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
    A proof system that presupposes more powerful foundationa... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→Non-standard analysis provides simpler and more intuitive proofs of many theorems of standard real analysis.

    A proof system that presupposes more powerful foundational machinery cannot be deemed simpler in any epistemically rigorous sense.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Epistemic simplicity requires minimal foundational assumptions; presupposing powerful machinery increases total theoretical commitments.
      ?

      Think about whether this reason is strong or weak

    • 2.A proof system's justificatory burden includes justifying its foundations; more powerful foundations demand stronger justification.
      ?

      Think about whether this reason is strong or weak

    • 3.Cognitive accessibility and pedagogical clarity correlate with foundational minimalism, which is a legitimate epistemic virtue.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Simplicity can mean brevity of proofs or fewer proof steps; powerful foundations often reduce derivation length significantly.
      ?

      Think about whether this reason is strong or weak

    • 2.Well-understood powerful axioms (like ZFC) may be epistemically simpler than laboriously reconstructing mathematics from minimal bases.
      ?

      Think about whether this reason is strong or weak

    • 3.Foundational power and justificatory rigor are distinct; powerful systems needn't be less justified if their axioms have strong warrant.
      ?

      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.

    Connections

    1 topic

    Truth & Knowledge1 linked

    Related

    A proof system's justificatory burden includes justifying its foundations; more ...Cognitive accessibility and pedagogical clarity correlate with foundational mini...Epistemic simplicity requires minimal foundational assumptions; presupposing pow...Foundational power and justificatory rigor are distinct; powerful systems needn'...
    +3 moreShow less
    Non-standard analysis provides simpler and more intuitive proofs of many theorem...Simplicity can mean brevity of proofs or fewer proof steps; powerful foundations...Well-understood powerful axioms (like ZFC) may be epistemically simpler than lab...

    Details

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