Hume separates his distinction of truths of into two categories. They are
Relation of Ideas (ROF) and Matter of Fact (MOF). Hume states Relation of Ideas
are always true based on how all its component parts relate. However, Matter of
Fact can and cannot be true depending on circumstance. If its components do not
relate it can not be truth. For example of ROF, all bachelors are unmarried.
This is truth based on that a bachelor is an unmarried man. An example of MOF is
that all bachelors are lonely. This can not be true because even though a
bachelor is unmarried it does not necessarily mean he is lonely. The component
parts of ROF relate when the components of MOF do not. Hume distinguishes
amongst the two categories by two determinings of truths. Analytic Propositions
and Synthetic determines truths of ROF and MOF. Analytic Propositions of ROF is
the idea that its truths depends on how each idea is analyzed and built up to
make it truth. ROF is necessary truth, which is called contrary impossible. It
has got to be true. As for MOF, Synthetic means the ability for MOF truths to be
demonstrative certain and intuitively certain. Demonstrative certain is when one
can not tell if it is certain by looking at it. Intuitively certain is when one
can look at it and know it is certain. MOF can be contingent, which is the
capability of being false. 2 Also known as contrary possible. Hume also states
that truths of ROF are found by a priori knowledge. Its truth is discovered by
operation of thought. Knowledge of experience is not needed. As long as one can
understand the ideas, they do not need any experience to tell if it is truth. On
the contrary, truths of MOF depends on experience; a posteriori knowledge. Based
on what exists it may or may not be true. Hume strongly believes in truths of
MOF that all ideas arise from experience. Experience of cause and effect
determines whether something is true of MOF. Even after experience of cause and
effect, a conclusion from that experience is not found by thinking it out nor by
any method of understanding. So, therefore that experience determines whether it
can be true or false. However, truths of ROF are inconceivably contrary. It is
never perceived as either/or nor “as a result of”, but as a relation of
ideas that are always true. Truths of MOF are contrary conceivable. They can be
understood as true or false by experience. It is not a matter of thinking it out
and relating the idea why one infers one from the other (truth from falsity),
but by experience. To conclude, Hume distinguishes truths of Relation of Ideas
and Matter of Fact by Sub categorizing the two into Analytical Propositions and
Synthetic. He later distinguishes truth that depends on ROI and MOF by factors
of certain/not certain, a priori/posteriori knowledge, contrary
impossible/contrary possible, and inconceivably contrary/contrary conceivable.