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<p>Is the Continuum Hypothesis true? Or is it false? Any discussion of the problem requires a preliminary discussion of the nature of Mathematical Truth. This is of course because by the results of Gödel and Cohen, there is no answer based on just the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{ZFC}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>ZFC</mtext> </math></EquationSource> </InlineEquation> axioms of Set Theory. We define and defend the <i>V</i>-view of Mathematical Truth in an account that is directed more to Mathematicians than to Philosophers. The reason is simply that the view through the Mathematician’s lens is much easier to discuss. In the <i>V</i>-view, the Continuum Hypothesis has an answer, as do all the formal questions of Set Theory.</p>

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What a set is: the V-view

  • 期刊论文

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  • 发表日期：

    2025年5月8日

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  • W. Hugh Woodin

摘要

Is the Continuum Hypothesis true? Or is it false? Any discussion of the problem requires a preliminary discussion of the nature of Mathematical Truth. This is of course because by the results of Gödel and Cohen, there is no answer based on just the \(\textrm{ZFC}\) ZFC axioms of Set Theory. We define and defend the V-view of Mathematical Truth in an account that is directed more to Mathematicians than to Philosophers. The reason is simply that the view through the Mathematician’s lens is much easier to discuss. In the V-view, the Continuum Hypothesis has an answer, as do all the formal questions of Set Theory.