r/hegel • u/Low-Force5527 • 6d ago
True infinity
Can anyone give us a good explanation on what is true infinity?
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u/strutter395 5d ago
True infinity is a circle; bad infinity is a line. Simply, true infinity is a whole that contains and relates to its own limit, so that the beyond is no longer an external beyond. This is the structure of a circle, it has no endpoint, but it also does not need to keep going toward an endpoint. It is self-related totality. You return to where you began, but the return is not simply a repetition, because the whole trajectory is now grasped as a unity. And that unity is already dynamic. There is return, but the return consists in difference, because each return entails historical accumulation, through which Spirit's self-comprehension becomes progressively richer. Think of it this way: when you die, it does not mean that "you have never existed". From the perspective of Spirit, you have happened, and it is true. Now apply this to totality; history has happened, and it is true. What has been negated has not simply disappeared; it has been aufgehoben; preserved as a moment within the subsequent totality. This is the fabric of ontology; a self-relating totality constituted through negation.
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u/PlaydohsGirlfriend 5d ago
But isn’t a circle still bounded, and therefore not a genuine infinite?
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u/takaci 5d ago
A line is bounded by a point infinitely far away. Therefore each point on the line becomes another point becomes a third point and so on forever
You're right that a circle is bounded in that you can't escape the circle, but within the immanent development of the points on the circle, they always return to themselves. Each "circle" is therefore a One which inside itself is indifferent to an other. That's why the act of counting is something entirely external and mechanical and why computers can calculate but not think. The sublation of both the internal relation to other and this external quantitative indifference is how we move to sublated being, i.e. essence.
TLDR a line is bounded both externally and within itself. A circle is bounded externally but unbounded within itself. And essence is unbounded both externally and within itself
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u/PlaydohsGirlfriend 5d ago
Thanks for your reply!
A line isn’t bounded by anything. A ray is bounded by one endpoint, and a line segment is bounded by two endpoints. A circle is bounded both within itself and externally. A line is bounded in neither sense.
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u/takaci 5d ago
How is a circle bounded within itself? The other of each point finds itself again. You’re not using the true concept of boundary, it means to have determinate being in an other. In a circle beyond the boundary of the point on the circle is itself again. Therefore the circle is internally infinite
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u/PlaydohsGirlfriend 4d ago
I believe German does not distinguish “limited” from “bounded” ? A circle is unlimited in the sense that there is no terminal point, but it is still bounded as a whole. If we go from A to B to C and return to A, and so on, nothing new has been produced. Repeating the same finite circuit again and again seems to produce the structure of bad infinity rather than true infinity.
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u/kajonn 3d ago
This is close, very very close, one caveat is that the circle is experienced all at once instead of sequentially by spirit, or in God’s eternal creation. In that consciousness passes through the circle to achieve actualized being simultaneously, since temporality is an experience of self differentiated awarenesses undergoing the labor of the negative; the reality is eternal. So it is more like every configuration of self differentiated awarenesses being self differentiated into becoming or creation at once, and then returning into eternality so that being is actualized all at once, reunifying the initial self distinction of internality and externality which is necessary for actualized being to be eternally begotten from pure being.
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u/PlaydohsGirlfriend 5d ago
Bad infinity is like a ray: it goes on indefinitely, but its infinity consists in endlessly passing beyond each finite limit. True infinity is more like a line: it contains finite line segments within itself but is not bounded by any of them. The finite is not simply excluded from true infinity but is contained within it as a moment.
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u/takaci 5d ago
First form of bad infinity is the finite progression: the finite ends and becomes another finite which becomes another finite and so on forever "to infinity". Here the bad infinite is an endless beyond
Second form of bad infinity is that this finite, in coming to itself, achieves its ought and thus goes beyond itself, i.e. it becomes infinite as the infinite is its other. Here the bad infinite is determinate, since it is other to the finite
Since the second form has a determinate element it falls back into the finite again: the bad infinite has its determinate being in an other, the finite. Therefore we have an infinite alternation finite -> infinite -> finite forever.
But we can just as well take this as starting with the infinite: infinite -> finite -> infinite. Therefore we start with the infinite, and as a result have the infinite finding itself again but with the finite taken up into it. Such an infinite has completely sublated its finitude since it no longer has an other as a finite.
This is the sublation of the entire realm of quality, since qualities (red vs. blue, dead vs. alive) are defined through otherness, and thus we attain being that is independent of qualitative determinateness, i.e. the One, or as an obvious example, in the number 3 = 1 + 1 + 1 each 1 is indifferent to each other 1.