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It is not the case that Brouwer's intuitionism holds that the continuum is a primitive intuition not constructed by adding elements to a discrete base.
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Reasons For
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Reason for
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1.
If the continuum is primitive and intuitive, it remains unclear how to rigorously formalize its structure without appealing to discrete operations.
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2.
Our temporal intuition may reflect cognitive limitations rather than mathematical reality, making it an unreliable guide to mathematical primitives.
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3.
Constructible reals from recursive sequences have proven mathematically fertile; primitive continuity offers fewer tools for proof and computation.
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Reasons Against
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Reason against
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1.
Temporal experience directly presents continuous flow, not discrete points, suggesting continuity is fundamental to intuition itself.
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2.
Constructing reals from discrete elements requires infinite procedures that are never completed, making discreteness an inadequate foundation.
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3.
The continuum's density and lack of gaps reflect an immediate phenomenological given that logically precedes any point-based decomposition.
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