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    The existence of partial formalization constitutes progre... — Carmelics
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    Challenges→The project of formalizing analogical inference in terms of one or more simple formal schemata is doomed.

    The existence of partial formalization constitutes progress toward adequacy, not evidence that formalization is 'doomed', as Polya's work on plausible reasoning shows cumulative refinement is possible.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Polya demonstrated that plausible reasoning admits systematic rules, showing informality is not inherently irreducible to principled structure.
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    • 2.Partial formalizations (logic, probability, decision theory) solve real problems, suggesting progress toward adequacy rather than diminishing returns.
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    • 3.Historical trajectory shows formalization expanding scope: classical logic → modal logic → fuzzy logic, indicating cumulative refinement remains possible.
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    Reasons Against

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    Reason against
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    • 1.Polya's rules for plausible reasoning capture pattern-matching, not the creative insight generating new conjectures—formalization misses the harder part.
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    • 2.Gap between formal systems and their application (interpretation problem) may be irreducible, making partial formalization inherently limited rather than progressive.
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    • 3.Extending formalization to new domains (fuzzy logic, abduction) requires informal meta-reasoning outside the formalism itself, suggesting an inescapable ceiling.
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    Key Terms

    Cumulative refinement(as used in philosophy of science and epistemology)
    The idea that by making small improvements and corrections over time, you gradually build toward a better understanding or solution, even if you never reach perfection.
    Formalization(describing what Frege did with existence)
    The process of taking an idea and expressing it precisely using logical symbols and strict rules, like translating messy everyday language into mathematical logic.
    Plausible reasoning(as Polya's main area of study)
    A way of thinking where you make an educated guess or draw a likely conclusion based on available evidence, even though you don't have complete proof.
    Polya, George(as a referenced philosopher/mathematician)
    A 20th-century mathematician and educator who studied how people solve problems and reason through uncertain situations, arguing that practical, step-by-step reasoning can lead to reliable conclusions.
    adequacy(as used in evaluating philosophical theories)
    How well a theory works or how successfully it explains what it's supposed to explain.

    Connections

    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Extending formalization to new domains (fuzzy logic, abduction) requires informa...Gap between formal systems and their application (interpretation problem) may be...Historical trajectory shows formalization expanding scope: classical logic → mod...Partial formalizations (logic, probability, decision theory) solve real problems...
    +3 moreShow less
    Polya demonstrated that plausible reasoning admits systematic rules, showing inf...Polya's rules for plausible reasoning capture pattern-matching, not the creative...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    The project of formalizing analogical inference in terms of one or more simple f...