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
    Strict finitists anticipated the complexity-theoretic ins... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Modality & Possibility
    HistoryEditSee Inverse

    Strict finitists anticipated the complexity-theoretic insight that exponentiation marks the boundary between the feasible and the infeasible.

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    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.

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Van Dantzig (1955) held that feasible numbers are closed under addition and multiplication.
      ?

      Think about whether this reason is strong or weak

    • 2.Yessenin-Volpin (1970) explicitly stated that feasible numbers should not be regarded as closed under exponentiation.
      ?

      Think about whether this reason is strong or weak

    • 3.The particular examples of infeasible numbers put forward by Yessenin-Volpin and others use exponential or iterated exponential notations such as n₁^n₂ or n₁^(n₂^n₃).
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Strict finitists like Yessenin-Volpin were concerned with ontological limits on which numbers exist, not computational resource bounds on algorithms.
      ?

      Think about whether this reason is strong or weak

    • 2.Complexity theory's feasibility boundary is defined relative to input-size scaling of machine operations, a framework entirely absent from strict finitist writings.
      ?

      Think about whether this reason is strong or weak

    • 3.Attributing anticipation of a concept to thinkers who lacked its constitutive framework conflates surface terminological resemblance with genuine theoretical insight.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.The polynomial/exponential boundary in complexity theory is a formal, machine-model-relative result dependent on Church-Turing thesis assumptions that strict finitists explicitly rejected.
      ?

      Think about whether this reason is strong or weak

    • 2.Yessenin-Volpin's rejection of exponential closure was motivated by sorites-style vagueness concerns about feasibility, not by worst-case algorithmic analysis.
      ?

      Think about whether this reason is strong or weak

    • 3.Two positions can share a conclusion about exponentiation while differing so fundamentally in justification that no genuine anticipation relation holds between them.
      ?

      Think about whether this reason is strong or weak

    Topics

    Modality & PossibilityTruth & Knowledge

    Connections

    1 topic

    Proof of definition segments1 linked

    Related

    Attributing anticipation of a concept to thinkers who lacked its constitutive fr...Complexity theory's feasibility boundary is defined relative to input-size scali...In complexity theory, polynomial (sub-exponential) orders of growth are feasible...Strict finitists like Yessenin-Volpin were concerned with ontological limits on ...
    +6 moreShow less
    The particular examples of infeasible numbers put forward by Yessenin-Volpin and...The polynomial/exponential boundary in complexity theory is a formal, machine-mo...Two positions can share a conclusion about exponentiation while differing so fun...Van Dantzig (1955) held that feasible numbers are closed under addition and mult...Yessenin-Volpin (1970) explicitly stated that feasible numbers should not be reg...Yessenin-Volpin's rejection of exponential closure was motivated by sorites-styl...

    Similar

    Strict finitism anticipates concerns that also inspired the developmen...79%Strict finitism anticipates concerns that also motivated the developme...78%In complexity theory, feasibility applies to orders of growth of time ...77%In complexity theory, feasibility is a property of time complexity fun...76%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    If we regard such expressions as tokens rather than types, then it makes sense to consider the task of concretely ‘counting up to’ a number by constructing its unary representation in the sense described by Yessenin-Volpin. g. the unary numerals are generated by applying the formation rule \(\sigma \mapsto \sigma'\) to the initial symbol \(0\). e. [49] In attempting to accommodate (S1)–(S3) simultaneously, we must confront a tension which has led many authors to follow Dummett (1975) in conclu
    Extraction notes

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

    Details

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