Hume in his book differentiates the two objects of human reason or enquiry. These objects are the relations of ideas and matters of fact. Every idea relation is either automatically or obviously certain. These relations are mathematical and the amount concerning a relationship of idea is right by quality of its rational status. The matters of fact on the other side are the objects of human reason. These objects are not attached to any kind of necessity. A suggestion about matters of fact are not essentially true. As Hume proclaims “the contrary of every matter fact is still possible; because it can never imply a contradiction” although it contradicts to declare that a circle is not circular, it does not contradict in any way to say that the sun will not rise tomorrow.
The propositions which give the picture of relations of ideas are considered to be true through operation of thoughts with no dependence on where else does the same exist in the world. propositions looking into the matters of fact are easy to be known through the same way. People have a notion that events are informally related in such a way that knowledge of one event leads to believing of the second event. These events are not in any case linked by the logic that guides relations of ideas. these events are not contingent when put on the principle of noncontradiction. In contrary, these events are linked by supposing that there is a joining between the existing fact and that which is inferred from it. This link is action and it is brought about by experience, when one finds out that any specific objects are always adjoined with each other.
Experience gives the best situation for determining cause-and-effect relations. With no experiments, it is no possible for someone to be able to know that “two smooth pieces of marble will adhere to each other”. And also, no analysis whatsoever can result to contradiction that they will not stick together. From what Hume asserts, experimental deductions are not based on demonstrative reasoning. In contrary, only experience makes it possible for one to bring events together in a casual manner. A single experience of two events cannot rightfully be casually associated. Casual judgement, which is in other words referred to as “inductive inference” is arbitrary. It is by means of analogy, experience and observation that a general association of events can be made. The vivacity, force and frequency of two events experienced at the same time result in one being certain and gives self-assurance in hoping for the second one when the first one takes place.
In conclusion, it is clear that a matter-of-fact-inference is with no doubt a casual inference. In turn a casual inference is entirely based on experience. A pure reason does not play any role anywhere. How ideas are related and matters of fact are the two names used to denote modes of reasoning. The understanding of humans is based on propositions that are either certain or probable. Assertion of the relation of ideas is to make a reasonably essential judgement. Assertion of matters of fact is making an experimental judgement. Conclusions drawn from relations of ideas is that it is certain by nature. Conclusions subsequent from matters of facts are that they are probable by nature. Relation of ideas is mathematical while matters of fact is experimental.