Unlimited

Use in the book

Anaximander’s principle is reported as the unlimited. The atomist report distinguishes infinitely many atoms from a void infinite in extent. Aristotle’s report on division allows division without limit potentially, while denying its accomplishment actually.

Places to read

1. I.10.12.2The unlimited is the principle attributed to Anaximander.
2. I.18.1a.3Infinity of number is distinguished from infinity of extent.
3. I.14.1bPotentially unlimited division is distinguished from actual division.

Translation in this edition

“Unlimited” suits the substantive principle; “infinite” often suits number or extent; “without limit” can preserve the force of a process. The object of the qualification remains essential.

Use in the book

Traherne uses the word to loosen the reader’s customary boundaries. The world first appears a bounded collection of physical objects; entered through its value and service, it becomes a field of inexhaustible variety. The point is an enlargement of enjoyment, not merely an increase in size. His round earth is also called illimited because the traveller finds no enclosing wall or final edge. Yet the same meditation expressly leaves undecided whether the universe is infinite.

This distinction matters: experiential openness, endless circulation, and divine infinity can illuminate one another without becoming identical propositions. The word often marks the passage from counting possessions to discovering a world in which attention can continually advance.

Places to read

1. I.18The world becomes an illimited field when its value and service are perceived.
2. II.21The round earth has no terminal border; the universe’s actual infinitude remains undecided.

In this edition

Read illimited as unbounded in its immediate context. II.21 prevents treating every occurrence as a literal assertion of infinite physical extension.

Use in the book

B 28 describes the rounded Sphere as equal from all sides and wholly without limit. Roundedness and limitless extent present an interpretive tension. One may consider an absence of distinguishing boundaries or an emphatic completeness, but the fragment does not explicitly supply such a gloss. It is safer to preserve the difficulty than to force an infinite geometric sphere with a measurable surface.

B 39 challenges talk of boundless depths of earth and ample aither, attributing that confident speech to people who have seen only a little of the All. The opening conditional and fragmentary end mean the full argument is missing. Nonetheless, the passage plainly criticises an ungrounded cosmological assertion; it cannot be cited as Empedocles' straightforward affirmation that earth extends infinitely downward.

B 172's boundless height of air and B 16's boundless time occur in different settings. The former characterises a vast constituent or region; the latter denies a future empty of the two powers. B 135 extends law through aither and boundless light. These uses give the language of scope several functions, quantitative, temporal, and normative, rather than one settled mathematical definition.

Places to read

1. B 28The rounded Sphere is called altogether without limit.
2. B 39A conditional challenge criticises claims about boundless depths of earth and ample aither.
3. B 17.18The height of air is called boundless.
4. B 16Boundless time will not be emptied of the two powers.
5. B 135Boundless light expresses the uninterrupted reach of what is lawful.

Translation in this edition

The same English word covers different Greek expressions. The entry therefore records the actual forms and avoids converting all of them into a single doctrine of the Infinite. B 39 should retain its questioning or conditional force.