Aristotle remarked of Anaximander that his positing of the first or primary principle [to life/existence] as “the Unbounded” is done in part so as to allow that things may not be destroyed by another’s unboundness. The elements were conceived in their pure form, the property abstracted from that to which the property attaches, as essentially unbounded, but Anaximander realised that if any one of these were essentially unbounded the others must eventually cease to be, being overtaken by the unbounded (infinite) nature of the other. Thus no single element can be the primary unbounded principle (Thales had proposed this principle was “water”). Anaximander wisely noted the error in this thought, and posited not a single unbounded element but the notion of the unbounded itself as primary. This is a huge conceptual leap. Aristotle interpreted Anaximander’s unbounded as an “internal undifferentiation”, the mixing of all opposites (hot and cold, warm and dry, etc) together such that no quality is left of the originals, nothing but a singular undifferentiated and indeterminate “boundlessness” remains. It is then from this that all other differences arise, being separated out from the originary “whole” and entering into their common oppositional relationships.
Interestingly modern notions of difference in philosophy posit a similar “internal nondifferentiation”, e.g. repetition of the same, to account for that from which difference arises. Nietzsche metaphorically conceived of this thought as the Eternal Recurrence/Return; Deleuze took up the thought and naturalised it further, positing an internal principle of difference, absence or void, as fundamental to everything (to “all forces”) in so far as separation of quality effects inherent distancing and division. Even at the level of pure quantity space/time effects this separation, and this goes all the way back to Aristotle’s formulation “A is A”. So “space/time” is then seen only as the basic principle of repetition through which “the same” (difference/absence in itself [the “Unbounded”]) is manifest “physically” or on the level of force-interaction.
Also interesting to note that Anaximander was perhaps the first human to conceive of the notion of evolution, stating that humans must have originally been born of other creatures; this thought he derived from the observation that man is a creature which is helpless upon birth and requires much support, nurturing and protection, thus man could not have initially survived if this has been his original situation. Man must have come from another creature, as other creatures are born immediately or near immediately capable of surviving. Evolution pre-Darwin, circa 560 BC. Nice.
There are two possible exceptions [to universal unboundedness] that come to mind;
If there is only one object or entity of existence; this would mean that the destruction of one thing would be the allowance of another, such that the unbounded essentiality of the oneness would retain its integrity.
An infinite holographic reality; if an aspect of a hologram [e.g. universe] is destroyed then the underlying eidos or information set would remain, resulting in its holographic projection occurring elsewhere.
…Perhaps it could occur at another time within the same hologram e.g. a foetus dies but its information remains, another foetus is formed in the same or another womb, and the information is placed in that incarnation.
Wishful thinking I know.
I must say I like the idea of unboundedness as it doesn’t necessarily have to be infinite to the fullest degree [stateless/void]. It brings to mind fractals and other potential infinities and collections thereof.
Isn’t it also strikingly funny that any notion of the “Unbounded” is automatically a bound, placed on the “thing” described, the target of our references.
“Well then, if it’s unbounded, then surely it’s not not-unbounded, and therefore it doesn’t very well impinge into where the bounded things may reside ,does it. And therefore, there you have it, it has a bound!”
What at first seems to be a useless exercise in sophistry could for us serve to illuminate inherent and inescapable limitations in linguistic thinking. I invite everyone to consider any conception arising as a result of logical derivation either as exemplary dementia or pedagogic tool (summoned to give students a taste of the teacher’s prior, unspoken insight). To emplace the NOTION itself, of the unbounded, as the functional object of worship and target of our linguistic references is surely a stroke of pedagogic genius. Thus NOTION, and no thing; perspective, and no truth.
can it not be unbounded in and of itself? In other words, it doesn’t have to include all [although my exceptions did include all, or so I thought] it just has to be unbounded according to itself.
An emptiness is unbounded, but including a bound would be denying its unboundedness as an emptiness. A fractal may be unbounded, it completely goes by its infinite coding without including anything bar tself.
The birth of the Platonic Forms.
And now perhaps to undo all this; first relate the notion back from the notion of a thing in itself to the notion of a notion, and then back to the thing it is a notion of… and finally, to see if it is still there.
In the case of the unbounded, the notion may be the only form in which this thing exists, and so also, the only notion that is justified as being approached as an object.
The unbounded has been described perhaps most technically (and perhaps most fittingly) by the Jews:
the no-thingness coming to thing-ness in three linguistic steps, :
Ein (not/no)
Ein Soph (no limit) and
Ein Soph Aur (light of no limit/limitness light).
leading up to the geometrical model of the Tree of Life: The Thing (not the notion of it, but a representation) in perhaps the most comprehensive meaning: Man as the world, composed of a “tree” developing / ranging in multiple directions from force to form, in representation of ten different “Gods”, or really, ways of man to relate to himself, worlds in which man finds the occurrence of his self consciousless to come into particular expressions.
Anyway the Hebrews saw it fit to retrospectively derive this differentiated Thing, this bound-ness, from something thereby the be identified, which they apparently wanted to understand as an unbounded, and therefore had to formulate as a negative.