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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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The former encourages and advances science--although to the prejudice of the practical; the latter presents us with excellent principles for the investigation of the practical, but, in relation to everything regarding which we can attain to speculative cognition, permits reason to append idealistic explanations of natural phenomena, to the great injury of physical investigation.

 I need not observe, that it is no just objection to the present doctrine, that we can reason upon our past conclusions or principles, without having recourse to those impressions, from which they first arose. Thus the empiricism of transcendentally idealizing reason is robbed of all popularity; and, however prejudicial it may be to the highest practical principles, there is no fear that it will ever pass the limits of the schools, or acquire any favour or influence in society or with the multitude. Instead of any such attempt, I confine myself to the examination of reason alone and its pure thought; and I do not need to seek far for the sum-total of its cognition, because it has its seat in my own mind.  But in order to bestow on this system its full force and evidence, we must carry our eye from it a moment to consider its consequences, and explain from the same principles some other species of reasoning, which are derived from the same origin. 
Above them all, there is the ideal teacher, who employs them as instruments for the advancement of the essential aims of human reason.
 See our privacy policy for details.  Mathematics, indeed, are useful in all mechanical operations, and arithmetic in almost every art and profession: But it is not of themselves they have any influence: Mechanics are the art of regulating the motions of bodies to some designed end or purpose; and the reason why we employ arithmetic in fixing the proportions of numbers, is only that we may discover the proportions of their influence and operation. For the same reason the attempt to prove a synthetical proposition by means of mere conceptions, for example; "Everything that exists contingently has a cause," has never succeeded. It will be incumbent on those, who affirm that memory produces entirely our personal identity, to give a reason why we cm thus extend our identity beyond our memory. And to convince us the more fully of this truth, we may here stop a moment, and from a review of the preceding reasonings may draw some new arguments, to prove that those laws, however necessary, are entirely artificial, and of human invention; and consequently that justice is an artificial, and not a natural virtue.