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    Demonstrating the formal invalidity of an argument via co... — Carmelics
    Home/Philosophy of Language
    HistoryEditSee Inverse

    Demonstrating the formal invalidity of an argument via counterexample presupposes a principled way of discerning the full logical structure of that argument, and hence of distinguishing logical constants from nonlogical constants.

    Truth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.A genuine counterexample to the formal validity of an argument must exhibit the full logical structure of that argument, not merely a surface propositional form.
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    • 2.The Demarcater insists that the full logical structure of the firefighter argument is the quantificational form, not the mere propositional form.
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    • 3.Other arguments sharing only the propositional form but having true premises and a false conclusion do not count as genuine counterexamples to the firefighter argument's validity.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Counterexample validity in natural language reasoning is established by semantic content, not by prior commitment to a canonical logical form.
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    • 2.Quine's substitutional account shows formal invalidity can be demonstrated by uniform substitution of nonlogical terms without presupposing a fixed logical/nonlogical distinction.
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    • 3.If counterexamples can succeed by semantic transparency rather than structural analysis, the demarcation of logical constants is a post-hoc theoretical artifact, not a presupposition.
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    Reason against 2 of 2
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    • 1.Etchemendy's critique shows that Tarskian logical consequence already conflates model-theoretic stipulation with genuine necessity, undermining the authority of any formal structural reading.
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    • 2.If the formal structure assigned to an argument is itself theory-laden and revisable, then 'presupposing' that structure is not a precondition of counterexample practice but a contested theoretical choice.
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    Topics

    Philosophy of LanguageTruth & Knowledge

    Key Terms

    Formal invalidity(as used in logic)
    When an argument's conclusion doesn't logically follow from its premises, even if the premises were true—basically, the reasoning structure itself is broken.
    Logical structure(as used in logic)
    The underlying pattern of how an argument is organized—which statements connect to which, and how they're supposed to support each other.
    Nonlogical constants(as used in logic)
    The actual content or specific words in an argument—like 'cat,' 'blue,' or 'happiness'—that give the argument its particular meaning but aren't part of the logical structure itself.
    counterexample([IHT] arg. 2)
    A possible obligational situation (casus possibilis positus) that verifies the antecedent and falsifies the consequent of an inference
    logical constants
    The special expressions whose meanings must be fixed in order to evaluate the formal validity of an inference or the truth of a logical truth.

    Related

    A genuine counterexample to the formal validity of an argument must exhibit the ...Counterexample validity in natural language reasoning is established by semantic...Etchemendy's critique shows that Tarskian logical consequence already conflates ...If counterexamples can succeed by semantic transparency rather than structural a...
    +4 moreShow less
    If the formal structure assigned to an argument is itself theory-laden and revis...

    Source

    AI-extracted1/3 agreementValid
    SEP: logical-constants
    View source passageHide passage
    As Massey (1975) reminds us, the fact that there are other arguments with the form \(\refp{propform}\) that have true premises and a false conclusion does not show that \(\refp{firefighter}\) is invalid (or even that it is “formally” invalid). The Demarcater will insist that a genuine counterexample to the formal validity of \(\refp{firefighter}\) would have to exhibit the full logical structure of \(\refp{firefighter}\), which is not \(\refp{propform}\) but \(\refp{quantform}\). Thus the Demar
    Extraction notes

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

    Details

    Other arguments sharing only the propositional form but having true premises and...
    Quine's substitutional account shows formal invalidity can be demonstrated by un...
    The Demarcater insists that the full logical structure of the firefighter argume...

    Similar

    A genuine counterexample to the formal validity of an argument must ex...86%It is conceivable that the non-logical constants of an argument can be...83%There is no systematic theory of invalidity — the only way to prove an...81%Modern logical validity is indifferent to irrelevance and permits addi...80%
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit