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
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Claiming the totality is non-arithmetical in a unique sen... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→The totality of transfinite cardinal numbers is absolutely infinite in a sui generis non-arithmetical sense, rather than having a cardinal number of its own.

    Claiming the totality is non-arithmetical in a unique sense smuggles in an unexplained primitive that violates the principle of ontological parsimony (Ockham's razor) in mathematical ontology.

    ?Rate how convincing each reason is below to see the overall strength.

    No one has weighed in yet. Be the first to share reasons for or against this statement.

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

    Key Terms

    Mathematical ontology(what the indispensability argument is trying to ground or justify)
    The question of what kinds of mathematical objects exist (like numbers, sets, or equations) and whether they're real or just useful inventions.
    Ockham's razor(named after medieval philosopher William of Ockham)
    A principle that says the simplest explanation is usually the best one—don't add extra complications or assumptions unless you really need them.
    Ontology(Carnap argues this enterprise is based on a mistake)
    The philosophical discipline that tries to answer hard questions about what there really is.
    Primitive (in ontology)(referring to unexplained assumptions in a philosophical argument)
    A basic concept or thing that is assumed to exist without being explained or derived from anything else.

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    Totality(referring to a complete set of causes)
    A complete set or collection of all the things involved in a situation—think of it as the 'whole package' of causes or explanations for something.
    non-arithmetical(Complexity classification of dependence logic validity)
    Not decidable within the arithmetical hierarchy
    ontological parsimony(methodology / theory choice)
    The theoretical virtue of preferring theories that posit fewer entities; an economical ontology over an expansive one

    Connections

    1 topic

    Divine Attributes1 linked

    Related

    The totality of transfinite cardinal numbers is absolutely infinite in a sui gen...

    Details

    Type
    claim
    Perspectives
    0 (0 for, 0 against)
    Edits
    1 edit

    Open for perspectives

    This idea is waiting for its first supporting or challenging perspective.

    Share the first perspective