6 ideas
| 17423 | The essence of natural numbers must reflect all the functions they perform [Sicha] |
| Full Idea: What is really essential to being a natural number is what is common to the natural numbers in all the functions they perform. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2) | |
| A reaction: I could try using natural numbers as insults. 'You despicable seven!' 'How dare you!' I actually agree. The question about functions is always 'what is it about this thing that enables it to perform this function'. |
| 17425 | To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha] |
| Full Idea: A knowledge of 'how many' cannot be inferred from the equinumerosity of two collections; a numerical quantifier statement is needed. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 3) |
| 17424 | Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha] |
| Full Idea: Counting is the activity of putting an initial segment of a serially ordered string in 1-1 correspondence with some other collection of entities. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2) |
| 20646 | Helmholtz used 'energy' to mathematically link heat, light, electricity and magnetism [Helmholtz, by Watson] |
| Full Idea: Helmholtz provided the requisite mathematical formulation linking heat, light, electricity and magnetism, by treating these phenomena as different manifestations of 'energy'. | |
| From: report of Hermann von Helmholtz (On the Conservation of Force [1847]) by Peter Watson - Convergence 01 'Human' | |
| A reaction: I'm increasingly struck by the neglect by philosophers of nature of these amazing developments in 19th century physics, because they prefer the excitement of the latest nuclear physics. There is more philosophical interest in the earlier stages. |
| 20973 | All forces conserve the sum of kinetic and potential energy [Helmholtz, by Papineau] |
| Full Idea: Helmholtz crucially asserted that all forces conserve the sum of kinetic and potential energy; superficially non-conservative forces like friction are simply macroscopic manifestations of more fundamental forces conserving energy at the micro-level. | |
| From: report of Hermann von Helmholtz (On the Conservation of Force [1847]) by David Papineau - Thinking about Consciousness App 4.3 | |
| A reaction: Friction had been a problem case, because it appeared not to conserve energy when it slowed movement down. |
| 20713 | God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B] |
| Full Idea: Rachels argues 1) If any being is God, he must be a fitting object of worship, 2) No being could be a fitting object of worship, since worship requires the abandonment of one's role as an autonomous moral agent, so 3) There cannot be a being who is God. | |
| From: report of James Rachels (God and Human Attributes [1971], 7 p.334) by Brian Davies - Introduction to the Philosophy of Religion 9 'd morality' | |
| A reaction: Presumably Lionel Messi can be a fitting object of worship without being God. Since the problem is with being worshipful, rather than with being God, should I infer that Messi doesn't exist? |