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    The proposition '2+2=4' is a necessary truth because it r... — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    The proposition '2+2=4' is a necessary truth because it reduces to an identity statement

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.A proposition is necessary if, upon analysis, it reduces to a statement of identities
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    • 2.'2' is defined as '1+1' and '4' is defined as '1+1+1+1'
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    • 3.Substituting these definitions into '2+2=4' yields '1+1+1+1 = 1+1+1+1', which is an identity
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.The necessity of '2+2=4' depends on prior definitional choices, and definitions are conventional, not logically necessary.
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    • 2.Frege and Russell showed that arithmetic reduces to logic only through contested axioms like Hume's Principle, which are not self-evident identities.
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    • 3.A truth whose necessity is inherited from definitions cannot be necessary in an absolute, mind-independent sense, only relative to a chosen system.
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    Reason against 2 of 2
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    • 1.Kant argued that '7+5=12' is synthetic a priori, not analytic, because the concept of 12 is not contained in the mere combination of 7 and 5.
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    • 2.If arithmetic propositions require pure intuition of successive addition to be known, their necessity derives from the structure of cognition, not from conceptual identity.
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    • 3.Leibniz's reduction procedure presupposes that substitution of definitional equivalents preserves meaning, but Frege's puzzle shows co-referential terms are not always intersubstitutable salva veritate in all contexts.
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    Topics

    Modality & PossibilityTruth & Knowledge

    Connections

    1 topic

    Philosophy of Language2 linked

    Related

    '2' is defined as '1+1' and '4' is defined as '1+1+1+1'A proposition is necessary if, upon analysis, it reduces to a statement of ident...A truth whose necessity is inherited from definitions cannot be necessary in an ...Frege and Russell showed that arithmetic reduces to logic only through contested...
    +6 moreShow less
    If arithmetic propositions require pure intuition of successive addition to be k...Kant argued that '7+5=12' is synthetic a priori, not analytic, because the conce...Leibniz's reduction procedure presupposes that substitution of definitional equi...Substituting these definitions into '2+2=4' yields '1+1+1+1 = 1+1+1+1', which is...The concept of the predicate '4' is contained in the subject '2+2'The necessity of '2+2=4' depends on prior definitional choices, and definitions ...

    Similar

    A proposition is necessary if, upon analysis, it reduces to a statemen...83%Every necessary truth is entailed by every proposition.79%Substituting these definitions into '2+2=4' yields '1+1+1+1 = 1+1+1+1'...78%The relation between a true proposition and the corresponding fact is ...78%

    Source

    AI-extracted1/3 agreementValid
    SEP: leibniz-modal
    View source passageHide passage
    In other words, a proposition is necessary (or expresses a necessary truth) if, in analyzing it, one arrives at a statement of identities. A simple example can be found in arithmetic: “2+2 = 4.” Since “2 = 1+1” and “4 = 1+1+1+1”, we can easily show that the original statement can be reduced to “1+1+1+1 = 1+1+1+1.” Here we have an obvious case of an identity and one where we can say that the concept of the predicate – in this case, “4” – is contained is contained in the subject, “2+2” (or “(1+1)
    Extraction notes

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

    Details

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