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In his Enquiry concerning human understanding, Hume provides the following definition:

All the objects of human reason or enquiry 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; and in short, every affirmation which is either intuitively or demonstratively certain.

He does not go any further in the explanation of this concept(at least as far as I've read), and I'm not sure I've understood well what a "relation of ideas" is. Is it the same as the analytic a priori judgment?

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    'Analytic a priori judgement' sounds like a Kantian-type statement; and Kants protagonist was Hume; I wouldn't say its exactly the same, because I expect they used it for differing purposes; but its in the same sense. – Mozibur Ullah Mar 29 '15 at 19:52
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    This is one of the weirder points if you're doing a grand arc history of philosophy approach -- one of Kant's famous ideas that supposedly is the death knell of empiricism is wholly found in Hume who is supposedly one of those empiricists. – virmaior Mar 30 '15 at 1:44
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Yes. Both features of the relations of ideas, analyticity and a-priority, are spelled out in §30 of the Enquiry, a bit after the one you quoted from.

Hume associates relations of ideas with demonstrative reasoning:

All reasonings may be divided into two kinds, namely, demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence.

He then associates demonstrative reasoning with the law of non-contradiction:

That there are no demonstrative arguments in the case seems evident; since it implies no contradiction that the course of nature may change, and that an object, seemingly like those which we have experienced, may be attended with different or contrary effects.

This implies that relations of ideas are analytic, in Kant's sense of the word. Hume then associates demonstrative arguments, and non-contradiction, also with abstract a priori reasoning:

Now whatever is intelligible, and can be distinctly conceived, implies no contradiction, and can never be proved false by any demonstrative argument or abstract reasoning a priori.

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