Across
- 2. a system that is based on a small number of statements that are accepted as self-evident
- 4. he proved the “second incompleteness theorem”
- 5. according to the “mathematics is discovered” position, truth lies outside of mathematics itself, in other words, the criterion of truth is ……-mathematical
- 8. reasoning from particular instances to a generalized law
- 9. an observed regularity in mathematics that is hypothesized to be true, but has not been proven with certainty
- 10. the property of an axiomatic system to be able to prove contradictory statements from the same set of axioms
- 12. a proven statement in mathematics
Down
- 1. if this is generated by an axiomatic system, we consider this system to be inconsistent
- 3. a property of deductive proof that sets it apart from scientific evidence
- 6. reasoning from the general to the particular
- 7. the process of mathematical reasoning in which it is demonstrated that a statement logically follows from other, previously accepted statements
- 11. test for truth that forms the basis of the “mathematics is invented” position