Friday, December 09, 2011

Ockham and Bradley's regress

I am currently working on chapter 51 of Ockham’s Summa Logicae, and I have spotted something that looks very much like Bradley’s regress. He writes
Nec illud quod subiungitur de materia et forma, subiecto et accidente, toto et partibus, et spiritibus unitis corporibus concludit rem relativam mediam inter illa unita. Eadem enim quaestio remaneret de illa re media: quomodo facit unum cum eo in quo poneretur? Aut enim se ipsa, et eadem ratione standum fuit in primis unibilibus; aut alia unione, et tunc procedetur in infinitum.
I am still working on a translation, but it means something like this. The context is Ockham’s argument against the existence of relation as a distinct category of thing separate from the things that are related. He says that the joining of matter and form, subject and accident, whole and parts etc into one object does not imply the existence of a relation-entity intermediate between the two. For the same question would apply to the relation-entity. How is the relation made one with the thing (such as the unity of matter and from) in which it is posited? Either by itself, and by the same reasoning we should have stopped at the first two things capable of being united (e.g. matter and form alone), or by another union, and then there would be an infinite regress.

But this is Bradley’s regress, or something very similar to it.  Bradley did not invent his regress!

An interesting side note: the Latin phrase eadem ratione standum fuit in primo seems to be a stock phrase always used in the context of regress proofs. Burley uses the same argument, and the same phrase here, arguing that if something X exists, this is either because of its essence, or from something added to its essence. If because of its essence, then existence is part of essence. If because of something else Y added to the essence, then Y exists either because of its essence, or by something added to its essence. If by something Z added to Y, then we have to ask the same thing about Z, and so on ad infinitum. But if by its essence, then by the same reasoning we should have stopped in the first place (eadem ratione fuit standum in primo). I.e. if it is enough for Y to exist because of its essence, the same reasoning applies to the starting point X, and we should have stopped there.

A similar argument, and the same phrase, is used by Thomas in lecture 3 on Book 10 of the Metaphysics. When a man is said to be one, the term one does not express a different nature from man, just as being does not express a different nature from the ten categories; for, if it did express a different nature, an infinite regress would necessarily result, since that nature too would be said to be one and a being. And if being were to express a nature different from these things, an infinite regress would also follow; but if not, then by the same reasoning we should have stopped at the first instance (pari ratione standum fuit in primo). See also Summa I Q6 a3 arg3, where he argues that good is good essentially, and not by something added to it, Summa I Q27 a3 arg1, where he argues that no other procession exists in God besides that of the Word, Summa IIa Q109 a6 arg3, arguing that a man does not need grace in order to prepare for grace, and De Potentia Q3 arg 7 arg7, arguing that the forces of nature suffice for the action of nature without God operating therein.

See also Albertus, Metaphysics IV iv (scanned but not corrected or translated), where he argues that there is no medium between odd and even.

It’s interesting because the stock phrase suggests a stock argument, and therefore its use by writers prior to Ockham suggests the argument did not originate with him. But it is a stock argument against multiplying entities. We must choose reason 1 which tells us not to multiply entities, and reason 2 which tells us we must multiply. If we choose reason 2, we get another entity, but then must choose between reason 1a, which tells us to stop there, and 2b which tells us to continue multiplying. But if we choose 2b, we get an infinite regress. Therefore choose reason 1a. But now the crucial point: reason 1a is the same as reason 1, therefore by the same reason whoy not just stop at 1 - pari ratione standum fuit in primo.

Ockham uses this argument all over the place in the Summa, and it is pretty much the basis of his nominalism. But the examples above suggest that it did not originate with him. His genius lay in seeing its application in metaphysics and logic, in using it as the foundation for his nominalistic program, and in writing the Summa, which is a masterpiece of extended argument, intermixed with polemic and some entertaining ranting and abuse. (More on the ranting and abuse later).

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Blogger J said...

More nominalist errors or at least difficulties..Relations imply classes and attributes. "SF is north of LA". Ie, facts about a sphere named earth, with cardinal points, one called " North" (does that mean another class, Northness? perhaps. But does not seem to be a regress). Not real deep but workable; from a galaxic POV...problematic perhaps least given earthly coordinates, meaningful. Russell hints at Bradley's view which he calls monistic. And rejects it.

4:13 pm  

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