17 ideas
10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
16659 | Relations do not add anything to reality, though they are real aspects of the world [Olivi] |
16673 | Quantity just adds union and location to the extension of parts [Olivi] |
16663 | Things are limited by the species to certain modes of being [Olivi] |