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Semantic issues can be resolved by more precise definitions. That's why we must circumscribe, dispensing with the notion means we can't investigate it.
In geometry, there exist a set of axioms from which sprout the various laws and relationships that can be proven and tested against one another. However, the axioms must be taken on faith. There is no way to proove them. In fact it has been shown that it is impossible to proove them. Hence mathematics (geometry is a specific example, but the idea of axioms permeates throughout the whole of mathematics) is a field built entirely on faith.
The concept is problematic, but it is also self consistant. If you accept that faith is necessary for mathematics, life and anything else (it is the hidden axiom if you will), then you solve the paradox, the problem becomes null and avenues hitherto shut open themselves up for exploration.
What then becomes important is not the concept of belief itself, but what you believe in and how closely that belief matches reality.
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