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To know is not too demanding: it merely requires memory and time. But to understand is quite a different matter: it requires intellectual ability and training, a self conscious awareness of what one is doing, experience in techniques of analysis and synthesis, and above all, perspective.

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A lot of people have thought of understanding as just knowledge of true causes, but then there is a problem of why we value knowledge - if not to understand things. And in effect understanding is what underwrites the desire for knowledge in the context of science.

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The most difficult thing is to know what we do know, and what we do not know. Therefore, desiring to know anything, we shall before all else determine WHAT we accept as given, and WHAT as demanding definition and proof; that is, determine WHAT we know already, and WHAT we wish to know. In relation to the knowledge of the world and of ourselves, the conditions would be ideal could we venture to accept nothing as given, and count all as demanding definition and proof. In other words, it would be best to assume that we know nothing, and make this our point of departure. But unfortunately such conditions are impossible to create. Knowledge must start from some foundation, something must be recognized as known; otherwise we shall be obliged always to define one unknown by means of another.

According to Wertheimer, reaching an understanding involves many aspects of learners, such as their emotions, attitudes, and perceptions, as well as their intellects. In gaining insight into the solution to a problem, a student need not—in fact, should not—be logical. Rather, the student should cognitively arrange and rearrange the components of the problem until a solution based on understanding is reached. Exactly how this process is done will vary from student to student.

Knowing, whatever its level, is not the act by which a subject transformed into an object docilely and passively accepts the contents others give or impose on him or her. Knowledge, on the contrary, necessitates the curious presence of subjects confronted with the world. It requires their transforming action on reality. It demands a constant searching. It implies invention and reinvention. It claims from each person a reflection on the very act of knowing.

is — it is necessary to come first to an understanding concerning knowledge, which is looked upon as the instrument by which to take possession of the Absolute, or as the means through which to get a sight of it.

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'Yes, Professor, knowledge and understanding are quite different. Only understanding can lead to being, whereas knowledge is but a passing presence in it. New knowledge displaces the old and the result is, as it were, a pouring from the empty into the void.

We cannot understand without wanting to understand, that is, without wanting to let something be said. It would be an inadmissible abstraction to contend that we must first have achieved a contemporaneousness with the author or the original reader by means of a reconstruction of his historical horizon before we could begin to grasp the meaning of what is said. A kind of anticipation of meaning guides the effort to understand from the very beginning.

It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way… Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.

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