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    Probabilistic reasoning does not yield a conclusion that ... — Carmelics
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    Home/Modality & Possibility
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    Probabilistic reasoning does not yield a conclusion that the next ball will be a certain color, but rather that certain future observations are very likely given past observations

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Observing 90 white balls out of 100 yields a probability of 91/102 ≈ 0.89 for the next ball being white via the rule of succession
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    • 2.Even when all 100 observed balls are white, yielding a probability of 0.99, there remains a nonzero probability the next ball is not white
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    • 3.A nonzero probability of the contrary outcome means the conclusion is not guaranteed
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Reichenbach's pragmatic vindication shows that if any method can establish stable frequencies, the straight rule of induction will converge to the same limit.
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    • 2.Convergence to limiting frequencies constitutes a form of practical certainty that dissolves the epistemic gap between 'very likely' and 'guaranteed' for scientific purposes.
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    • 3.The claim illicitly imports a metaphysical standard of certainty that probabilistic reasoning was never designed to meet, making the critique a category error.
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    Reason against 2 of 2
    ?
    • 1.Carnap's inductive logic demonstrates that logical probability relations between evidence and hypothesis are analytic truths, not contingent guesses about future observations.
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    • 2.If the inferential link from past to future observations is itself a logical necessity within a confirmed probability framework, then the conclusion carries modal force beyond mere likelihood.
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    Related

    A nonzero probability of the contrary outcome means the conclusion is not guaran...Carnap's inductive logic demonstrates that logical probability relations between...Convergence to limiting frequencies constitutes a form of practical certainty th...Even when all 100 observed balls are white, yielding a probability of 0.99, ther...
    +4 moreShow less
    If the inferential link from past to future observations is itself a logical nec...Observing 90 white balls out of 100 yields a probability of 91/102 ≈ 0.89 for th...Reichenbach's pragmatic vindication shows that if any method can establish stabl...The claim illicitly imports a metaphysical standard of certainty that probabilis...

    Similar

    Demonstrative reasoning cannot bridge the gap between past observation...81%Analogical reasoning can be directed primarily toward prior probabilit...80%Beliefs about colors do not appear to be grounded in inference to the ...78%If the conclusion is already known (e.g. perceptually), inference does...78%

    Source

    AI-extracted1/3 agreementValid
    SEP: induction-problem
    View source passageHide passage
    This is Laplace’s famous “rule of succession” (1814). Suppose on the basis of observing 90 white balls out of 100, we calculate by the rule of succession that the probability of the next ball being white is \(91/102=0.89\). It is quite conceivable that the next ball might be black. Even in the case, where all 100 balls have been white, so that the probability of the next ball being white is 0.99, there is still a small probability that the next ball is not white. What the probabilistic reasoning
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit