18 ideas
| 7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
| 9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
| 22276 | Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter] |
| 17264 | Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder] |
| 12232 | A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano] |
| 12233 | The ground of a pure conceptual truth is only in other conceptual truths [Bolzano] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |