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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
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    42
    A genuine counter-example to an inference rule must be de... — Carmelics
    Home/Proof of definition segments
    HistoryEditSee Inverse

    A genuine counter-example to an inference rule must be defined in terms of presence ranges, not absence ranges

    Proof of definition segments
    ?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.When properties are partially located, a property P has both a presence range (P+) and an absence range (P−) that may overlap
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    • 2.A place where the reason property is present and the inferred property is absent but also present is not a real refutation of the inference
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    • 3.Only a case in the presence range of the reason property that falls outside the presence range of the inferred property constitutes a real counter-example
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.In Navya-Nyāya epistemology, a counter-example (vyabhicāra) is defined by the co-absence of hetu and sādhya, making absence ranges logically prior to presence ranges in falsification.
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    • 2.Gaṅgeśa's Tattvacintāmaṇi establishes that pervasion (vyāpti) is undermined precisely when the reason is present alongside the confirmed absence of the probandum, not merely its non-presence.
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    • 3.A definition of counter-example that excludes absence ranges cannot account for cases where partial location generates genuine epistemic defeat of the inference relation itself.
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    Reason against 2 of 2
    ?
    • 1.The Mīmāṃsā principle of arthāpatti holds that inferential rules must be tested against all evidential contexts, including cases where absence is the primary epistemic datum.
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    • 2.If a counter-example is restricted to presence ranges only, inference rules become unfalsifiable in domains where properties are known primarily through their absences, violating the Nyāya norm of testability.
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    Topics

    Proof of definition segments

    Connections

    1 topic

    Modality & Possibility1 linked

    Related

    A definition of counter-example that excludes absence ranges cannot account for ...A place where the reason property is present and the inferred property is absent...Gaṅgeśa's Tattvacintāmaṇi establishes that pervasion (vyāpti) is undermined prec...If a counter-example is restricted to presence ranges only, inference rules beco...
    +4 moreShow less
    In Navya-Nyāya epistemology, a counter-example (vyabhicāra) is defined by the co...Only a case in the presence range of the reason property that falls outside the ...The Mīmāṃsā principle of arthāpatti holds that inferential rules must be tested ...When properties are partially located, a property P has both a presence range (P...

    Similar

    Only a case in the presence range of the reason property that falls ou...82%Definition V1 counts a place as a counter-example to an inference if t...80%The standard definition V1 of a counter-example is inadequate when pro...74%A place where the reason property is present and the inferred property...74%

    Source

    AI-extracted1/3 agreementValid
    SEP: early-modern-india
    View source passageHide passage
    The main effect of admitting partially located properties into the system is that it is no longer the case that a property, P, and its complement, P′, are disjoint: they may now intersect. If the inferred property is partially located, then the class of “agreeing cases” (sapakṣas - places where the inferred property is present) and the class of “disagreeing cases” (vipakṣas—places where the inferred property is absent) overlap rather than being distinct classes. To put it another way, a property
    Extraction notes

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

    Details

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