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It is not the case that The necessity required for demonstration applies to all things under the subject on account of what they are.
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Reasons For
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Reason for 1 of 2
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1.
Aristotle's own Posterior Analytics distinguishes per se necessity from mere universal predication, allowing accidental universals that don't ground demonstration.
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2.
If necessity were solely grounded in what subjects are, mathematical truths about physical objects would require no empirical supplementation, which Aristotle denies in Physics II.
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Reason for 2 of 2
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1.
Aquinas and Scotus both argue that essential predication admits degrees of necessity, so 'on account of what they are' underdetermines which essentialist claims license demonstration.
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2.
A subject's essence can ground conflicting demonstrative necessities when the same subject falls under multiple scientific domains, as in the case of harmonics and arithmetic.
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Reasons Against
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Reason against
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1.
Demonstrative necessity is characterized as de omni, per se, and universale.
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2.
This kind of necessity is universal and grounded in the essence of the things under the subject.
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