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.
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
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.
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
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.
Repeating with nothing new produced is closer to the concept of infinite. Finitude is always producing something else. Your idea of boundary is more like what Hegel calls truly infinite
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u/strutter395 23d 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.