What is Poincaré's view on mathematical truth?
Mathematical truths are not etched in some pre-existing reality waiting to be unearthed, as some might believe. Instead, they are born from a process of selection, a 'choice among conventions.' Our minds, with their inherent sense of order and harmony, gravitate towards certain frameworks because they are useful, elegant, and facilitate further exploration. It is by logic that we prove, yes, but it is through intuition that we discover. This intuition guides our choices, allowing us to build coherent systems that reflect a kind of beauty, a harmony that resonates with our innate mental faculties. The power lies not in discovery, but in the discerning selection.
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