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Click on the phrases to see them in context. The original texts by Immanuel Kant and David Hume are available from the Gutenberg Projet.

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Devoid, however, of a true and objectively valid a priori intuition, they can neither furnish any basis for the possibility of mathematical cognitions a priori, nor bring the propositions of experience into necessary accordance with those of mathematics.

 I should not hesitate to stake my all on the truth of the proposition- if there were any possibility of bringing it to the test of experience--that, at least, some one of the planets, which we see, is inhabited. 
This hypothesis is founded on sufficient experience.
 Home based business wage earner's success rate is over 85% compared with small businesses like retail shops and restaurants, at about 95% failure rate after 5 years. Experience is an empirical cognition; that is to say, a cognition which determines an object by means of perceptions. For the conception merely enables me to cogitate an object as according with the general conditions of experience; while the existence of the object permits me to cogitate it as contained in the sphere of actual experience. The principle of these is; Experience is possible only through the representation of a necessary connection of Perceptions. The same demand must again be made of the cause itself--as a datum of experience.