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Mathematical knowledge may, just like our scientific knowledge, be deep and broad, it may be subtle and wonderfully explanatory, it may be uncontroversially accepted; but it cannot be certain. (Ch. 10)

 

David Deutsch

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Induction was shown to be untenable as a scientific method by Popper in The Logic of Scientific Discovery (1959). Instead, advances in scientific understanding come ideally from hypothetico-deductivism: firstly, development of a hypothesis in relation to a problem situation, and secondly, its testing in relation to all relevant knowledge and furthermore by its great explanatory power.

 

John Carew Eccles

 

Knowledge is also inferred from what is accepted as established knowledge, with new knowledge being based on the best explanation. This includes possible truths subject to proof.

 

Nayef Al-Rodan

 

In our time of ever-increasing specialization, there is a tendency to concern ourselves with relatively narrow scientific problems. The broad foundations of our present-day scientific knowledge and its historical development tend to be forgotten too often. This is an unfortunate trend, not only because our horizon becomes rather limited and our perspective somewhat distorted, but also because there are many valuable lessons to be learned in looking back over the years during which the basic concepts and the fundamental laws of a particular scientific discipline were first formulated.

 

Emil Wolf

 

Up until the publication of Thomas Kuhn's The Structure of Scientific Revolutions in 1962, the history, philosophy, and sociology of science maintained an internalist approach to scientific knowledge claims. Science was seen as somehow above any social, political, or cultural influences, and therefore, the examinations of scientific knowledge focused on areas such as 'discoveries,' 'famous men,' and 'the scientific revolution in the West.' When Kuhn opened the door to the possibility that external factors were involved in the development of scientific paradigms, science studies assumed a more critical tone.

 

Thomas Samuel Kuhn

 

Knowledge is necessary to act in the sense of my going home from here to the place I live; I must have knowledge for this; I must have knowledge to speak English; I must have knowledge to write a letter and so on. Knowledge as function, mechanical function, is necessary. Now if I use that knowledge in my relationship with you, another human being, I am bringing about a barrier, a division between you and me, namely the observer. That is, knowledge, in relationship, in human relationship, is destructive. That is knowledge which is the tradition, the memory, the image, which the mind has built about you, that knowledge is separative and therefore creates conflict in our relationship.

 

Jiddu Krishnamurti