Sensory experience is only one of several different types of experience
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For the enduring strength of science – the reason it can indeed plop a person on the moon – is that it always attempts, as best it can, to rest its assertions on evidence and experience. But sensory experience is only one of several different but equally legitimate types of experience, which is precisely why mathematics – seen only inwardly, with the mind's eye – is still considered scientific (in fact, is usually considered extremely scientific!).