Wednesday, March 23, 2011

The Anti-Razor

Dr Feser fairly recently had a post about Ockham's razor, and perhaps it was remembering this that made me sit up when I came across the "anti-razor", formulated in the Scotist work (anonymous, despite the title) Logica Campsale Anglicj, valde utilis et realis contra Ockham, that is, The Logic of the Englishman Campsall, very useful and realist, against Ockham. It goes like this:

Whenever some affirmative proposition is verified about things, if one thing does not suffice to verify such such a proposition, one must posit two, and if two do not suffice, three, and so on to infinity.

In his preface to the critical edition to Ockham's Quodlibeta Septem, Joseph Wey notes that the same principle was formulated by Walter of Chatton. I translate from p. *35:

It may be useful to note here that Chatton also frequently employs a limiting principle or rule . . . which can be called a certain "anti-razor" or complement of the principle of parsimony, namely 'When a proposition is verified about things, if two things do not suffice to verify the proposition, one must posit a third.' Ockham does not accept this rule, but rather vehemently opposes it.

Gideon Gal discusses the authorship of pseudo-Campsall's anti-Ockhamist logic in the preface to the critical edition of Ockham's Summa Logicae. There's a funny remark in there which seems to imply that the logical debates in early 14th-century Franciscan England were damaging to fraternal charity. The Campsall-logic can't have been by John of Rodington, he says on *60-*61:

Furthermore, John of Rodington, who as they say was a very holy man, did not adhere so faithfully to the doctrine of the Subtle Doctor nor so bitterly opposed the doctrine of the Inceptor as the author of the Logic against Ockham. If anyone were to say that the author is John of Reading, we could well believe him . . . It seems to us that some of the things he said and wrote are very similar to those which William Ockham found vain and ridiculous and rebuked in the Summa Logicae . . . this can easily explain the acrimony of the author against Ockham, especially if their contention took place in a single academic community [coram scholaribus communibus].

Gal goes on to discuss the anti-razor as well as the case for and against Walter of Chatton and the anti-Ockham being one and the same.

In any case, as the editor of the anti-Ockham notes, the anti-razor has been independently formulated by a modern author, K. Menger, in "A Counterpart of Ockham's Razor in Pure and Applied Mathematics: Ontological Uses," Synthese 12 (1960), 415:

. . . what is needed is a counterpart to the Law of Parsimony - so to speak, a law against Miserliness - stipulating that entities must not be reduced to the point of inadequacy and, more generally, that it is vain to try to do with fewer what requires more.

The benefit, such as it is, of the Ockhamist metaphysics is that it's clean and tidy, wiping all the conceptual barnacles and encrustments off the mental slate. The main critique of the formalizantes must always be that its wild and florid growth produces a profusion of pseudo-entities multiplying out of control. The goal of metaphysics, however, is not to produce either an invigoratingly pure and arid conceptual desert, nor an exciting and exotic conceptual rainforest, but to understand reality as it is. So metaphysics will have to do with the right amount of entities, neither more nor less than necessity demands.

If Faber and I ever get around to producing for public consumption an edition or translation or modern rewriting of the Diologus curiosus inter Dunxsistam et Okamistam, "A Curious Dialogue between a Scotist and an Ockhamist," no doubt the anti-razor will resurface.


Eric said...

Rondo Keele has a nice discussion of Chatton's version of the Anti-Razor in his Stanford Encyclopedia article on Chatton.

Also, though I would be the first to agree that Ockham's ontological elimination goes too far, I think a number of his critics (and perhaps his interpreters as well) misunderstand the purpose of the razor. At least when it comes to his reduction of the categories -- which almost always depends upon the razor -- I take it that Ockham's project isn't to provide a full listing of reality, but instead to make clear what can be established demonstratively by philosophy alone.

As Ockham sees it, since God isn't under any compulsion to follow the principle of parsimony, He could create a world in which there are entities corresponding to each of the categories. But such a world would be indistinguishable -- for us -- from the world we actually inhabit. The razor is meant to demonstrate the bare minimum that God needs to create the world as we see it, but it doesn't entail that God did it just that way.

This is why, for instance, Ockham makes explicit that, though the razor implies that there need be no such things as relations in the world, we should believe that there are at least some relational entities: for revelation teaches that there are such things (in particular, in the Trinity and the Incarnation).

Were we angels, we could just look at the world and intuitively see its metaphysical structure; since we're not, the best we can do, Ockham thinks, is use philosophy to find the bare minimum structure and trust God to reveal to us any other important bits that He thinks we should know about.

His arguments against universals, on the other hand, typically don't depend on the razor, but instead upon the principle of non-contradiction; here Ockham does think that philosophy can make progress in determining the structure of the world, since God is not capable of performing the logically impossible.

Michael Sullivan said...

Eric, many thanks for the reference and comment.