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
    An inductive proof proves the inductive base φ(1) and the... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Proof of definition segments
    HistoryEditSee Inverse

    Part of a larger discussion

    Supports→An inductive proof enables us to perceive that a direct proof of any particular proposition can be constructed, even though it cannot prove the infinite possibility of application.

    An inductive proof proves the inductive base φ(1) and the inductive step φ(n) → φ(n+1).

    Proof of definition segments
    ?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.

    Topics

    Proof of definition segments

    Connections

    2 topics

    Truth & Knowledge2 linkedPhilosophy of Language1 linked

    Next step

    Based on where you are in your exploration

    Browse more in Proof of definition segments
    Related propositions within the same area of thought.

    Related

    An inductive proof enables us to perceive that a direct proof of any particular ...Once the inductive base and inductive step are proved, we need not reiterate mod...The proxy statement φ(m) is an eliminable pseudo-proposition standing proxy for ...

    Similar

    Every step of the proof can be derived from the axioms74%A demonstration that φ is not in n-PROVABILITY_T for sufficiently larg...72%The proof proposed in Appendix B purports to derive the principle of I...69%The Main Theorem establishes that Γ ⊨_MSL φ if and only if Trans(Γ) ∪ ...67%

    Source

    AI-extracted
    SEP: wittgenstein-mathematics
    View source passageHide passage
    Here the ‘conclusion’ of an inductive proof [i.e., “what is to be proved” (PR §164)] uses ‘\(m\)’ rather than ‘\(n\)’ to indicate that ‘\(m\)’ stands for any particular number, while ‘\(n\)’ stands for any arbitrary number. For Wittgenstein, the proxy statement “\(\phi(m)\)” is not a mathematical proposition that “assert[s] its generality” (PR §168), it is an eliminable pseudo-proposition standing proxy for the proved inductive base and inductive step. Though an inductive proof cannot prove “the

    Details

    Type
    premise
    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