History and Philosophy of Logic 13 (2):203-213 (1992)

Intuitionistically. a set has to be given by a finite construction or by a construction-project generating the elements of the set in the course of time. Quantification is only meaningful if the range of each quantifier is a well-circumscribed set. Thinking upon the meaning of quantification, one is led to insights?in particular, the so-called continuity principles?which are surprising from a classical point of view. We believe that such considerations lie at the basis of Brouwer?s reconstruction of mathematics. The predicate ?α is lawless? is not acceptable, the lawless sequences do not form a well-circumscribed intuitionistic set, and quantification over lawless sequences does not make sense
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DOI 10.1080/01445349208837203
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References found in this work BETA

Analysing Choice Sequences.A. S. Troelstra - 1983 - Journal of Philosophical Logic 12 (2):197 - 260.
The Continuum Hypothesis in Intuitionism.W. Gielen, H. de Swart & W. Veldman - 1981 - Journal of Symbolic Logic 46 (1):121-136.

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Realizing Brouwer's Sequences.Richard E. Vesley - 1996 - Annals of Pure and Applied Logic 81 (1-3):25-74.

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