How does knowledge grow? It may reorganize itself by which conclusions become explicit that were hidden before. Some rules are needed to make this consistent. These rules should be known as well. So next to the knowledge specific for some topic, say biology, transformation rules have to be available. Examples of such rules are arithmetic and logic.
A second way how knowledge can grow is by the combination of two sources of knowledge, e.g. biology and physics. This is only possible if these two sources can be phrased in the same terms. They should be combined and so a common language is needed by which elements of the two domains can be related. This is not always a simple step. The participation of experts in both fields can be very helpful in such an integration.
The third way is even one step more complicated: the integration of new observations in existing knowledge. First these observations have to generate knowledge themselves. This can already be judged as a miracle. Then it may be needed to convert this new knowledge into the domain of the existing knowledge and finally it should be combined, e.g. by the rules of logic.
Let us look how this works in a famous example by Aristotle.
- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal
The first line, all mean are mortal, should be interpreted as given knowledge. We may wonder how Aristotle has gained this knowledge. It might be phrased as common knowledge, but from a strict scientific point of view the statement is just a hypothesis as there are still seven billion people alive. Let us accept it for the moment as available knowledge.
Next a new observation. Aristotle looks and sees. What does he see? It is Socrates. How does he know? This is the miracle of human recognition. We see and we know. Arguments may be given if somebody questions the observation: it is the bench that is always be used by Socrates. It is an old men with a very similar beard and smile and he is raising the familiar type of questions. Such properties come usual second. The first thing that pops up in the mind is: there is Socrates.
In order to combine the first statement, phrasing our knowledge with the observation: there is Socrates, we have to bring these two items in the same language. This is done by stating that Socrates is a man. This is a conversion of knowledge. The ‘concept’ Socrates is enlarged, generalized into ‘man’. This conversion can only be made on the basis of prior knowledge. Alternatively we may directly observe, walking to the bench and hearing Socrates arguing: Socrates is a man.
Finally, by the rules of logic it can be inferred from the two statements 1 and 2 that Socrates is mortal, a fact that in this hypothetical simple example was not known before.
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