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    The inference from 'certain problems appear inherently se... — Carmelics
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    Challenges→NC is expected to be properly contained in P (NC ≠ P)

    The inference from 'certain problems appear inherently sequential' to 'NC ≠ P' commits the same epistemic error Lakatos identified in naive falsificationism: apparent resistance to a method does not establish principled impossibility.

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    Key Terms

    Lakatos
    Imre Lakatos was a 20th-century Hungarian philosopher of science who developed an influential theory about how science actually progresses. Rather than seeing scientific progress as a simple accumulation of facts or sudden breakthroughs, Lakatos argued that science advances through competing research programs that protect their core ideas while adjusting their supporting beliefs based on new evidence. His work remains important because it offers a more realistic picture of how science develops than earlier theories, explaining why scientists don't immediately abandon ideas when faced with contradictory evidence.
    NC ≠ P(computational complexity theory)
    A mathematical claim stating that problems solvable quickly with many parallel computers are fundamentally different from (and likely harder than) problems solvable quickly with a single computer.
    Naive falsificationism(as used in philosophy of science)
    The oversimplified idea that you can prove a scientific theory wrong just by finding one case that contradicts it, without considering how theories might be revised or protected from single counterexamples.
    Principled impossibility

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    (as used in logical and mathematical reasoning)
    Something that is impossible not just in practice, but for deep, fundamental reasons—not just because we haven't figured out how to do it yet.
    Sequential(as used in describing problem-solving processes)
    Happening in a specific order, one after another, where each step depends on completing the previous one.
    epistemic error(as used in epistemology)
    A mistake in knowledge or understanding—believing something false about what we can know or how we know it.
    inference(Nyāya epistemology)
    A component of epistemology in Nyāya philosophy; a veritable inference yields knowledge about the world and must have premises that are themselves known

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    Modality & Possibility1 linkedSkepticism1 linked

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    NC is expected to be properly contained in P (NC ≠ P)

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