What follows is neither proof nor argument, nor philosophy of any sort, but rather an exercise in sociolinguistics. [And as such, a sort of sociological preparation for the thread announced here.] The point is simply to exhibit a common way of talking among contemporary mathematicians, as well as some physicists and philosophers -- an easy style of conversation that you would never imagine exists, if most of your acquaintance with science and its philosophy is mediated by figures like Daniel Dennett and Richard Dawkins.
To cite evidence of theistic talk from the learned men of history, from antiquity through the nineteenth century, would be pointless, since the mode was well-nigh universal, at all times and in all realms. Yet in our present day, most of the habitués of faculty clubs and coffee-houses have managed to satisfy themselves, that all those who ever lived, in history, from Pythagorus to the Einstein of “Der Herrgott würfelt nicht”, were, without exception, imbeciles, and simply didn’t know what they were talking about, when they talked that way. At last mankind has seen the light (or the darkness, rather); we speak only of what is sensible and sniffable, like Donald Trump. And who should be so rash as to cite the testimony of a mere Plato, or Galileo, or Cantor, or Gödel, against the brass certitude of so eminent a scholar as Sir Christopher Hitchens, Ph.D?
Therefore I shall limit myself to recent citations. A few examples from among many, snatched at random from recent reading.
Again, note: I am not implying anything about the theology, per se, of the people here quoted, let alone suggesting that they never miss Mass. Indeed a Dennett -- a roaring atheist -- can still indulge in such turns of phrases as "we can take advantage of the God's-eye perspective we have temporarily adopted" (the Devil can quote Scripture to his purpose). So far, this is just corpus linguistics; but more anon.
(1) Theistic language
(a) mathematics
Arthur Koestler, The Act of Creation (1964):
Karl Friedrich Gauss described how he finally proved a theorem on which he had worked unsuccessfully for four years: “At last, two days ago, I succeeded, not by dint of painful effort, but so to speak by the grace of God.”
Thomas Tymoczko, ed., New Directions in the Philosophy of Mathematics (1986, rev. 1998), p. 219:
In one of the most cited discussions in his much-quoted book, Kuhn [1962] talks of scientific decision in terms of “conversion experience” and “faith”.
Richard de Millo et al., “Social Processes and Proofs”, in Thomas Tymoczko, ed., New Directions in the Philosophy of Mathematics (1986, rev. 1998), p. 271:
The classical view does not require that an ordinary proof be accompanied by its formal counterpart; on the contrary, there are mathematically sound reasons for allowing the gods to formalize most of our arguments.
Similar language is often used in formulating the contemporary concept of a “hypertask”. Cf. likewise
Shaughan Lavine, Understanding the Infinite (1994), p. 55:
For Cantor … “countable” meant countable by God.
and similarly
Michael Potter, Set Theory and its Philosophy (2004), p. 250, re the plausibility of the Axiom of Choice:
… generalizing to the uncountable case by appeal to the idea than an ideal being could achieve the choices required of him (or perhaps Him).
If we adopt some particular postulate system for abstract set theory, and agree that the criterion for accepting an intuitive set-theoretic argument is that its analogue can be justified by the postuates, then we are in efect agreeing that the set of all intuitive sets endowed with the membership relation is a configuration satisfying the postulates. We can have at best intuitive reasons for believing this. It is really an act of faith.
-- Andrew Gleason, Fundamentals of Abstract Analysis (1966), p. 153
Gregory Chaitin, “Gödel’s Theorem and Information”, in Thomas Tymoczko, ed., New Directions in the Philosophy of Mathematics (1986, rev. 1998), p. 306:
If God tells one how many different programs of size less than N halt, this can be expressed as an N-bit base-two numeral, and from it one could eventually deduce which of these programs half and which do not. An alternative divine revelation would be knowing that program of size less than N which takes longest to halt.
Robin Wilson, Four Colors Suffice (2002), p. 214, recounting a mathematician’s reaction to the immensely long and repetitive, unsurveyable, computer-aided proof of the Four Color Conjecture:
God wouldn’t let the theorem be proved by a method as terrible as that!
(b) physics
Hermann Weyl, Symmetry (1952):
Contingency is an essential feature of the world. Clarke in his controversy with Leibniz admitted the latter’s principle of sufficient reason, but added that the sufficient reason often lies in the mere will of God. I think, here Leibniz the rationalist is definitely wrong, and Clarke [the theist] on the right track. But it would have been more sincere to deny the principle of sufficient reason altogether, instead of making God responsible for all that is unreason in the world.
Abdus Salam (1988):
God created just two dimensions -- one of space and one of time. … At a later epoch, there was a phase transition to four dimensions, plus six internal ones.
Stephen Hawking, A Brief History of Time (1988; 2nd edn. 1996) p. 91, alludes to Roger Penrose’s paraphrase of cosmic censorship: “God abhors a naked singularity.” The (jocularly) theistic language is especially odd and noteworthy, since the epigram here being echoed -- “Nature abhors a vacuum” (Latin: horror vacui) does not use it.
Stephen Hawking, A Brief History of Time (1988; 2nd edn. 1996) p. 126f.:
These laws [of physics] may have originally been decreed by God, but it appears that he has since left the universe to evolve according to them and does not now intervene…
That, then (for that author) leaves only the explanation of the settings of the parameters for initial conditions:
One possible answer is to say that God chose the initial configuration of the universe for reasons that we cannot hope to understand. This would certainly have been within the power of an omnipotent being, but if he had started it off in such an incomprehensible way, why did he choose to let it evolve according to laws that we could understand?
Simon Blackburn, Think (1999), p. 69, in a section called “A Scientific Model”:
Classical physics identifies the temperature of a gas with the mean kinetic energies of the molecules that compose it. So in making hot gases, God has only one thing to fix…
Blackburn is a philosopher, not a physicist; as commonly in that community, he is writing in an “as if” mode; but still, the choice of words is noteworthy.
John Gribbin & Martin Rees, quoted in Edward Harrison, Cosmology (2nd edn. 2000), p. 489: Absent the strong anthropic principle,
If there is a unique ‘theory of everything’, then … we would have to accept it as genuinely coincidental, or even providential, that the constants determined by high-energy physics happen to lie in the narrowly restricted range that allows complexity and consciousness to evolve…
(“Providential”… a lovely word…)
Paul Davies, The Goldilocks Enigma (2006), p. 3:
It appeared to Hoyle as if a superintellect had been ‘monkeying’ with the laws of physics. … Like the porridge in the tale of Goldilocks … the universe seems to be ‘just right’ for life.
Paul Davies, The Goldilocks Enigma (2006), p. 236:
Most theoretical physicists are Platonists in the way they conceptualize the laws of physics as precise mathematical relationships possessing a real, independent existence…
Shing-Tung Yau, The Shape of Inner Space (2010), p. 101:
As Robert Greene puts it, “you’re trying to find the one metric given you by God.”
Michael Atiyah re string theory, quoted in Shing-Tung Yau, The Shape of Inner Space (2010), p. 292:
They’re onto something, obviously. Whether that something is what God’s created for the universe remains to be seen. But if He didn’t do it for the universe, it must have been for something.
This statement is reminiscent of the Principle of Plenitude; and recalls Einstein’s celebrated quip, anent the possible failure of an experiment to confirm his prediction: "Da täte mir halt der liebe Gott leid; die Theorie stimmt doch."
Less seriously, but using a religious metaphor: J. L. Synge, Relativity: The General Theory (1960), p. ix:
It is to support Minkowski’s way of looking at relativity that I find myself pursuing the hard path of a missionary.
More serious is the following. The author is discussing the vexed question of the Collapse of the Wave-Packet upon observation (related to: If a tree falls in a forest, and no-one’s around, does it make a sound? -- here rewritten in Oxford terms, replacing the forest by a quad), and quotes the old limerick:
Dear Sir, Your astonishment’s odd;
I am always about in the Quad.
And that’s why the tree
Will continue to be,
Since observed by Yours faithfully, God.
He comments (J. C. Polkinghorne, The Quantum World (1984), p. 67):
Divine reduction of wavepackets would be an overkill, since it would operate everywhere and always, forcing the electron each time to go through a definite slit. The point about measurement is that it only occurs spasmodically.
Note the predicted empirical consequences of God in the Quad! Then, between square brackets, the author adds:
This observation is in accord with the classic theological understanding of creation, which sees God as the ground and support of all that is (in our terms, the guarantor of the Schrödinger equation), but not as an object among objects (no collapser of wavepackets).
This aside is in fact central: by the time he wrote this, Polkinghorne had quit his endowed Chair in physics to become a village vicar.
(c ) analytical philosophy
Michael Dummett, Truth and other enigmas (1978), p. 15, discussing character as (it may be, untested) hidden propensities:
If B still wishes to maintain the necessity of ‘Either Jones was brave or he was not’, he will have to old either that there must be some fact of the sort to which we usually appeal … or else that there is some fact of an extraordinary kind, perhaps known only to God.
Dummett’s use of the term, to characterise the viewpoint of a hypothetical philosopher inclined to Realism, is so to speak opaque, not representing his own view, which is rather (id, p. 150) that “only a philosophically quite naïve person would adopt realist view of statements about character”. Only such, or Saint Peter.
(2) Realist language
Arthur Koestler, The Act of Creation (1964):
Gauss is reported to have said: “I have had my solutions for a long time, but I do not yet know how I am to arrive at them.”
Klaus Jänich, Topology (1980; Eng. trans. 1984), p. 35:
When topological groups are found in nature [emphasis added], they are generally not given abstractly as a set G with a composition law and a topology, but concretely, as a group of transformations…
This is not really anymore outrageously realist than saying “When a set of six objects is found in nature…” (say, the familiar six-pack; although the one at my side is already down to five, and it’s not even noon).
And again, p. 157:
Covering spaces very often “occur in nature”: that is, one comes across them spontaneously, while studying entirely different problems.
Shaughan Lavine, Understanding the Infinite (1994), p. 160:
We seem to have nontrivial intuitions concerning the infinite, going far beyond simple things like Extensionality, Pairing, or even Power Set.
Shing-Tung Yau, The Shape of Inner Space (2010), p. ix:
The strength of this discipline [i.e., mathematics] lies not simply in its ability to explain physical reality…, because to a mathematician, mathematics is reality.
If all you know of math is elementary arithmetic, this statement may lack punch. But in the upper reaches of set theory, topology and so on, it embraces a world of miracles and of monsters.
~ ~ ~
It is important to note, that this is the way Realists talk en famille. The talk is casual, often not literal, yet is meant in some serious sense. It is not to be compared with the tawdry pseudo-theological, pseudo-mystical sort of gibberish that popular authors (and even some serious ones, yielding no doubt to the Satanic promptings of the marketing department) use to gin up their pap for the masses -- like “God particle” for the freaking Higgs boson.
It may be objected (it will be objected; it has been objected) that such expressions, in a modern mouth, are a mere façon de parler. To which we reply (with Whorf), that a façon de parler tends to cohere with a façon de penser.
Nor is it a refutation of the point here made, to adduce agnostic pseudepigrapha from any of the gentlemen here quoted. We are each a walking contradiction; we contain multitudes. C.S. Lewis himself confessed that he tended to be a cranky agnostic at dawn, but a theist later, when he’d had tea and was more himself.
Once again: The point here is not to assert that so-and-so among our near contemporaries is or is not a believer. Indeed it will strengthen my eventual case, if many of them are not in fact believers, yet find themselves attracted, or guided, or driven, to Realist or Theistic language, whether for convenience, or (in the case of Cantor, Gödel, and Einstein) something deeper.
So, a very modest initial move, a sort of pawn to king’s four. (Only later -- much later -- shall we see if we can capture Satan’s Queen.) So far we hold simply, that occasional use of Realist or Theist language, in serious discourse, is not in and of itself diagnostic for Trisomy 21.
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