| Relations of Ideas | Matters of Fact | |
| sphere: | mathematics | (science) | 
| certainty: | intuitively or demonstratively certain | not certain | 
| example: | Three times five is equal to half of thirty. | The sun will rise tomorrow. | 
| knowable: | by the mere operation of thought | (by experience) | 
| dependence: | not dependent on existence | (dependent on existence) | 
| possibility: | contrary is not possible | contrary is possible |