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Inverse View
It is not the case that For appearances, both the Thesis (divisions of matter are finite) and the Antithesis (divisions of matter are infinite) are false.
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
Mathematical predicates like 'finite' and 'infinite' apply to sets defined by their structural properties, not by epistemic completability.
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2.
The series of natural numbers is actually infinite regardless of whether any mind completes enumeration of it.
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3.
Therefore, the divisibility of matter can coherently bear a determinate infinite or finite cardinality independent of experiential limits.
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Reason for 2 of 2
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1.
Aristotle's distinction between potential and actual infinity allows 'infinite' to apply meaningfully to an incompletable process of division.
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2.
If matter is potentially infinitely divisible, the predicate 'infinite' applies in its potential sense without requiring a completed sequence.
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3.
Kant's inference that incompletability entails neither-finite-nor-infinite conflates epistemic inaccessibility with ontological indeterminacy.
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Reasons Against
1 perspective
Reason against
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1.
For appearances, divisions of matter into parts are not completable in experience.
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2.
The predicates 'finite' and 'infinite' apply only to a completed or completable sequence of divisions.
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3.
A sequence that is not completable in experience can be considered neither finite nor infinite.
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