“Mathematics is the most pure of all sciences”

Directly quoted from Randall Munroe, https://xkcd.com/435/ Edit citation

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"A science would have to be more of a "pure science" than another if the nature of its subject entirely determines the nature of the other's subject."

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July 27th, 2022 20:46
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What determines purity? It is possible (though unlikely) that an observed effect resulting from an experiment in chemistry could contradict established theories of physics. As long as the experiment stands up to a greater deal of scientific scrutiny than prior observations in physics which contradict it, physics must be ammended.

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August 3rd, 2022 08:29

This statement is about the nature of of the subject not about the practice of the science itself, which seems to be what you're talking about. I'm not sure how this goes towards improving this premise, which is what discussions about the premise are supposed to be. Maybe the statement can be clarified? It does say, "the nature of its subject", which is pretty explicit. The easiest criticism I can make about this statement is just that the practice of a science might matter more, which would actually belong in a challenge to the statement.

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"Mathematics does not require observations."

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July 27th, 2022 20:34
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Define observation. By attempting to calculate the circumference of a circle using a similar shape with an increasing number of sides, it becomes apparent that the ratio of circumference (perimeter) to Diameter tends towards pi. Why is this distinct from a scientific observation?

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August 3rd, 2022 08:06

This is an interesting thought. I think it would make sense to add the second sentence as a challenge to this statement. (If you click on the statement you can see where to add challenges.)

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