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
    Leibniz's conception requires differentials that obey the... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Philosophy of Language
    HistoryEditSee Inverse

    Part of a larger discussion

    Supports→To do full justice to both Leibniz's and Nieuwentijdt's conceptions of infinitesimals, two distinct sorts of infinitesimals are required.

    Leibniz's conception requires differentials that obey the same algebraic laws as finite quantities.

    Philosophy of LanguageTruth & Knowledge
    ?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

    Philosophy of LanguageTruth & Knowledge

    Connections

    1 topic

    Modality & Possibility2 linked

    Related

    Next step

    Based on where you are in your exploration

    Browse more in Philosophy of Language
    Related propositions within the same area of thought.
    Leibniz recognized the need for differentials but not nilsquare infinitesimals, ...Nieuwentijdt's conception requires nilsquare infinitesimals that measure the len...Nilsquare infinitesimals are necessarily smaller than Leibnizian differentials.To do full justice to both Leibniz's and Nieuwentijdt's conceptions of infinites...

    Similar

    Leibniz recognized the need for differentials but not nilsquare infini...79%Since P_f presupposes differential structure, one cannot use P_f in th...74%Moral laws can be known with the same necessity as mathematical princi...73%To do full justice to both Leibniz's and Nieuwentijdt's conceptions of...73%

    Source

    AI-extracted
    SEP: continuity
    View source passageHide passage
    Now Leibniz could retort that that this argument depends crucially on the assumption that the portion of the curve between abscissae 0 and \(\Dx\) is indeed straight. If this be denied, then of course it does not follow that \(\Dx ^2 = 0\). But if one grants, as Leibniz does, that that there is an infinitesimal straight stretch of the curve (a side, that is, of an infinilateral polygon coinciding with the curve) between abscissae 0 and \(e\), say, which does not reduce to a single point then \(e

    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