| 11. | Since the first two were existential axioms, Russell phrased mathematical statements depending on them as conditionals.
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| 12. | :Every mathematical statement involving complex numbers can be rephrased as a statement involving only real numbers.
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| 13. | Fundamental physical entities are defined mathematically, and the physicalist must consider what makes mathematical statements true.
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| 14. | Structuralism is an epistemologically realistic view in that it holds that mathematical statements have an objective truth value.
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| 15. | :The number of quantifiers in a mathematical statement gives a rough measure of the statement s complexity.
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| 16. | A mathematician friend recently explained that there is a whole class of mathematical statements that can be called independent.
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| 17. | Mathematical statements have their own moderately complex taxonomy, being divided into axioms, conjectures, theorems, corollaries.
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| 18. | He spent several days rewriting it and now has it down to three normal-looking pages of mathematical statements.
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| 19. | The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true.
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| 20. | Nuprl uses a type system based on Martin-L�f intuitionistic type theory to model mathematical statements in a digital library.
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