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But, an implicit assumption in that process is that mathematical principles (most importantly, the Law of Identity) can be applied to those representations of reality (integrated through time).
This isn't a trivial assumption.
Additionally, your words highlight the issue of not knowing whether or not the original premises are true. The only ways we have to determine the truth of assumptions like "F = ma" always lead us back to induction. And we all know about the problem of induction.
But, to put the first part more flippantly:
This isn't a trivial assumption.
Additionally, your words highlight the issue of not knowing whether or not the original premises are true. The only ways we have to determine the truth of assumptions like "F = ma" always lead us back to induction. And we all know about the problem of induction.
But, to put the first part more flippantly:
Prove it.Because mathematical deduction never produces false results from true premises we preserve the same level of truth.
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