On the verification of a proof of ‘God’s existence’
Der Spiegel online offered an eye-cathcing headline last week: ‘Computer Scientists “Prove” God Exists’ (article here). The article referred to a pre-publication report of a paper submitted to arxiv.org last month, entitled ‘Formalization, Mechanization and Automation of Gödel’s Proof of God’s Existence’ (here). Essentially, the paper claims – it is more of an abstract and statement of results – that (a form of) Kurt Gödel’s modal ontological argument had been successfully coded, and that its validity had been demonstrated using – the detail I rather liked – programs running on a MacBook. As my colleague Alan Torrance pointed out on FB, this is not surprising; there has been a fairly general acceptance of Gödel’s logic for a while now. And as Der Spiegel pointed out, the point of the research was not to prove God’s existence but to demonstrate the possibility of computerised verification of logical arguments, using an argument of some fame, and of acknowledged complexity, as a test case. That said, the statement that a proof of God’s existence has been shown to be valid is not uninteresting – and that it is a version of the (in)famous ontological argument is very pleasing to those, like me, who see a restless fascination with the ontological argument as the infallible mark of a truly philosophical mind… Attentive readers will have noted some variation in use of scare quotes in the various headlines: the original piece used none; the newspaper article suggested ‘proof’ was being used wrongly; my title suggests the issue lies with ‘God’s existence’. Obviously, I think my usage is correct, but these differences highlight what is at stake. In defence of the original authors, they were referring to ‘Gödel’s proof of God’s existence’ in the same way they might have referenced ‘Fermat’s last theorem’: it is a well-known logical conundrum of interest to logicians because it appears correct but seeming has proved difficult to demonstrate completely. Der Spiegel‘s headline (at least in translation; I could not find an easy way to navigate to a German original of the article) suggested that the ‘proof’ was dubious; this is precisely wrong; assuming the correctness of the results reported, the heart of the research findings is the fact that the proof is certain, and demonstrated to be so. But what has been proved? Deductive logic always proves the same thing: that, given a certain set of axioms and definitions, a certain set of conclusions follows from a certain set of premises. (In modal logic there is an added complication of which modal logic is in play; if you are interested in the technical details of modal logics, go and get a life the paper claims that KB is sufficient for the proof to work; S5 is not needed.) In serious logic, the axioms and definitions are necessarily seriously abstruse and formal (here, Definition 3 asserts ‘Necessary existence of an individual is the necessary exemplification of all its essences’). The precise proof is that, given five axioms and accepting three definitions, it can be shown that a ‘God-like being’ necessarily exists, where ‘God-like’ means ‘possessing all positive properties’ (this is essentially a formalisation of perfect being theology). So what hesitations might we have before claiming ‘scientists have proved that God exists?’ Two, one more (theologically) significant than the other. First, and less significant, the proof is uninteresting (except as a neat bit of demonstrated logic) if any of the axioms or definitions are dubious. The three required definitions and five stated axioms are as follows (you can look up the symbolic logic in the paper above if you are interested): D1 A ‘God-like’ being possesses all positive properties. D2 An ‘essence’ of an individual is a property possessed by it and necessarily implying any of its properties. D3 ‘Necessary existence’ of an individual is the necessary exemplification of all its essences. A1 Either a property or its negation is positive, but not both. A2 A property necessarily implied by a positive property is positive. A3 The property of being ‘God-like’ is positive. A4 Positive properties are necessarily positive. A5 Necessary existence is a positive property. Now, anyone at all familiar with debate over the ontological argument in its various forms will fairly quickly spot the first point of attack here: is the concept of ‘necessary existence’ coherent/meaningful? (And, concomitantly, is the claim that it is a positive property if coherent justified?) As the authors say in their concluding paragraph, ‘[t]he critical discussion of the underlying concepts, definitions and axioms remains a human responsibility…’ (In reading the proof, I am also struck by the unspecified value-judgement implied in the word ‘positive’; A3, A5, and probably D1 seem to me to smuggle in...
Read MoreWhy read theology?
I am thinking about the curriculum for a new compulsory module I have to teach entitled ‘Readings in Medieval Theology,’ and doing the usual academic thing with a new module, particularly a new module you didn’t design, of trying to work out some intentionality: why am I teaching this (beyond the fact that I have to)?; what do I want the students to get out of it? There are various levels at which I can answer the question. The module exists in part because we believe that reading primary sources in the tradition should be a part of a theology degree (there are other compulsory modules in patristics, Reformation, and modern theology). This is in part about content: I occasionally apply the ‘graduation test’ to the curricula I teach: what would really embarrass me if it suddenly struck me at a graduation ceremony that someone was on stage getting a theology degree without having read it? Amongst the medievals, only Thomas’ Summa Theologica really passes that test for me. (And so I have always taken every opportunity to get primary reading in the ST in – together with a well-honed piece on how to read the text, beginning ‘The Summa is divided into five parts, helpfully numbered one to three…’) There is also a skills element: reading primary texts, particularly ancient texts, intelligently is, or should be, a core skill in any humanities degree. Like most skills, it is gained only by practice, so compulsory readings modules have become a significant component of our degrees. I want to go deeper than either of those answers, however. Why should anyone do a theology degree at all? Some of our students are preparing for Christian ministry, but even there – why does a pastor need to have read Thomas Aquinas, still less Teresa of Avila, Catherine of Siena, John of Damascus, or John Major (all of whom will feature in my module)? My answer comes straight from the medieval universities that Thomas and John Major taught in: we read theologians to learn how to think theologically. The texts we read are, at one level, entirely irrelevant. We are trying to learn an art, and thinking along with good practitioners of the art will help us to learn it. Thinking along with the greatest practitioners will help us to fly as high as we can, which is why undergraduates really should read Thomas (and Augustine, and Calvin, and Schleiermacher, and Barth) – and why graduate students should pick a great mind to live with for their three years of formation. (And why those of us who presume to teach should be reading the greats very regularly…) The point of a theology degree is not that you know what Thomas or Calvin thought about this or that; the point is that, when asked what a Christian should think about this or that, you are a bit more able to give a worthwhile answer than you would have been had you not done the degree. (Of course, giving the time you spent doing the degree to prayer, or evangelism, or serving people who are poor and/or marginalised, would have been far more productive in these terms, but…) You know where to look for answers, have a sense of which logical distinctions might become important, and are just skilled, in a thousand subtle ways, at thinking in this mode. (This generalises, of course. The point of doing any degree – possibly with the exceptions of medicine and law, amongst the traditional subjects – is to learn to think. The knowledge you acquire along the way is entirely accidental; what you (should…) gain is an ability to address any question, any problem,...
Read MoreRob Bell, Love Wins 5
One more post on chapter 1, looking again at complaints about Bell’s ‘orthodoxy.’ The chapter begins with a story that Bell told in the promotional video, and which has therefore become famous. An art exhibition at church included an exhibit with a quotation from Gandhi; someone attached a post-it note reading ‘Reality check: he’s in hell.’ Bell writes: Really? Gandhi’s in hell? He is? We have confirmation of this? Somebody knows this? Without any doubt? And his pre-publication detractors once again took him to task. And again, they were badly wrong – in my view, and in the view of (here) virtually the entire Christian tradition. Remember Johann Heidegger from a couple of posts back? He was the Reformed writer who held that the number of the saved would indeed be small. Shedd and Warfield condemn him for being far too conservative in his theology. Heidegger wrote about precisely this question, and said this: No one except those who sin unto death ought to or can determine anything certain before the end of life, concerning the eternal reprobation of himself or of others. Of others indeed we must have good hopes by the judgement of love, 1. Cor.13:7 (beareth, believeth, hopeth, endureth all things)… (q. ET from Heppe, p. 188, with error silently corrected). Let’s do a kind of scale of theological conservatism here, shall we? Shedd and Warfield are conservative – I believe that will be generally granted. They reprove Heidegger for being far too conservative. That makes him, what? Ultra-conservative? Heidegger then rejects as far too conservative the position that we can know for certain that any other human being is damned. We’re somewhere off the scale now, in the company of those who think the Taliban are dangerously liberal. I have thought hard about anyone in the Christian tradition who held to this position, that we can know for certain that a particular person is in hell. There were, to be fair, some Landmarkian Baptists. And Dante, I suppose, although he might claim his allegory was not meant to be taken like that. Certainly, there are not many. And yet when Bell doesn’t even say that this is wrong, but merely questions whether it is right, we are told that he has committed an error so grave that he must be publicly castigated. I can’t quite decide whether this is simply brilliant debating work from Bell, enticing his opponents to defend a position so extreme that no one in their right mind would touch it, or whether his opponents really, genuinely, don’t realise just how far behind they have left anything resembling historic orthodoxy. This is not mere theological hair-splitting. This point is pastorally vital. Bell’s other example concerns an atheist teenager, killed in a car crash. ‘There’s no hope, then,’ comes the comment, reflecting this ridiculously extreme position. All of us who are Christian pastors have performed funeral services for those with no visible faith, and have been offered care and counsel to those, actively Christian or not, who have lost an apparently-unbelieving family member or friend. The first rule of such pastoral engagement has always been not to speculate about the fate of the dead person. One speaks with confidence the promises of Jesus, proclaims the sure and certain hope of the resurrection of the dead, announces with utter conviction the defeat of death and sin and hell in the cross, and invites, implicitly or explicitly, the hearers to place their own faith and trust in these realities. The one who has died is in God’s hands, and it is not for us to judge. The gospel of Jesus is never, ever, ‘there’s no hope, then.’ This point is utterly vital, and Bell is simply...
Read MoreA call for conceptual clarity about conceptual clarity
(A title of which Doyeweerd would have been proud…) The collection Analytic Theology (OUP, 2009; ed. by Oliver Crisp and Mike Rea) contains several excellent and entertaining pieces, clustered around a claim that theologians ought to be attentive to the turn to explication of core Christian doctrines by analytic philosophers of religion. The claim seems to me a necessary one; as Thomas McCall puts it elsewhere ‘[s]ome theologians are surprised to learn that theological issues are under consideration at all in the analytic community, while other theologians are skeptical – to say that they are dubious that any good could come out of Notre Dame is to put it mildly.’ (Whose Trinity? Which Monotheism? (Eerdmans, 2010; p.1). For me, ever since interacting with Paul Helm – and indeed Oliver Crisp – when I was a doctoral student, the use and attraction of analytic tools has been obvious. It is simply a given, as far as I can see, that all intellectual work benefits from conceptual clarity, that analytic tools are finely honed precision instruments for the clarifying of concepts, and that contemporary theology has (famous and influential) exemplars whose lack of conceptual clarity is astonishing (see Randy Rauser’s entertaining and sharp application of Harry Frankfurt’s category of ‘bullshit’ to the writings of certain contemporary theologians in Analytic Theology). That said, the pursuit of conceptual clarity using analytic tools has certain limitations, which we need to be clear about. The most purely ‘analytic’ thinker in the Christian tradition is, I think, Eunomius, the primary heresiarch of the fourth century (far more so than Arius). Eunomius worked with a philosophy of language (probably derived via Porphyry from Plato’s Cratylus) in which words, properly used, corresponded to things in a one-one mapping. The proper name of God, naming that which is essential to be divine, is ‘unbegotten’; therefore the Son is not God. The Cappadocian logic which opposed this insisted on a doctrine of ‘analogy’ (to use an anachronistic word – their word was epinoia – have a look just how central this term is to the arguments of Basil and Gregory Nyssan’s books contra Eunomius) – the way words refer to the divine, in particular, is profoundly complex and irreducibly hesitant. There are no words (no, not ‘person’ or ‘relation’, regardless of modern fashions) that do more than gesture mutely and almost ineffectually towards divine reality. For many contemporary theologians some realisation of this problem of language leads to a neglect of analytic philosophy. If contemporary philosophy is to be mined, veins of gold will be sought in Ricouer or (for the intellectually serious) Heidegger, not in the giants of the analytic tradition. This seems to me to be a mistake; as St Thomas (more than any other) shows, it is precisely because our language has such limited purchase when referring to God that we need to pursue conceptual clarity about the precise locations of the limits of our language. However, I confess to not seeing much of this sort of analysis in contemporary analytics. Rather too often, it seems to me, the analytic philosopher lines up a set of well-defined concepts which are either assumed to correspond in an uncomplicated way to reality, or perhaps which have no direct correspondence to reality. To borrow the terms of a different philosophical discourse, clarity about the proper relations of the signifiers is too often achieved at the expense of clarity about how the signifiers might relate to the signified, making the exercise, for the theologian, largely irrelevant. (I do not think I have read an analytic treatment of trinitarian doctrine – a favourite theme – which does not fall foul of this to some extent; I’d be very happy to be pointed to one.) So – yes, yes, and thrice yes, to the attempt to bring the finely-honed tools of analytics into theological discourse, to call theologians to use words with precision and responsibility, and to refuse, ever, to substitute rhetoric for argument – certainly to refuse the temptation to descend into Frankfurtian bull-sessions. But can we say more about the limits of our analysis? Can we be clear and precise about the places where our concepts necessarily lack full clarity and precision? Can we own and never forget that there are some realities that our, unquestionably excellent, dissecting tools cannot pare apart and expose in fine anatomical detail? Only if we can, will we be able to speak more clearly, more analytically, of the ineffable and incomprehensible One who has graciously met us in Jesus...
Read MorePolanus on interpreting Scripture
‘The interpretation of H. Scripture is the exposition (explicatio) of its true sense and use, arranged in clear words (verbis perspicuis instituta), to the glory of God and the edification of the church.’ Even in my inelegant translation, that’s not a bad opening gambit. The (long…) section ends with a paragraph ‘on the use of H. Scripture for consolation’: ‘…therefore however grave the evil, so great and certain is the good set against it, that it is an effective remedy for sorrow. A most beautiful example (exemplum pulcherrinendum) is Isa. 41:26 ff. …’ The words are from Amandus Polanus’s Syntagma Theologiae Christianae; it was never going to be a big seller, even in theological terms. The edition in our library, published in Geneva in 1617, runs to something over 700 pages in folio, with two columns of (I estimate) six point Latin text on each. Oh, and the printer’s Greek font is all-but-illegible, at least to my eyes. If that wasn’t bad enough, the ‘Synopsis’ at the start of the book is a masterpiece of Ramist bifurcations (I counted six levels of subdivision on the definition of theology alone), and the text itself is in classical scholastic quaestiones form. What was it Barth said of Heppe? ‘Dry and dusty as a table of logarithms …’ I pulled it out the library to check a reference. I suspect I am its first reader in living memory; it is not yet on our electronic catalogue (most of our best books aren’t…), and was apparently misplaced in the stacks, so the librarian took a while to find it. Her perseverance seemed to demand some from me; and in between the anti-Roman polemic, and the fading and tiny Latin print, I found my heart strangely...
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