Abstraction

(For this section one should include more results from cognitive psychology and phenomenological research)

In everyday life abstraction shows up as the ability of people to talk about concrete things with general concepts like 'chair', 'table', 'glass' etc. although the concrete objects mentioned are usually 'different'. In a classroom there can be different kinds of chairs but we are talking about 'chairs'. The same with 'table' and 'glass'. There are different concrete real things but we are using one concept to talk about them. A possible explanation is the selection of a set of properties which are common to all these different concrete objects and use this selection as a kind of signature, as y key to identify these objects. A key is the intersection $\kappa$ of different objects. Thus we can use the key of different objects to form a concept $c_{i}$ representing some common properties of all these objects.

$$\kappa : \{o_{1}, ..., o_{m}\} \longmapsto \bigcap\{o_{1}, ..., o_{m}\}$$ (6.22)

$$c_{i} = \kappa(\{o_{1}, ..., o_{m}\})$$ (6.23)

Thus we can form as many abstractions from objects as there are possible selections of properties of these objects, which can be distinguished.