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RolfAndreassen comments on About addition and truth - Less Wrong
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Well, perhaps my question is better phrased as, "What is the referent of mathematics which does not describe objects in the universe?"
It's a certain model that exists within your mind and your mathematics textbook. :)
Models are tested by reference to experiment. If the model only exists in my head, what is the experiment that tests it? If there is no external reference, then in what sense can anything at all be said to contradict the model?
Are models tested by reference to experiment? You can demonstrate that a model is inapplicable in some cases; if it's inapplicable in all cases, it is useless; I don't know if it means anything to say that the model itself is false.
This is doubly so when applied to mathematics; mathematics (specifically, logic) is the model that gives a context to the term "contradiction"; that tells what it means and how we know it applies.