20 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| 6303 | Sets are positions in patterns [Resnik] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| 22167 | Our images of bodies are not produced by the bodies, but by our own minds [Augustine, by Aquinas] |
| 22117 | Our minds grasp reality by direct illumination (rather than abstraction from experience) [Augustine, by Matthews] |
| 22118 | Augustine created the modern concept of the will [Augustine, by Matthews] |
| 23903 | When we admire a work, we see ourselves as its creator [Weil] |
| 4348 | Love, and do what you will [Augustine] |
| 7821 | Pagans produced three hundred definitions of the highest good [Augustine, by Grayling] |
| 22119 | Augustine said (unusually) that 'ought' does not imply 'can' [Augustine, by Matthews] |
| 23901 | Relationships depend on equality, so unequal treatment kills them [Weil] |
| 22116 | Augustine identified Donatism, Pelagianism and Manicheism as the main heresies [Augustine, by Matthews] |
| 23904 | The cruelty of the Old Testament put me off Christianity [Weil] |
| 23902 | I attach little importance to immortality, which is an undecidable fact, and irrelevant to us [Weil] |
| 19338 | Augustine said evil does not really exist, and evil is a limitation in goodness [Augustine, by Perkins] |