display all the ideas for this combination of texts
3 ideas
| 24036 | I can only see the proportion of two to three if there is a common measure - their unity [Descartes] |
| Full Idea: I do not recognise what the proportion of magnitude is between two and three, unless I consider a third term, namely unity, which is the common measure of the one and the other. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 14) | |
| A reaction: A striking defence of the concept of the need for the unit in arithmetic. To say 'three is half as big again', you must be discussing the same size of 'half' in each instance. |
| 24035 | Unity is something shared by many things, so in that respect they are equals [Descartes] |
| Full Idea: Unity is that common nature in which all things that are compared with each other must participate equally. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 14) | |
| A reaction: A lovely explanation of the concept of 'units' for counting. Fregeans hate units, but we Grecian thinkers love them. |
| 17462 | A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt] |
| Full Idea: One requirement for a successful count is that double counting should be avoided: a single object should not be counted twice. ...but that is to make a knowledgeable judgement of distinctness - to resolve a question of identity in the negative. | |
| From: Ian Rumfitt (Concepts and Counting [2002], III) | |
| A reaction: He also notes later (p.65) that you must count all and only the right things. |