Has Grafen formalized Darwin?Biology & Philosophy


Jonathan Birch
Agricultural and Biological Sciences (all) / History and Philosophy of Science / Philosophy


Symbols and Nomenclature


The crucifixion in photography

Darwin Marable

Flowers of the Primrose destroyed by Birds



Has Grafen formalized Darwin?

Commentary on Grafen’s ‘The Formal Darwinism project in outline’

Jonathan Birch

Accepted: 23 December 2013 / Published online: 25 January 2014  Springer Science+Business Media Dordrecht 2014

Abstract One key aim of Grafen’s Formal Darwinism project is to formalize ‘modern biology’s understanding and updating of Darwin’s central argument’. In this commentary, I consider whether Grafen has succeeded in this aim.

Keywords Formal Darwinism  Darwin  Cumulative adaptation  Apparent design

In the first paragraph of his target article, Grafen tells us that the goal of the ‘Formal

Darwinism’ project is to ‘construct a mathematical bridge’ between formal representations of selection and formal representations of design. But is the bridge to be built for its own sake, or to serve a grander purpose? Later in the paper, Grafen reveals a much bolder end: it is also his hope that the project will be ‘accepted as articulating modern biology’s understanding and updating of Darwin’s central argument’ (14).1 In this commentary, I consider what it would take to formalize

Darwin, and assess whether Grafen’s framework is adequate to this formidable task.

Darwin’s ‘central argument’

I will follow Grafen in taking Darwin’s ‘central argument’ to be, in broad terms, the argument ‘that the mechanics of inheritance and reproduction give rise to the

J. Birch (&)

Christ’s College, St Andrew’s Street, Cambridge CB2 3BU, UK e-mail: jgb37@cam.ac.uk 1 Page references, unless stated otherwise, refer to Grafen’s target article, ‘The Formal Darwinism project in outline’. 123

Biol Philos (2014) 29:175–180

DOI 10.1007/s10539-013-9421-z appearance of design’ (Grafen 2007, 1243). Naturally, the Origin contains other arguments: for instance, the argument that all species are genealogically connected, and the argument that natural selection is responsible for their divergence. There is room for disagreement as to which of these arguments is the ‘central’ one (cf. Sober 2011), but I will not address this here.

In what way do the mechanics of inheritance and reproduction give rise to the appearance of design? Darwin’s claim in a nutshell, of course, is that they do so through natural selection. But there is more to the argument than this. Darwin’s claim is that natural selection assembles apparently designed objects cumulatively and gradually, through the step-by-step selection of incremental improvements. He expresses the idea beautifully in the following paragraph, which, familiar as it is, is well worth quoting in full:

If we must compare the eye to an optical instrument, we ought in imagination to take a thick layer of transparent tissue, with a nerve sensitive to light beneath, and then suppose every part of this layer to be continually changing slowly in density, so as to separate into layers of different densities and thicknesses, placed at different distances from each other, and with the surfaces of each layer slowly changing in form. Further we must suppose that there is a power always intently watching each slight accidental alteration in the transparent layers; and carefully selecting each alteration which, under varied circumstances, may in any way, or in any degree, tend to produce a distincter image. We must suppose each new state of the instrument to be multiplied by the million; and each to be preserved till a better be produced, and then the old ones to be destroyed. In living bodies, variation will cause the slight alterations, generation will multiply them almost infinitely, and natural selection will pick out with unerring skill each improvement. Let this process go on for millions on millions of years; and during each year on millions of individuals of many kinds; and may we not believe that a living optical instrument might thus be formed as superior to one of glass, as the works of the Creator are to those of man? (Darwin 1859, 188–189)

This passage vividly illustrates the way in which Darwin blends the language of evolution with the language of design. Natural selection, he tells us, favours and preserves ‘improvements’ on existing structures, leading eventually to a ‘living optical instrument’ of ‘superior’ design to those of human construction.

Grafen’s central (and, it has to be said, rather troubling) insight is that no theorem or principle in classical population genetics even comes close to providing a formal vindication of this informal argument, because nowhere in classical population genetics do we find any attempt to represent the notions of ‘improvement’ or ‘good design’ in formal terms. His ‘Formal Darwinism’ project seeks to close this lacuna in two stages. The first is to introduce a new formalism (in part borrowed from economics) intended to capture the notion of ‘apparent design’. The second is to derive links between this new formalism and the well-known Price formalism for evolutionary change: links intended to embody, and thus formally vindicate, the premises of Darwin’s central argument. The project is ambitious; its goal is admirable. But has Grafen succeeded? 176 J. Birch 123

The elusive notion of ‘apparent design’

My first reason for doubt on this score arises from Grafen’s formal treatment of the notion of ‘apparent design’. Grafen suggests that the ‘appearance of design’ exhibited by eyes, hearts and other complex adaptations can be captured formally using the apparatus of optimization programmes. He provides no explicit argument for this claim, however, and it is likely to raise a few philosophers’ eyebrows.

Perhaps ‘appearing designed’ and ‘solving an optimization programme’ can be equated in some cases, but I do not think they can be equated in general.

This is easiest to see in non-biological examples. Consider a ball in a crater, rolling around until it comes to rest in the centre. We could define an optimization programme with possible positions of the ball as the ‘strategy set’ and (the negative of) potential energy as the ‘maximand’, and we could prove links between this optimization programme and Newtonian mechanics. Indeed, we could show that, on a smooth enough surface, the ball would reliably solve the programme. Yet it would be wrong to equate solving the programme with ‘appearing designed’, since balls at the bottom of potential wells do not appear any more designed than balls at the top.