Free choice sequences play a key role in the Brouwerian continuum. Using recent modal analysis of potential infinity, we can make sense of free choice sequences as potentially infinite sequences of natural numbers without adopting Brouwer’s distinctive idealistic metaphysics. This provides classicists with a means to make sense of intuitionistic ideas from their own classical perspective. I develop a modal-potentialist theory of real numbers that suffices to capture the most distinctive features of intuitionistic analysis, such as Brouwer’s continuity theorem, the existence of a sequence that is monotone, bounded, and non-convergent, and the inability to decompose the continuum non-trivially.

中文翻译：

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直觉分析的潜在主义观点


自由选择序列在 Brouwerian 连续体中起着关键作用。使用最近对潜在无穷大的模态分析，我们可以将自由选择序列理解为潜在的无限自然数序列，而无需采用 Brouwer 独特的唯心主义形而上学。这为古典主义者提供了一种从他们自己的古典角度理解直觉主义思想的方法。我发展了一种实数的模态潜力主义理论，该理论足以捕捉直觉分析的最独特特征，例如 Brouwer 连续性定理，存在单调、有界和非收敛的序列，以及无法非平凡地分解连续体。