Are you skilled in the art of Arithmetic?

How things can be both Created and Eternal


The Monad that ate Aachen!

by Richard Murdey, November 27, 1994


An Apology:

In the final essay of this series, it was originally planned to investigate how the thought of John Scottus Erigena might be applied, or at least related to, some aspect of today's technological world. Alas, discretion was once again found to be the better part of valour: that task would require a mind of greater capacity than my own. Moreover, the more I consider the matter, the more I come to believe that such a feat, were it even possible, would prove to be an unwieldy piece of scholarship. As Dermot Moran points out in his concluding remarks, you cannot make Erigena a modernist simply by "isolating some of his more modern sounding statements and translating them into the vocabulary of recent critical philosophy." 1

Oddly enough, Moran does actually argue that Erigena was a modernist 2, mainly on the strength that his two "closest intellectual followers" 3 were Meister Eckhart of Hochheim (c. 1260 - c. 1329) and Nicholas of Cusa (1401-64). This is simply bad reasoning: The correct inference to make from the connection is that the aforementioned pair were dark-ageist in their philosophical outlook.

It is unfair to assign people to a single word of terminology at the best of times, but when that person pre-dates the terminology by ten centuries it's downright muddleheaded.

In order to understand, and, I say, appreciate the work of John Scottus, the modern reader has to drop about a millennia's worth of intellectual baggage. Imagine, if you can, life in the year 865. Of the great civilisation yet to come, Erigena had no knowledge. What is etched deeply into his mind, as with all the scholars of the age, is instead the memory of a glorious world in the distant and fading past.

Fix your minds eye on that golden age. Now move slowly across the centuries, and watch it recede into the past. Yet not so far as its light does not shed some warmth. Sunset, not dusk.

Are you skilled in the art of Arithmetic?

John Scottus Erigena's greatest work is the Periphyseon, or On the Division of Nature. The divisions to which the title refers to are, foremost, being and non-being. On another level, though, there are four divisions, centered on the idea of creation. They are:

1 : That which creates but is not itself created.

2 : That which both creates and is created.

3 : That which is created but can not create.

4 : That which neither creates nor is created.

It is easy to see the logical completeness of these divisions, as they are an exhaustive list of all binary pairs, namely 1:(1,0), 2:(1,1), 3:(0,1), and 4:(0,0). Writing it this way also highlights the logical relation of the first division to the third, and likewise the second with the last. The source of this idea is a sentence from Augustine, "The cause of things, therefore, which makes but is not made, is God; but all other causes both make and are made." 4 God, as both the source and end of everything, corresponds to the first and the last division. The third is the created universe.

Of particular interest to us here is the second division, that which is created by God, but also creates. Belonging here are said to be the primordial causes, one of which is the monad, the source of all numbers. Conflict arises, however, when the Platonic doctrine of eternal forms, of which the monad must be considered a constituent part, is brought to be subservient to the Christian doctrine of creation. The question that must be addressed is, to put it shortly, how something can be both created and eternal.

Erigena provides the answer through a discussion in Book III of the Periphyseon that treats the monad as a 'test case', if you will, for all the primordial causes. 5

The discussion is divided into two chapters. The first considers the reasons for thinking of the monad as eternal, the next shows how the monad, and all numbers, must be necessarily created.

On the Division of Nature is written as a dialogue between the master and his disciple, or, as some early manuscripts have it, between two anonymous philosophers, Nutritor and Alumnus. 6 While the ideas of the master always have priority, the student is not unskilled, for it is he who lays out the arguments for the eternity of the monad, though the more complex task of explaining its creative nature is left to the master. 7

Part 1 : How the monad is eternal.

M: Are you skilled in the art of Arithmetic?

D: I am, unless I'm mistaken. I have studied it from early childhood.

M: Well then, define it clearly and briefly.

D: Arithmetic is the science of numbers, not those which, but those according to which, we count. 8

The distinction 'according to which' is fundamental. The numbers themselves are not perceived in any substance, either corporeal or incorporeal: Arithmetic is not concerned about trees, pens, or oranges, but rather about those numbers present in knowledge and intellect by which we count these objects.

When we count pens, for example, one pen, two pens, three pens... there is nothing in the pen, either in matter or form, that makes it one pen. We are able to assign it to unity only by comparison with the idea of unity present in the intellect. The cause of this idea, and by extension all the other numbers, is the monad, without which we are not able to do other than make statements about individual objects, red pen, blue pen, green pen...

How, then, are all numbers contained within the monad? Reason teaches us, answers the disciple, that they exist in it causally and eternally, causally because the monad "subsists as the beginning of all numbers" 9, eternally because since "the monad extends to infinity" 10 it cannot be conceived of as having a beginning. 11

The monad is infinite because all numbers spring from it, and an infinite cannot have a finite source. The monad "is the beginning, middle, and end of all numbers - for they proceed from it, move through it, make their way toward it, and end in it." 12

Here we see how the discussion of the relationship of numbers to the monad is parallel to the relationship of all things to God. For God, St Dionysius the Areopagite tells us, "is both the Maker of all things and is made in all things" 13 and as we have seen from the divisions of nature, He is also both the beginning and end of all things. Erigena even goes so far as to refer to God as "that Monad which is sole Cause and Creator of all things visible and invisible" 14.

The numbers, then, exist eternally in an eternal monad. They do not cease to be part of it when they flow from it, for the monad is a part of the "natural state" 15 of all numbers. When numbers are multiplied or completely reduced they come forth from it, or return to it "according to the rules of the discipline which oversees their reasons." 16

Part 2: How the monad, and the numbers, are made.

God is the creator of all things, so the monad is created. 17 The created monad is that "in which all numbers always subsist causally, uniformly, and according to their reasons, and from which they emerge in many forms." 18

The starting point for this part in the discussion is the idea, expressed by the disciple, that numbers are eternal in the monad, but made in their multiples. For example, the number 6 exists potentially in the monad, as does all the other numbers, but takes on actual existence as an intelligible number. 19

For the numbers, as they exist in the monad, "by their ineffable unity surpass every intellect except the divine, which nothing anywhere eludes." 20 Since they are beyond doubt actually found in the human intellect, then surely they have been made, placed there by God, "the Creator, Multiplier, and Orderer of all things." 21

Consistent with the hierarchy of being found throughout the Periphyseon, numbers are said to 'descend' from the monad though a series of steps, rather like a waterfall, splashing down from ledge to ledge. From the monad to the intellect, from the intellect to reason, from reason to memory, then to the senses and finally visible figures. 22

The eternal numbers are said to be made both in their presence in the intellect, as pure numbers devoid of any form other than themselves; one, two, three... , and again as they combine with the form of a corporeal being present as a phantasm in the memory; one pen, two pens, three pens...

Conclusion

That the nature of numbers can be thought of as both eternal and made has been demonstrated. One might, though, be tempted to ask, as does the disciple, just where this gets us when considering the larger problem of "how everything from God is at once eternal and made; and especially how God Himself is both the Maker of everything and made in everything." 23 Does this not lead one to the 'monstrous conclusion' that "God is all things and all things are God" 24? For this, surely, cannot be reconciled with the idea that God is one, the perfect unity.

Well, Erigena replies, we saw that the numbers, while always existing causally in the monad, and, even while existing in their multiplicity, still having the monad as part of their nature, are still, as they exist in both the memory and the intellect, considered created, and thus are separate from the monad.

The problem is how assign to created numbers an individual nature distinct from, but still a part of, the unity that is the monad. That is what the question of how numbers can be both eternal and made really addresses. If that question can be answered effectively, then by extension, it can be applied to all created natures in their relationship to the uncreated Monad, God.

Does Eriugena answer the question effectively? I do not know. Have I managed to fully outline the crucial points of his arguments in this essay? Probably not. For him all the beings in the created universe are considered as theophanies 25 but that does not mean that in all things is to be found God. The answer is, I can only propose, is that God, in the act of creation, makes it so. Only thus can natural beings be given any autonomy at all.


1 Moran, p286
2 modernist - well, not quite so modern. The term means belonging of the modern age, which, according to Moran, began c. 1450. (p279)
3 Moran, p279
4 Bett, p21
5 Apology : I'm using words like 'primordial causes', 'Divine ideas', and 'Forms' without really knowing what I'm talking about in terms of the finer distinctions between them. In a general way, I take the second division to contain that which acts as an intermediary to His creative will. Oh dear, help!
6 Moran, p58
7 The dialogue is a sadly neglected method of philosophical inquiry. The Periphyseon offers stimulating dialogue between two quite distinct characters, and the ability of the student to speak for the reader, demanding further explanation, or asking for a restatement of previous conclusions, is highly useful.
8 Eriugena, p163
9 Eriugena, p164
10 Eriugena, p165
11 For the art of Arithmetic, there are the reasons by which the numbers are ordered (the rules of mathmatics) and the numbers themselves. To generate all numbers, however, only the number one is needed, for, using the reasons, all numbers can subsequently be generated from it. 1+1=2, 1+2=3, 2+2=4, 2+3=5 etc... This is why the number one, or the idea of unity, is of prime (excuse the pun) importance in medieval Arithmetic.
12 Eriugena, p165
13 Eriugena, p162
14 Eriugena, p172
15 Eriugena, p166
16 Eriugena, p166
17 Creation may, or it may not, imply a temporal component. God created the universe in time, but he created the monad eternally. So what Erigena is considering later is specifically how numbers are made in time, rather than eternally, in the monad.
18 Eriugena, p173
19 Eriugena, p170
20 Eriugena, p172
21 Eriugena, p171
22 Eriugena, p171
23 Eriugena, p175
24 Eriugena, p162
25 theophany - the manifestation or appearance of God to man.

Bibliography

Bett, Henry
Johannes Scotus Erigena Russell & Russell, Inc., New York, 1964

Eriugena, Joannes Scotus
On The Division Of Nature The Bobbs-Merrill Company, Inc., 1976

Moran, Dermot
The Philosophy of John Scotus Eriugena Cambridge University Press 1989


Richard Murdey

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