Infinite thoughts
What follows is a “twisting around” - through contemporary history - of Parmenides' statement that “what is” is 'like a sphere' (the most perfect form of sacred geometry), en peirasi – (related to peras limited/bounded) and atelés – purposeless (i.e. what is complete, has no purpose – it just “is”)...
NOTE: the Greek notion of peras ≠ finite !!! It has nothing to do with temporality – and yet makes temporality possible...
One should also note that Parmenides is expressing “reality” with a prose poem – not a literal “language game.”
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An interesting expression for finite occurs in Parmenides (6th C. BC). Actually … the Parmenidean notion of finite is nearer to our conception of complete than to our true conception of finite … Parmenides constructs out of his own imagery, an extraordinary universe, a kind of sphere (sphaira), in which cosmological and ontological features strangely blend. This sphere is in some sense finite, and Parmenides expresses this by saying, twice, that it is en peirasi, which can be translated by: in bounds, or by within bounds (or limits). The second translation has the advantage, if an advantage it be, that in present day mathematics it could pass as an equivalent for the technical term finite; although, in its own contexts in Parmenides, the word peiras exudes a vigor and mystique of poetry.
Collected Papers of Salomon Bochner by Salomon Bochner p. 4 http://books.google.nl/books?id=qCPazSkvigMC&pg=PA218&lpg=PA218&dq=parmenides+%22finite%22+peras&source=web&ots=VWNi9Pyilp&sig=bbb4b7L4zjvQbdHuM9BN1TO4PXI&hl=en&sa=X&oi=book_result&resnum=2&ct=result#PPA218,M1
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One of Parmenides' descriptions of Being states that Being is finite (i.e., not indeterminate). According to Parmenides, that Being is atelés (without-telos=infinite, limitless) means that Being is incomplete (atelés means purposeless or endless) and something lacking. Thus Being is shaped as spherical, thus limited, and qualitatively equal everywhere, and is finite. http://www.csudh.edu/phenom_studies/greekphil/greek06.htm
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6. Freeman uses the term 'infinite' in her translation of fragments 1 and 3; the Greek word is 'apeiron', which can mean "infinite", "indefinite", "indeterminate", "unlimited".
http://www.gmu.edu/courses/phil/ancient/pzm2.htm
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The Greek term Apeiron, meaning originally "boundless" rather than "infinite," was used by Anaximander for the ultimate source of his universe. He probably meant by it something spatially unbounded, but since out of it arose the primary opposite substances (such as the hot and the cold, the dry and the wet) it may have been regarded also as qualitatively indeterminate. Aristotle, summarizing the views of certain early Pythagoreans (Metaphysics A, 5), puts the pair Peras ("Limit") and Apeiron ("Unlimited") at the head of a list of ten opposites. Peras is equated with (numerical) oddness, unity, rest, goodness, and so on; Apeiron is equated with evenness, plurality, motion, badness. The two principles Peras and Apeiron constituted an ultimate dualism, being not merely attributes but also themselves the substance of the things of which they are predicated. From the Pythagoreans on, the opposition of Peras and Apeiron was a standard theme in Greek philosophy.
Parmenides (fr. 8, 42ff.) seems to have accepted Limit and rejected the Unlimited for his One Being. The later Pythagoreans removed unity from the list of identities with Peras and argued that unity was the product of the imposition of the Peras upon the Apeiron, or else it was the source of both of them. Plato in the Philebus regards Peras and Apeiron as contained in all things, and supposes that it is through limit that intelligibility and beauty are manifested in the realm of Becoming. Exactly how the Ideas fit into this scheme is controversial, but in the doctrine of ideal numbers which Aristotle attributes to him Plato seems finally to have identified a material principle with the Apeiron and a formal principle with the Peras. Both principles apply to the ideal as well as to the sensible world. This leads in due course to the doctrine in Proclus (Elementa 89–90) that true being is composed of Peras and Apeiron, and beyond being there is a first Peras and a first Apeiron. The Christian writer known as Dionysius the Areopagite identified this doubled First Principle with God.
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The concept of infinity, for long wrongly regarded as contrary to the whole tenor of Greek classicism, was in fact a Greek discovery, and by the fifth century BCE the normal meaning of Apeiron was "infinite." Infinite spatial extension was implied in the doctrines of Anaximander, Anaximenes, and Xenophanes and was made explicit by the Pythagoreans (see Aristotle, Physics IV, 6). Denied by Parmenides, it was reasserted for the Eleatics by Melissus (frs. 3–4) and adopted by the Atomists. Plato, however (in the Timaeus), and Aristotle (Physics III) insisted upon a finite universe, and in this they were followed by the Stoics and most subsequent thinkers until the Renaissance. Aristotle had, however, admitted that infinity could occur in counting and he stated the concept clearly for the first time. He also accepted infinite divisibility (Physics VI), which had been "discovered" by Zeno and adopted wholeheartedly by Anaxagoras. It was rejected by the Atomists. Plato rejected it in the Timaeus, although he seems to have admitted it at the precosmic stage in Parmenides 158B–D, 164C–165C. Aristotle accepted infinite divisibility for movements, for magnitudes in space, and for time. The concept of a continuum so reached has been a basic concept in physical theory ever since. The mathematical concept of infinitesimal numbers associated with infinite divisibility and also with the doctrine of incommensurables remained important until the development of calculus in modern times.
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The Shape of Ancient Thought by Thomas McEvilley (p.314) (http://books.google.nl/books?id=vTfm8KHn900C&pg=PA314&lpg=PA314&dq=parmenides+%22finite%22&source=web&ots=I93JnSznWs&sig=HdhPyqw-8lMoFayNNMfASLTh39E&hl=en&sa=X&oi=book_result&resnum=4&ct=result#PPA314,M1 )
Those thinkers who pressed for the finity of things- the Pythagoreans, Parmenides, Empedocles – were concerned with knowability, the mind’s ability to appropriate Being into its system of order. To be knowable the universe must have limits or the time that it takes to inspect it and come to know it would be infinite and could not be contained within a human lifetime.
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Two more aspects of Parmenidean thought caused Plato to revise his early theory of forms as presented in the Phaedo (74-75, 92d & 100c) and Republic (596a & 597c), thus inducing him to write the Parmenides, where:
1. immanence (μετέχειν) and transcendence (μίμησις) are shown to be separately untenable but mutually interdependent;
and
2. the One (τὸ ἕν) is defined antinomially as one, whole and finite (142d) and many, divided and infinite (144c).
http://www.pacitti.org/books_00199104.htm
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You must not forget that Being is only grasped by intellectual insight, not by the senses. So it is not a body in the space, like the earth, but it is a logical, geometrical figure. Parmenides has to say that being is finite, because if it were not finite, it would be the apeiron (="the unlimited"). Anaximander named the primary substance "the apeiron", it was the originating cause of all things in the world. We can imagine it as an infinite and inexhaustible amount of undifferentiated matter. The apeiron is contrary to Parmenides' being - it is not motionless and not indivisible, because it creates the natural things out of itself by division and motion. But the apeiron was the only Greek conception of infinity. So, if being cannot be the apeiron, it must have limits. It's just logic.
http://www.ilovephilosophy.com/phpbb/viewtopic.php?f=1&t=142733&p=1623436&hilit=flux
16. Parmenides may have been a pupil of Xenophanes and, more probably, an associate of the Pythagorean Ameinias whom in the end he followed and “was led to stillness” by him (DL IX, 21).This “stillness” or quietude hesuchia συχία was indeed , as we saw (§12), characteristic of the Pythagoreans ; so Parmenides was connected with them. He lived in Elea (=Velia), flourished in the first half of the 5th century and framed laws for the city which were preserved for a long time (Plutarch Against Colotes 1126AB ; DL IX, 23). His poem “On Nature,” written in ungainly hexameters, falls into three sections: the first is a prologue, the second deals with the way of truth and the last with the way of opinion. The prologue and most of the way of truth have been preserved but only fragments of the way of opinion.
The way of truth (the first part of the poem proper) speaks of the One Being (or Entity) eon (=on ‘being’) which is discovered by, and related to, nous νους ‘mind, intelligence’. Now, this Being, which is the Reality, has certain attributes (=predicates): it is one, holding in itself all that is/are; it is ever present; it is full, complete, all inclusive; it is unmoving, indivisible, homogeneous; it is uncreated, changeless and imperishable. It is perfect – like a sphere. So Being eon/on is related to and apprehended by mind nous. However, as many scholars appreciate (eg KRS 253), a sphere implies limits and a limited form, however perfect, implies the existence of something other than itself, so that Reality is not one. Indeed, Parmenides says explicitly that Reality/Being is bound within limits (peirasi desmoan πεiραsi δεσμων) by Necessity (ananke). The only solution is to see the bonds of necessity as some kind of determinacy implying that Reality is what is and could not be otherwise; but the form of the sphere remains bothersome.
The way of opinion doxa δόξα belongs to the senses of mortals and deals with what appears to be, not what is. Motion, change and multiplicity belong to doxa. This motion and change is thought of as ‘coming to be’ and this is utterly wrong since “to-be” has no precedent, itself being always. So the senses are deceptive. Sensory perceptions are composed of opposites and change and perish like the things themselves. All changes are just names which men give to things.
Thus Parmenides uses terms that will become customary and fundamental in subsequent philosophical enquiries by dealing with ontology (=being) and suggesting the division between the intelligible and the sensible more clearly than anyone before him.
17. However, there is another side to Parmenides. Plato writes that Socrates, when very young, met him and was impressed by his “depth which was absolutely noble” and thereafter revered him above all other thinkers (Theat, 183E). He was connected with Pythagoreanism, as we saw in §16, but also Orphism and the worship of Persephone, goddess of the Underworld, and Apollo Oulios (‘destroyer who heals’) or Apollo of the incubation Phoaleuterios Φωλευτήριος– and it should be noted that one myth has Orpheus serve as priest of Apollo (Graves 28) while another has Apollo mate with Persephone (Kingsley 1999: 102). The prelude of Parmenides’s poem contains several not obvious allusions to these cults. For instance, the poet is escorted by the Daughters of the Sun (=Apollo) who had left the mansions of the Night (=Persephone) and now lead him to the gates of the paths of Night and Day which are blocked by giant doors with bronze axles and a lintel and a stone threshold and which open back to a gaping chasm whereat the Goddess receives him kindly. This location reminds of the Hesiodic picture of the extremity of the world where are the sources of Earth, Tartaros etc (§6 above) and beyond, in the West, the outermost limit is Night (§8, above). The “goddess” who receives the poet is given no name and this usually indicates Persephone. Parmenides is describing a descent into Hades/Tartaros (like that of Orpheus) so that true knowledge might be obtained. There has been found epigraphic evidence that he was a doctor-priest iatromantis, leader of a sect in Elea that practised incubation (pholarchos φώλαρχος), or something similar, aiming at higher states of consciousness, or divinization (Kingsley 1999)14 .
http://www.omilosmeleton.gr/pdf/en/philosophy/GPA.pdf
