Hume 206: More on relations of ideas & matters of fact.

Hume has argued that all ideas are based on impressions, that you cannot have an idea without first having some appropriate experience. However, once you have certain ideas you can manipulate them in certain ways and gain new knowledge but this isn’t knowledge of the world. Once you know a bit of geometry you can work out the what the internal angles of a hexagon must add up to without measuring them but this doesn’t tell you whether there are any hexagons out there in the world. To find that out you will have to go out and check.

Possible objections to Hume's distinction:

1. The distinction may be self-defeating as you can ask whether the distinction is itself a relation of ideas or a matter of fact. If it is a relation of ideas then, according to Hume, it doesn’t necessarily tell us anything about the way the world really is; if it is a matter of fact then the contrary is possible and it leaves open the possibility that Hume is wrong in his claim that this is the way to divide up ‘the objects of human reason or enquiry’.
   
   
2. There are possible counter-examples. It seems that some matters of fact can be known prior to, i.e. before, experience:
• Galileo determining by thought experiment that objects of different weights must fall at the same rate in a vacuum. (Galileo also did actual experiments rolling balls of different weights down slopes but the thought experiment of dropping differing weights either connected or not connected would seem to suffice.)
• Einstein calculating how much gravity will bend light. [This second example also seems to be a counter-example to Hume’s claim that knowledge of cause and effect can only be found through experience.]

Why is this important?

Hume is going to rely on this distinction when he argues some of our important conclusions about the world are not based on reasoning. However, if the distinction he is making here is incorrect then any arguments based on it are thrown into doubt.

Hume says that we move from observing that something has always happened to concluding that it will always happen—the dropped stone always has fallen towards the ground so the dropped stone always will fall towards the ground.

However, he claims that this move isn't based on any kind of reasoning. It can't be, according to Hume, because it isn't a relation of ideas ("since there is no outright contradiction in supposing that the course of nature will change") but all reasonings concerning matters of fact depend on the assumption that the way things happen will remain as they have been in the past. We can't use that assumption to justify that assumption as that would be a circular argument. He says: