18 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] |
| 21110 | An understanding of the most basic physics should explain all of the subject's mysteries [Krauss] |
| 21105 | In 1676 it was discovered that water is teeming with life [Krauss] |
| 21109 | Space itself can expand (and separate its contents) at faster than light speeds [Krauss] |
| 21104 | General Relativity: the density of energy and matter determines curvature and gravity [Krauss] |
| 21107 | Uncertainty says that energy can be very high over very short time periods [Krauss] |
| 21106 | Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss] |
| 21112 | Empty space contains a continual flux of brief virtual particles [Krauss] |
| 21108 | The universe is precisely 13.72 billion years old [Krauss] |
| 21111 | It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |