Matters of Fact and Relations of Ideas

All the objects of human reason or inquiry may naturally be divided into two kinds, to wit, relations of ideas, and matters of fact.  Of the first kind are the sciences of geometry, algebra, and arithmetic. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is any where existent in the universe... .  Matters of fact, which are the second objects of human reason, are not ascertained in the same manner ... . The contrary of every matter of fact is still possible ... .
- David Hume, An Enquiry Concerning Human Understanding (1748)

Are there any truths which are not known through observation or reasoning?

Leibniz made a distinction between two kinds of truth: Truths of fact, such as "The cat is under the bed," and truths of reason, such as "A square has four sides." Truths of fact are known in virtue of factual observations, and truths or reason are true in virtue of the meanings of words.

Truths of fact have also been called contingent, and truths of reason have been called necessary.  For truths of fact depend on observable facts. They are contingent on the facts. Truths of reason are necessary because they don't depend on any facts, but are true by definition. They are also called "tautologies."

In Hume's writings we meet these two kinds of truth under the names of "matter of fact" and "relations of ideas." Hume believed that all worthwhile knowledge must be one or the other. And what about any so-called "truth" that is neither? "[C]ommit it then to the flames. for it can contain nothing but sophistry and illusion."

So theology, ethics and metaphysics are ...nonsense? And what about the truths of fiction and poetry?

Was Hume right? Can you conceive of a meaningful sentence that does not report either a matter of fact or a relation of ideas?

We shall encounter this distinction again in the philosophy of Kant, and still again in the writings of the Vienna Circle school of logical positivists of the 1930's.

Bibliography

Hume, David. An Inquiry Concerning Human Understanding, The Liberal Arts Press,New York, 1955.

McNabb, D.G.C., "David Hume," Encyclopedia of Philosophy, Collier-Macmillan, New York, 1967, Vol. 4, pp. 74-90.