| 476 | Self-created numbers make the universe stable [Philolaus] |
| Full Idea: Number is the ruling and self-created bond which maintains the everlasting stability of the contents of the universe. | |
| From: Philolaus (On the Cosmos (lost) [c.435 BCE], B23), quoted by (who?) - where? |
| 17008 | You have discovered that elliptical orbits result just from gravitation and planetary movement [Newton, by Leibniz] |
| Full Idea: You have made the astonishing discovery that Kepler's ellipses result simply from the conception of attraction or gravitation and passage in a planet. | |
| From: report of Isaac Newton (Principia Mathematica [1687]) by Gottfried Leibniz - Letter to Newton 1693.03.07 | |
| A reaction: I quote this to show that Newton made 'an astonishing discovery' of a connection in nature, and did not merely produce an equation which described a pattern of behaviour. The simple equation is the proof of the connection. |
| 17010 | We have given up substantial forms, and now aim for mathematical laws [Newton] |
| Full Idea: The moderns - rejecting substantial forms and occult qualities - have undertaken to reduce the phenomena of nature to mathematical laws. | |
| From: Isaac Newton (Principia Mathematica [1687], Preface) | |
| A reaction: This is the simplest statement of the apparent anti-Aristotelian revolution in the seventeenth century. |
| 8656 | The laws of number are not laws of nature, but are laws of the laws of nature [Frege] |
| Full Idea: The laws of number are not applicable to external things, and are not laws of nature, but they are applicable to judgements of external things: they are laws of the laws of nature. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §87) | |
| A reaction: We seem to be somewhere between pythagoreanism and 'the mind of God'. I feel fairly strongly that we are looking through the wrong end of the telescope here. The laws of nature 'emerge' from nature, and high-level abstractions emerge with them. |
| 8381 | The constancy of scientific laws rests on differential equations, not on cause and effect [Russell] |
| Full Idea: It is not in the sameness of causes and effects that the constancy of scientific law consists, but in sameness of relations. And even 'sameness of relations' is too simple a phrase; 'sameness of differential equations' is the only correct phrase. | |
| From: Bertrand Russell (On the Notion of Cause [1912], p.186) | |
| A reaction: This seems to be a commitment to the regularity view, since there is nothing more to natural law than that the variables keeping obeying the equations. It also seems to be a very instrumentalist view. |
| 15125 | We only know the mathematical laws, but not much else [Hawthorne] |
| Full Idea: We know the laws of the physical world, in so far as they are mathematical, pretty well, but we know nothing else about it. | |
| From: John Hawthorne (Causal Structuralism [2001], Ch.25) | |
| A reaction: Lovely remark [spotted by Hawthorne]. This sums up exactly what I take to be the most pressing issue in philosophy of science - that we develop a view of science that has space for the next step in explanation. |