A Relation of Ideas, in the Humean

David Hume

David Hume was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment...

 sense, is the type of knowledge that can be characterized as arising out of pure conceptual thought and logical operations (in contrast to a Matter of Fact

Matter of Fact

A Matter of Fact, in the Humean sense, is the type of knowledge that can be characterized as arising out of one's interaction with and experience in the external world . In a Kantian framework, it is equivalent to the synthetic a posteriori.Examples:-The sun will come out tomorrow. -There are...

). In a Kantian

Immanuel Kant

Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....

 philosophy, it is equivalent to the analytic a priori

A priori and a posteriori (philosophy)

The terms a priori and a posteriori are used in philosophy to distinguish two types of knowledge, justifications or arguments...

. It is also closely coincident with the so-called Truths of Reason of Leibniz, which are defined as those statements whose denials are self-contradictory

Contradiction

In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...

.

Examples:

Mathematics: 8 x 10 = 80.

Logic/Definitions: All islands are surrounded by water (by definition).

How We Know:

-We can demonstrate these truths.

-Denying these will lead to a logical contradiction.