mbd_map 19: A Dedication homepage homepage forum lectures 1: A Word of Encouragement 2: Dar al-Hikma 3: Proclus' Elements 4: Reversion in the Corporeal 5: Mathematical Recursion 6: Episodic Memory 7: Mortality 7 Supplement: Classical Mortality Arguments 8: Personal Identity 9: Existential Passage 10: Precedent at Dar al-Hikma 10 Supplement: Images of Dar al-Hikma 11: Passage Types 12: A Metaphysical Grammar 13: Merger Probability 14: Ex Nihilo Probability 15: Noetic Reduction 16: Summary of Mathematical Results 17: Application to Other Species 18: Potential Benefits 19: A Dedication appendices works cited
 

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A Word of Encouragement

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Dar al-Hikma

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Proclus' Elements

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Reversion in the Corporeal

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Mathematical Recursion

6

Episodic Memory

7

Mortality

7s

Classical Mortality Arguments

8

Personal Identity
1   2   3   4  

9

Existential Passage
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10

Precedent at Dar al-Hikma

10s

Images of Dar al-Hikma

11

Passage Types

12

A Metaphysical Grammar

13

Merger Probability

14

Ex Nihilo Probability

15

Noetic Reduction

16

Summary of Mathematical Results

17

Application to Other Species
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18

Potential Benefits

19

A Dedication

Appendices

Works Cited



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Chapter 4
Reversion in the Corporeal


Proclus makes an elegant argument for the soul's indestructible and imperishable nature.  His orderly conclusions build upon each other in a logical manner.  So has Proclus demonstrated the immortality of the soul?  This depends upon what we judge to be a satisfactory "demonstration."  What does it really mean, to say that a metaphysical argument demonstrates something?
       One meaning of "demonstrate" is to "show by reasoning."  That much Proclus has accomplished:  most of his reasoning is sound in the Elements.[1]
       "Demonstrate" has a second, stronger meaning:  to "show how something works."  Proclus alludes to this second meaning in the Elements:  "The task of science is the recognition of causes, and only when we recognize the causes of things do we say that we know them."[2]  Causes, Proclus insists, are not isolated, but ordered within a structured hierarchy of causation.  Quoting his description of cyclic activity:  "There are greater circuits and lesser, in that some revert upon their immediate priors, others upon the superior causes, even to the beginning of all things."[3]
       (Proclus' hierarchy of causes enchanted medieval scholars.  The book's popular abridgment acquired a title [Book of Causes] that suited scholarly interest.)
       So Proclus acknowledges the need to pursue causes towards their source, as the way of knowing things as they really are — knowing how they work.  And this is a sound principle.  A hierarchy of causes certainly affects physical bodies; as, for example, in the motion of a car.  The proximate, direct cause of motion is merely the rotation of its wheels.  This rotation has in turn a cause:  the force exerted through the pistons.  And that force likewise has a cause, in the combustion of gasoline.  Our understanding proceeds onward through the hierarchy of known causes.  As we learn the several causes of the car's motion, we improve our understanding of the car.
       Turning now to the ten propositions quoted previously, we see that they state several types of causation.  The first two propositions touch upon physical, corporeal causes, which Proclus mentions in Propositions 33 and 17.[4]   His examination of causes continues in Proposition 15, wherein Proclus makes a sharp distinction between corporeal and incorporeal causes.  Thereafter the remaining propositions elaborate incorporeal causes exclusively.[5]
       Table 4.1 arranges Proclus' causes by proposition, with the general nature of each cause summarized at right.

Table 4.1 
Ten selected propositions from Proclus' Elements of Theology
Proposition
Cause
Nature
33
cyclic motion
corporeal
17
self-motion
both corporeal and incorporeal
15
self-reversion
incorporeal
16
self-reversion
separable from corporeal
43
self-reversion
self-constituted
46
self-constitution
imperishable
49
self-constitution
perpetual
83
self-knowledge
all self-reversive and
     self-constituted natures

186
soul
all self-knowing natures; hence
     incorporeal, separable

187
soul
all natures of Prop. 186;[6]
     hence indestructible,
     imperishable

Reading the table row-by-row, from the top down, we can see how Proclus has built his case.
       The success of Proclus' argument for immortality is tied to the success he has enjoyed in puzzling out the hierarchy of corporeal and incorporeal causes at work in the human body.  Proclus' corporeal causes rise no higher than simple self-motion, and not even that rudimentary degree of dynamism is guaranteed to be entirely corporeal.[7]  Above self-motion the incorporeal hierarchy of causes takes control, producing all greater human qualities through means independent of the corporeal body.
       This is the division of causes which Proclus maintains.  It makes sense, when viewed through the eyes of a Neoplatonist.  However, modern readers may find that this division of causes raises some questions.  Do corporeal causes truly reach their zenith at self-motion?  Or does self-motion engender higher levels of causation within the human body?  And if so, how far might corporeal causation within the body progress towards the soul?
       Answers to these questions might very well disentangle the knot of Proclus' argument — if only to spool his Neoplatonism in, and then out again, as thread for a metaphysical panoply of modern cut.  To that end a review of relevant facts will be worthwhile.



The review begins at what Proclus thought the most potent of corporeal causes:  self-motion.  Proclus does not detail the living functions he thought to be self-motivated, so it's hard to guess just which self-motions he imagined the body capable of executing.  Perhaps the flow of blood through the circulatory system appeared to him as a self-moving stream.  Or he may have been impressed by the autonomous motion of muscular reflexes.  But this is speculation — he may not have pondered these functions at all.  The Elements focus on mental functions, mentioning the human body only as a participating repository of the soul.[8]  So examples of bodily self-motion are not to be found in Proclus' text.
       We might have better luck if we look to Proclus' next higher cause, self-reversion.

"Everything originally self-moving is capable of reversion upon itself." [9]
Proposition 17 delves into the reversive activity of self-motion.  Apparently Proclus is speaking here of reversion in all types of bodies, biological and other; but this is uncertain because nowhere does Proclus define the literal meaning of "reversion."[10]  The proposition does at least give us some working definitions of self-reversion, as expressed through self-motion:
"...motive activity is directed upon itself..."
"...mover and moved exist simultaneously as one thing..."
"...one and the same thing moves and is moved..."
Proclus' definitions are slippery fish.  In Proposition 17 the catch slides en masse towards the prosaic end of the boat.  These reversions are closer to mere "recursion" than to the spiritual cycles Proclus describes elsewhere — recursion being understood first as a "mechanically operated cyclic motion."
       If we allow ourselves this simplification we can gain entry into Proclus' argument.  Recursion, unlike reversion, has technical definitions.  Mathematical, computational and biological examples of recursion exist.  So a study of recursion would raise this critique upon a scaffolding of fact.
       Recursion has an additional advantage in being an ancient concept.  As the mathematician Robin Gandy reminds us, "The use of recursion in computation is at least as old as Euclid, though the word is recent."[11]  So its properties have been known for a long time.  Those factual properties would be germane to Proclus' argument, where they could be shown to free powers in the body more causative than mere self-motion.  And so these are the powers to target with a selective history of recursive systems, which follows.



next    Chapter 5:  Mathematical Recursion


Chapter 4 Endnotes

[1] Again, for examples of logical weakness, see Dodds 1963, xi-xiii.
[2] Dodds 13.
[3] Dodds 37.
[4] Proclus' differentiation of corporeal and incorporeal causations is anything but clear-cut.  For such clarification as may be possible, see Lucas Siorvanes, Proclus: Neo-Platonic Philosophy and Science (Edinburgh: Edinburgh University Press, 1996) 86-110; A. C. Lloyd, The Anatomy of Neoplatonism (Oxford: Clarendon Press, 1990) 98-135.
        Proclus deposits Nature at the lowest stratum of causation; yet even natural objects have both corporeal and incorporeal aspects in his scheme.  (Here Proclus is following Aristotle's example.)  The matter comprising physical bodies Proclus considers to be inert; it is instead the "enmattered form" (physis) which gives that matter its useful properties.  A body's physis, while technically incorporeal, is nonetheless inseparable from its matter; so physis is the most "tangible" sort of incorporeality to be found in Proclus' universe.  See Siorvanes 136-37.
[5] Or they would, if Proclus had numbered his propositions more to this critic's liking.   As it happens, his numbering scheme throws up a few exceptions to my tidy rule.  An example:  Props. 25 through 39 develop the principles of procession and reversion.   For Proclus, these broad principles undergird both corporeal and incorporeal existence.  (Cyclic activity, described therein in Prop. 33, reads as one of the more corporeal aspects.)
[6] Prop. 187 calls upon Prop. 186 as an authoritative axiom.  The properties listed in Prop. 187 are properties which have been derived in the build-up towards Prop. 186.
[7] See Chapter 3, note 10 for the syllogism in question.  Proclus' pronouncements on self-motion are rather problematic.  In Prop. 14 Proclus states that some existents are "intrinsically moved."  (Unfortunately, he does not provide a list of these existents.)  In Prop. 20 he specifically denies self-motive powers to the human body, stating that "self-movement is contrary to its nature."  Yet, "[w]hen soul is present, the body is in some sense self-moved..."  The cloudy phrase, "in some sense," is a miniature of Proclus' greater difficulty with the concept of self-motion.  Dodds 201-08 provides some helpful commentary on Props. 14-20.  See also note 8, below, concerning the soul's life-giving relation to the body.
[8] Dodds 165.  Quoting from Prop. 188:  "For that into which soul enters necessarily lives, and when a body is deprived of soul it is thereupon left lifeless...."  Siorvanes details Proclus' "subtle bodies" and "soul vehicles" in Siorvanes 131-33.
[9] Dodds 19-21.
[10] Proclus may not have wanted us to assign a literal meaning to "reversion."  Quoting Lloyd 124, 126-27:
"It is difficult, perhaps impossible, to find a consistent theory of reversion in Neoplatonism....
       [T]he term translated 'reversion' — epistrophe — is doubly ambiguous.  First, we find it used sometimes with its strict meaning of 'being turned towards' something, in other words to refer to an inclination, sometimes with a much fuller meaning of 'returning' or 'having returned' to it; and there are times when the reader is unsure which is meant...."
Proclus describes reversion via abstract analogies — a method common among Neoplatonic philosophers.  See Siorvanes 105-09.
[11] For a short sketch of the development of the mathematical term "recursion," see Robin Gandy, "The Confluence of Ideas in 1936," The Universal Turing Machine — A Half-Century Survey, ed. Rolf Herken (Oxford: Oxford University Press, 1988) 72-73.
 
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Wayne Stewart
Last update 4/19/11