Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Certain paradoxes arise from attempting to form an illegi... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Modality & Possibility
    HistoryEditSee Inverse

    Certain paradoxes arise from attempting to form an illegitimate totality by collecting into a single totality a collection whose members presuppose the existence of that totality

    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.The set of all non-self-membered sets is a member of itself if and only if it is not a member of itself
      ?

      Think about whether this reason is strong or weak

    • 2.The sentence 'This sentence is false' is true if and only if it is false
      ?

      Think about whether this reason is strong or weak

    • 3.These contradictions result from treating a self-presupposing collection as a completed whole
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Russell's paradox is dissolved by type theory without invoking 'illegitimate totalities'—the restriction is syntactic, not metaphysical.
      ?

      Think about whether this reason is strong or weak

    • 2.Zermelo-Fraenkel set theory blocks paradox via the axiom schema of separation without presupposing any notion of self-presupposing collections.
      ?

      Think about whether this reason is strong or weak

    • 3.The 'illegitimate totality' diagnosis is one interpretive gloss among several, not a discovered metaphysical fact about why paradoxes arise.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Priest's dialetheism accepts that some contradictions—including the Liar—are true, rendering paradox-avoidance an optional rather than mandatory theoretical virtue.
      ?

      Think about whether this reason is strong or weak

    • 2.If contradictions arising from totalities can be tolerated within paraconsistent logic, the claim that such totalities are 'illegitimate' loses its normative force.
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.

    Topics

    Modality & PossibilityTruth & Knowledge

    Connections

    1 topic

    Philosophy of Language1 linked

    Related

    If contradictions arising from totalities can be tolerated within paraconsistent...Priest's dialetheism accepts that some contradictions—including the Liar—are tru...Russell's paradox is dissolved by type theory without invoking 'illegitimate tot...The 'illegitimate totality' diagnosis is one interpretive gloss among several, n...
    +4 moreShow less
    The sentence 'This sentence is false' is true if and only if it is falseThe set of all non-self-membered sets is a member of itself if and only if it is...These contradictions result from treating a self-presupposing collection as a co...Zermelo-Fraenkel set theory blocks paradox via the axiom schema of separation wi...

    Similar

    Allowing a totality to be a member of itself generates paradoxes84%If the totality of cardinals were measured by a cardinal, or the total...84%Quantification over infinite totalities is the root of logical paradox...80%The paradox appears only when one wrongly believes one can do somethin...79%

    Source

    AI-extracted1/3 agreementValid
    SEP: categories
    View source passageHide passage
    Thus, e.g., Russell and Whitehead introduced type theory (which might in some sense be considered a theory of categories) to avoid a certain form of paradox found in Fregean set theory (where we must consider the putative set of all non-self membered sets, which is a member of itself if and only if it is not a member of itself), liar’s paradoxes (“This sentence is false”, which is true if and only if it is false), etc. On their analysis, paradoxes like these arise from the attempt to form an ill
    Extraction notes

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

    Details

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