Infinite

In philosophy, “infinite” refers to something that is absolutely without limit, like God for Descartes or Leibniz, while “indefinite” describes something without a limit that is recognizable or comprehensible to us, but might still have a hidden or structural limit. The key distinction is between a metaphysical, absolute non-finitude (infinite) and an epistemic, iterative, or incomprehensible non-finitude (indefinite).

Infinite

• Definition: Absolutely unlimited in all respects, or a completed totality of infinitely many things.
• Nature: Metaphysical and absolute. It is a positive, actual characteristic, not merely the absence of limits we can perceive.
• Examples:
  • God: Descartes and Leibniz reserved the term “infinite” for God alone, the one being whose nature is to have no limits whatsoever.
  • Actual Infinity: In mathematics, actual infinity refers to a completed, definite set with infinitely many members, such as the set of all integers.

Indefinite

• Definition: Lacking any recognized or conceivable limit, even though it may have limits that are unknown or incomprehensible to us.
• Nature: Epistemic or structural. It can be an iterative process without end, such as the potential for endless division of a line, or simply something that is beyond our ability to grasp all its limits.
• Examples:
  • The material world: Descartes argued the universe is indefinite because we cannot find a limit, but he did not assert there are absolutely no limits.
  • Potential Infinity: In contrast to actual infinity, potential infinity (or indefinite) is a process that can always be continued but is never completed, like counting numbers or dividing a line segment.

Key distinctions

AI responses may include mistakes.

[1] https://www.academia.edu/20213750/The_Infinite_The_Indefinite_and_attitudes_towards_infinity_Leibniz_s_response_to_Descartes

[2] https://www.tandfonline.com/doi/full/10.1080/09608788.2020.1818055

[3] https://philpapers.org/rec/SCHTOA-10

[4] https://www.tandfonline.com/doi/full/10.1080/00751634.2024.2383545

[5] wikipedia/en/Actual_and_potential_infinity

[6] https://medium.com/@timah/philosophy-and-mathematics-when-infinity-reveals-its-two-faces-1ddf1b4f62f7

[7] https://www.tandfonline.com/doi/pdf/10.1080/09608788.2020.1818055

[8] https://inters.org/infinity

[9] https://www.marxists.org/archive/marx/works/1883/don/appendix1.htm

[10] https://www.beyng.com/docs/Adorno-BeingExistence.html

[11] https://www.encyclopedia.com/religion/encyclopedias-almanacs-transcripts-and-maps/finite-being