display all the ideas for this combination of philosophers
4 ideas
| 17185 | Mathematics deals with the essences and properties of forms [Spinoza] |
| Full Idea: Mathematics does not deal with ends, but with the essences and properties of forms (figures), …and has placed before us another rule of truth. | |
| From: Baruch de Spinoza (The Ethics [1675], IApp) | |
| A reaction: Just what I need - a nice clear assertion of essentialism in mathematics. Many say maths is all necessary, so essence is irrelevant, but I say explanations occur in mathematics, and that points to essentialism. |
| 17222 | The sum of its angles follows from a triangle's nature [Spinoza] |
| Full Idea: It follows from the nature of a triangle that its three angles are equal to two right angles. | |
| From: Baruch de Spinoza (The Ethics [1675], IV Pr 57) | |
| A reaction: This is the essentialist view of mathematics, which I take to be connected to explanation, which I take to be connected to the direction of explanation. |
| 17197 | The idea of a triangle involves truths about it, so those are part of its essence [Spinoza] |
| Full Idea: The idea of the triangle must involve the affirmation that its three angles are equal to two right angles. Therefore this affirmation pertains to the essence of the idea of a triangle. | |
| From: Baruch de Spinoza (The Ethics [1675], II Pr 49) | |
| A reaction: This seems to say that the essence is what is inescapable when you think of something. Does that mean that brandy is part of the essence of Napoleon? (Presumably not) Spinoza is ignoring the direction of explanation here. |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal. | |
| From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'. |