16 ideas
12215 | The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K] |
10185 | Set theory is the standard background for modern mathematics [Burgess] |
10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
12211 | It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K] |
12209 | The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K] |
12214 | 'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' [Fine,K] |
12212 | Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K] |
12216 | Real objects are those which figure in the facts that constitute reality [Fine,K] |
12218 | Being real and being fundamental are separate; Thales's water might be real and divisible [Fine,K] |
12217 | For ontology we need, not internal or external views, but a view from outside reality [Fine,K] |
12213 | Ontological claims are often universal, and not a matter of existential quantification [Fine,K] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |