It is sufficient, to disprove materialism, to say that the glasses on the table are irreducibly two, or whatever number. Real numbers are a wholly conceptual universal, which is instantiated throughout the universe, and on which the whole universe is founded quite apart from relativity or fine-tuned cosmological constants. This fact shows that the mathematical concept is more fundamental than matter. And therefore matter/energy cannot be either the whole of reality, or the primary reality.
Although famously an agnostic, Berlinski introduced the philosophy of George Berkeley: if numbers are essentially a concept, then where was this concept when there were no human minds to conceive them before the Big Bang? Steve Meyer, a Christian, replied that the most parsimonious answer is that they originated and reside in the mind of an eternal Creator, “whom we call God,” as Aquinas said. Since mathematics is conceptually rational, then this God must be rational too.
I think it was Robinson who responded that Berkeley also suggested that matter itself, like number, is only a reality in the mind of God. Meyer dismissed this, saying (echoing Dr Johnson’s misunderstanding, I suppose) that the material world is a created reality, not an abstract concept.
I’m a fan of George Berkeley, and I argued here that the progress of science and information theory has only strengthened the appeal of his “subjective idealism.” Both “matter” and “reality” are extraordinarily hard concepts to demonstrate. But mind we experience directly. One you’ve read through that article (!) I want here to add some further thoughts on how it makes more sense of the reality of biblical creation than does the idea of a material world apart from God, which I suppose Steve Meyer holds. Not that Mayer would be interested in my views – nowadays he’s interacting with Sir Roger Penrose!
We start with the creation of all things by the Father’s Spirit, through his Word, which Word John shows us is nothing other than the Only-begotten Son. Human speech is immaterial thought expressed in breath, and can be regarded either as something external to the speaker, or as an aspect of himself. As the idiom says, “I gave him a piece of my mind.” So the divine analogy to this has the sense both of internality and externality to the mind of God. And yet unlike human speech, both the Word and Spirit are immaterial, so where, and what, is the “matter” so created?
That ambiguity carries on in the theology of the written word of God, which, Paul teaches, when internalised gives us “the mind of Christ.” Likewise the dabar of God in the prophets did not simply predict the future – like the speech-acts in Genesis 1 it brought it into being, because it was itself divine.
From my last post, where I distinguished the presence of the Word, in the word of Scripture, from the physical world, there is clearly a sense in which the distinction from God that Steve Meyer sees in creation is real. God is not present in nature in the same way he is in the “living and active” word. This is analogous, perhaps, with the way that our ideas need not reflect our own character: I once wrote a song from a bigot’s point of view, to criticise bigotry rather than to express my own.
Yet the intimacy of God’s involvement in the world pushes very much in Berkeley’s direction. To begin with, the creative role of the Word is not one-off, as in Deism, but ongoing: “in him all things hold together” (Colossians 1:17). A creation that would immediately cease to exist without the ongoing power of the divine Word is scarcely independent of God.
Our very existence is in God: “In him we live and move and have our being” (Acts 17:28). Conversely, God is said to be ubiquitous within creation, as the Psalmist discovers (Psalm 139:7-10), and Ephesians 1:23 says that Christ the Word “fills everything in every way.” Paul clearly does not mean to suggest pantheism or panentheism by this, for in Romans 1:20 he limits what may be known of God from nature to his “eternal power and deity.” Nevertheless the complete interpenetration of creation by God, acted out most visibly in providence, excludes a stark deistic duality from biblical theology.
The fact that God “works out everything in conformity with the purpose of his will” (Ephesians 1:11), and the classic examples of that such as Genesis 45:5-8, also emphasise the difficulty of separating God’s mind from the ongoing unfolding of creation-history. All analogies fall short over the vexed question of human free-will, but that is no more problematic for a creation in God’s mind than for a material world governed by providence.
I’ve heard it said that Nicolas Tesla was such a genius that he could plan a project in detail in his mind, without recourse to either pen and paper or trial and error. True or not, we can imagine such a situation as self-evident for God. There is no great conceptual problem for an infinite and omniscient God to hold the entire creation, in every detail and for all time, in his mind. And if he doesn’t, some other deity must have created the details. But Jesus said that the very hairs on our head are numbered. If the entire Creation is, then, encompassed in God’s mind, why is a separate material entity matching it not superfluous?
Now, imagine a sorcerer in a cartoon film, a veritable Nicolas Tesla in intellect, who, by a supreme effort of will and the pronouncing of the Magic Syllable of El-Tarah, mentally conceives of an entire world the size of a grapefruit. By his magic arts he then projects it to hover six feet in front of his face, sweating with the extreme mental strain. His cartoon apprentice, examining it closely, can see tiny creatures crawling about on a miniscule landscape. The servant-girl at the keyhole can see the apparition too. But as the sorcerer’s breath is exhausted, and the Magic Syllable is silenced, he slumps to the floor senseless, and the magic world dissipates.
Now in that thought-experiment, in what sense can we say that, although accessible to “public knowledge,” this magic apparition was anything else but a thought in the sorcerer’s mind? Can we say confidently that it had a separate existence in the world, or was its appearance to the onlookers, perhaps, an effect of the sorcerer’s mind on theirs? And would the difference actually matter? In Berkeley’s thought, the communion of minds is the most parsimonious explanation of reality, without the superfluous imposition of a dubious thing called “matter.” And of course, God never runs out of breath… and neither was there a pre-existing space outside himself into which he could project the actual Creation.
One of the modern theologians (was it Moltmann, or Hick?) supposed that for God to create, he has to diminish himself kenotically to “make room” for creation. This is as foolish, in my view, as suggesting that Beethoven had to make his mind smaller to make room for symphonies. Creation is if anything an increase, not a diminution, of God’s being. Yet the idea does highlight the problem of where, outside an infinite God, the cosmos could exist. There is no such problem in Berkeley’s framework.
So what would be the difference between such a real world as a thought in God’s mind, and other ideas flitting across his imagination? In Molinism, God deliberates between different ideas in his mind before deciding which world actually to create. But in classical theism, because God, who is pure Spirit and pure Act, knows himself perfectly, he has no need of deliberation. What he wills to create is not just one idea among many, but simply the Truth, for God is simply Truth, and, Knowledge, and Wisdom, and Liberty. Does that mean that God creates from necessity? No more than the fact that he cannot be other than good limits his freedom. One can say that God-as-Creator is exclusively expressed in the actual Creation, just as God as self-giving Servant is wholly expressed in the Incarnation of the Son.
Furthermore, were we naively to follow Dr Johnson in fearing that Berkeley’s conceptual world lacks solidity, remember what C. S. Lewis said on a number of occasions: the world of the Spirit is not invisible and nebulous to us because it is insubstantial, but because we are. There can be nothing more solid and substantial than an idea in the mind of the God of Truth.
Isn’t this all angels on heads of pins stuff? I think not, and not just (as I wrote in my 2019 piece) because it solves the problems raised by Descartes’ substance dualism, and by modern science’s “bit before it” conundrum. If our own mental picture of the world grasps the intimacy with which we are present to God, and he to us, and fully appreciates that it is the realm of the spirit that is our true dwelling, then we’re going to be immune to materialism, more alive to God in his world, more connected to his will, more faithful in prayer, and even more appreciative of the wonder of a creation that, like mathematics, is full of God’s glory.
