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    If incompatibility of opposite-of-consequent with anteced... — Carmelics
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    Challenges→An inference is formally valid in the restricted sense if the opposite of its consequent is formally incompatible with its antecedent, but not every application of that form is valid

    If incompatibility of opposite-of-consequent with antecedent does not guarantee universal validity, the incompatibility relation itself must be non-formal, undermining the original classification.

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    Key Terms

    Antecedent(referring to causal conditions that would exist before Plato's decision)
    Something that comes before something else in time; in this case, an earlier event or cause.
    Consequent(as used in logic)
    The 'then' part of an if-then statement—the result that follows from the condition.
    Non-formal(in logic and philosophy)
    Not following strict, fixed logical rules or structure; instead depending on content, context, or meaning rather than pure logical form.
    Opposite-of-consequent(in logical analysis)
    The logical negation or opposite of what would result from an if-then statement; basically saying 'the 'then' part is false.'
    classification(Kitcher's framework for analyzing argument patterns in scientific explanation)

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    A description of which sentences in a schematic argument are premises and which are conclusions, together with a specification of what rules of inference are used.
    incompatibility(Characterized as an apparently negative notion, which creates a problem for the positive truth-maker proposal.)
    A relation that obtains between two states when it is not possible for them to obtain together.
    universal validity(Proposed as both necessary and sufficient for logical truth in a standard mathematical characterization alternative to derivability.)
    A sentence is universally valid when no collective assignment of meanings to the variables and the schematic letters in its logical form would turn that form into a false sentence.

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    Modality & Possibility1 linkedPhilosophy of Language1 linked

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    An inference is formally valid in the restricted sense if the opposite of its co...

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