Source: p 115, Philosophy: A Complete Introduction (2012) by Prof Sharon Kaye (MA PhD in Philosophy, U. Toronto). Caution: I rewrote numerals as integers for easier reading.
1 Relations of ideas are logical truths, such as '2 + 2 = 4'. These are necessary because the attempt to deny them results in a contradiction.
If 2 + 2 = 5, then 1 + 1 + 1 + 1 is not 1 + 1 + 1 + 1, which is a contradiction.
2 Matters of fact are observed truths, such as 'bread nourishes'. These are contingent (meaning 'not necessary') because you can deny them without producing a contradiction. [3.] The idea of bread poisoning instead of nourishing involves no conceptual impossibility. [4.] We can prove this by imagining a world where bread poisons instead of nourishes.
Hume points out that the assertion 'A causes B' is a matter of fact, not a relation of ideas. Therefore it can't be necessary.
Of course, everyone recognizes instances when matters of fact go differently from usual. We've all eaten something that usually nourishes us, only to find that, this time, it made us sick. When this happens, we are liable to look for a hidden cause — some microscopic bacteria in the food that gave us food poisoning.
But when Hume calls the nourishing effect of bread a matter of fact, he isn't saying that there may be hidden causes that make things turn out differently this time. [5.] He's saying that the bread could suddenly have a completely different effect without any different causes at all.
To insist that there would have to be different cause in order to produce a different effect would be to cast the nourishing effect of bread as a relation of ideas like '2 + 2 = 4'. Because human beings are creatures of habit, we constantly view causal connections as logical connections. But this is a conceptual confusion we must overcome, in Hume's view.
What abstract distinctions between 1 and 2 have I neglected? I do not understand
3 and 4: because one necessary condition for 'bread nourishes' is: the bread is not poisoned (with bacteria). They are mutually exclusive.
5: how can no change in any cause still cause completely different effects? With no change in any cause, how can nourishing bread suddenly mutate into poisoned bread?