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EXPLAIN HUMES DISTINCTION BETWEEN TRUTHS OF MOF AND THOSE OF ROI

EXPLAIN HUME'S DISTINCTION
BETWEEN 
TRUTHS WHICH DEPEND ON ROI AND THOSE WHICH DEPEND ON MOF
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.

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