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