Discuss the claim that some areas of knowledge are discovered and others are invented

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Daniel Bregman                14/07/2011

Discuss the claim that some areas of knowledge are discovered and others are invented.

In many areas of knowledge we feel as though we are explorers in a realm of understanding, uncovering new ideas that were previously hidden. It is sometimes tempting to assign this model of knowledge as discovery to all subjects. However, this may not be an accurate description of the origin of our knowledge claims. In this essay I will explore the distinction between knowledge-as-discovery and knowledge-as-invention, and aim to show that the field which can truly be described as discovery is in fact much smaller than might be expected. But what does it mean to say that knowledge is invented? If we use the commonly-accepted definition of knowledge as justified true belief, invented knowledge is knowledge that fundamentally originates from the self (or another person’s self) rather than the external world.

One area of knowledge that would seem, prima facie, to be discovered rather than invented is the area of mathematics. In my own studies of the subject I have had the experience of proving a statement, or calculating a result, and this feels like an exploration of a structure already extant: participating in mathematical study feels like the discovery – not invention – of information. However, I believe that this initial impression is misleading, and in fact mathematics does not come under the category of discovered knowledge. Consider a circle. Its mathematical definition is ‘the locus of a point at fixed distance from another fixed point’. This would imply that the circumference is infinitely thin, and infinitely smooth, but such a construction cannot physically exist. What, then, do theorems about circles mean? For example, one simple theorem is that a triangle whose points are on the circumference of a circle, with one side forming the diameter of the circle, has an angle of 90°. Where does this knowledge come from, if the shapes do not and cannot exist?

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We have two possibilities open to us. The first option is that perfect shapes do exist, in some transcendent non-physical form. This belief is based on that posited by Plato, the ancient Greek philosopher. He held that objects in the material world are ‘shadows’ of an immaterial realm known as the realm of Forms. We recognise circles because of the Form of Circle, and our mathematical knowledge is knowledge about the relevant Forms. However, this view seems somewhat unpalatable. It is unclear how Plato’s Forms can interact with the real world, and provide knowledge to it. Plato himself suggests ...

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